TSTP Solution File: SET151-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET151-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 09:11:45 EDT 2024
% Result : Unsatisfiable 4.11s 0.94s
% Output : Refutation 4.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f10086,plain,
$false,
inference(subsumption_resolution,[],[f10082,f113]) ).
fof(f113,axiom,
universal_class != complement(null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complement_of_null_class_1) ).
fof(f10082,plain,
universal_class = complement(null_class),
inference(resolution,[],[f10028,f206]) ).
fof(f206,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ),
inference(resolution,[],[f7,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f10028,plain,
subclass(universal_class,complement(null_class)),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f423,f194,f26,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1540,f1542,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1646,f1647,f1648,f1651,f1652,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f2983,f3592,f3599,f3600,f3601,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3945,f3948,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886,f554,f6039,f6040,f6041,f6042,f6043,f6044,f6045,f6046,f6047,f6048,f6049,f6050,f6051,f6057,f6060,f6062,f6067,f6160,f6244,f6245,f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).
fof(f9988,plain,
! [X0] :
( subclass(universal_class,complement(null_class))
| member(not_subclass_element(universal_class,complement(null_class)),X0)
| null_class = X0 ),
inference(resolution,[],[f9921,f291]) ).
fof(f10027,plain,
subclass(universal_class,complement(null_class)),
inference(subsumption_resolution,[],[f9987,f2]) ).
fof(f9987,plain,
( subclass(universal_class,complement(null_class))
| ~ member(not_subclass_element(universal_class,complement(null_class)),universal_class) ),
inference(resolution,[],[f9921,f612]) ).
fof(f9985,plain,
subclass(universal_class,complement(null_class)),
inference(resolution,[],[f9921,f4212]) ).
fof(f9984,plain,
! [X2,X0,X1] :
( subclass(universal_class,complement(restrict(X0,X1,X2)))
| member(not_subclass_element(universal_class,complement(restrict(X0,X1,X2))),X0) ),
inference(resolution,[],[f9921,f495]) ).
fof(f9983,plain,
! [X2,X0,X1] :
( subclass(universal_class,complement(restrict(X0,X1,X2)))
| member(not_subclass_element(universal_class,complement(restrict(X0,X1,X2))),cross_product(X1,X2)) ),
inference(resolution,[],[f9921,f496]) ).
fof(f9982,plain,
( subclass(universal_class,complement(symmetric_difference(inverse(subset_relation),subset_relation)))
| member(not_subclass_element(universal_class,complement(symmetric_difference(inverse(subset_relation),subset_relation))),complement(identity_relation)) ),
inference(resolution,[],[f9921,f3843]) ).
fof(f9981,plain,
! [X0] :
( subclass(universal_class,complement(symmetric_difference(null_class,X0)))
| member(not_subclass_element(universal_class,complement(symmetric_difference(null_class,X0))),complement(null_class)) ),
inference(resolution,[],[f9921,f3991]) ).
fof(f9980,plain,
! [X0] :
( subclass(universal_class,complement(symmetric_difference(X0,singleton(X0))))
| member(not_subclass_element(universal_class,complement(symmetric_difference(X0,singleton(X0)))),successor(X0)) ),
inference(resolution,[],[f9921,f6656]) ).
fof(f9979,plain,
! [X0] :
( subclass(universal_class,complement(symmetric_difference(X0,null_class)))
| member(not_subclass_element(universal_class,complement(symmetric_difference(X0,null_class))),complement(null_class)) ),
inference(resolution,[],[f9921,f4123]) ).
fof(f9978,plain,
! [X0,X1] :
( subclass(universal_class,complement(symmetric_difference(X0,X1)))
| member(not_subclass_element(universal_class,complement(symmetric_difference(X0,X1))),union(X0,X1)) ),
inference(resolution,[],[f9921,f1660]) ).
fof(f9977,plain,
! [X0,X1] :
( subclass(universal_class,complement(symmetric_difference(X0,X1)))
| ~ member(not_subclass_element(universal_class,complement(symmetric_difference(X0,X1))),intersection(X0,X1)) ),
inference(resolution,[],[f9921,f3825]) ).
fof(f9975,plain,
! [X0] :
( subclass(universal_class,complement(complement(X0)))
| ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0) ),
inference(resolution,[],[f9921,f24]) ).
fof(f9973,plain,
! [X0,X1] :
( subclass(universal_class,complement(intersection(X0,X1)))
| member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X0) ),
inference(resolution,[],[f9921,f21]) ).
fof(f9972,plain,
! [X0,X1] :
( subclass(universal_class,complement(intersection(X0,X1)))
| member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X1) ),
inference(resolution,[],[f9921,f22]) ).
fof(f9971,plain,
! [X0,X1] :
( subclass(universal_class,complement(cross_product(X0,X1)))
| not_subclass_element(universal_class,complement(cross_product(X0,X1))) = ordered_pair(first(not_subclass_element(universal_class,complement(cross_product(X0,X1)))),second(not_subclass_element(universal_class,complement(cross_product(X0,X1))))) ),
inference(resolution,[],[f9921,f17]) ).
fof(f10023,plain,
! [X0,X1] :
( singleton(X0) = not_subclass_element(universal_class,complement(ordered_pair(X0,X1)))
| unordered_pair(X0,singleton(X1)) = not_subclass_element(universal_class,complement(ordered_pair(X0,X1))) ),
inference(subsumption_resolution,[],[f9970,f692]) ).
fof(f9970,plain,
! [X0,X1] :
( subclass(universal_class,complement(ordered_pair(X0,X1)))
| singleton(X0) = not_subclass_element(universal_class,complement(ordered_pair(X0,X1)))
| unordered_pair(X0,singleton(X1)) = not_subclass_element(universal_class,complement(ordered_pair(X0,X1))) ),
inference(resolution,[],[f9921,f693]) ).
fof(f9969,plain,
! [X0] :
( subclass(universal_class,complement(singleton(X0)))
| not_subclass_element(universal_class,complement(singleton(X0))) = X0 ),
inference(resolution,[],[f9921,f650]) ).
fof(f9968,plain,
! [X0,X1] :
( subclass(universal_class,complement(unordered_pair(X0,X1)))
| not_subclass_element(universal_class,complement(unordered_pair(X0,X1))) = X0
| not_subclass_element(universal_class,complement(unordered_pair(X0,X1))) = X1 ),
inference(resolution,[],[f9921,f8]) ).
fof(f9967,plain,
! [X0,X1] :
( subclass(universal_class,complement(X0))
| ~ subclass(X0,X1)
| member(not_subclass_element(universal_class,complement(X0)),X1) ),
inference(resolution,[],[f9921,f1]) ).
fof(f9921,plain,
! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ),
inference(duplicate_literal_removal,[],[f9897]) ).
fof(f9897,plain,
! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) ),
inference(resolution,[],[f421,f2]) ).
fof(f9964,plain,
! [X0] :
( subclass(X0,power_class(image(element_relation,null_class)))
| member(not_subclass_element(X0,power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class)))
| ~ member(not_subclass_element(X0,power_class(image(element_relation,null_class))),universal_class) ),
inference(forward_demodulation,[],[f9963,f664]) ).
fof(f9963,plain,
! [X0] :
( member(not_subclass_element(X0,power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class)))
| ~ member(not_subclass_element(X0,power_class(image(element_relation,null_class))),universal_class)
| subclass(X0,complement(image(element_relation,power_class(universal_class)))) ),
inference(forward_demodulation,[],[f9917,f664]) ).
fof(f9917,plain,
! [X0] :
( ~ member(not_subclass_element(X0,power_class(image(element_relation,null_class))),universal_class)
| member(not_subclass_element(X0,complement(image(element_relation,power_class(universal_class)))),image(element_relation,power_class(universal_class)))
| subclass(X0,complement(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f421,f664]) ).
fof(f9962,plain,
! [X0] :
( subclass(X0,power_class(universal_class))
| member(not_subclass_element(X0,power_class(universal_class)),image(element_relation,null_class))
| ~ member(not_subclass_element(X0,power_class(universal_class)),universal_class) ),
inference(forward_demodulation,[],[f9961,f616]) ).
fof(f9961,plain,
! [X0] :
( member(not_subclass_element(X0,power_class(universal_class)),image(element_relation,null_class))
| ~ member(not_subclass_element(X0,power_class(universal_class)),universal_class)
| subclass(X0,complement(image(element_relation,null_class))) ),
inference(forward_demodulation,[],[f9916,f616]) ).
fof(f9916,plain,
! [X0] :
( ~ member(not_subclass_element(X0,power_class(universal_class)),universal_class)
| member(not_subclass_element(X0,complement(image(element_relation,null_class))),image(element_relation,null_class))
| subclass(X0,complement(image(element_relation,null_class))) ),
inference(superposition,[],[f421,f616]) ).
fof(f9960,plain,
! [X0,X1] :
( subclass(X1,power_class(X0))
| member(not_subclass_element(X1,power_class(X0)),image(element_relation,complement(X0)))
| ~ member(not_subclass_element(X1,power_class(X0)),universal_class) ),
inference(forward_demodulation,[],[f9959,f55]) ).
fof(f9959,plain,
! [X0,X1] :
( member(not_subclass_element(X1,power_class(X0)),image(element_relation,complement(X0)))
| ~ member(not_subclass_element(X1,power_class(X0)),universal_class)
| subclass(X1,complement(image(element_relation,complement(X0)))) ),
inference(forward_demodulation,[],[f9915,f55]) ).
fof(f9915,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,power_class(X0)),universal_class)
| member(not_subclass_element(X1,complement(image(element_relation,complement(X0)))),image(element_relation,complement(X0)))
| subclass(X1,complement(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f421,f55]) ).
fof(f9958,plain,
! [X2,X0,X1] :
( subclass(X2,diagonalise(cross_product(X0,X1)))
| member(not_subclass_element(X2,diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1)))
| ~ member(not_subclass_element(X2,diagonalise(cross_product(X0,X1))),universal_class) ),
inference(forward_demodulation,[],[f9957,f541]) ).
fof(f9957,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1)))
| ~ member(not_subclass_element(X2,diagonalise(cross_product(X0,X1))),universal_class)
| subclass(X2,complement(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(forward_demodulation,[],[f9914,f541]) ).
fof(f9914,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,diagonalise(cross_product(X0,X1))),universal_class)
| member(not_subclass_element(X2,complement(domain_of(restrict(identity_relation,X0,X1)))),domain_of(restrict(identity_relation,X0,X1)))
| subclass(X2,complement(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f421,f541]) ).
fof(f9956,plain,
! [X0,X1] :
( subclass(X1,diagonalise(X0))
| member(not_subclass_element(X1,diagonalise(X0)),domain_of(intersection(X0,identity_relation)))
| ~ member(not_subclass_element(X1,diagonalise(X0)),universal_class) ),
inference(forward_demodulation,[],[f9955,f76]) ).
fof(f9955,plain,
! [X0,X1] :
( member(not_subclass_element(X1,diagonalise(X0)),domain_of(intersection(X0,identity_relation)))
| ~ member(not_subclass_element(X1,diagonalise(X0)),universal_class)
| subclass(X1,complement(domain_of(intersection(X0,identity_relation)))) ),
inference(forward_demodulation,[],[f9913,f76]) ).
fof(f9913,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,diagonalise(X0)),universal_class)
| member(not_subclass_element(X1,complement(domain_of(intersection(X0,identity_relation)))),domain_of(intersection(X0,identity_relation)))
| subclass(X1,complement(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f421,f76]) ).
fof(f9954,plain,
! [X2,X0,X1] :
( subclass(X2,union(X0,domain_of(intersection(X1,identity_relation))))
| member(not_subclass_element(X2,union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1)))
| ~ member(not_subclass_element(X2,union(X0,domain_of(intersection(X1,identity_relation)))),universal_class) ),
inference(forward_demodulation,[],[f9953,f446]) ).
fof(f9953,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1)))
| ~ member(not_subclass_element(X2,union(X0,domain_of(intersection(X1,identity_relation)))),universal_class)
| subclass(X2,complement(intersection(complement(X0),diagonalise(X1)))) ),
inference(forward_demodulation,[],[f9912,f446]) ).
fof(f9912,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,union(X0,domain_of(intersection(X1,identity_relation)))),universal_class)
| member(not_subclass_element(X2,complement(intersection(complement(X0),diagonalise(X1)))),intersection(complement(X0),diagonalise(X1)))
| subclass(X2,complement(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f421,f446]) ).
fof(f9952,plain,
! [X2,X0,X1] :
( subclass(X2,union(X0,image(element_relation,complement(X1))))
| member(not_subclass_element(X2,union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1)))
| ~ member(not_subclass_element(X2,union(X0,image(element_relation,complement(X1)))),universal_class) ),
inference(forward_demodulation,[],[f9951,f445]) ).
fof(f9951,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1)))
| ~ member(not_subclass_element(X2,union(X0,image(element_relation,complement(X1)))),universal_class)
| subclass(X2,complement(intersection(complement(X0),power_class(X1)))) ),
inference(forward_demodulation,[],[f9911,f445]) ).
fof(f9911,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,union(X0,image(element_relation,complement(X1)))),universal_class)
| member(not_subclass_element(X2,complement(intersection(complement(X0),power_class(X1)))),intersection(complement(X0),power_class(X1)))
| subclass(X2,complement(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f421,f445]) ).
fof(f9950,plain,
! [X1] :
( subclass(X1,complement(null_class))
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9949,f4134]) ).
fof(f9949,plain,
! [X0,X1] :
( subclass(X1,union(X0,universal_class))
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9948,f615]) ).
fof(f9948,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| subclass(X1,complement(intersection(complement(X0),null_class))) ),
inference(subsumption_resolution,[],[f9947,f4212]) ).
fof(f9947,plain,
! [X0,X1] :
( member(not_subclass_element(X1,complement(null_class)),null_class)
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| subclass(X1,complement(intersection(complement(X0),null_class))) ),
inference(forward_demodulation,[],[f9946,f4080]) ).
fof(f9946,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| member(not_subclass_element(X1,complement(intersection(complement(X0),null_class))),intersection(complement(X0),null_class))
| subclass(X1,complement(intersection(complement(X0),null_class))) ),
inference(forward_demodulation,[],[f9910,f4134]) ).
fof(f9910,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,union(X0,universal_class)),universal_class)
| member(not_subclass_element(X1,complement(intersection(complement(X0),null_class))),intersection(complement(X0),null_class))
| subclass(X1,complement(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f421,f615]) ).
fof(f9945,plain,
! [X0] :
( subclass(X0,complement(null_class))
| ~ member(not_subclass_element(X0,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9944,f4134]) ).
fof(f9944,plain,
! [X0] :
( subclass(X0,union(universal_class,universal_class))
| ~ member(not_subclass_element(X0,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9943,f796]) ).
fof(f9943,plain,
! [X0] :
( ~ member(not_subclass_element(X0,complement(null_class)),universal_class)
| subclass(X0,complement(intersection(null_class,null_class))) ),
inference(subsumption_resolution,[],[f9942,f4212]) ).
fof(f9942,plain,
! [X0] :
( member(not_subclass_element(X0,complement(null_class)),null_class)
| ~ member(not_subclass_element(X0,complement(null_class)),universal_class)
| subclass(X0,complement(intersection(null_class,null_class))) ),
inference(forward_demodulation,[],[f9941,f4080]) ).
fof(f9941,plain,
! [X0] :
( ~ member(not_subclass_element(X0,complement(null_class)),universal_class)
| member(not_subclass_element(X0,complement(intersection(null_class,null_class))),intersection(null_class,null_class))
| subclass(X0,complement(intersection(null_class,null_class))) ),
inference(forward_demodulation,[],[f9909,f4134]) ).
fof(f9909,plain,
! [X0] :
( ~ member(not_subclass_element(X0,union(universal_class,universal_class)),universal_class)
| member(not_subclass_element(X0,complement(intersection(null_class,null_class))),intersection(null_class,null_class))
| subclass(X0,complement(intersection(null_class,null_class))) ),
inference(superposition,[],[f421,f796]) ).
fof(f9940,plain,
! [X2,X3,X0,X1] :
( subclass(X3,union(X0,intersection(complement(X1),complement(X2))))
| member(not_subclass_element(X3,union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2)))
| ~ member(not_subclass_element(X3,union(X0,intersection(complement(X1),complement(X2)))),universal_class) ),
inference(forward_demodulation,[],[f9939,f447]) ).
fof(f9939,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(X3,union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2)))
| ~ member(not_subclass_element(X3,union(X0,intersection(complement(X1),complement(X2)))),universal_class)
| subclass(X3,complement(intersection(complement(X0),union(X1,X2)))) ),
inference(forward_demodulation,[],[f9908,f447]) ).
fof(f9908,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X3,union(X0,intersection(complement(X1),complement(X2)))),universal_class)
| member(not_subclass_element(X3,complement(intersection(complement(X0),union(X1,X2)))),intersection(complement(X0),union(X1,X2)))
| subclass(X3,complement(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f421,f447]) ).
fof(f9938,plain,
! [X2,X0,X1] :
( subclass(X2,union(domain_of(intersection(X0,identity_relation)),X1))
| member(not_subclass_element(X2,union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(domain_of(intersection(X0,identity_relation)),X1)),universal_class) ),
inference(forward_demodulation,[],[f9937,f443]) ).
fof(f9937,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(domain_of(intersection(X0,identity_relation)),X1)),universal_class)
| subclass(X2,complement(intersection(diagonalise(X0),complement(X1)))) ),
inference(forward_demodulation,[],[f9907,f443]) ).
fof(f9907,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,union(domain_of(intersection(X0,identity_relation)),X1)),universal_class)
| member(not_subclass_element(X2,complement(intersection(diagonalise(X0),complement(X1)))),intersection(diagonalise(X0),complement(X1)))
| subclass(X2,complement(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f421,f443]) ).
fof(f9936,plain,
! [X2,X0,X1] :
( subclass(X2,union(image(element_relation,complement(X0)),X1))
| member(not_subclass_element(X2,union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(image(element_relation,complement(X0)),X1)),universal_class) ),
inference(forward_demodulation,[],[f9935,f442]) ).
fof(f9935,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(image(element_relation,complement(X0)),X1)),universal_class)
| subclass(X2,complement(intersection(power_class(X0),complement(X1)))) ),
inference(forward_demodulation,[],[f9906,f442]) ).
fof(f9906,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,union(image(element_relation,complement(X0)),X1)),universal_class)
| member(not_subclass_element(X2,complement(intersection(power_class(X0),complement(X1)))),intersection(power_class(X0),complement(X1)))
| subclass(X2,complement(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f421,f442]) ).
fof(f9934,plain,
! [X1] :
( subclass(X1,complement(null_class))
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9933,f3967]) ).
fof(f9933,plain,
! [X0,X1] :
( subclass(X1,union(universal_class,X0))
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class) ),
inference(forward_demodulation,[],[f9932,f614]) ).
fof(f9932,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| subclass(X1,complement(intersection(null_class,complement(X0)))) ),
inference(subsumption_resolution,[],[f9931,f4212]) ).
fof(f9931,plain,
! [X0,X1] :
( member(not_subclass_element(X1,complement(null_class)),null_class)
| ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| subclass(X1,complement(intersection(null_class,complement(X0)))) ),
inference(forward_demodulation,[],[f9930,f3938]) ).
fof(f9930,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| member(not_subclass_element(X1,complement(intersection(null_class,complement(X0)))),intersection(null_class,complement(X0)))
| subclass(X1,complement(intersection(null_class,complement(X0)))) ),
inference(forward_demodulation,[],[f9905,f3967]) ).
fof(f9905,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,union(universal_class,X0)),universal_class)
| member(not_subclass_element(X1,complement(intersection(null_class,complement(X0)))),intersection(null_class,complement(X0)))
| subclass(X1,complement(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f421,f614]) ).
fof(f9929,plain,
! [X2,X3,X0,X1] :
( subclass(X3,union(intersection(complement(X0),complement(X1)),X2))
| member(not_subclass_element(X3,union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2)))
| ~ member(not_subclass_element(X3,union(intersection(complement(X0),complement(X1)),X2)),universal_class) ),
inference(forward_demodulation,[],[f9928,f444]) ).
fof(f9928,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(X3,union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2)))
| ~ member(not_subclass_element(X3,union(intersection(complement(X0),complement(X1)),X2)),universal_class)
| subclass(X3,complement(intersection(union(X0,X1),complement(X2)))) ),
inference(forward_demodulation,[],[f9904,f444]) ).
fof(f9904,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X3,union(intersection(complement(X0),complement(X1)),X2)),universal_class)
| member(not_subclass_element(X3,complement(intersection(union(X0,X1),complement(X2)))),intersection(union(X0,X1),complement(X2)))
| subclass(X3,complement(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f421,f444]) ).
fof(f9927,plain,
! [X2,X0,X1] :
( subclass(X2,union(X0,X1))
| member(not_subclass_element(X2,union(X0,X1)),intersection(complement(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(X0,X1)),universal_class) ),
inference(forward_demodulation,[],[f9926,f26]) ).
fof(f9926,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X2,union(X0,X1)),intersection(complement(X0),complement(X1)))
| ~ member(not_subclass_element(X2,union(X0,X1)),universal_class)
| subclass(X2,complement(intersection(complement(X0),complement(X1)))) ),
inference(forward_demodulation,[],[f9903,f26]) ).
fof(f9903,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X2,union(X0,X1)),universal_class)
| member(not_subclass_element(X2,complement(intersection(complement(X0),complement(X1)))),intersection(complement(X0),complement(X1)))
| subclass(X2,complement(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f421,f26]) ).
fof(f9924,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) ),
inference(subsumption_resolution,[],[f9918,f4]) ).
fof(f9918,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ),
inference(duplicate_literal_removal,[],[f9901]) ).
fof(f9901,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) ),
inference(resolution,[],[f421,f160]) ).
fof(f9923,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| null_class = singleton(not_subclass_element(X0,complement(X1))) ),
inference(subsumption_resolution,[],[f9900,f4]) ).
fof(f9900,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(universal_class,universal_class)
| null_class = singleton(not_subclass_element(X0,complement(X1))) ),
inference(resolution,[],[f421,f3115]) ).
fof(f9919,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) ),
inference(duplicate_literal_removal,[],[f9899]) ).
fof(f9899,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1))
| subclass(intersection(X0,universal_class),complement(X1)) ),
inference(resolution,[],[f421,f133]) ).
fof(f9920,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) ),
inference(duplicate_literal_removal,[],[f9898]) ).
fof(f9898,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1))
| subclass(intersection(universal_class,X0),complement(X1)) ),
inference(resolution,[],[f421,f128]) ).
fof(f9896,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| null_class = singleton(not_subclass_element(X0,complement(X1))) ),
inference(resolution,[],[f421,f3114]) ).
fof(f9922,plain,
! [X0] :
( member(not_subclass_element(identity_relation,complement(X0)),X0)
| subclass(identity_relation,complement(X0)) ),
inference(duplicate_literal_removal,[],[f9895]) ).
fof(f9895,plain,
! [X0] :
( member(not_subclass_element(identity_relation,complement(X0)),X0)
| subclass(identity_relation,complement(X0))
| subclass(identity_relation,complement(X0)) ),
inference(resolution,[],[f421,f1146]) ).
fof(f421,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) ),
inference(resolution,[],[f25,f3]) ).
fof(f9888,plain,
! [X0] :
( subclass(cantor(inverse(null_class)),image(regular(cross_product(X0,universal_class)),X0))
| null_class = cross_product(X0,universal_class) ),
inference(superposition,[],[f4151,f526]) ).
fof(f9885,plain,
subclass(cantor(inverse(subset_relation)),image(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class)),
inference(superposition,[],[f4151,f2004]) ).
fof(f9884,plain,
! [X2,X0,X1] : subclass(cantor(inverse(restrict(cross_product(X2,universal_class),X0,X1))),image(cross_product(X0,X1),X2)),
inference(superposition,[],[f4151,f527]) ).
fof(f9883,plain,
! [X2,X0,X1] : subclass(cantor(inverse(restrict(cross_product(X2,universal_class),X0,X1))),image(cross_product(X0,X1),X2)),
inference(superposition,[],[f4151,f527]) ).
fof(f9882,plain,
! [X0,X1] :
( member(null_class,image(X0,X1))
| ~ inductive(cantor(inverse(restrict(X0,X1,universal_class)))) ),
inference(resolution,[],[f4151,f158]) ).
fof(f9881,plain,
! [X0,X1] :
( ~ subclass(image(X0,X1),cantor(inverse(restrict(X0,X1,universal_class))))
| image(X0,X1) = cantor(inverse(restrict(X0,X1,universal_class))) ),
inference(resolution,[],[f4151,f7]) ).
fof(f4151,plain,
! [X0,X1] : subclass(cantor(inverse(restrict(X0,X1,universal_class))),image(X0,X1)),
inference(superposition,[],[f3963,f42]) ).
fof(f211,plain,
! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ),
inference(resolution,[],[f7,f35]) ).
fof(f9879,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f9876,f3484]) ).
fof(f9876,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| subclass(singleton(X0),null_class)
| singleton(X0) = null_class ),
inference(superposition,[],[f160,f3588]) ).
fof(f9871,plain,
! [X0] :
( singleton(singleton(X0)) = not_subclass_element(ordered_pair(singleton(X0),X0),null_class)
| null_class = singleton(singleton(singleton(X0))) ),
inference(superposition,[],[f3588,f4463]) ).
fof(f3588,plain,
! [X0] :
( not_subclass_element(singleton(X0),null_class) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f3484,f652]) ).
fof(f1544,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(composition_function)))
| compose(X0,X1) = X2 ),
inference(resolution,[],[f787,f96]) ).
fof(f1537,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(cross_product(X0,X1))))
| member(X2,X0) ),
inference(resolution,[],[f787,f14]) ).
fof(f1536,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(cross_product(X0,X1))))
| member(X2,X1) ),
inference(resolution,[],[f787,f15]) ).
fof(f210,plain,
! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ),
inference(resolution,[],[f7,f32]) ).
fof(f8482,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| ~ subclass(universal_class,intersection(X0,X1)) ),
inference(resolution,[],[f6452,f163]) ).
fof(f9838,plain,
! [X0] : member(singleton(singleton(singleton(singleton(X0)))),singleton(singleton(ordered_pair(singleton(X0),X0)))),
inference(forward_demodulation,[],[f9828,f4463]) ).
fof(f9828,plain,
! [X0] : member(ordered_pair(singleton(singleton(X0)),singleton(X0)),singleton(singleton(ordered_pair(singleton(X0),X0)))),
inference(superposition,[],[f8458,f4463]) ).
fof(f9823,plain,
! [X0] : member(ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))),singleton(singleton(singleton(ordered_pair(singleton(X0),X0))))),
inference(superposition,[],[f8458,f4463]) ).
fof(f9821,plain,
! [X0,X1] :
( ~ subclass(singleton(singleton(singleton(singleton(X0)))),X1)
| member(ordered_pair(singleton(X0),X0),X1) ),
inference(resolution,[],[f8458,f1]) ).
fof(f8458,plain,
! [X0] : member(ordered_pair(singleton(X0),X0),singleton(singleton(singleton(singleton(X0))))),
inference(superposition,[],[f5413,f4463]) ).
fof(f9785,plain,
! [X0,X1] :
( ~ member(omega,symmetric_difference(complement(X0),complement(X1)))
| ~ subclass(universal_class,symmetric_difference(union(X0,X1),union(complement(X0),complement(X1)))) ),
inference(superposition,[],[f6452,f1654]) ).
fof(f9817,plain,
! [X0,X1] :
( symmetric_difference(complement(X0),complement(X1)) = union(complement(X0),complement(X1))
| ~ subclass(union(complement(X0),complement(X1)),symmetric_difference(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f9783,f1654]) ).
fof(f9783,plain,
! [X0,X1] :
( ~ subclass(union(complement(X0),complement(X1)),symmetric_difference(complement(X0),complement(X1)))
| union(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f4078,f1654]) ).
fof(f9781,plain,
! [X0,X1] : subclass(symmetric_difference(union(X0,X1),union(complement(X0),complement(X1))),complement(symmetric_difference(complement(X0),complement(X1)))),
inference(superposition,[],[f3947,f1654]) ).
fof(f9816,plain,
! [X0,X1] :
( union(X0,X1) = symmetric_difference(complement(X0),complement(X1))
| ~ subclass(union(X0,X1),symmetric_difference(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f9780,f1654]) ).
fof(f9780,plain,
! [X0,X1] :
( ~ subclass(union(X0,X1),symmetric_difference(complement(X0),complement(X1)))
| union(X0,X1) = intersection(union(X0,X1),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f3936,f1654]) ).
fof(f9769,plain,
! [X0,X1] :
( ~ member(null_class,symmetric_difference(complement(X0),complement(X1)))
| ~ inductive(symmetric_difference(union(X0,X1),union(complement(X0),complement(X1)))) ),
inference(superposition,[],[f1693,f1654]) ).
fof(f9768,plain,
! [X0,X1] :
( member(null_class,complement(symmetric_difference(complement(X0),complement(X1))))
| ~ inductive(symmetric_difference(union(X0,X1),union(complement(X0),complement(X1)))) ),
inference(superposition,[],[f1662,f1654]) ).
fof(f9767,plain,
! [X2,X0,X1] :
( member(X2,complement(symmetric_difference(complement(X0),complement(X1))))
| ~ member(X2,symmetric_difference(union(X0,X1),union(complement(X0),complement(X1)))) ),
inference(superposition,[],[f1659,f1654]) ).
fof(f9766,plain,
! [X0,X1] : symmetric_difference(union(X0,X1),union(complement(X0),complement(X1))) = intersection(complement(symmetric_difference(complement(X0),complement(X1))),union(union(X0,X1),union(complement(X0),complement(X1)))),
inference(superposition,[],[f1614,f1654]) ).
fof(f9765,plain,
! [X2,X3,X0,X1] :
( ~ subclass(symmetric_difference(complement(X0),complement(X1)),X2)
| ~ member(X3,union(X0,X1))
| ~ member(X3,union(complement(X0),complement(X1)))
| member(X3,X2) ),
inference(superposition,[],[f747,f1654]) ).
fof(f9764,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(ordered_pair(X2,X3),union(X0,X1)) ),
inference(superposition,[],[f719,f1654]) ).
fof(f9763,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(ordered_pair(X2,X3),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f718,f1654]) ).
fof(f9762,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(unordered_pair(X2,X3),union(X0,X1)) ),
inference(superposition,[],[f265,f1654]) ).
fof(f9761,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(unordered_pair(X2,X3),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f264,f1654]) ).
fof(f9758,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(singleton(X2),union(X0,X1)) ),
inference(superposition,[],[f177,f1654]) ).
fof(f9757,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(singleton(X2),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f176,f1654]) ).
fof(f9756,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1)))
| member(omega,union(X0,X1)) ),
inference(superposition,[],[f173,f1654]) ).
fof(f9815,plain,
! [X2,X0,X1] :
( subclass(symmetric_difference(complement(X0),complement(X1)),X2)
| member(not_subclass_element(symmetric_difference(complement(X0),complement(X1)),X2),union(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f9754,f1654]) ).
fof(f9754,plain,
! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(complement(X0),complement(X1)),X2),union(complement(X0),complement(X1)))
| subclass(intersection(union(X0,X1),union(complement(X0),complement(X1))),X2) ),
inference(superposition,[],[f133,f1654]) ).
fof(f9814,plain,
! [X0,X1] :
( null_class = symmetric_difference(complement(X0),complement(X1))
| member(regular(symmetric_difference(complement(X0),complement(X1))),union(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f9753,f1654]) ).
fof(f9753,plain,
! [X0,X1] :
( member(regular(symmetric_difference(complement(X0),complement(X1))),union(complement(X0),complement(X1)))
| null_class = intersection(union(X0,X1),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f132,f1654]) ).
fof(f9813,plain,
! [X2,X0,X1] :
( subclass(symmetric_difference(complement(X0),complement(X1)),X2)
| member(not_subclass_element(symmetric_difference(complement(X0),complement(X1)),X2),union(X0,X1)) ),
inference(forward_demodulation,[],[f9751,f1654]) ).
fof(f9751,plain,
! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(complement(X0),complement(X1)),X2),union(X0,X1))
| subclass(intersection(union(X0,X1),union(complement(X0),complement(X1))),X2) ),
inference(superposition,[],[f128,f1654]) ).
fof(f9812,plain,
! [X0,X1] :
( null_class = symmetric_difference(complement(X0),complement(X1))
| member(regular(symmetric_difference(complement(X0),complement(X1))),union(X0,X1)) ),
inference(forward_demodulation,[],[f9750,f1654]) ).
fof(f9750,plain,
! [X0,X1] :
( member(regular(symmetric_difference(complement(X0),complement(X1))),union(X0,X1))
| null_class = intersection(union(X0,X1),union(complement(X0),complement(X1))) ),
inference(superposition,[],[f127,f1654]) ).
fof(f9749,plain,
! [X0,X1] :
( ~ inductive(symmetric_difference(complement(X0),complement(X1)))
| member(null_class,union(X0,X1)) ),
inference(superposition,[],[f126,f1654]) ).
fof(f9748,plain,
! [X2,X0,X1] :
( member(X2,symmetric_difference(complement(X0),complement(X1)))
| ~ member(X2,union(complement(X0),complement(X1)))
| ~ member(X2,union(X0,X1)) ),
inference(superposition,[],[f23,f1654]) ).
fof(f9746,plain,
! [X2,X0,X1] :
( ~ member(X2,symmetric_difference(complement(X0),complement(X1)))
| member(X2,union(X0,X1)) ),
inference(superposition,[],[f21,f1654]) ).
fof(f9745,plain,
! [X0] : symmetric_difference(complement(X0),power_class(image(element_relation,null_class))) = intersection(union(X0,image(element_relation,power_class(universal_class))),union(complement(X0),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f1654,f664]) ).
fof(f9744,plain,
! [X0] : symmetric_difference(complement(X0),power_class(universal_class)) = intersection(union(X0,image(element_relation,null_class)),union(complement(X0),power_class(universal_class))),
inference(superposition,[],[f1654,f616]) ).
fof(f9743,plain,
! [X0,X1] : symmetric_difference(complement(X1),power_class(X0)) = intersection(union(X1,image(element_relation,complement(X0))),union(complement(X1),power_class(X0))),
inference(superposition,[],[f1654,f55]) ).
fof(f9742,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),diagonalise(cross_product(X0,X1))) = intersection(union(X2,domain_of(restrict(identity_relation,X0,X1))),union(complement(X2),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f1654,f541]) ).
fof(f9741,plain,
! [X0,X1] : symmetric_difference(complement(X1),diagonalise(X0)) = intersection(union(X1,domain_of(intersection(X0,identity_relation))),union(complement(X1),diagonalise(X0))),
inference(superposition,[],[f1654,f76]) ).
fof(f9740,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),union(X0,domain_of(intersection(X1,identity_relation)))) = intersection(union(X2,intersection(complement(X0),diagonalise(X1))),union(complement(X2),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f1654,f446]) ).
fof(f9739,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),union(X0,image(element_relation,complement(X1)))) = intersection(union(X2,intersection(complement(X0),power_class(X1))),union(complement(X2),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f1654,f445]) ).
fof(f9736,plain,
! [X2,X3,X0,X1] : symmetric_difference(complement(X3),union(X0,intersection(complement(X1),complement(X2)))) = intersection(union(X3,intersection(complement(X0),union(X1,X2))),union(complement(X3),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f1654,f447]) ).
fof(f9735,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),union(domain_of(intersection(X0,identity_relation)),X1)) = intersection(union(X2,intersection(diagonalise(X0),complement(X1))),union(complement(X2),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f1654,f443]) ).
fof(f9734,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),union(image(element_relation,complement(X0)),X1)) = intersection(union(X2,intersection(power_class(X0),complement(X1))),union(complement(X2),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f1654,f442]) ).
fof(f9732,plain,
! [X2,X3,X0,X1] : symmetric_difference(complement(X3),union(intersection(complement(X0),complement(X1)),X2)) = intersection(union(X3,intersection(union(X0,X1),complement(X2))),union(complement(X3),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f1654,f444]) ).
fof(f9731,plain,
! [X2,X0,X1] : symmetric_difference(complement(X2),union(X0,X1)) = intersection(union(X2,intersection(complement(X0),complement(X1))),union(complement(X2),union(X0,X1))),
inference(superposition,[],[f1654,f26]) ).
fof(f9805,plain,
! [X0] : symmetric_difference(complement(X0),null_class) = intersection(complement(null_class),union(complement(X0),null_class)),
inference(forward_demodulation,[],[f9730,f4134]) ).
fof(f9730,plain,
! [X0] : symmetric_difference(complement(X0),null_class) = intersection(union(X0,universal_class),union(complement(X0),null_class)),
inference(superposition,[],[f1654,f603]) ).
fof(f9729,plain,
! [X0] : symmetric_difference(power_class(image(element_relation,null_class)),complement(X0)) = intersection(union(image(element_relation,power_class(universal_class)),X0),union(power_class(image(element_relation,null_class)),complement(X0))),
inference(superposition,[],[f1654,f664]) ).
fof(f9728,plain,
! [X0] : symmetric_difference(power_class(universal_class),complement(X0)) = intersection(union(image(element_relation,null_class),X0),union(power_class(universal_class),complement(X0))),
inference(superposition,[],[f1654,f616]) ).
fof(f9727,plain,
! [X0,X1] : symmetric_difference(power_class(X0),complement(X1)) = intersection(union(image(element_relation,complement(X0)),X1),union(power_class(X0),complement(X1))),
inference(superposition,[],[f1654,f55]) ).
fof(f9726,plain,
! [X2,X0,X1] : symmetric_difference(diagonalise(cross_product(X0,X1)),complement(X2)) = intersection(union(domain_of(restrict(identity_relation,X0,X1)),X2),union(diagonalise(cross_product(X0,X1)),complement(X2))),
inference(superposition,[],[f1654,f541]) ).
fof(f9725,plain,
! [X0,X1] : symmetric_difference(diagonalise(X0),complement(X1)) = intersection(union(domain_of(intersection(X0,identity_relation)),X1),union(diagonalise(X0),complement(X1))),
inference(superposition,[],[f1654,f76]) ).
fof(f9724,plain,
! [X2,X0,X1] : symmetric_difference(union(X0,domain_of(intersection(X1,identity_relation))),complement(X2)) = intersection(union(intersection(complement(X0),diagonalise(X1)),X2),union(union(X0,domain_of(intersection(X1,identity_relation))),complement(X2))),
inference(superposition,[],[f1654,f446]) ).
fof(f9723,plain,
! [X2,X0,X1] : symmetric_difference(union(X0,image(element_relation,complement(X1))),complement(X2)) = intersection(union(intersection(complement(X0),power_class(X1)),X2),union(union(X0,image(element_relation,complement(X1))),complement(X2))),
inference(superposition,[],[f1654,f445]) ).
fof(f9720,plain,
! [X2,X3,X0,X1] : symmetric_difference(union(X0,intersection(complement(X1),complement(X2))),complement(X3)) = intersection(union(intersection(complement(X0),union(X1,X2)),X3),union(union(X0,intersection(complement(X1),complement(X2))),complement(X3))),
inference(superposition,[],[f1654,f447]) ).
fof(f9719,plain,
! [X2,X0,X1] : symmetric_difference(union(domain_of(intersection(X0,identity_relation)),X1),complement(X2)) = intersection(union(intersection(diagonalise(X0),complement(X1)),X2),union(union(domain_of(intersection(X0,identity_relation)),X1),complement(X2))),
inference(superposition,[],[f1654,f443]) ).
fof(f9718,plain,
! [X2,X0,X1] : symmetric_difference(union(image(element_relation,complement(X0)),X1),complement(X2)) = intersection(union(intersection(power_class(X0),complement(X1)),X2),union(union(image(element_relation,complement(X0)),X1),complement(X2))),
inference(superposition,[],[f1654,f442]) ).
fof(f9716,plain,
! [X2,X3,X0,X1] : symmetric_difference(union(intersection(complement(X0),complement(X1)),X2),complement(X3)) = intersection(union(intersection(union(X0,X1),complement(X2)),X3),union(union(intersection(complement(X0),complement(X1)),X2),complement(X3))),
inference(superposition,[],[f1654,f444]) ).
fof(f9715,plain,
! [X2,X0,X1] : symmetric_difference(union(X0,X1),complement(X2)) = intersection(union(intersection(complement(X0),complement(X1)),X2),union(union(X0,X1),complement(X2))),
inference(superposition,[],[f1654,f26]) ).
fof(f9798,plain,
! [X0] : symmetric_difference(null_class,complement(X0)) = intersection(complement(null_class),union(null_class,complement(X0))),
inference(forward_demodulation,[],[f9714,f3967]) ).
fof(f9714,plain,
! [X0] : symmetric_difference(null_class,complement(X0)) = intersection(union(universal_class,X0),union(null_class,complement(X0))),
inference(superposition,[],[f1654,f603]) ).
fof(f9797,plain,
! [X0] : symmetric_difference(null_class,complement(X0)) = intersection(complement(null_class),union(null_class,complement(X0))),
inference(forward_demodulation,[],[f9711,f603]) ).
fof(f9711,plain,
! [X0] : symmetric_difference(complement(universal_class),complement(X0)) = intersection(complement(null_class),union(complement(universal_class),complement(X0))),
inference(superposition,[],[f1654,f3967]) ).
fof(f9796,plain,
! [X0] : symmetric_difference(complement(X0),null_class) = intersection(complement(null_class),union(complement(X0),null_class)),
inference(forward_demodulation,[],[f9710,f603]) ).
fof(f9710,plain,
! [X0] : symmetric_difference(complement(X0),complement(universal_class)) = intersection(complement(null_class),union(complement(X0),complement(universal_class))),
inference(superposition,[],[f1654,f4134]) ).
fof(f9709,plain,
! [X0] : symmetric_difference(complement(X0),complement(singleton(X0))) = intersection(successor(X0),union(complement(X0),complement(singleton(X0)))),
inference(superposition,[],[f1654,f43]) ).
fof(f1654,plain,
! [X0,X1] : symmetric_difference(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1))),
inference(superposition,[],[f1614,f26]) ).
fof(f9687,plain,
! [X0] :
( ~ member(omega,symmetric_difference(X0,regular(X0)))
| ~ subclass(universal_class,symmetric_difference(complement(null_class),union(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f6452,f1645]) ).
fof(f9685,plain,
! [X0] :
( ~ subclass(union(X0,regular(X0)),symmetric_difference(X0,regular(X0)))
| union(X0,regular(X0)) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f4078,f1645]) ).
fof(f9683,plain,
! [X0] :
( subclass(symmetric_difference(complement(null_class),union(X0,regular(X0))),complement(symmetric_difference(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f3947,f1645]) ).
fof(f9682,plain,
! [X0] :
( ~ subclass(complement(null_class),symmetric_difference(X0,regular(X0)))
| complement(null_class) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f3936,f1645]) ).
fof(f9671,plain,
! [X0] :
( ~ member(null_class,symmetric_difference(X0,regular(X0)))
| ~ inductive(symmetric_difference(complement(null_class),union(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f1693,f1645]) ).
fof(f9670,plain,
! [X0] :
( member(null_class,complement(symmetric_difference(X0,regular(X0))))
| ~ inductive(symmetric_difference(complement(null_class),union(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f1662,f1645]) ).
fof(f9669,plain,
! [X0,X1] :
( member(X1,complement(symmetric_difference(X0,regular(X0))))
| ~ member(X1,symmetric_difference(complement(null_class),union(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f1659,f1645]) ).
fof(f9668,plain,
! [X0] :
( symmetric_difference(complement(null_class),union(X0,regular(X0))) = intersection(complement(symmetric_difference(X0,regular(X0))),union(complement(null_class),union(X0,regular(X0))))
| null_class = X0 ),
inference(superposition,[],[f1614,f1645]) ).
fof(f9667,plain,
! [X2,X0,X1] :
( ~ subclass(symmetric_difference(X0,regular(X0)),X1)
| ~ member(X2,complement(null_class))
| ~ member(X2,union(X0,regular(X0)))
| member(X2,X1)
| null_class = X0 ),
inference(superposition,[],[f747,f1645]) ).
fof(f9666,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(ordered_pair(X1,X2),complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f719,f1645]) ).
fof(f9665,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(ordered_pair(X1,X2),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f718,f1645]) ).
fof(f9664,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(unordered_pair(X1,X2),complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f265,f1645]) ).
fof(f9663,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(unordered_pair(X1,X2),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f264,f1645]) ).
fof(f9660,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(singleton(X1),complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f177,f1645]) ).
fof(f9659,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,regular(X0)))
| member(singleton(X1),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f176,f1645]) ).
fof(f9656,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,regular(X0)),X1),union(X0,regular(X0)))
| subclass(intersection(complement(null_class),union(X0,regular(X0))),X1)
| null_class = X0 ),
inference(superposition,[],[f133,f1645]) ).
fof(f9655,plain,
! [X0] :
( member(regular(symmetric_difference(X0,regular(X0))),union(X0,regular(X0)))
| null_class = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f132,f1645]) ).
fof(f9653,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,regular(X0)),X1),complement(null_class))
| subclass(intersection(complement(null_class),union(X0,regular(X0))),X1)
| null_class = X0 ),
inference(superposition,[],[f128,f1645]) ).
fof(f9652,plain,
! [X0] :
( member(regular(symmetric_difference(X0,regular(X0))),complement(null_class))
| null_class = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f127,f1645]) ).
fof(f9650,plain,
! [X0,X1] :
( member(X1,symmetric_difference(X0,regular(X0)))
| ~ member(X1,union(X0,regular(X0)))
| ~ member(X1,complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f23,f1645]) ).
fof(f9648,plain,
! [X0,X1] :
( ~ member(X1,symmetric_difference(X0,regular(X0)))
| member(X1,complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f21,f1645]) ).
fof(f9647,plain,
! [X0] :
( union(null_class,intersection(complement(X0),complement(regular(X0)))) = complement(symmetric_difference(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f447,f1645]) ).
fof(f9646,plain,
( symmetric_difference(universal_class,regular(universal_class)) = intersection(complement(null_class),complement(null_class))
| universal_class = null_class ),
inference(superposition,[],[f1645,f3967]) ).
fof(f9698,plain,
! [X0] :
( symmetric_difference(singleton(X0),X0) = intersection(complement(null_class),union(singleton(X0),X0))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f9645]) ).
fof(f9645,plain,
! [X0] :
( symmetric_difference(singleton(X0),X0) = intersection(complement(null_class),union(singleton(X0),X0))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f1645,f656]) ).
fof(f1645,plain,
! [X0] :
( symmetric_difference(X0,regular(X0)) = intersection(complement(null_class),union(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f1614,f67]) ).
fof(f9524,plain,
! [X2,X0,X1] :
( member(X2,image(X0,X1))
| ~ member(X2,universal_class)
| null_class = restrict(inverse(restrict(X0,X1,universal_class)),singleton(X2),universal_class) ),
inference(superposition,[],[f1493,f42]) ).
fof(f9523,plain,
! [X0] :
( ~ member(apply(choice,complement(range_of(X0))),universal_class)
| null_class = restrict(inverse(X0),singleton(apply(choice,complement(range_of(X0)))),universal_class)
| ~ member(complement(range_of(X0)),universal_class)
| null_class = complement(range_of(X0)) ),
inference(resolution,[],[f1493,f880]) ).
fof(f9535,plain,
! [X0] :
( null_class = restrict(inverse(X0),singleton(regular(complement(range_of(X0)))),universal_class)
| null_class = complement(range_of(X0)) ),
inference(subsumption_resolution,[],[f9518,f8509]) ).
fof(f9518,plain,
! [X0] :
( ~ member(regular(complement(range_of(X0))),universal_class)
| null_class = restrict(inverse(X0),singleton(regular(complement(range_of(X0)))),universal_class)
| null_class = complement(range_of(X0)) ),
inference(resolution,[],[f1493,f120]) ).
fof(f9528,plain,
! [X2,X0,X1] :
( null_class = restrict(inverse(X2),singleton(ordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(range_of(X2))) ),
inference(subsumption_resolution,[],[f9511,f696]) ).
fof(f9511,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),universal_class)
| null_class = restrict(inverse(X2),singleton(ordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(range_of(X2))) ),
inference(resolution,[],[f1493,f698]) ).
fof(f9527,plain,
! [X0,X1] :
( null_class = restrict(inverse(X1),singleton(singleton(X0)),universal_class)
| ~ subclass(universal_class,complement(range_of(X1))) ),
inference(subsumption_resolution,[],[f9510,f118]) ).
fof(f9510,plain,
! [X0,X1] :
( ~ member(singleton(X0),universal_class)
| null_class = restrict(inverse(X1),singleton(singleton(X0)),universal_class)
| ~ subclass(universal_class,complement(range_of(X1))) ),
inference(resolution,[],[f1493,f175]) ).
fof(f9525,plain,
! [X2,X0,X1] :
( null_class = restrict(inverse(X2),singleton(unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(range_of(X2))) ),
inference(subsumption_resolution,[],[f9508,f11]) ).
fof(f9508,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| null_class = restrict(inverse(X2),singleton(unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(range_of(X2))) ),
inference(resolution,[],[f1493,f263]) ).
fof(f9507,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(range_of(X0)),X1),universal_class)
| null_class = restrict(inverse(X0),singleton(not_subclass_element(complement(range_of(X0)),X1)),universal_class)
| subclass(complement(range_of(X0)),X1) ),
inference(resolution,[],[f1493,f121]) ).
fof(f9506,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,range_of(X1)),universal_class)
| null_class = restrict(inverse(X1),singleton(not_subclass_element(X0,range_of(X1))),universal_class)
| subclass(X0,range_of(X1)) ),
inference(resolution,[],[f1493,f3]) ).
fof(f9505,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(inverse(X1),singleton(X0),universal_class)
| ~ subclass(range_of(X1),X2)
| member(X0,X2) ),
inference(resolution,[],[f1493,f1]) ).
fof(f1493,plain,
! [X0,X1] :
( member(X1,range_of(X0))
| ~ member(X1,universal_class)
| null_class = restrict(inverse(X0),singleton(X1),universal_class) ),
inference(superposition,[],[f31,f39]) ).
fof(f9486,plain,
! [X0] : member(ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))),singleton(ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))))),
inference(superposition,[],[f5439,f4463]) ).
fof(f9485,plain,
! [X0,X1] :
( ~ subclass(singleton(ordered_pair(singleton(X0),X0)),X1)
| member(ordered_pair(singleton(X0),X0),X1) ),
inference(resolution,[],[f5439,f1]) ).
fof(f5439,plain,
! [X0] : member(ordered_pair(singleton(X0),X0),singleton(ordered_pair(singleton(X0),X0))),
inference(superposition,[],[f5369,f4463]) ).
fof(f9478,plain,
! [X0] :
( subclass(symmetric_difference(singleton(X0),X0),complement(null_class))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f9477]) ).
fof(f9477,plain,
! [X0] :
( subclass(symmetric_difference(singleton(X0),X0),complement(null_class))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f4669,f656]) ).
fof(f9475,plain,
! [X0] :
( null_class = X0
| ~ subclass(complement(null_class),symmetric_difference(X0,regular(X0)))
| complement(null_class) = symmetric_difference(X0,regular(X0)) ),
inference(resolution,[],[f4669,f7]) ).
fof(f4669,plain,
! [X0] :
( subclass(symmetric_difference(X0,regular(X0)),complement(null_class))
| null_class = X0 ),
inference(superposition,[],[f3947,f67]) ).
fof(f9473,plain,
! [X0,X1] :
( subset_relation = restrict(identity_relation,X0,X1)
| ~ subclass(subset_relation,restrict(identity_relation,X0,X1)) ),
inference(forward_demodulation,[],[f9471,f29]) ).
fof(f9471,plain,
! [X0,X1] :
( ~ subclass(subset_relation,restrict(identity_relation,X0,X1))
| subset_relation = intersection(cross_product(X0,X1),identity_relation) ),
inference(superposition,[],[f4097,f29]) ).
fof(f4097,plain,
! [X0] :
( ~ subclass(subset_relation,intersection(X0,identity_relation))
| subset_relation = intersection(X0,identity_relation) ),
inference(resolution,[],[f4062,f7]) ).
fof(f9467,plain,
! [X0] :
( range_of(X0) = cantor(inverse(X0))
| ~ subclass(range_of(X0),cantor(inverse(X0))) ),
inference(forward_demodulation,[],[f9460,f39]) ).
fof(f9460,plain,
! [X0] :
( ~ subclass(range_of(X0),cantor(inverse(X0)))
| domain_of(inverse(X0)) = cantor(inverse(X0)) ),
inference(superposition,[],[f3959,f39]) ).
fof(f9466,plain,
! [X0] :
( inverse(X0) = cantor(flip(cross_product(X0,universal_class)))
| ~ subclass(inverse(X0),cantor(flip(cross_product(X0,universal_class)))) ),
inference(forward_demodulation,[],[f9459,f38]) ).
fof(f9459,plain,
! [X0] :
( ~ subclass(inverse(X0),cantor(flip(cross_product(X0,universal_class))))
| domain_of(flip(cross_product(X0,universal_class))) = cantor(flip(cross_product(X0,universal_class))) ),
inference(superposition,[],[f3959,f38]) ).
fof(f9463,plain,
! [X0] :
( sum_class(X0) = cantor(restrict(element_relation,universal_class,X0))
| ~ subclass(sum_class(X0),cantor(restrict(element_relation,universal_class,X0))) ),
inference(forward_demodulation,[],[f9457,f53]) ).
fof(f9457,plain,
! [X0] :
( ~ subclass(sum_class(X0),cantor(restrict(element_relation,universal_class,X0)))
| domain_of(restrict(element_relation,universal_class,X0)) = cantor(restrict(element_relation,universal_class,X0)) ),
inference(superposition,[],[f3959,f53]) ).
fof(f3959,plain,
! [X0] :
( ~ subclass(domain_of(X0),cantor(X0))
| domain_of(X0) = cantor(X0) ),
inference(resolution,[],[f3948,f7]) ).
fof(f9455,plain,
! [X2,X0,X1] :
( member(apply(X0,X1),cantor(X2))
| ~ member(apply(X0,X1),domain_of(X2))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X2)))
| ~ function(X0) ),
inference(resolution,[],[f925,f3109]) ).
fof(f9454,plain,
! [X2,X0,X1] :
( member(image(X0,X1),cantor(X2))
| ~ member(image(X0,X1),domain_of(X2))
| ~ function(X0)
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X2)))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f925,f554]) ).
fof(f9453,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),cantor(X2))
| ~ member(ordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X2))) ),
inference(resolution,[],[f925,f697]) ).
fof(f9452,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),cantor(X2))
| ~ member(ordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,complement(complement(diagonalise(compose(inverse(element_relation),X2))))) ),
inference(resolution,[],[f925,f787]) ).
fof(f9451,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),cantor(X2))
| ~ member(unordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X2))) ),
inference(resolution,[],[f925,f161]) ).
fof(f9450,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),cantor(X2))
| ~ member(unordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,complement(complement(diagonalise(compose(inverse(element_relation),X2))))) ),
inference(resolution,[],[f925,f471]) ).
fof(f9449,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),cantor(X2))
| ~ member(not_subclass_element(X0,X1),domain_of(X2))
| ~ subclass(X0,diagonalise(compose(inverse(element_relation),X2)))
| subclass(X0,X1) ),
inference(resolution,[],[f925,f160]) ).
fof(f9448,plain,
! [X0,X1] :
( member(apply(choice,X0),cantor(X1))
| ~ member(apply(choice,X0),domain_of(X1))
| ~ member(X0,universal_class)
| ~ subclass(X0,diagonalise(compose(inverse(element_relation),X1)))
| null_class = X0 ),
inference(resolution,[],[f925,f875]) ).
fof(f9447,plain,
! [X0,X1] :
( member(regular(intersection(X0,diagonalise(compose(inverse(element_relation),X1)))),cantor(X1))
| ~ member(regular(intersection(X0,diagonalise(compose(inverse(element_relation),X1)))),domain_of(X1))
| null_class = intersection(X0,diagonalise(compose(inverse(element_relation),X1))) ),
inference(resolution,[],[f925,f132]) ).
fof(f9446,plain,
! [X0,X1] :
( member(regular(X0),cantor(X1))
| ~ member(regular(X0),domain_of(X1))
| ~ subclass(X0,diagonalise(compose(inverse(element_relation),X1)))
| null_class = X0 ),
inference(resolution,[],[f925,f159]) ).
fof(f9445,plain,
! [X0,X1] :
( member(power_class(X0),cantor(X1))
| ~ member(power_class(X0),domain_of(X1))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f925,f165]) ).
fof(f9444,plain,
! [X0,X1] :
( member(sum_class(X0),cantor(X1))
| ~ member(sum_class(X0),domain_of(X1))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f925,f164]) ).
fof(f9443,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),cantor(X1))
| ~ member(ordered_pair(X0,domain_of(X0)),domain_of(X1))
| ~ subclass(domain_relation,diagonalise(compose(inverse(element_relation),X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f925,f318]) ).
fof(f9442,plain,
! [X0,X1] :
( member(singleton(X0),cantor(X1))
| ~ member(singleton(X0),domain_of(X1))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X1))) ),
inference(resolution,[],[f925,f162]) ).
fof(f9441,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,diagonalise(compose(inverse(element_relation),X1))),X2),cantor(X1))
| ~ member(not_subclass_element(intersection(X0,diagonalise(compose(inverse(element_relation),X1))),X2),domain_of(X1))
| subclass(intersection(X0,diagonalise(compose(inverse(element_relation),X1))),X2) ),
inference(resolution,[],[f925,f133]) ).
fof(f9440,plain,
! [X0,X1] :
( member(X0,cantor(X1))
| ~ member(X0,domain_of(X1))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X1)))
| singleton(X0) = null_class ),
inference(resolution,[],[f925,f3115]) ).
fof(f9439,plain,
! [X0] :
( member(apply(choice,diagonalise(compose(inverse(element_relation),X0))),cantor(X0))
| ~ member(apply(choice,diagonalise(compose(inverse(element_relation),X0))),domain_of(X0))
| null_class = diagonalise(compose(inverse(element_relation),X0))
| ~ member(diagonalise(compose(inverse(element_relation),X0)),universal_class) ),
inference(resolution,[],[f925,f70]) ).
fof(f9434,plain,
! [X0,X1] :
( member(regular(intersection(diagonalise(compose(inverse(element_relation),X0)),X1)),cantor(X0))
| ~ member(regular(intersection(diagonalise(compose(inverse(element_relation),X0)),X1)),domain_of(X0))
| null_class = intersection(diagonalise(compose(inverse(element_relation),X0)),X1) ),
inference(resolution,[],[f925,f127]) ).
fof(f9432,plain,
! [X0] :
( member(regular(diagonalise(compose(inverse(element_relation),X0))),cantor(X0))
| ~ member(regular(diagonalise(compose(inverse(element_relation),X0))),domain_of(X0))
| null_class = diagonalise(compose(inverse(element_relation),X0)) ),
inference(resolution,[],[f925,f66]) ).
fof(f9431,plain,
! [X0] :
( member(omega,cantor(X0))
| ~ member(omega,domain_of(X0))
| ~ subclass(universal_class,diagonalise(compose(inverse(element_relation),X0))) ),
inference(resolution,[],[f925,f163]) ).
fof(f9428,plain,
! [X0] :
( member(null_class,cantor(X0))
| ~ member(null_class,domain_of(X0))
| ~ inductive(diagonalise(compose(inverse(element_relation),X0))) ),
inference(resolution,[],[f925,f47]) ).
fof(f9420,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(diagonalise(compose(inverse(element_relation),X0)),X1),X2),cantor(X0))
| ~ member(not_subclass_element(intersection(diagonalise(compose(inverse(element_relation),X0)),X1),X2),domain_of(X0))
| subclass(intersection(diagonalise(compose(inverse(element_relation),X0)),X1),X2) ),
inference(resolution,[],[f925,f128]) ).
fof(f9419,plain,
! [X0,X1] :
( member(not_subclass_element(diagonalise(compose(inverse(element_relation),X0)),X1),cantor(X0))
| ~ member(not_subclass_element(diagonalise(compose(inverse(element_relation),X0)),X1),domain_of(X0))
| subclass(diagonalise(compose(inverse(element_relation),X0)),X1) ),
inference(resolution,[],[f925,f2]) ).
fof(f925,plain,
! [X0,X1] :
( ~ member(X1,diagonalise(compose(inverse(element_relation),X0)))
| member(X1,cantor(X0))
| ~ member(X1,domain_of(X0)) ),
inference(superposition,[],[f23,f77]) ).
fof(f3957,plain,
( ~ subclass(cross_product(universal_class,universal_class),subset_relation)
| cross_product(universal_class,universal_class) = subset_relation ),
inference(resolution,[],[f3945,f7]) ).
fof(f9406,plain,
! [X0,X1] :
( subset_relation = restrict(identity_relation,X0,X1)
| ~ subclass(subset_relation,restrict(identity_relation,X0,X1)) ),
inference(forward_demodulation,[],[f9404,f28]) ).
fof(f9404,plain,
! [X0,X1] :
( ~ subclass(subset_relation,restrict(identity_relation,X0,X1))
| subset_relation = intersection(identity_relation,cross_product(X0,X1)) ),
inference(superposition,[],[f3953,f28]) ).
fof(f3953,plain,
! [X0] :
( ~ subclass(subset_relation,intersection(identity_relation,X0))
| subset_relation = intersection(identity_relation,X0) ),
inference(resolution,[],[f3921,f7]) ).
fof(f9347,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = apply(X1,X2)
| apply(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(universal_class,ordered_pair(X0,X3))
| ~ function(X1) ),
inference(resolution,[],[f693,f3109]) ).
fof(f9346,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = image(X1,X2)
| unordered_pair(X0,singleton(X3)) = image(X1,X2)
| ~ function(X1)
| ~ subclass(universal_class,ordered_pair(X0,X3))
| ~ member(X2,universal_class) ),
inference(resolution,[],[f693,f554]) ).
fof(f9345,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = ordered_pair(X1,X2)
| ordered_pair(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(universal_class,ordered_pair(X0,X3)) ),
inference(resolution,[],[f693,f697]) ).
fof(f9344,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = ordered_pair(X1,X2)
| ordered_pair(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(universal_class,complement(complement(ordered_pair(X0,X3)))) ),
inference(resolution,[],[f693,f787]) ).
fof(f9343,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = unordered_pair(X1,X2)
| unordered_pair(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(universal_class,ordered_pair(X0,X3)) ),
inference(resolution,[],[f693,f161]) ).
fof(f9342,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = unordered_pair(X1,X2)
| unordered_pair(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(universal_class,complement(complement(ordered_pair(X0,X3)))) ),
inference(resolution,[],[f693,f471]) ).
fof(f9341,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = not_subclass_element(X1,X2)
| not_subclass_element(X1,X2) = unordered_pair(X0,singleton(X3))
| ~ subclass(X1,ordered_pair(X0,X3))
| subclass(X1,X2) ),
inference(resolution,[],[f693,f160]) ).
fof(f9340,plain,
! [X2,X0,X1] :
( singleton(X0) = apply(choice,X1)
| apply(choice,X1) = unordered_pair(X0,singleton(X2))
| ~ member(X1,universal_class)
| ~ subclass(X1,ordered_pair(X0,X2))
| null_class = X1 ),
inference(resolution,[],[f693,f875]) ).
fof(f9339,plain,
! [X2,X0,X1] :
( singleton(X0) = regular(intersection(X1,ordered_pair(X0,X2)))
| unordered_pair(X0,singleton(X2)) = regular(intersection(X1,ordered_pair(X0,X2)))
| null_class = intersection(X1,ordered_pair(X0,X2)) ),
inference(resolution,[],[f693,f132]) ).
fof(f9338,plain,
! [X2,X0,X1] :
( singleton(X0) = regular(X1)
| regular(X1) = unordered_pair(X0,singleton(X2))
| ~ subclass(X1,ordered_pair(X0,X2))
| null_class = X1 ),
inference(resolution,[],[f693,f159]) ).
fof(f9337,plain,
! [X2,X0,X1] :
( singleton(X0) = power_class(X1)
| power_class(X1) = unordered_pair(X0,singleton(X2))
| ~ subclass(universal_class,ordered_pair(X0,X2))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f693,f165]) ).
fof(f9336,plain,
! [X2,X0,X1] :
( singleton(X0) = sum_class(X1)
| sum_class(X1) = unordered_pair(X0,singleton(X2))
| ~ subclass(universal_class,ordered_pair(X0,X2))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f693,f164]) ).
fof(f9335,plain,
! [X2,X0,X1] :
( singleton(X0) = ordered_pair(X1,domain_of(X1))
| ordered_pair(X1,domain_of(X1)) = unordered_pair(X0,singleton(X2))
| ~ subclass(domain_relation,ordered_pair(X0,X2))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f693,f318]) ).
fof(f9334,plain,
! [X2,X0,X1] :
( singleton(X0) = singleton(X1)
| singleton(X1) = unordered_pair(X0,singleton(X2))
| ~ subclass(universal_class,ordered_pair(X0,X2)) ),
inference(resolution,[],[f693,f162]) ).
fof(f9333,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = not_subclass_element(intersection(X1,ordered_pair(X0,X2)),X3)
| unordered_pair(X0,singleton(X2)) = not_subclass_element(intersection(X1,ordered_pair(X0,X2)),X3)
| subclass(intersection(X1,ordered_pair(X0,X2)),X3) ),
inference(resolution,[],[f693,f133]) ).
fof(f9332,plain,
! [X2,X0,X1] :
( singleton(X0) = X1
| unordered_pair(X0,singleton(X2)) = X1
| ~ subclass(universal_class,ordered_pair(X0,X2))
| singleton(X1) = null_class ),
inference(resolution,[],[f693,f3115]) ).
fof(f9355,plain,
! [X0,X1] :
( singleton(X0) = apply(choice,ordered_pair(X0,X1))
| unordered_pair(X0,singleton(X1)) = apply(choice,ordered_pair(X0,X1))
| ordered_pair(X0,X1) = null_class ),
inference(subsumption_resolution,[],[f9331,f696]) ).
fof(f9331,plain,
! [X0,X1] :
( singleton(X0) = apply(choice,ordered_pair(X0,X1))
| unordered_pair(X0,singleton(X1)) = apply(choice,ordered_pair(X0,X1))
| ordered_pair(X0,X1) = null_class
| ~ member(ordered_pair(X0,X1),universal_class) ),
inference(resolution,[],[f693,f70]) ).
fof(f9326,plain,
! [X2,X0,X1] :
( singleton(X0) = regular(intersection(ordered_pair(X0,X1),X2))
| unordered_pair(X0,singleton(X1)) = regular(intersection(ordered_pair(X0,X1),X2))
| null_class = intersection(ordered_pair(X0,X1),X2) ),
inference(resolution,[],[f693,f127]) ).
fof(f9324,plain,
! [X0,X1] :
( singleton(X0) = regular(ordered_pair(X0,X1))
| unordered_pair(X0,singleton(X1)) = regular(ordered_pair(X0,X1))
| ordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f693,f66]) ).
fof(f9323,plain,
! [X0,X1] :
( singleton(X0) = omega
| unordered_pair(X0,singleton(X1)) = omega
| ~ subclass(universal_class,ordered_pair(X0,X1)) ),
inference(resolution,[],[f693,f163]) ).
fof(f9320,plain,
! [X0,X1] :
( singleton(X0) = null_class
| unordered_pair(X0,singleton(X1)) = null_class
| ~ inductive(ordered_pair(X0,X1)) ),
inference(resolution,[],[f693,f47]) ).
fof(f9312,plain,
! [X2,X3,X0,X1] :
( singleton(X0) = not_subclass_element(intersection(ordered_pair(X0,X1),X2),X3)
| unordered_pair(X0,singleton(X1)) = not_subclass_element(intersection(ordered_pair(X0,X1),X2),X3)
| subclass(intersection(ordered_pair(X0,X1),X2),X3) ),
inference(resolution,[],[f693,f128]) ).
fof(f9311,plain,
! [X2,X0,X1] :
( singleton(X0) = not_subclass_element(ordered_pair(X0,X1),X2)
| unordered_pair(X0,singleton(X1)) = not_subclass_element(ordered_pair(X0,X1),X2)
| subclass(ordered_pair(X0,X1),X2) ),
inference(resolution,[],[f693,f2]) ).
fof(f693,plain,
! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton(X0) = X2
| unordered_pair(X0,singleton(X1)) = X2 ),
inference(superposition,[],[f8,f13]) ).
fof(f3603,plain,
! [X0] :
( ~ subclass(complement(inverse(subset_relation)),identity_relation)
| subclass(complement(inverse(subset_relation)),X0) ),
inference(resolution,[],[f2983,f2982]) ).
fof(f9277,plain,
! [X0] :
( ~ subclass(singleton(singleton(singleton(X0))),identity_relation)
| member(singleton(singleton(X0)),inverse(subset_relation)) ),
inference(superposition,[],[f3602,f4463]) ).
fof(f3602,plain,
! [X0,X1] :
( ~ subclass(ordered_pair(X0,X1),identity_relation)
| member(singleton(X0),inverse(subset_relation)) ),
inference(resolution,[],[f2983,f706]) ).
fof(f9267,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,universal_class)
| not_subclass_element(singleton(X0),identity_relation) = X0 ),
inference(resolution,[],[f3532,f652]) ).
fof(f3532,plain,
! [X0] :
( ~ subclass(singleton(X0),identity_relation)
| member(X0,subset_relation)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f2984,f168]) ).
fof(f9266,plain,
( null_class = singleton(apply(choice,complement(complement(null_class))))
| ~ member(complement(complement(null_class)),universal_class)
| null_class = complement(complement(null_class)) ),
inference(resolution,[],[f9239,f880]) ).
fof(f9261,plain,
( null_class = singleton(regular(complement(complement(null_class))))
| null_class = complement(complement(null_class)) ),
inference(resolution,[],[f9239,f120]) ).
fof(f9251,plain,
! [X0] :
( null_class = singleton(not_subclass_element(complement(complement(null_class)),X0))
| subclass(complement(complement(null_class)),X0) ),
inference(resolution,[],[f9239,f121]) ).
fof(f9250,plain,
! [X0] :
( null_class = singleton(not_subclass_element(X0,complement(null_class)))
| subclass(X0,complement(null_class)) ),
inference(resolution,[],[f9239,f3]) ).
fof(f9249,plain,
! [X0,X1] :
( singleton(X0) = null_class
| ~ subclass(complement(null_class),X1)
| member(X0,X1) ),
inference(resolution,[],[f9239,f1]) ).
fof(f9239,plain,
! [X1] :
( member(X1,complement(null_class))
| singleton(X1) = null_class ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886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).
fof(f9246,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = null_class ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977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).
fof(f9237,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| null_class = singleton(apply(choice,complement(X0)))
| ~ member(complement(X0),universal_class)
| complement(X0) = null_class ),
inference(resolution,[],[f3115,f880]) ).
fof(f9229,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| null_class = singleton(regular(complement(X0)))
| complement(X0) = null_class ),
inference(resolution,[],[f3115,f120]) ).
fof(f9245,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ subclass(universal_class,symmetric_difference(X0,X1)) ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977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).
fof(f9220,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = singleton(omega)
| ~ subclass(universal_class,symmetric_difference(X0,X1)) ),
inference(resolution,[],[f3115,f6452]) ).
fof(f9244,plain,
! [X0,X1] :
( null_class = singleton(image(X0,singleton(X1)))
| member(apply(X0,X1),universal_class) ),
inference(subsumption_resolution,[],[f9216,f4]) ).
fof(f9216,plain,
! [X0,X1] :
( ~ subclass(universal_class,universal_class)
| null_class = singleton(image(X0,singleton(X1)))
| member(apply(X0,X1),universal_class) ),
inference(resolution,[],[f3115,f316]) ).
fof(f9198,plain,
! [X0] :
( ~ subclass(universal_class,singleton(X0))
| null_class = singleton(null_class)
| singleton(X0) = null_class
| ~ inductive(X0) ),
inference(resolution,[],[f3115,f6274]) ).
fof(f9187,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,flip(X0))
| null_class = singleton(ordered_pair(ordered_pair(X1,X2),X3))
| member(ordered_pair(ordered_pair(X2,X1),X3),X0) ),
inference(resolution,[],[f3115,f36]) ).
fof(f9186,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,rotate(X0))
| null_class = singleton(ordered_pair(ordered_pair(X1,X2),X3))
| member(ordered_pair(ordered_pair(X2,X3),X1),X0) ),
inference(resolution,[],[f3115,f33]) ).
fof(f9172,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(X0))
| null_class = singleton(ordered_pair(X1,X2))
| ~ homomorphism(X3,X0,X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(X0,ordered_pair(X1,X2))) ),
inference(resolution,[],[f3115,f89]) ).
fof(f9148,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = singleton(not_subclass_element(complement(X0),X1))
| subclass(complement(X0),X1) ),
inference(resolution,[],[f3115,f121]) ).
fof(f9145,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = singleton(not_subclass_element(X1,X0))
| subclass(X1,X0) ),
inference(resolution,[],[f3115,f3]) ).
fof(f9143,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| singleton(X1) = null_class
| member(X1,range_of(X0)) ),
inference(resolution,[],[f3115,f6375]) ).
fof(f9142,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| singleton(X1) = null_class
| member(X1,domain_of(X0)) ),
inference(resolution,[],[f3115,f923]) ).
fof(f9140,plain,
! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| singleton(X1) = null_class
| ~ member(X1,X0)
| null_class = X0 ),
inference(resolution,[],[f3115,f6160]) ).
fof(f9135,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,image(X0,image(X1,singleton(X2))))
| null_class = singleton(X3)
| member(ordered_pair(X2,X3),compose(X0,X1))
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f3115,f59]) ).
fof(f9133,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| singleton(X1) = null_class
| ~ member(X1,power_class(X0)) ),
inference(resolution,[],[f3115,f152]) ).
fof(f9130,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| singleton(X1) = null_class
| ~ member(X1,diagonalise(X0)) ),
inference(resolution,[],[f3115,f155]) ).
fof(f9124,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| null_class = singleton(X3)
| member(X3,X0) ),
inference(resolution,[],[f3115,f495]) ).
fof(f9123,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| null_class = singleton(X3)
| member(X3,cross_product(X1,X2)) ),
inference(resolution,[],[f3115,f496]) ).
fof(f9240,plain,
! [X1] :
( singleton(X1) = null_class
| member(X1,complement(null_class)) ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886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).
fof(f9121,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(null_class,X0))
| singleton(X1) = null_class
| member(X1,complement(null_class)) ),
inference(resolution,[],[f3115,f3991]) ).
fof(f9120,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| singleton(X1) = null_class
| member(X1,successor(X0)) ),
inference(resolution,[],[f3115,f6656]) ).
fof(f9119,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,null_class))
| singleton(X1) = null_class
| member(X1,complement(null_class)) ),
inference(resolution,[],[f3115,f4123]) ).
fof(f9118,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| null_class = singleton(X2)
| member(X2,union(X0,X1)) ),
inference(resolution,[],[f3115,f1660]) ).
fof(f9117,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| null_class = singleton(X2)
| ~ member(X2,intersection(X0,X1)) ),
inference(resolution,[],[f3115,f3825]) ).
fof(f9115,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| singleton(X1) = null_class
| ~ member(X1,X0) ),
inference(resolution,[],[f3115,f24]) ).
fof(f9114,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(complement(X0),complement(X1)))
| null_class = singleton(X2)
| ~ member(X2,union(X0,X1)) ),
inference(resolution,[],[f3115,f448]) ).
fof(f9113,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = singleton(X2)
| member(X2,X0) ),
inference(resolution,[],[f3115,f21]) ).
fof(f9112,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = singleton(X2)
| member(X2,X1) ),
inference(resolution,[],[f3115,f22]) ).
fof(f9110,plain,
! [X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| singleton(X1) = null_class
| X0 = X1 ),
inference(resolution,[],[f3115,f650]) ).
fof(f9109,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| null_class = singleton(X2)
| X0 = X2
| X1 = X2 ),
inference(resolution,[],[f3115,f8]) ).
fof(f9108,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| singleton(X1) = null_class
| ~ subclass(X0,X2)
| member(X1,X2) ),
inference(resolution,[],[f3115,f1]) ).
fof(f3115,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(universal_class,X1)
| singleton(X0) = null_class ),
inference(resolution,[],[f3114,f1]) ).
fof(f9050,plain,
! [X0,X1] :
( member(X0,intersection(complement(X1),power_class(image(element_relation,null_class))))
| member(X0,union(X1,image(element_relation,power_class(universal_class))))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f449,f664]) ).
fof(f9049,plain,
! [X0,X1] :
( member(X0,intersection(complement(X1),power_class(universal_class)))
| member(X0,union(X1,image(element_relation,null_class)))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f449,f616]) ).
fof(f9048,plain,
! [X2,X0,X1] :
( member(X1,intersection(complement(X2),power_class(X0)))
| member(X1,union(X2,image(element_relation,complement(X0))))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f449,f55]) ).
fof(f9047,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),diagonalise(cross_product(X0,X1))))
| member(X2,union(X3,domain_of(restrict(identity_relation,X0,X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f541]) ).
fof(f9046,plain,
! [X2,X0,X1] :
( member(X1,intersection(complement(X2),diagonalise(X0)))
| member(X1,union(X2,domain_of(intersection(X0,identity_relation))))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f449,f76]) ).
fof(f9045,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),union(X0,domain_of(intersection(X1,identity_relation)))))
| member(X2,union(X3,intersection(complement(X0),diagonalise(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f446]) ).
fof(f9044,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),union(X0,image(element_relation,complement(X1)))))
| member(X2,union(X3,intersection(complement(X0),power_class(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f445]) ).
fof(f9041,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,intersection(complement(X4),union(X0,intersection(complement(X1),complement(X2)))))
| member(X3,union(X4,intersection(complement(X0),union(X1,X2))))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f449,f447]) ).
fof(f9040,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),union(domain_of(intersection(X0,identity_relation)),X1)))
| member(X2,union(X3,intersection(diagonalise(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f443]) ).
fof(f9039,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),union(image(element_relation,complement(X0)),X1)))
| member(X2,union(X3,intersection(power_class(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f442]) ).
fof(f9037,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,intersection(complement(X4),union(intersection(complement(X0),complement(X1)),X2)))
| member(X3,union(X4,intersection(union(X0,X1),complement(X2))))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f449,f444]) ).
fof(f9036,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(complement(X3),union(X0,X1)))
| member(X2,union(X3,intersection(complement(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f26]) ).
fof(f9034,plain,
! [X0,X1] :
( member(X0,intersection(power_class(image(element_relation,null_class)),complement(X1)))
| member(X0,union(image(element_relation,power_class(universal_class)),X1))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f449,f664]) ).
fof(f9033,plain,
! [X0,X1] :
( member(X0,intersection(power_class(universal_class),complement(X1)))
| member(X0,union(image(element_relation,null_class),X1))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f449,f616]) ).
fof(f9032,plain,
! [X2,X0,X1] :
( member(X1,intersection(power_class(X0),complement(X2)))
| member(X1,union(image(element_relation,complement(X0)),X2))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f449,f55]) ).
fof(f9031,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(diagonalise(cross_product(X0,X1)),complement(X3)))
| member(X2,union(domain_of(restrict(identity_relation,X0,X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f541]) ).
fof(f9030,plain,
! [X2,X0,X1] :
( member(X1,intersection(diagonalise(X0),complement(X2)))
| member(X1,union(domain_of(intersection(X0,identity_relation)),X2))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f449,f76]) ).
fof(f9029,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(union(X0,domain_of(intersection(X1,identity_relation))),complement(X3)))
| member(X2,union(intersection(complement(X0),diagonalise(X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f446]) ).
fof(f9028,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(union(X0,image(element_relation,complement(X1))),complement(X3)))
| member(X2,union(intersection(complement(X0),power_class(X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f445]) ).
fof(f9025,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,intersection(union(X0,intersection(complement(X1),complement(X2))),complement(X4)))
| member(X3,union(intersection(complement(X0),union(X1,X2)),X4))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f449,f447]) ).
fof(f9024,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(union(domain_of(intersection(X0,identity_relation)),X1),complement(X3)))
| member(X2,union(intersection(diagonalise(X0),complement(X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f443]) ).
fof(f9023,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(union(image(element_relation,complement(X0)),X1),complement(X3)))
| member(X2,union(intersection(power_class(X0),complement(X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f442]) ).
fof(f9021,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,intersection(union(intersection(complement(X0),complement(X1)),X2),complement(X4)))
| member(X3,union(intersection(union(X0,X1),complement(X2)),X4))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f449,f444]) ).
fof(f9020,plain,
! [X2,X3,X0,X1] :
( member(X2,intersection(union(X0,X1),complement(X3)))
| member(X2,union(intersection(complement(X0),complement(X1)),X3))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f449,f26]) ).
fof(f9073,plain,
! [X0,X1] :
( member(omega,union(X0,X1))
| ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1))) ),
inference(subsumption_resolution,[],[f9012,f52]) ).
fof(f9012,plain,
! [X0,X1] :
( member(omega,union(X0,X1))
| ~ member(omega,universal_class)
| ~ subclass(universal_class,symmetric_difference(complement(X0),complement(X1))) ),
inference(resolution,[],[f449,f6452]) ).
fof(f9000,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,intersection(complement(X1),complement(X2))),union(X1,X2))
| ~ member(not_subclass_element(X0,intersection(complement(X1),complement(X2))),universal_class)
| subclass(X0,intersection(complement(X1),complement(X2))) ),
inference(resolution,[],[f449,f3]) ).
fof(f8999,plain,
! [X2,X3,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,universal_class)
| ~ subclass(intersection(complement(X1),complement(X2)),X3)
| member(X0,X3) ),
inference(resolution,[],[f449,f1]) ).
fof(f8997,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,universal_class)
| member(X0,complement(X1)) ),
inference(resolution,[],[f449,f21]) ).
fof(f8996,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,universal_class)
| member(X0,complement(X2)) ),
inference(resolution,[],[f449,f22]) ).
fof(f449,plain,
! [X2,X0,X1] :
( member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f26]) ).
fof(f8993,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_of(restrict(identity_relation,X0,X1)))
| ~ subclass(universal_class,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f1928,f29]) ).
fof(f1928,plain,
! [X0] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(resolution,[],[f180,f163]) ).
fof(f8990,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(restrict(identity_relation,X0,X1)))
| ~ subclass(universal_class,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f1926,f29]) ).
fof(f1926,plain,
! [X0] :
( ~ subclass(universal_class,cantor(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(resolution,[],[f180,f949]) ).
fof(f8890,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(X0,intersection(complement(X1),complement(X2))),complement(singleton(intersection(complement(X0),union(X1,X2))))),successor(intersection(complement(X0),union(X1,X2)))),
inference(superposition,[],[f5658,f447]) ).
fof(f8883,plain,
! [X2,X3,X0,X1] : subclass(symmetric_difference(complement(X3),union(X0,intersection(complement(X1),complement(X2)))),union(X3,intersection(complement(X0),union(X1,X2)))),
inference(superposition,[],[f4681,f447]) ).
fof(f8882,plain,
! [X2,X3,X0,X1] : subclass(symmetric_difference(union(X0,intersection(complement(X1),complement(X2))),complement(X3)),union(intersection(complement(X0),union(X1,X2)),X3)),
inference(superposition,[],[f4681,f447]) ).
fof(f8927,plain,
! [X2,X3,X0,X1] :
( subclass(union(X0,intersection(complement(X1),complement(X2))),X3)
| ~ subclass(union(X0,intersection(complement(X1),complement(X2))),intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8873,f447]) ).
fof(f8873,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(X0,intersection(complement(X1),complement(X2))),intersection(complement(X0),union(X1,X2)))
| subclass(complement(intersection(complement(X0),union(X1,X2))),X3) ),
inference(superposition,[],[f2982,f447]) ).
fof(f8868,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f1358,f447]) ).
fof(f8924,plain,
! [X2,X0,X1] :
( null_class = union(X0,intersection(complement(X1),complement(X2)))
| ~ member(union(X0,intersection(complement(X1),complement(X2))),universal_class)
| ~ member(apply(choice,union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8923,f447]) ).
fof(f8923,plain,
! [X2,X0,X1] :
( ~ member(union(X0,intersection(complement(X1),complement(X2))),universal_class)
| ~ member(apply(choice,union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2)))
| null_class = complement(intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8867,f447]) ).
fof(f8867,plain,
! [X2,X0,X1] :
( ~ member(apply(choice,union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2)))
| ~ member(complement(intersection(complement(X0),union(X1,X2))),universal_class)
| null_class = complement(intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f880,f447]) ).
fof(f8918,plain,
! [X2,X0,X1] :
( null_class = union(X0,intersection(complement(X1),complement(X2)))
| ~ subclass(union(X0,intersection(complement(X1),complement(X2))),intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8862,f447]) ).
fof(f8862,plain,
! [X2,X0,X1] :
( ~ subclass(union(X0,intersection(complement(X1),complement(X2))),intersection(complement(X0),union(X1,X2)))
| null_class = complement(intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f600,f447]) ).
fof(f8861,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ member(omega,power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f567,f447]) ).
fof(f8860,plain,
! [X2,X0,X1] :
( ~ inductive(image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ member(null_class,power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f566,f447]) ).
fof(f8858,plain,
! [X2,X3,X0,X1] : complement(image(element_relation,union(X3,intersection(complement(X0),union(X1,X2))))) = power_class(intersection(complement(X3),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f450,f447]) ).
fof(f8857,plain,
! [X2,X3,X0,X1] : complement(image(element_relation,union(intersection(complement(X0),union(X1,X2)),X3))) = power_class(intersection(union(X0,intersection(complement(X1),complement(X2))),complement(X3))),
inference(superposition,[],[f450,f447]) ).
fof(f8856,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X3,intersection(complement(X4),union(X0,intersection(complement(X1),complement(X2)))))
| ~ member(X3,union(X4,intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f448,f447]) ).
fof(f8855,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X3,intersection(union(X0,intersection(complement(X1),complement(X2))),complement(X4)))
| ~ member(X3,union(intersection(complement(X0),union(X1,X2)),X4)) ),
inference(superposition,[],[f448,f447]) ).
fof(f8854,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),union(X1,X2)),domain_of(intersection(X3,identity_relation))) = complement(intersection(union(X0,intersection(complement(X1),complement(X2))),diagonalise(X3))),
inference(superposition,[],[f446,f447]) ).
fof(f8853,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),union(X1,X2)),image(element_relation,complement(X3))) = complement(intersection(union(X0,intersection(complement(X1),complement(X2))),power_class(X3))),
inference(superposition,[],[f445,f447]) ).
fof(f8852,plain,
! [X2,X3,X0,X1,X4] : union(intersection(complement(X3),complement(X4)),intersection(complement(X0),union(X1,X2))) = complement(intersection(union(X3,X4),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f444,f447]) ).
fof(f8851,plain,
! [X2,X3,X0,X1] : union(domain_of(intersection(X3,identity_relation)),intersection(complement(X0),union(X1,X2))) = complement(intersection(diagonalise(X3),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f443,f447]) ).
fof(f8850,plain,
! [X2,X3,X0,X1] : union(image(element_relation,complement(X3)),intersection(complement(X0),union(X1,X2))) = complement(intersection(power_class(X3),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f442,f447]) ).
fof(f8849,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(union(X0,intersection(complement(X1),complement(X2)))))
| member(singleton(X3),intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f426,f447]) ).
fof(f8848,plain,
! [X2,X3,X0,X1] :
( member(X3,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| member(X3,power_class(intersection(complement(X0),union(X1,X2))))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f424,f447]) ).
fof(f8847,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(union(X0,intersection(complement(X1),complement(X2))),X3)
| ~ member(X4,universal_class)
| member(X4,intersection(complement(X0),union(X1,X2)))
| member(X4,X3) ),
inference(superposition,[],[f420,f447]) ).
fof(f8846,plain,
! [X2,X0,X1] :
( ~ inductive(image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ inductive(power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f402,f447]) ).
fof(f8844,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,union(X0,intersection(complement(X1),complement(X2))))
| ~ subclass(universal_class,intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f276,f447]) ).
fof(f8841,plain,
! [X2,X0,X1] :
( ~ member(omega,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f179,f447]) ).
fof(f8840,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,union(X0,intersection(complement(X1),complement(X2))))
| ~ member(omega,intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f171,f447]) ).
fof(f8839,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ member(X3,power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f152,f447]) ).
fof(f8838,plain,
! [X2,X0,X1] :
( ~ member(null_class,image(element_relation,union(X0,intersection(complement(X1),complement(X2)))))
| ~ inductive(power_class(intersection(complement(X0),union(X1,X2)))) ),
inference(superposition,[],[f151,f447]) ).
fof(f8837,plain,
! [X2,X0,X1] : complement(image(element_relation,power_class(intersection(complement(X0),union(X1,X2))))) = power_class(image(element_relation,union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f150,f447]) ).
fof(f8917,plain,
! [X2,X3,X0,X1] :
( subclass(union(X0,intersection(complement(X1),complement(X2))),X3)
| ~ member(not_subclass_element(union(X0,intersection(complement(X1),complement(X2))),X3),intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8836,f447]) ).
fof(f8836,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(union(X0,intersection(complement(X1),complement(X2))),X3),intersection(complement(X0),union(X1,X2)))
| subclass(complement(intersection(complement(X0),union(X1,X2))),X3) ),
inference(superposition,[],[f121,f447]) ).
fof(f8916,plain,
! [X2,X0,X1] :
( null_class = union(X0,intersection(complement(X1),complement(X2)))
| ~ member(regular(union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2))) ),
inference(forward_demodulation,[],[f8835,f447]) ).
fof(f8835,plain,
! [X2,X0,X1] :
( ~ member(regular(union(X0,intersection(complement(X1),complement(X2)))),intersection(complement(X0),union(X1,X2)))
| null_class = complement(intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f120,f447]) ).
fof(f8834,plain,
! [X2,X0,X1] :
( ~ inductive(union(X0,intersection(complement(X1),complement(X2))))
| ~ member(null_class,intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f119,f447]) ).
fof(f8833,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X0,intersection(complement(X1),complement(X2))))) = power_class(intersection(complement(X0),union(X1,X2))),
inference(superposition,[],[f55,f447]) ).
fof(f8832,plain,
! [X2,X3,X0,X1] : union(X3,intersection(complement(X0),union(X1,X2))) = complement(intersection(complement(X3),union(X0,intersection(complement(X1),complement(X2))))),
inference(superposition,[],[f26,f447]) ).
fof(f8831,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),union(X1,X2)),X3) = complement(intersection(union(X0,intersection(complement(X1),complement(X2))),complement(X3))),
inference(superposition,[],[f26,f447]) ).
fof(f8830,plain,
! [X2,X3,X0,X1] :
( member(X3,union(X0,intersection(complement(X1),complement(X2))))
| member(X3,intersection(complement(X0),union(X1,X2)))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f25,f447]) ).
fof(f8829,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(complement(X1),complement(X2))))
| ~ member(X3,intersection(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f24,f447]) ).
fof(f8828,plain,
! [X2,X0,X1] : symmetric_difference(complement(X0),union(X1,X2)) = intersection(union(X0,intersection(complement(X1),complement(X2))),union(complement(X0),union(X1,X2))),
inference(superposition,[],[f1614,f447]) ).
fof(f8827,plain,
! [X2,X0,X1] :
( member(null_class,union(X0,intersection(complement(X1),complement(X2))))
| ~ inductive(symmetric_difference(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f1662,f447]) ).
fof(f8826,plain,
! [X2,X3,X0,X1] :
( member(X3,union(X0,intersection(complement(X1),complement(X2))))
| ~ member(X3,symmetric_difference(complement(X0),union(X1,X2))) ),
inference(superposition,[],[f1659,f447]) ).
fof(f8825,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X0),union(X1,X2)),union(X0,intersection(complement(X1),complement(X2)))),
inference(superposition,[],[f3947,f447]) ).
fof(f8824,plain,
complement(symmetric_difference(inverse(subset_relation),subset_relation)) = union(identity_relation,intersection(complement(inverse(subset_relation)),complement(subset_relation))),
inference(superposition,[],[f447,f1653]) ).
fof(f8823,plain,
! [X0,X1] : complement(symmetric_difference(X0,X1)) = union(intersection(X0,X1),intersection(complement(X0),complement(X1))),
inference(superposition,[],[f447,f1614]) ).
fof(f8818,plain,
! [X0,X1] : union(X1,intersection(complement(X0),complement(singleton(X0)))) = complement(intersection(complement(X1),successor(X0))),
inference(superposition,[],[f447,f43]) ).
fof(f8817,plain,
! [X0,X1] : union(image(element_relation,power_class(universal_class)),intersection(complement(X0),complement(X1))) = complement(intersection(power_class(image(element_relation,null_class)),union(X0,X1))),
inference(superposition,[],[f447,f664]) ).
fof(f8816,plain,
! [X0,X1] : union(image(element_relation,null_class),intersection(complement(X0),complement(X1))) = complement(intersection(power_class(universal_class),union(X0,X1))),
inference(superposition,[],[f447,f616]) ).
fof(f8815,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X0)),intersection(complement(X1),complement(X2))) = complement(intersection(power_class(X0),union(X1,X2))),
inference(superposition,[],[f447,f55]) ).
fof(f8814,plain,
! [X2,X3,X0,X1] : union(domain_of(restrict(identity_relation,X0,X1)),intersection(complement(X2),complement(X3))) = complement(intersection(diagonalise(cross_product(X0,X1)),union(X2,X3))),
inference(superposition,[],[f447,f541]) ).
fof(f8813,plain,
! [X2,X0,X1] : union(domain_of(intersection(X0,identity_relation)),intersection(complement(X1),complement(X2))) = complement(intersection(diagonalise(X0),union(X1,X2))),
inference(superposition,[],[f447,f76]) ).
fof(f8812,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),diagonalise(X1)),intersection(complement(X2),complement(X3))) = complement(intersection(union(X0,domain_of(intersection(X1,identity_relation))),union(X2,X3))),
inference(superposition,[],[f447,f446]) ).
fof(f8811,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),power_class(X1)),intersection(complement(X2),complement(X3))) = complement(intersection(union(X0,image(element_relation,complement(X1))),union(X2,X3))),
inference(superposition,[],[f447,f445]) ).
fof(f8808,plain,
! [X2,X3,X0,X1,X4] : union(intersection(complement(X0),union(X1,X2)),intersection(complement(X3),complement(X4))) = complement(intersection(union(X0,intersection(complement(X1),complement(X2))),union(X3,X4))),
inference(superposition,[],[f447,f447]) ).
fof(f8807,plain,
! [X2,X3,X0,X1] : union(intersection(diagonalise(X0),complement(X1)),intersection(complement(X2),complement(X3))) = complement(intersection(union(domain_of(intersection(X0,identity_relation)),X1),union(X2,X3))),
inference(superposition,[],[f447,f443]) ).
fof(f8806,plain,
! [X2,X3,X0,X1] : union(intersection(power_class(X0),complement(X1)),intersection(complement(X2),complement(X3))) = complement(intersection(union(image(element_relation,complement(X0)),X1),union(X2,X3))),
inference(superposition,[],[f447,f442]) ).
fof(f8804,plain,
! [X2,X3,X0,X1,X4] : union(intersection(union(X0,X1),complement(X2)),intersection(complement(X3),complement(X4))) = complement(intersection(union(intersection(complement(X0),complement(X1)),X2),union(X3,X4))),
inference(superposition,[],[f447,f444]) ).
fof(f8803,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X0),complement(X1)),intersection(complement(X2),complement(X3))) = complement(intersection(union(X0,X1),union(X2,X3))),
inference(superposition,[],[f447,f26]) ).
fof(f447,plain,
! [X2,X0,X1] : union(X2,intersection(complement(X0),complement(X1))) = complement(intersection(complement(X2),union(X0,X1))),
inference(superposition,[],[f26,f26]) ).
fof(f8699,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(intersection(complement(X0),complement(X1)),X2),complement(singleton(intersection(union(X0,X1),complement(X2))))),successor(intersection(union(X0,X1),complement(X2)))),
inference(superposition,[],[f5658,f444]) ).
fof(f8692,plain,
! [X2,X3,X0,X1] : subclass(symmetric_difference(complement(X3),union(intersection(complement(X0),complement(X1)),X2)),union(X3,intersection(union(X0,X1),complement(X2)))),
inference(superposition,[],[f4681,f444]) ).
fof(f8691,plain,
! [X2,X3,X0,X1] : subclass(symmetric_difference(union(intersection(complement(X0),complement(X1)),X2),complement(X3)),union(intersection(union(X0,X1),complement(X2)),X3)),
inference(superposition,[],[f4681,f444]) ).
fof(f8735,plain,
! [X2,X3,X0,X1] :
( subclass(union(intersection(complement(X0),complement(X1)),X2),X3)
| ~ subclass(union(intersection(complement(X0),complement(X1)),X2),intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8682,f444]) ).
fof(f8682,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(intersection(complement(X0),complement(X1)),X2),intersection(union(X0,X1),complement(X2)))
| subclass(complement(intersection(union(X0,X1),complement(X2))),X3) ),
inference(superposition,[],[f2982,f444]) ).
fof(f8677,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ subclass(universal_class,power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f1358,f444]) ).
fof(f8732,plain,
! [X2,X0,X1] :
( null_class = union(intersection(complement(X0),complement(X1)),X2)
| ~ member(union(intersection(complement(X0),complement(X1)),X2),universal_class)
| ~ member(apply(choice,union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8731,f444]) ).
fof(f8731,plain,
! [X2,X0,X1] :
( ~ member(union(intersection(complement(X0),complement(X1)),X2),universal_class)
| ~ member(apply(choice,union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2)))
| null_class = complement(intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8676,f444]) ).
fof(f8676,plain,
! [X2,X0,X1] :
( ~ member(apply(choice,union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2)))
| ~ member(complement(intersection(union(X0,X1),complement(X2))),universal_class)
| null_class = complement(intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f880,f444]) ).
fof(f8726,plain,
! [X2,X0,X1] :
( null_class = union(intersection(complement(X0),complement(X1)),X2)
| ~ subclass(union(intersection(complement(X0),complement(X1)),X2),intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8671,f444]) ).
fof(f8671,plain,
! [X2,X0,X1] :
( ~ subclass(union(intersection(complement(X0),complement(X1)),X2),intersection(union(X0,X1),complement(X2)))
| null_class = complement(intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f600,f444]) ).
fof(f8670,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ member(omega,power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f567,f444]) ).
fof(f8669,plain,
! [X2,X0,X1] :
( ~ inductive(image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ member(null_class,power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f566,f444]) ).
fof(f8667,plain,
! [X2,X3,X0,X1] : complement(image(element_relation,union(X3,intersection(union(X0,X1),complement(X2))))) = power_class(intersection(complement(X3),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f450,f444]) ).
fof(f8666,plain,
! [X2,X3,X0,X1] : complement(image(element_relation,union(intersection(union(X0,X1),complement(X2)),X3))) = power_class(intersection(union(intersection(complement(X0),complement(X1)),X2),complement(X3))),
inference(superposition,[],[f450,f444]) ).
fof(f8665,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X3,intersection(complement(X4),union(intersection(complement(X0),complement(X1)),X2)))
| ~ member(X3,union(X4,intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f448,f444]) ).
fof(f8664,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X3,intersection(union(intersection(complement(X0),complement(X1)),X2),complement(X4)))
| ~ member(X3,union(intersection(union(X0,X1),complement(X2)),X4)) ),
inference(superposition,[],[f448,f444]) ).
fof(f8663,plain,
! [X2,X3,X0,X1] : union(intersection(union(X0,X1),complement(X2)),domain_of(intersection(X3,identity_relation))) = complement(intersection(union(intersection(complement(X0),complement(X1)),X2),diagonalise(X3))),
inference(superposition,[],[f446,f444]) ).
fof(f8662,plain,
! [X2,X3,X0,X1] : union(intersection(union(X0,X1),complement(X2)),image(element_relation,complement(X3))) = complement(intersection(union(intersection(complement(X0),complement(X1)),X2),power_class(X3))),
inference(superposition,[],[f445,f444]) ).
fof(f8661,plain,
! [X2,X3,X0,X1] : union(domain_of(intersection(X3,identity_relation)),intersection(union(X0,X1),complement(X2))) = complement(intersection(diagonalise(X3),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f443,f444]) ).
fof(f8660,plain,
! [X2,X3,X0,X1] : union(image(element_relation,complement(X3)),intersection(union(X0,X1),complement(X2))) = complement(intersection(power_class(X3),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f442,f444]) ).
fof(f8659,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(union(intersection(complement(X0),complement(X1)),X2)))
| member(singleton(X3),intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f426,f444]) ).
fof(f8658,plain,
! [X2,X3,X0,X1] :
( member(X3,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| member(X3,power_class(intersection(union(X0,X1),complement(X2))))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f424,f444]) ).
fof(f8657,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(union(intersection(complement(X0),complement(X1)),X2),X3)
| ~ member(X4,universal_class)
| member(X4,intersection(union(X0,X1),complement(X2)))
| member(X4,X3) ),
inference(superposition,[],[f420,f444]) ).
fof(f8656,plain,
! [X2,X0,X1] :
( ~ inductive(image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ inductive(power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f402,f444]) ).
fof(f8654,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,union(intersection(complement(X0),complement(X1)),X2))
| ~ subclass(universal_class,intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f276,f444]) ).
fof(f8651,plain,
! [X2,X0,X1] :
( ~ member(omega,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ subclass(universal_class,power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f179,f444]) ).
fof(f8650,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,union(intersection(complement(X0),complement(X1)),X2))
| ~ member(omega,intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f171,f444]) ).
fof(f8649,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ member(X3,power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f152,f444]) ).
fof(f8648,plain,
! [X2,X0,X1] :
( ~ member(null_class,image(element_relation,union(intersection(complement(X0),complement(X1)),X2)))
| ~ inductive(power_class(intersection(union(X0,X1),complement(X2)))) ),
inference(superposition,[],[f151,f444]) ).
fof(f8647,plain,
! [X2,X0,X1] : complement(image(element_relation,power_class(intersection(union(X0,X1),complement(X2))))) = power_class(image(element_relation,union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f150,f444]) ).
fof(f8725,plain,
! [X2,X3,X0,X1] :
( subclass(union(intersection(complement(X0),complement(X1)),X2),X3)
| ~ member(not_subclass_element(union(intersection(complement(X0),complement(X1)),X2),X3),intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8646,f444]) ).
fof(f8646,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(union(intersection(complement(X0),complement(X1)),X2),X3),intersection(union(X0,X1),complement(X2)))
| subclass(complement(intersection(union(X0,X1),complement(X2))),X3) ),
inference(superposition,[],[f121,f444]) ).
fof(f8724,plain,
! [X2,X0,X1] :
( null_class = union(intersection(complement(X0),complement(X1)),X2)
| ~ member(regular(union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2))) ),
inference(forward_demodulation,[],[f8645,f444]) ).
fof(f8645,plain,
! [X2,X0,X1] :
( ~ member(regular(union(intersection(complement(X0),complement(X1)),X2)),intersection(union(X0,X1),complement(X2)))
| null_class = complement(intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f120,f444]) ).
fof(f8644,plain,
! [X2,X0,X1] :
( ~ inductive(union(intersection(complement(X0),complement(X1)),X2))
| ~ member(null_class,intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f119,f444]) ).
fof(f8643,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(complement(X0),complement(X1)),X2))) = power_class(intersection(union(X0,X1),complement(X2))),
inference(superposition,[],[f55,f444]) ).
fof(f8642,plain,
! [X2,X3,X0,X1] : union(X3,intersection(union(X0,X1),complement(X2))) = complement(intersection(complement(X3),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f26,f444]) ).
fof(f8641,plain,
! [X2,X3,X0,X1] : union(intersection(union(X0,X1),complement(X2)),X3) = complement(intersection(union(intersection(complement(X0),complement(X1)),X2),complement(X3))),
inference(superposition,[],[f26,f444]) ).
fof(f8640,plain,
! [X2,X3,X0,X1] :
( member(X3,union(intersection(complement(X0),complement(X1)),X2))
| member(X3,intersection(union(X0,X1),complement(X2)))
| ~ member(X3,universal_class) ),
inference(superposition,[],[f25,f444]) ).
fof(f8639,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,union(intersection(complement(X0),complement(X1)),X2))
| ~ member(X3,intersection(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f24,f444]) ).
fof(f8638,plain,
! [X2,X0,X1] : symmetric_difference(union(X0,X1),complement(X2)) = intersection(union(intersection(complement(X0),complement(X1)),X2),union(union(X0,X1),complement(X2))),
inference(superposition,[],[f1614,f444]) ).
fof(f8637,plain,
! [X2,X0,X1] :
( member(null_class,union(intersection(complement(X0),complement(X1)),X2))
| ~ inductive(symmetric_difference(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f1662,f444]) ).
fof(f8636,plain,
! [X2,X3,X0,X1] :
( member(X3,union(intersection(complement(X0),complement(X1)),X2))
| ~ member(X3,symmetric_difference(union(X0,X1),complement(X2))) ),
inference(superposition,[],[f1659,f444]) ).
fof(f8635,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(X0,X1),complement(X2)),union(intersection(complement(X0),complement(X1)),X2)),
inference(superposition,[],[f3947,f444]) ).
fof(f8634,plain,
! [X0,X1] : union(intersection(complement(X0),complement(X1)),image(element_relation,power_class(universal_class))) = complement(intersection(union(X0,X1),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f444,f664]) ).
fof(f8633,plain,
! [X0,X1] : union(intersection(complement(X0),complement(X1)),image(element_relation,null_class)) = complement(intersection(union(X0,X1),power_class(universal_class))),
inference(superposition,[],[f444,f616]) ).
fof(f8632,plain,
! [X2,X0,X1] : union(intersection(complement(X1),complement(X2)),image(element_relation,complement(X0))) = complement(intersection(union(X1,X2),power_class(X0))),
inference(superposition,[],[f444,f55]) ).
fof(f8631,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),domain_of(restrict(identity_relation,X0,X1))) = complement(intersection(union(X2,X3),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f444,f541]) ).
fof(f8630,plain,
! [X2,X0,X1] : union(intersection(complement(X1),complement(X2)),domain_of(intersection(X0,identity_relation))) = complement(intersection(union(X1,X2),diagonalise(X0))),
inference(superposition,[],[f444,f76]) ).
fof(f8629,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),intersection(complement(X0),diagonalise(X1))) = complement(intersection(union(X2,X3),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f444,f446]) ).
fof(f8628,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),intersection(complement(X0),power_class(X1))) = complement(intersection(union(X2,X3),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f444,f445]) ).
fof(f8625,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),intersection(diagonalise(X0),complement(X1))) = complement(intersection(union(X2,X3),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f444,f443]) ).
fof(f8624,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),intersection(power_class(X0),complement(X1))) = complement(intersection(union(X2,X3),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f444,f442]) ).
fof(f8622,plain,
! [X2,X3,X0,X1,X4] : union(intersection(complement(X3),complement(X4)),intersection(union(X0,X1),complement(X2))) = complement(intersection(union(X3,X4),union(intersection(complement(X0),complement(X1)),X2))),
inference(superposition,[],[f444,f444]) ).
fof(f8621,plain,
! [X2,X3,X0,X1] : union(intersection(complement(X2),complement(X3)),intersection(complement(X0),complement(X1))) = complement(intersection(union(X2,X3),union(X0,X1))),
inference(superposition,[],[f444,f26]) ).
fof(f8615,plain,
! [X0,X1] : union(intersection(complement(X0),complement(singleton(X0))),X1) = complement(intersection(successor(X0),complement(X1))),
inference(superposition,[],[f444,f43]) ).
fof(f444,plain,
! [X2,X0,X1] : union(intersection(complement(X0),complement(X1)),X2) = complement(intersection(union(X0,X1),complement(X2))),
inference(superposition,[],[f26,f26]) ).
fof(f8569,plain,
! [X0,X1] :
( null_class = X0
| ~ subclass(universal_class,X1)
| member(regular(X0),X1) ),
inference(resolution,[],[f8509,f1]) ).
fof(f8509,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0 ),
inference(resolution,[],[f7726,f114]) ).
fof(f8559,plain,
( member(regular(application_function),universal_class)
| null_class = application_function ),
inference(resolution,[],[f7726,f105]) ).
fof(f8558,plain,
( member(regular(domain_relation),universal_class)
| null_class = domain_relation ),
inference(resolution,[],[f7726,f98]) ).
fof(f8557,plain,
( member(regular(composition_function),universal_class)
| null_class = composition_function ),
inference(resolution,[],[f7726,f95]) ).
fof(f8556,plain,
! [X0] :
( member(regular(compose_class(X0)),universal_class)
| null_class = compose_class(X0) ),
inference(resolution,[],[f7726,f92]) ).
fof(f8555,plain,
! [X0] :
( member(regular(cantor(X0)),universal_class)
| null_class = cantor(X0) ),
inference(resolution,[],[f7726,f4091]) ).
fof(f8554,plain,
! [X0] :
( member(regular(cantor(restrict(element_relation,universal_class,X0))),universal_class)
| null_class = cantor(restrict(element_relation,universal_class,X0)) ),
inference(resolution,[],[f7726,f3961]) ).
fof(f8553,plain,
! [X0] :
( member(regular(cantor(inverse(X0))),universal_class)
| null_class = cantor(inverse(X0)) ),
inference(resolution,[],[f7726,f3963]) ).
fof(f8552,plain,
! [X0] :
( member(regular(cantor(flip(cross_product(X0,universal_class)))),universal_class)
| null_class = cantor(flip(cross_product(X0,universal_class))) ),
inference(resolution,[],[f7726,f3962]) ).
fof(f8551,plain,
! [X0] :
( member(regular(cantor(X0)),universal_class)
| null_class = cantor(X0) ),
inference(resolution,[],[f7726,f3948]) ).
fof(f8550,plain,
( member(regular(subset_relation),universal_class)
| null_class = subset_relation ),
inference(resolution,[],[f7726,f3945]) ).
fof(f8547,plain,
! [X0] :
( member(regular(compose(X0,inverse(X0))),universal_class)
| null_class = compose(X0,inverse(X0))
| ~ function(X0) ),
inference(resolution,[],[f7726,f63]) ).
fof(f8546,plain,
! [X0,X1] :
( member(regular(compose(X0,X1)),universal_class)
| null_class = compose(X0,X1) ),
inference(resolution,[],[f7726,f57]) ).
fof(f8545,plain,
! [X0] :
( member(regular(omega),universal_class)
| null_class = omega
| ~ inductive(X0) ),
inference(resolution,[],[f7726,f51]) ).
fof(f8544,plain,
( member(regular(successor_relation),universal_class)
| null_class = successor_relation ),
inference(resolution,[],[f7726,f44]) ).
fof(f8543,plain,
! [X0] :
( member(regular(image(successor_relation,X0)),universal_class)
| null_class = image(successor_relation,X0)
| ~ inductive(X0) ),
inference(resolution,[],[f7726,f48]) ).
fof(f8542,plain,
! [X0] :
( member(regular(flip(X0)),universal_class)
| null_class = flip(X0) ),
inference(resolution,[],[f7726,f35]) ).
fof(f8541,plain,
! [X0] :
( member(regular(rotate(X0)),universal_class)
| null_class = rotate(X0) ),
inference(resolution,[],[f7726,f32]) ).
fof(f8537,plain,
! [X0,X1] :
( member(regular(restrict(identity_relation,X0,X1)),universal_class)
| null_class = restrict(identity_relation,X0,X1) ),
inference(resolution,[],[f7726,f3956]) ).
fof(f8536,plain,
! [X0,X1] :
( member(regular(restrict(identity_relation,X0,X1)),universal_class)
| null_class = restrict(identity_relation,X0,X1) ),
inference(resolution,[],[f7726,f4015]) ).
fof(f8535,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),universal_class)
| null_class = restrict(X0,X1,X2) ),
inference(resolution,[],[f7726,f3944]) ).
fof(f8534,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),universal_class)
| null_class = restrict(X0,X1,X2) ),
inference(resolution,[],[f7726,f3942]) ).
fof(f8532,plain,
( member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),universal_class)
| null_class = symmetric_difference(inverse(subset_relation),subset_relation) ),
inference(resolution,[],[f7726,f4529]) ).
fof(f8531,plain,
! [X0] :
( member(regular(symmetric_difference(null_class,X0)),universal_class)
| null_class = symmetric_difference(null_class,X0) ),
inference(resolution,[],[f7726,f4678]) ).
fof(f8529,plain,
! [X0] :
( member(regular(symmetric_difference(complement(X0),complement(singleton(X0)))),universal_class)
| null_class = symmetric_difference(complement(X0),complement(singleton(X0))) ),
inference(resolution,[],[f7726,f5658]) ).
fof(f8528,plain,
! [X0,X1] :
( member(regular(symmetric_difference(complement(X0),complement(X1))),universal_class)
| null_class = symmetric_difference(complement(X0),complement(X1)) ),
inference(resolution,[],[f7726,f4681]) ).
fof(f8527,plain,
! [X0] :
( member(regular(symmetric_difference(universal_class,X0)),universal_class)
| null_class = symmetric_difference(universal_class,X0) ),
inference(resolution,[],[f7726,f4491]) ).
fof(f8526,plain,
! [X0] :
( member(regular(symmetric_difference(X0,singleton(X0))),universal_class)
| null_class = symmetric_difference(X0,singleton(X0)) ),
inference(resolution,[],[f7726,f4489]) ).
fof(f8525,plain,
! [X0] :
( member(regular(symmetric_difference(X0,null_class)),universal_class)
| null_class = symmetric_difference(X0,null_class) ),
inference(resolution,[],[f7726,f4671]) ).
fof(f8524,plain,
! [X0,X1] :
( member(regular(symmetric_difference(X0,X1)),universal_class)
| symmetric_difference(X0,X1) = null_class ),
inference(resolution,[],[f7726,f3947]) ).
fof(f8523,plain,
! [X0] :
( member(regular(symmetric_difference(X0,universal_class)),universal_class)
| null_class = symmetric_difference(X0,universal_class) ),
inference(resolution,[],[f7726,f4490]) ).
fof(f8522,plain,
! [X0,X1] :
( member(regular(symmetric_difference(X0,X1)),universal_class)
| symmetric_difference(X0,X1) = null_class ),
inference(resolution,[],[f7726,f4089]) ).
fof(f8521,plain,
! [X0] :
( member(regular(intersection(X0,identity_relation)),universal_class)
| null_class = intersection(X0,identity_relation) ),
inference(resolution,[],[f7726,f4062]) ).
fof(f8520,plain,
! [X0] :
( member(regular(intersection(identity_relation,X0)),universal_class)
| null_class = intersection(identity_relation,X0) ),
inference(resolution,[],[f7726,f3921]) ).
fof(f8519,plain,
! [X0] :
( member(regular(intersection(X0,identity_relation)),universal_class)
| null_class = intersection(X0,identity_relation) ),
inference(resolution,[],[f7726,f4061]) ).
fof(f8518,plain,
! [X0] :
( member(regular(intersection(identity_relation,X0)),universal_class)
| null_class = intersection(identity_relation,X0) ),
inference(resolution,[],[f7726,f3920]) ).
fof(f8517,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),universal_class)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f7726,f4063]) ).
fof(f8516,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),universal_class)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f7726,f3922]) ).
fof(f8514,plain,
! [X0,X1] :
( member(regular(singleton(X0)),universal_class)
| singleton(X0) = null_class
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[],[f7726,f652]) ).
fof(f8560,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0 ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f444,f447,f449,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f889,f878,f879,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2005,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886,f554,f6039,f6040,f6041,f6042,f6043,f6044,f6045,f6046,f6047,f6048,f6049,f6050,f6051,f6057,f6060,f6062,f6067,f6160,f6244,f6245,f6250,f6251,f6256,f6257,f6258,f6259,f6260,f6261,f6262,f6263,f6264,f6265,f6266,f6267,f6268,f6269,f6271,f6248,f920,f6374,f6377,f6408,f6409,f6410,f6411,f6384,f6386,f6390,f6391,f6392,f6393,f6394,f6395,f6396,f6397,f6406,f6375,f6412,f6413,f6418,f6419,f6424,f6425,f6427,f6428,f6429,f6430,f6431,f6432,f6433,f6434,f6435,f6436,f6437,f3825,f6447,f6448,f6453,f6454,f6459,f6460,f6461,f6462,f6463,f6464,f6465,f6466,f6467,f6468,f6469,f6470,f6471,f6472,f3843,f6473,f6474,f6478,f6479,f6480,f6485,f6486,f6487,f6488,f6489,f6490,f6491,f6492,f6493,f6494,f6495,f6496,f6497,f6498,f4483,f6499,f6249,f6511,f1514,f6522,f6523,f6525,f956,f6528,f2428,f6531,f6532,f6538,f6544,f6549,f6550,f6551,f3109,f6561,f6562,f6563,f6564,f6565,f6566,f6567,f6568,f6570,f6571,f6572,f6573,f6574,f6575,f6576,f6582,f6585,f6587,f6592,f6594,f6595,f6601,f1658,f6648,f6652,f6653,f6654,f6657,f6691,f6692,f6693,f6694,f6665,f6666,f6667,f6670,f6671,f6672,f6673,f6674,f6675,f6676,f6677,f6686,f215,f6656,f6846,f6847,f6854,f6855,f6860,f6861,f6862,f6863,f6864,f6865,f6866,f6867,f6868,f6869,f6870,f6871,f6872,f6873,f6874,f6875,f3936,f6879,f6899,f6901,f6902,f6908,f6909,f6910,f6911,f6912,f4078,f6913,f6917,f6933,f6920,f6934,f6935,f6937,f6938,f6939,f6941,f6942,f4308,f4513,f216,f219,f221,f526,f7218,f7232,f7231,f7230,f747,f7468,f7469,f7470,f7472,f7486,f7487,f7475,f7488,f7479,f7480,f7481,f7483,f7484,f7485,f754,f7542,f7543,f7544,f7545,f7546,f7547,f7552,f7467,f7604,f7605,f7617,f7618,f7623,f7624,f7629,f7630,f7631,f7692,f7707,f875,f7770,f7771,f7772,f7773,f7774,f7775,f7776,f7777,f7778,f7780,f7781,f7782,f7783,f7784,f7785,f7786,f7787,f7793,f7795,f7796,f7797,f7798,f7800,f7801,f7802,f7803,f7804,f7805,f7806,f7812,f880,f7873,f7843,f7844,f7845,f7846,f7847,f7849,f7850,f7852,f7853,f7857,f7882,f7885,f7887,f7891,f7893,f7895,f7897,f7899,f7904,f7954,f8036,f8040,f2004,f8076,f8077,f8089,f8085,f2007,f8322,f8324,f8325,f8326,f8327,f8329,f8330,f8336,f8340,f320,f8424,f5348,f8441,f8446,f5413,f8450,f8452,f8463,f8458,f6274,f8468,f8467,f8474,f6452,f8479,f8482,f8484,f8487,f8491,f8492,f8493,f8495,f8497,f321,f8503,f8504,f8507,f7726,f8509,f8510,f8511]) ).
fof(f8511,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0
| ~ function(X0) ),
inference(resolution,[],[f7726,f62]) ).
fof(f8510,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0 ),
inference(resolution,[],[f7726,f4]) ).
fof(f7726,plain,
! [X2,X0] :
( ~ subclass(X0,X2)
| member(regular(X0),universal_class)
| null_class = X0 ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f444,f447,f449,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5348,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5413,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886,f554,f6039,f6040,f6041,f6042,f6043,f6044,f6045,f6046,f6047,f6048,f6049,f6050,f6051,f6057,f6060,f6062,f6067,f6160,f6244,f6245,f6250,f6251,f6256,f6257,f6258,f6259,f6260,f6261,f6262,f6263,f6264,f6265,f6266,f6267,f6268,f6269,f6271,f6248,f6274,f920,f6374,f6377,f6408,f6409,f6410,f6411,f6384,f6386,f6390,f6391,f6392,f6393,f6394,f6395,f6396,f6397,f6406,f6375,f6412,f6413,f6418,f6419,f6424,f6425,f6427,f6428,f6429,f6430,f6431,f6432,f6433,f6434,f6435,f6436,f6437,f3825,f6447,f6448,f6452,f6453,f6454,f6459,f6460,f6461,f6462,f6463,f6464,f6465,f6466,f6467,f6468,f6469,f6470,f6471,f6472,f3843,f6473,f6474,f6478,f6479,f6480,f6485,f6486,f6487,f6488,f6489,f6490,f6491,f6492,f6493,f6494,f6495,f6496,f6497,f6498,f4483,f6499,f6249,f6511,f1514,f6522,f6523,f6525,f956,f6528,f2428,f6531,f6532,f6538,f6544,f6549,f6550,f6551,f3109,f6561,f6562,f6563,f6564,f6565,f6566,f6567,f6568,f6570,f6571,f6572,f6573,f6574,f6575,f6576,f6582,f6585,f6587,f6592,f6594,f6595,f6601,f1658,f6648,f6652,f6653,f6654,f6657,f6691,f6692,f6693,f6694,f6665,f6666,f6667,f6670,f6671,f6672,f6673,f6674,f6675,f6676,f6677,f6686,f215,f6656,f6846,f6847,f6854,f6855,f6860,f6861,f6862,f6863,f6864,f6865,f6866,f6867,f6868,f6869,f6870,f6871,f6872,f6873,f6874,f6875,f3936,f6879,f6899,f6901,f6902,f6908,f6909,f6910,f6911,f6912,f4078,f6913,f6917,f6933,f6920,f6934,f6935,f6937,f6938,f6939,f6941,f6942,f4308,f4513,f216,f219,f221,f526,f7218,f7232,f7231,f7230,f747,f7468,f7469,f7470,f7472,f7486,f7487,f7475,f7488,f7479,f7480,f7481,f7483,f7484,f7485,f754,f7542,f7543,f7544,f7545,f7546,f7547,f7552,f7467,f7604,f7605,f7617,f7618,f7623,f7624,f7629]) ).
fof(f8507,plain,
! [X0] :
( member(ordered_pair(restrict(element_relation,universal_class,range_of(null_class)),apply(null_class,X0)),domain_relation)
| ~ member(restrict(element_relation,universal_class,range_of(null_class)),universal_class) ),
inference(superposition,[],[f321,f4437]) ).
fof(f8504,plain,
! [X0,X1] :
( member(ordered_pair(restrict(element_relation,universal_class,image(X0,singleton(X1))),apply(X0,X1)),domain_relation)
| ~ member(restrict(element_relation,universal_class,image(X0,singleton(X1))),universal_class) ),
inference(superposition,[],[f321,f68]) ).
fof(f8503,plain,
! [X0,X1] :
( ~ member(restrict(element_relation,universal_class,X0),universal_class)
| ~ subclass(domain_relation,X1)
| member(ordered_pair(restrict(element_relation,universal_class,X0),sum_class(X0)),X1) ),
inference(resolution,[],[f321,f1]) ).
fof(f321,plain,
! [X0] :
( member(ordered_pair(restrict(element_relation,universal_class,X0),sum_class(X0)),domain_relation)
| ~ member(restrict(element_relation,universal_class,X0),universal_class) ),
inference(superposition,[],[f100,f53]) ).
fof(f8497,plain,
! [X0] :
( ~ member(omega,cantor(inverse(X0)))
| ~ subclass(universal_class,symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))) ),
inference(superposition,[],[f6452,f920]) ).
fof(f8495,plain,
! [X0] :
( ~ member(omega,cantor(X0))
| ~ subclass(universal_class,symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))) ),
inference(superposition,[],[f6452,f77]) ).
fof(f8493,plain,
( ~ member(omega,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ subclass(universal_class,symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation))) ),
inference(superposition,[],[f6452,f1653]) ).
fof(f8492,plain,
! [X0] :
( ~ member(omega,symmetric_difference(X0,singleton(X0)))
| ~ subclass(universal_class,symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0))) ),
inference(superposition,[],[f6452,f1658]) ).
fof(f8491,plain,
! [X0,X1] :
( ~ member(omega,symmetric_difference(X0,X1))
| ~ subclass(universal_class,symmetric_difference(complement(intersection(X0,X1)),union(X0,X1))) ),
inference(superposition,[],[f6452,f1614]) ).
fof(f8487,plain,
! [X2,X0,X1] :
( ~ member(omega,restrict(X2,X0,X1))
| ~ subclass(universal_class,symmetric_difference(cross_product(X0,X1),X2)) ),
inference(superposition,[],[f6452,f29]) ).
fof(f8484,plain,
! [X2,X0,X1] :
( ~ member(omega,restrict(X0,X1,X2))
| ~ subclass(universal_class,symmetric_difference(X0,cross_product(X1,X2))) ),
inference(superposition,[],[f6452,f28]) ).
fof(f8479,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| ~ member(omega,X1)
| ~ member(omega,X0) ),
inference(resolution,[],[f6452,f23]) ).
fof(f6452,plain,
! [X0,X1] :
( ~ member(omega,intersection(X0,X1))
| ~ subclass(universal_class,symmetric_difference(X0,X1)) ),
inference(resolution,[],[f3825,f163]) ).
fof(f8474,plain,
! [X0] :
( ~ inductive(ordered_pair(singleton(X0),X0))
| ~ inductive(singleton(singleton(X0)))
| null_class = singleton(singleton(singleton(X0))) ),
inference(superposition,[],[f8467,f4463]) ).
fof(f8467,plain,
! [X0] :
( ~ inductive(singleton(X0))
| ~ inductive(X0)
| singleton(X0) = null_class ),
inference(resolution,[],[f6274,f47]) ).
fof(f8468,plain,
! [X0] :
( ~ member(null_class,ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(singleton(X0)))
| ~ inductive(singleton(singleton(X0))) ),
inference(superposition,[],[f6274,f4463]) ).
fof(f6274,plain,
! [X0] :
( ~ member(null_class,singleton(X0))
| singleton(X0) = null_class
| ~ inductive(X0) ),
inference(duplicate_literal_removal,[],[f6273]) ).
fof(f6273,plain,
! [X0] :
( ~ inductive(X0)
| singleton(X0) = null_class
| ~ member(null_class,singleton(X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f6248,f656]) ).
fof(f8463,plain,
! [X0,X1] : member(singleton(singleton(singleton(singleton(X0)))),ordered_pair(ordered_pair(singleton(X0),X0),X1)),
inference(forward_demodulation,[],[f8457,f4463]) ).
fof(f8457,plain,
! [X0,X1] : member(ordered_pair(singleton(singleton(X0)),singleton(X0)),ordered_pair(ordered_pair(singleton(X0),X0),X1)),
inference(superposition,[],[f5413,f4463]) ).
fof(f8452,plain,
! [X0,X1] : member(ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))),ordered_pair(singleton(ordered_pair(singleton(X0),X0)),X1)),
inference(superposition,[],[f5413,f4463]) ).
fof(f8450,plain,
! [X2,X0,X1] :
( ~ subclass(ordered_pair(singleton(singleton(X0)),X1),X2)
| member(ordered_pair(singleton(X0),X0),X2) ),
inference(resolution,[],[f5413,f1]) ).
fof(f5413,plain,
! [X0,X1] : member(ordered_pair(singleton(X0),X0),ordered_pair(singleton(singleton(X0)),X1)),
inference(superposition,[],[f702,f4463]) ).
fof(f8446,plain,
! [X0] :
( ~ member(singleton(ordered_pair(singleton(X0),X0)),element_relation)
| member(singleton(singleton(X0)),singleton(X0)) ),
inference(superposition,[],[f5348,f4463]) ).
fof(f8441,plain,
! [X0] :
( ~ member(singleton(singleton(ordered_pair(singleton(X0),X0))),element_relation)
| member(singleton(singleton(singleton(X0))),singleton(singleton(X0))) ),
inference(superposition,[],[f5348,f4463]) ).
fof(f5348,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),element_relation)
| member(singleton(X0),X0) ),
inference(superposition,[],[f19,f4463]) ).
fof(f8424,plain,
! [X0,X1] :
( ~ member(flip(cross_product(X0,universal_class)),universal_class)
| ~ subclass(domain_relation,X1)
| member(ordered_pair(flip(cross_product(X0,universal_class)),inverse(X0)),X1) ),
inference(resolution,[],[f320,f1]) ).
fof(f320,plain,
! [X0] :
( member(ordered_pair(flip(cross_product(X0,universal_class)),inverse(X0)),domain_relation)
| ~ member(flip(cross_product(X0,universal_class)),universal_class) ),
inference(superposition,[],[f100,f38]) ).
fof(f8340,plain,
( ~ member(apply(choice,complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),subset_relation)
| ~ member(complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),universal_class)
| null_class = complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(resolution,[],[f2007,f880]) ).
fof(f8336,plain,
( ~ member(regular(complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),subset_relation)
| null_class = complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(resolution,[],[f2007,f120]) ).
fof(f8330,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),subset_relation)
| ~ subclass(universal_class,complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(resolution,[],[f2007,f698]) ).
fof(f8329,plain,
! [X0] :
( ~ member(singleton(X0),subset_relation)
| ~ subclass(universal_class,complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(resolution,[],[f2007,f175]) ).
fof(f8327,plain,
! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| ~ subclass(universal_class,complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(resolution,[],[f2007,f263]) ).
fof(f8326,plain,
! [X0] :
( ~ member(not_subclass_element(complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),X0),subset_relation)
| subclass(complement(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),X0) ),
inference(resolution,[],[f2007,f121]) ).
fof(f8325,plain,
! [X0] :
( ~ member(not_subclass_element(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),subset_relation)
| subclass(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(resolution,[],[f2007,f3]) ).
fof(f8324,plain,
! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),X1)
| member(X0,X1) ),
inference(resolution,[],[f2007,f1]) ).
fof(f8322,plain,
! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),inverse(element_relation)))) ),
inference(resolution,[],[f2007,f495]) ).
fof(f2007,plain,
! [X0] :
( member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ member(X0,subset_relation) ),
inference(superposition,[],[f22,f1933]) ).
fof(f8085,plain,
subclass(subset_relation,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),
inference(superposition,[],[f3942,f2004]) ).
fof(f8089,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(subsumption_resolution,[],[f8084,f496]) ).
fof(f8084,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f754,f2004]) ).
fof(f8077,plain,
! [X0] :
( ~ member(X0,subset_relation)
| member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f495,f2004]) ).
fof(f8076,plain,
image(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class) = range_of(subset_relation),
inference(superposition,[],[f42,f2004]) ).
fof(f2004,plain,
subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),
inference(superposition,[],[f1933,f29]) ).
fof(f8040,plain,
! [X0] :
( member(singleton(singleton(singleton(X0))),element_relation)
| ~ member(singleton(X0),X0)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f7954,f4463]) ).
fof(f8036,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ subclass(element_relation,X2)
| member(ordered_pair(X0,X1),X2) ),
inference(resolution,[],[f7954,f1]) ).
fof(f7954,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(subsumption_resolution,[],[f1582,f7467]) ).
fof(f7904,plain,
( null_class = power_class(image(element_relation,null_class))
| ~ member(power_class(image(element_relation,null_class)),universal_class)
| ~ member(apply(choice,power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f7903,f664]) ).
fof(f7903,plain,
( ~ member(power_class(image(element_relation,null_class)),universal_class)
| ~ member(apply(choice,power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class)))
| null_class = complement(image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f7871,f664]) ).
fof(f7871,plain,
( ~ member(apply(choice,power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class)))
| ~ member(complement(image(element_relation,power_class(universal_class))),universal_class)
| null_class = complement(image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f880,f664]) ).
fof(f7899,plain,
! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| ~ member(apply(choice,power_class(X0)),image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f7898,f55]) ).
fof(f7898,plain,
! [X0] :
( ~ member(power_class(X0),universal_class)
| ~ member(apply(choice,power_class(X0)),image(element_relation,complement(X0)))
| null_class = complement(image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f7869,f55]) ).
fof(f7869,plain,
! [X0] :
( ~ member(apply(choice,power_class(X0)),image(element_relation,complement(X0)))
| ~ member(complement(image(element_relation,complement(X0))),universal_class)
| null_class = complement(image(element_relation,complement(X0))) ),
inference(superposition,[],[f880,f55]) ).
fof(f7897,plain,
! [X0,X1] :
( null_class = diagonalise(cross_product(X0,X1))
| ~ member(diagonalise(cross_product(X0,X1)),universal_class)
| ~ member(apply(choice,diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f7896,f541]) ).
fof(f7896,plain,
! [X0,X1] :
( ~ member(diagonalise(cross_product(X0,X1)),universal_class)
| ~ member(apply(choice,diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1)))
| null_class = complement(domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f7868,f541]) ).
fof(f7868,plain,
! [X0,X1] :
( ~ member(apply(choice,diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1)))
| ~ member(complement(domain_of(restrict(identity_relation,X0,X1))),universal_class)
| null_class = complement(domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f880,f541]) ).
fof(f7895,plain,
! [X0] :
( null_class = diagonalise(X0)
| ~ member(diagonalise(X0),universal_class)
| ~ member(apply(choice,diagonalise(X0)),domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f7894,f76]) ).
fof(f7894,plain,
! [X0] :
( ~ member(diagonalise(X0),universal_class)
| ~ member(apply(choice,diagonalise(X0)),domain_of(intersection(X0,identity_relation)))
| null_class = complement(domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f7867,f76]) ).
fof(f7867,plain,
! [X0] :
( ~ member(apply(choice,diagonalise(X0)),domain_of(intersection(X0,identity_relation)))
| ~ member(complement(domain_of(intersection(X0,identity_relation))),universal_class)
| null_class = complement(domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f880,f76]) ).
fof(f7893,plain,
! [X0,X1] :
( null_class = union(X0,domain_of(intersection(X1,identity_relation)))
| ~ member(union(X0,domain_of(intersection(X1,identity_relation))),universal_class)
| ~ member(apply(choice,union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f7892,f446]) ).
fof(f7892,plain,
! [X0,X1] :
( ~ member(union(X0,domain_of(intersection(X1,identity_relation))),universal_class)
| ~ member(apply(choice,union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1)))
| null_class = complement(intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f7866,f446]) ).
fof(f7866,plain,
! [X0,X1] :
( ~ member(apply(choice,union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1)))
| ~ member(complement(intersection(complement(X0),diagonalise(X1))),universal_class)
| null_class = complement(intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f880,f446]) ).
fof(f7891,plain,
! [X0,X1] :
( null_class = union(X0,image(element_relation,complement(X1)))
| ~ member(union(X0,image(element_relation,complement(X1))),universal_class)
| ~ member(apply(choice,union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f7890,f445]) ).
fof(f7890,plain,
! [X0,X1] :
( ~ member(union(X0,image(element_relation,complement(X1))),universal_class)
| ~ member(apply(choice,union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1)))
| null_class = complement(intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f7865,f445]) ).
fof(f7865,plain,
! [X0,X1] :
( ~ member(apply(choice,union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1)))
| ~ member(complement(intersection(complement(X0),power_class(X1))),universal_class)
| null_class = complement(intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f880,f445]) ).
fof(f7887,plain,
! [X0,X1] :
( null_class = union(domain_of(intersection(X0,identity_relation)),X1)
| ~ member(union(domain_of(intersection(X0,identity_relation)),X1),universal_class)
| ~ member(apply(choice,union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f7886,f443]) ).
fof(f7886,plain,
! [X0,X1] :
( ~ member(union(domain_of(intersection(X0,identity_relation)),X1),universal_class)
| ~ member(apply(choice,union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1)))
| null_class = complement(intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f7862,f443]) ).
fof(f7862,plain,
! [X0,X1] :
( ~ member(apply(choice,union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1)))
| ~ member(complement(intersection(diagonalise(X0),complement(X1))),universal_class)
| null_class = complement(intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f880,f443]) ).
fof(f7885,plain,
! [X0,X1] :
( null_class = union(image(element_relation,complement(X0)),X1)
| ~ member(union(image(element_relation,complement(X0)),X1),universal_class)
| ~ member(apply(choice,union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f7884,f442]) ).
fof(f7884,plain,
! [X0,X1] :
( ~ member(union(image(element_relation,complement(X0)),X1),universal_class)
| ~ member(apply(choice,union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1)))
| null_class = complement(intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f7861,f442]) ).
fof(f7861,plain,
! [X0,X1] :
( ~ member(apply(choice,union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1)))
| ~ member(complement(intersection(power_class(X0),complement(X1))),universal_class)
| null_class = complement(intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f880,f442]) ).
fof(f7882,plain,
! [X0,X1] :
( union(X0,X1) = null_class
| ~ member(union(X0,X1),universal_class)
| ~ member(apply(choice,union(X0,X1)),intersection(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f7881,f26]) ).
fof(f7881,plain,
! [X0,X1] :
( ~ member(union(X0,X1),universal_class)
| ~ member(apply(choice,union(X0,X1)),intersection(complement(X0),complement(X1)))
| complement(intersection(complement(X0),complement(X1))) = null_class ),
inference(forward_demodulation,[],[f7859,f26]) ).
fof(f7859,plain,
! [X0,X1] :
( ~ member(apply(choice,union(X0,X1)),intersection(complement(X0),complement(X1)))
| ~ member(complement(intersection(complement(X0),complement(X1))),universal_class)
| complement(intersection(complement(X0),complement(X1))) = null_class ),
inference(superposition,[],[f880,f26]) ).
fof(f7857,plain,
! [X0] :
( ~ member(complement(diagonalise(compose(inverse(element_relation),X0))),universal_class)
| null_class = complement(diagonalise(compose(inverse(element_relation),X0)))
| ~ member(apply(choice,complement(diagonalise(compose(inverse(element_relation),X0)))),cantor(X0)) ),
inference(resolution,[],[f880,f924]) ).
fof(f7853,plain,
! [X2,X0,X1] :
( ~ member(complement(image(X0,image(X1,singleton(X2)))),universal_class)
| null_class = complement(image(X0,image(X1,singleton(X2))))
| ~ member(ordered_pair(X2,apply(choice,complement(image(X0,image(X1,singleton(X2)))))),compose(X0,X1)) ),
inference(resolution,[],[f880,f58]) ).
fof(f7852,plain,
( ~ member(complement(inverse(subset_relation)),universal_class)
| null_class = complement(inverse(subset_relation))
| ~ member(apply(choice,complement(inverse(subset_relation))),identity_relation) ),
inference(resolution,[],[f880,f129]) ).
fof(f7850,plain,
! [X0] :
( ~ member(complement(domain_of(X0)),universal_class)
| null_class = complement(domain_of(X0))
| ~ member(apply(choice,complement(domain_of(X0))),universal_class)
| null_class = restrict(X0,singleton(apply(choice,complement(domain_of(X0)))),universal_class) ),
inference(resolution,[],[f880,f31]) ).
fof(f7849,plain,
! [X2,X0,X1] :
( ~ member(complement(restrict(X0,X1,X2)),universal_class)
| null_class = complement(restrict(X0,X1,X2))
| ~ member(apply(choice,complement(restrict(X0,X1,X2))),cross_product(X1,X2))
| ~ member(apply(choice,complement(restrict(X0,X1,X2))),X0) ),
inference(resolution,[],[f880,f754]) ).
fof(f7847,plain,
( ~ member(complement(complement(null_class)),universal_class)
| null_class = complement(complement(null_class))
| ~ member(apply(choice,complement(complement(null_class))),universal_class) ),
inference(resolution,[],[f880,f4833]) ).
fof(f7846,plain,
! [X0,X1] :
( ~ member(complement(complement(intersection(X0,X1))),universal_class)
| null_class = complement(complement(intersection(X0,X1)))
| ~ member(apply(choice,complement(complement(intersection(X0,X1)))),symmetric_difference(X0,X1)) ),
inference(resolution,[],[f880,f1659]) ).
fof(f7845,plain,
! [X0] :
( ~ member(complement(complement(X0)),universal_class)
| null_class = complement(complement(X0))
| member(apply(choice,complement(complement(X0))),X0)
| ~ member(apply(choice,complement(complement(X0))),universal_class) ),
inference(resolution,[],[f880,f25]) ).
fof(f7844,plain,
! [X0,X1] :
( ~ member(complement(intersection(X0,X1)),universal_class)
| complement(intersection(X0,X1)) = null_class
| ~ member(apply(choice,complement(intersection(X0,X1))),X1)
| ~ member(apply(choice,complement(intersection(X0,X1))),X0) ),
inference(resolution,[],[f880,f23]) ).
fof(f7843,plain,
( ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
| null_class = complement(cross_product(universal_class,universal_class))
| ~ member(apply(choice,complement(cross_product(universal_class,universal_class))),subset_relation) ),
inference(resolution,[],[f880,f2006]) ).
fof(f7873,plain,
! [X0] :
( ~ member(complement(X0),universal_class)
| complement(X0) = null_class
| ~ subclass(universal_class,X0) ),
inference(subsumption_resolution,[],[f7840,f69]) ).
fof(f7840,plain,
! [X0] :
( ~ member(complement(X0),universal_class)
| complement(X0) = null_class
| ~ subclass(universal_class,X0)
| ~ function(choice) ),
inference(resolution,[],[f880,f3109]) ).
fof(f880,plain,
! [X0] :
( ~ member(apply(choice,complement(X0)),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = null_class ),
inference(resolution,[],[f70,f24]) ).
fof(f7812,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f7809,f118]) ).
fof(f7809,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(singleton(X0),universal_class)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f7808]) ).
fof(f7808,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(singleton(X0),universal_class)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f875,f890]) ).
fof(f7806,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,cantor(inverse(X1)))
| null_class = X0
| member(apply(choice,X0),range_of(X1)) ),
inference(resolution,[],[f875,f6375]) ).
fof(f7805,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,cantor(X1))
| null_class = X0
| member(apply(choice,X0),domain_of(X1)) ),
inference(resolution,[],[f875,f923]) ).
fof(f7804,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,subset_relation)
| null_class = X0
| apply(choice,X0) = ordered_pair(first(apply(choice,X0)),second(apply(choice,X0))) ),
inference(resolution,[],[f875,f2058]) ).
fof(f7803,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,regular(X1))
| null_class = X0
| ~ member(apply(choice,X0),X1)
| null_class = X1 ),
inference(resolution,[],[f875,f6160]) ).
fof(f7802,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,identity_relation)
| null_class = X0
| member(apply(choice,X0),X1)
| ~ subclass(subset_relation,X1) ),
inference(resolution,[],[f875,f170]) ).
fof(f7801,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,identity_relation)
| null_class = X0
| member(apply(choice,X0),universal_class) ),
inference(resolution,[],[f875,f1143]) ).
fof(f7800,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,identity_relation)
| null_class = X0
| apply(choice,X0) = ordered_pair(first(apply(choice,X0)),second(apply(choice,X0))) ),
inference(resolution,[],[f875,f2428]) ).
fof(f7798,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,image(X1,image(X2,singleton(X3))))
| null_class = X0
| member(ordered_pair(X3,apply(choice,X0)),compose(X1,X2))
| ~ member(ordered_pair(X3,apply(choice,X0)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f875,f59]) ).
fof(f7797,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,image(element_relation,null_class))
| null_class = X0
| ~ member(apply(choice,X0),power_class(universal_class)) ),
inference(resolution,[],[f875,f621]) ).
fof(f7796,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,image(element_relation,complement(X1)))
| null_class = X0
| ~ member(apply(choice,X0),power_class(X1)) ),
inference(resolution,[],[f875,f152]) ).
fof(f7795,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,inverse(subset_relation))
| null_class = X0
| ~ member(apply(choice,X0),subset_relation)
| member(apply(choice,X0),identity_relation) ),
inference(resolution,[],[f875,f757]) ).
fof(f7793,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,domain_of(intersection(X1,identity_relation)))
| null_class = X0
| ~ member(apply(choice,X0),diagonalise(X1)) ),
inference(resolution,[],[f875,f155]) ).
fof(f7787,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,restrict(X1,X2,X3))
| null_class = X0
| member(apply(choice,X0),X1) ),
inference(resolution,[],[f875,f495]) ).
fof(f7786,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,restrict(X1,X2,X3))
| null_class = X0
| member(apply(choice,X0),cross_product(X2,X3)) ),
inference(resolution,[],[f875,f496]) ).
fof(f7785,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| null_class = X0
| member(apply(choice,X0),complement(identity_relation)) ),
inference(resolution,[],[f875,f3843]) ).
fof(f7784,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(null_class,X1))
| null_class = X0
| member(apply(choice,X0),complement(null_class)) ),
inference(resolution,[],[f875,f3991]) ).
fof(f7783,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(X1,singleton(X1)))
| null_class = X0
| member(apply(choice,X0),successor(X1)) ),
inference(resolution,[],[f875,f6656]) ).
fof(f7782,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(X1,null_class))
| null_class = X0
| member(apply(choice,X0),complement(null_class)) ),
inference(resolution,[],[f875,f4123]) ).
fof(f7781,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(X1,X2))
| null_class = X0
| member(apply(choice,X0),union(X1,X2)) ),
inference(resolution,[],[f875,f1660]) ).
fof(f7780,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,symmetric_difference(X1,X2))
| null_class = X0
| ~ member(apply(choice,X0),intersection(X1,X2)) ),
inference(resolution,[],[f875,f3825]) ).
fof(f7778,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(apply(choice,X0),X1) ),
inference(resolution,[],[f875,f24]) ).
fof(f7777,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,intersection(complement(X1),complement(X2)))
| null_class = X0
| ~ member(apply(choice,X0),union(X1,X2)) ),
inference(resolution,[],[f875,f448]) ).
fof(f7776,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(apply(choice,X0),X1) ),
inference(resolution,[],[f875,f21]) ).
fof(f7775,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(apply(choice,X0),X2) ),
inference(resolution,[],[f875,f22]) ).
fof(f7774,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,cross_product(X1,X2))
| null_class = X0
| apply(choice,X0) = ordered_pair(first(apply(choice,X0)),second(apply(choice,X0))) ),
inference(resolution,[],[f875,f17]) ).
fof(f7773,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,singleton(X1))
| null_class = X0
| apply(choice,X0) = X1 ),
inference(resolution,[],[f875,f650]) ).
fof(f7772,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| apply(choice,X0) = X1
| apply(choice,X0) = X2 ),
inference(resolution,[],[f875,f8]) ).
fof(f7771,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| null_class = X0
| ~ subclass(X1,X2)
| member(apply(choice,X0),X2) ),
inference(resolution,[],[f875,f1]) ).
fof(f7770,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| null_class = X0
| ~ member(apply(choice,X0),X2)
| member(apply(choice,X0),universal_class) ),
inference(resolution,[],[f875,f7467]) ).
fof(f875,plain,
! [X0,X1] :
( member(apply(choice,X0),X1)
| ~ member(X0,universal_class)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f70,f1]) ).
fof(f7707,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| member(X0,universal_class)
| ~ member(ordered_pair(X2,X0),compose(X3,X4)) ),
inference(resolution,[],[f7467,f58]) ).
fof(f7692,plain,
! [X0,X1] :
( ~ member(regular(cantor(X0)),X1)
| member(regular(cantor(X0)),universal_class)
| null_class = cantor(X0) ),
inference(resolution,[],[f7467,f950]) ).
fof(f7631,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| ~ subclass(X0,X3)
| subclass(X0,X1) ),
inference(resolution,[],[f7467,f160]) ).
fof(f7630,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(X0,X1)),X2)
| member(regular(intersection(X0,X1)),universal_class)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f7467,f132]) ).
fof(f7629,plain,
! [X2,X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| ~ subclass(X0,X2)
| null_class = X0 ),
inference(resolution,[],[f7467,f159]) ).
fof(f7624,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(X0,X1),X2),universal_class)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f7467,f133]) ).
fof(f7623,plain,
! [X0,X1] :
( ~ member(apply(choice,X0),X1)
| member(apply(choice,X0),universal_class)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(resolution,[],[f7467,f70]) ).
fof(f7618,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(X0,X1)),X2)
| member(regular(intersection(X0,X1)),universal_class)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f7467,f127]) ).
fof(f7617,plain,
! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| null_class = X0 ),
inference(resolution,[],[f7467,f66]) ).
fof(f7605,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(X0,X1),X2),universal_class)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f7467,f128]) ).
fof(f7604,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f7467,f2]) ).
fof(f7467,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f747,f4]) ).
fof(f7552,plain,
! [X2,X0,X1] :
( ~ member(regular(complement(restrict(X0,X1,X2))),cross_product(X1,X2))
| ~ member(regular(complement(restrict(X0,X1,X2))),X0)
| null_class = complement(restrict(X0,X1,X2)) ),
inference(resolution,[],[f754,f120]) ).
fof(f7547,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(ordered_pair(X0,X1),X4)
| ~ subclass(universal_class,complement(restrict(X4,X2,X3))) ),
inference(resolution,[],[f754,f698]) ).
fof(f7546,plain,
! [X2,X3,X0,X1] :
( ~ member(singleton(X0),cross_product(X1,X2))
| ~ member(singleton(X0),X3)
| ~ subclass(universal_class,complement(restrict(X3,X1,X2))) ),
inference(resolution,[],[f754,f175]) ).
fof(f7545,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(unordered_pair(X0,X1),X4)
| ~ subclass(universal_class,complement(restrict(X4,X2,X3))) ),
inference(resolution,[],[f754,f263]) ).
fof(f7544,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(complement(restrict(X0,X1,X2)),X3),cross_product(X1,X2))
| ~ member(not_subclass_element(complement(restrict(X0,X1,X2)),X3),X0)
| subclass(complement(restrict(X0,X1,X2)),X3) ),
inference(resolution,[],[f754,f121]) ).
fof(f7543,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,restrict(X1,X2,X3)),cross_product(X2,X3))
| ~ member(not_subclass_element(X0,restrict(X1,X2,X3)),X1)
| subclass(X0,restrict(X1,X2,X3)) ),
inference(resolution,[],[f754,f3]) ).
fof(f7542,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(X0,X3)
| ~ subclass(restrict(X3,X1,X2),X4)
| member(X0,X4) ),
inference(resolution,[],[f754,f1]) ).
fof(f754,plain,
! [X2,X3,X0,X1] :
( member(X3,restrict(X0,X1,X2))
| ~ member(X3,cross_product(X1,X2))
| ~ member(X3,X0) ),
inference(superposition,[],[f23,f28]) ).
fof(f7485,plain,
! [X2,X0,X1] :
( ~ subclass(cantor(inverse(X0)),X1)
| ~ member(X2,range_of(X0))
| ~ member(X2,diagonalise(compose(inverse(element_relation),inverse(X0))))
| member(X2,X1) ),
inference(superposition,[],[f747,f920]) ).
fof(f7484,plain,
! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,inverse(subset_relation))
| ~ member(X1,subset_relation)
| member(X1,X0) ),
inference(superposition,[],[f747,f75]) ).
fof(f7483,plain,
! [X2,X0,X1] :
( ~ subclass(cantor(X0),X1)
| ~ member(X2,domain_of(X0))
| ~ member(X2,diagonalise(compose(inverse(element_relation),X0)))
| member(X2,X1) ),
inference(superposition,[],[f747,f77]) ).
fof(f7481,plain,
! [X0,X1] :
( ~ subclass(symmetric_difference(inverse(subset_relation),subset_relation),X0)
| ~ member(X1,complement(identity_relation))
| ~ member(X1,union(inverse(subset_relation),subset_relation))
| member(X1,X0) ),
inference(superposition,[],[f747,f1653]) ).
fof(f7480,plain,
! [X2,X0,X1] :
( ~ subclass(symmetric_difference(X0,singleton(X0)),X1)
| ~ member(X2,complement(intersection(X0,singleton(X0))))
| ~ member(X2,successor(X0))
| member(X2,X1) ),
inference(superposition,[],[f747,f1658]) ).
fof(f7479,plain,
! [X2,X3,X0,X1] :
( ~ subclass(symmetric_difference(X0,X1),X2)
| ~ member(X3,complement(intersection(X0,X1)))
| ~ member(X3,union(X0,X1))
| member(X3,X2) ),
inference(superposition,[],[f747,f1614]) ).
fof(f7488,plain,
! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| member(X1,X0) ),
inference(subsumption_resolution,[],[f7476,f496]) ).
fof(f7476,plain,
! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| member(X1,X0) ),
inference(superposition,[],[f747,f1933]) ).
fof(f7475,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(restrict(X2,X0,X1),X3)
| ~ member(X4,cross_product(X0,X1))
| ~ member(X4,X2)
| member(X4,X3) ),
inference(superposition,[],[f747,f29]) ).
fof(f7487,plain,
! [X2,X0] :
( ~ member(X2,singleton(X0))
| ~ member(X2,X0)
| singleton(X0) = null_class ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f444,f447,f449,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5348,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5413,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460,f5464,f446,f5466,f5468,f5469,f5472,f5473,f5474,f5475,f5476,f5477,f5478,f5480,f5481,f5482,f5483,f5484,f5485,f5486,f5487,f5488,f5489,f5544,f5545,f5492,f5493,f5494,f5495,f5496,f5499,f5501,f5502,f5503,f5504,f5505,f5506,f5507,f5508,f5509,f5511,f5512,f5546,f5518,f5553,f3533,f5555,f4681,f5628,f5629,f5631,f5633,f5634,f5637,f5638,f5639,f5640,f5641,f5642,f5643,f5645,f5647,f5648,f5651,f5652,f5653,f5654,f5655,f5656,f5657,f5377,f450,f5686,f5688,f5689,f5692,f5693,f5694,f5695,f5696,f5697,f5698,f5700,f5702,f5703,f5706,f5707,f5708,f5709,f5710,f5711,f5712,f5715,f5716,f5658,f5763,f5764,f5766,f5768,f5769,f5772,f5773,f5774,f5775,f5776,f5777,f5778,f5779,f3991,f5801,f5802,f5807,f5808,f5813,f5814,f5815,f5816,f5817,f5818,f5819,f5820,f5821,f5822,f5823,f5824,f5825,f527,f5828,f5834,f5835,f5838,f5839,f5840,f5841,f5847,f5848,f5851,f5852,f5853,f4123,f5854,f5855,f5860,f5861,f5866,f5867,f5868,f5869,f5870,f5871,f5872,f5873,f5874,f5875,f5876,f5877,f5878,f4161,f5879,f5881,f5880,f5883,f5882,f4163,f5886,f554,f6039,f6040,f6041,f6042,f6043,f6044,f6045,f6046,f6047,f6048,f6049,f6050,f6051,f6057,f6060,f6062,f6067,f6160,f6244,f6245,f6250,f6251,f6256,f6257,f6258,f6259,f6260,f6261,f6262,f6263,f6264,f6265,f6266,f6267,f6268,f6269,f6271,f6248,f6274,f920,f6374,f6377,f6408,f6409,f6410,f6411,f6384,f6386,f6390,f6391,f6392,f6393,f6394,f6395,f6396,f6397,f6406,f6375,f6412,f6413,f6418,f6419,f6424,f6425,f6427,f6428,f6429,f6430,f6431,f6432,f6433,f6434,f6435,f6436,f6437,f3825,f6447,f6448,f6452,f6453,f6454,f6459,f6460,f6461,f6462,f6463,f6464,f6465,f6466,f6467,f6468,f6469,f6470,f6471,f6472,f3843,f6473,f6474,f6478,f6479,f6480,f6485,f6486,f6487,f6488,f6489,f6490,f6491,f6492,f6493,f6494,f6495,f6496,f6497,f6498,f4483,f6499,f6249,f6511,f1514,f6522,f6523,f6525,f956,f6528,f2428,f6531,f6532,f6538,f6544,f6549,f6550,f6551,f3109,f6561,f6562,f6563,f6564,f6565,f6566,f6567,f6568,f6570,f6571,f6572,f6573,f6574,f6575,f6576,f6582,f6585,f6587,f6592,f6594,f6595,f6601,f1658,f6648,f6652,f6653,f6654,f6657,f6691,f6692,f6693,f6694,f6665,f6666,f6667,f6670,f6671,f6672,f6673,f6674,f6675,f6676,f6677,f6686,f215,f6656,f6846,f6847,f6854,f6855,f6860,f6861,f6862,f6863,f6864,f6865,f6866,f6867,f6868,f6869,f6870,f6871,f6872,f6873,f6874,f6875,f3936,f6879,f6899,f6901,f6902,f6908,f6909,f6910,f6911,f6912,f4078,f6913,f6917,f6933,f6920,f6934,f6935,f6937,f6938,f6939,f6941,f6942,f4308,f4513,f216,f219,f221,f526,f7218,f7232,f7231,f7230,f747,f7467,f7468,f7469,f7470,f7472,f7486]) ).
fof(f7486,plain,
! [X2,X0,X1] :
( ~ member(X2,singleton(X0))
| ~ member(X2,X0)
| member(X2,X1)
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f7474,f3077]) ).
fof(f7474,plain,
! [X2,X0,X1] :
( ~ subclass(null_class,X1)
| ~ member(X2,singleton(X0))
| ~ member(X2,X0)
| member(X2,X1)
| singleton(X0) = null_class ),
inference(superposition,[],[f747,f767]) ).
fof(f7472,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(restrict(X0,X1,X2),X3)
| ~ member(X4,X0)
| ~ member(X4,cross_product(X1,X2))
| member(X4,X3) ),
inference(superposition,[],[f747,f28]) ).
fof(f7470,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,subset_relation)
| ~ subclass(intersection(X1,X2),identity_relation) ),
inference(resolution,[],[f747,f2984]) ).
fof(f7469,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,inverse(subset_relation))
| ~ subclass(intersection(X1,X2),identity_relation) ),
inference(resolution,[],[f747,f2983]) ).
fof(f7468,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) ),
inference(resolution,[],[f747,f62]) ).
fof(f747,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f7230,plain,
! [X0,X1] :
( second(not_subclass_element(null_class,null_class)) = range(regular(cross_product(singleton(X0),X1)),X0,X1)
| null_class = cross_product(singleton(X0),X1) ),
inference(superposition,[],[f41,f526]) ).
fof(f7231,plain,
! [X0] :
( ~ member(X0,domain_of(regular(cross_product(singleton(X0),universal_class))))
| null_class = cross_product(singleton(X0),universal_class) ),
inference(trivial_inequality_removal,[],[f7229]) ).
fof(f7229,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(regular(cross_product(singleton(X0),universal_class))))
| null_class = cross_product(singleton(X0),universal_class) ),
inference(superposition,[],[f30,f526]) ).
fof(f7232,plain,
! [X0,X1] :
( single_valued3(null_class) = domain(regular(cross_product(X0,singleton(X1))),X0,X1)
| null_class = cross_product(X0,singleton(X1)) ),
inference(forward_demodulation,[],[f7228,f5880]) ).
fof(f7228,plain,
! [X0,X1] :
( first(not_subclass_element(null_class,null_class)) = domain(regular(cross_product(X0,singleton(X1))),X0,X1)
| null_class = cross_product(X0,singleton(X1)) ),
inference(superposition,[],[f40,f526]) ).
fof(f7218,plain,
! [X0] :
( range_of(null_class) = image(regular(cross_product(X0,universal_class)),X0)
| null_class = cross_product(X0,universal_class) ),
inference(superposition,[],[f42,f526]) ).
fof(f526,plain,
! [X0,X1] :
( null_class = restrict(regular(cross_product(X0,X1)),X0,X1)
| cross_product(X0,X1) = null_class ),
inference(superposition,[],[f29,f67]) ).
fof(f221,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
inference(resolution,[],[f7,f105]) ).
fof(f219,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f7,f95]) ).
fof(f216,plain,
! [X0] :
( ~ subclass(identity_relation,compose(X0,inverse(X0)))
| compose(X0,inverse(X0)) = identity_relation
| ~ function(X0) ),
inference(resolution,[],[f7,f63]) ).
fof(f4513,plain,
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(omega,complement(identity_relation)) ),
inference(superposition,[],[f173,f1653]) ).
fof(f4308,plain,
! [X0] :
( ~ subclass(domain_relation,subset_relation)
| ~ member(X0,universal_class)
| member(domain_of(X0),universal_class) ),
inference(resolution,[],[f318,f2065]) ).
fof(f6942,plain,
! [X0] :
( diagonalise(compose(inverse(element_relation),inverse(X0))) = cantor(inverse(X0))
| ~ subclass(diagonalise(compose(inverse(element_relation),inverse(X0))),cantor(inverse(X0))) ),
inference(forward_demodulation,[],[f6931,f920]) ).
fof(f6931,plain,
! [X0] :
( ~ subclass(diagonalise(compose(inverse(element_relation),inverse(X0))),cantor(inverse(X0)))
| diagonalise(compose(inverse(element_relation),inverse(X0))) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f4078,f920]) ).
fof(f6941,plain,
! [X0] :
( diagonalise(compose(inverse(element_relation),X0)) = cantor(X0)
| ~ subclass(diagonalise(compose(inverse(element_relation),X0)),cantor(X0)) ),
inference(forward_demodulation,[],[f6929,f77]) ).
fof(f6929,plain,
! [X0] :
( ~ subclass(diagonalise(compose(inverse(element_relation),X0)),cantor(X0))
| diagonalise(compose(inverse(element_relation),X0)) = intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f4078,f77]) ).
fof(f6939,plain,
( symmetric_difference(inverse(subset_relation),subset_relation) = union(inverse(subset_relation),subset_relation)
| ~ subclass(union(inverse(subset_relation),subset_relation),symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(forward_demodulation,[],[f6927,f1653]) ).
fof(f6927,plain,
( ~ subclass(union(inverse(subset_relation),subset_relation),symmetric_difference(inverse(subset_relation),subset_relation))
| union(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f4078,f1653]) ).
fof(f6938,plain,
! [X0] :
( successor(X0) = symmetric_difference(X0,singleton(X0))
| ~ subclass(successor(X0),symmetric_difference(X0,singleton(X0))) ),
inference(forward_demodulation,[],[f6926,f1658]) ).
fof(f6926,plain,
! [X0] :
( ~ subclass(successor(X0),symmetric_difference(X0,singleton(X0)))
| successor(X0) = intersection(complement(intersection(X0,singleton(X0))),successor(X0)) ),
inference(superposition,[],[f4078,f1658]) ).
fof(f6937,plain,
! [X0,X1] :
( union(X0,X1) = symmetric_difference(X0,X1)
| ~ subclass(union(X0,X1),symmetric_difference(X0,X1)) ),
inference(forward_demodulation,[],[f6925,f1614]) ).
fof(f6925,plain,
! [X0,X1] :
( ~ subclass(union(X0,X1),symmetric_difference(X0,X1))
| union(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
inference(superposition,[],[f4078,f1614]) ).
fof(f6935,plain,
( restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| ~ subclass(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),subset_relation) ),
inference(forward_demodulation,[],[f6922,f29]) ).
fof(f6922,plain,
( ~ subclass(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),subset_relation)
| restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class) = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f4078,f1933]) ).
fof(f6934,plain,
! [X2,X0,X1] :
( restrict(X2,X0,X1) = X2
| ~ subclass(X2,restrict(X2,X0,X1)) ),
inference(forward_demodulation,[],[f6921,f29]) ).
fof(f6921,plain,
! [X2,X0,X1] :
( ~ subclass(X2,restrict(X2,X0,X1))
| intersection(cross_product(X0,X1),X2) = X2 ),
inference(superposition,[],[f4078,f29]) ).
fof(f6920,plain,
! [X0] :
( ~ subclass(X0,null_class)
| intersection(singleton(X0),X0) = X0
| singleton(X0) = null_class ),
inference(superposition,[],[f4078,f767]) ).
fof(f6933,plain,
! [X2,X0,X1] :
( restrict(X0,X1,X2) = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),restrict(X0,X1,X2)) ),
inference(forward_demodulation,[],[f6918,f28]) ).
fof(f6918,plain,
! [X2,X0,X1] :
( ~ subclass(cross_product(X1,X2),restrict(X0,X1,X2))
| cross_product(X1,X2) = intersection(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f4078,f28]) ).
fof(f6917,plain,
! [X0] :
( ~ subclass(regular(X0),null_class)
| regular(X0) = intersection(X0,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f4078,f67]) ).
fof(f6913,plain,
! [X0,X1] :
( singleton(X1) = intersection(X0,singleton(X1))
| not_subclass_element(singleton(X1),intersection(X0,singleton(X1))) = X1 ),
inference(resolution,[],[f4078,f652]) ).
fof(f4078,plain,
! [X0,X1] :
( ~ subclass(X0,intersection(X1,X0))
| intersection(X1,X0) = X0 ),
inference(resolution,[],[f4063,f7]) ).
fof(f6912,plain,
! [X0] :
( range_of(X0) = cantor(inverse(X0))
| ~ subclass(range_of(X0),cantor(inverse(X0))) ),
inference(forward_demodulation,[],[f6897,f920]) ).
fof(f6897,plain,
! [X0] :
( ~ subclass(range_of(X0),cantor(inverse(X0)))
| range_of(X0) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f3936,f920]) ).
fof(f6911,plain,
! [X0] :
( domain_of(X0) = cantor(X0)
| ~ subclass(domain_of(X0),cantor(X0)) ),
inference(forward_demodulation,[],[f6895,f77]) ).
fof(f6895,plain,
! [X0] :
( ~ subclass(domain_of(X0),cantor(X0))
| domain_of(X0) = intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f3936,f77]) ).
fof(f6910,plain,
( complement(identity_relation) = symmetric_difference(inverse(subset_relation),subset_relation)
| ~ subclass(complement(identity_relation),symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(forward_demodulation,[],[f6893,f1653]) ).
fof(f6893,plain,
( ~ subclass(complement(identity_relation),symmetric_difference(inverse(subset_relation),subset_relation))
| complement(identity_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f3936,f1653]) ).
fof(f6909,plain,
! [X0] :
( symmetric_difference(X0,singleton(X0)) = complement(intersection(X0,singleton(X0)))
| ~ subclass(complement(intersection(X0,singleton(X0))),symmetric_difference(X0,singleton(X0))) ),
inference(forward_demodulation,[],[f6892,f1658]) ).
fof(f6892,plain,
! [X0] :
( ~ subclass(complement(intersection(X0,singleton(X0))),symmetric_difference(X0,singleton(X0)))
| complement(intersection(X0,singleton(X0))) = intersection(complement(intersection(X0,singleton(X0))),successor(X0)) ),
inference(superposition,[],[f3936,f1658]) ).
fof(f6908,plain,
! [X0,X1] :
( complement(intersection(X0,X1)) = symmetric_difference(X0,X1)
| ~ subclass(complement(intersection(X0,X1)),symmetric_difference(X0,X1)) ),
inference(forward_demodulation,[],[f6891,f1614]) ).
fof(f6891,plain,
! [X0,X1] :
( ~ subclass(complement(intersection(X0,X1)),symmetric_difference(X0,X1))
| complement(intersection(X0,X1)) = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
inference(superposition,[],[f3936,f1614]) ).
fof(f6902,plain,
( cross_product(universal_class,universal_class) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| ~ subclass(cross_product(universal_class,universal_class),subset_relation) ),
inference(forward_demodulation,[],[f6888,f29]) ).
fof(f6888,plain,
( ~ subclass(cross_product(universal_class,universal_class),subset_relation)
| cross_product(universal_class,universal_class) = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f3936,f1933]) ).
fof(f6901,plain,
! [X2,X0,X1] :
( cross_product(X0,X1) = restrict(X2,X0,X1)
| ~ subclass(cross_product(X0,X1),restrict(X2,X0,X1)) ),
inference(forward_demodulation,[],[f6887,f29]) ).
fof(f6887,plain,
! [X2,X0,X1] :
( ~ subclass(cross_product(X0,X1),restrict(X2,X0,X1))
| cross_product(X0,X1) = intersection(cross_product(X0,X1),X2) ),
inference(superposition,[],[f3936,f29]) ).
fof(f6899,plain,
! [X2,X0,X1] :
( restrict(X0,X1,X2) = X0
| ~ subclass(X0,restrict(X0,X1,X2)) ),
inference(forward_demodulation,[],[f6884,f28]) ).
fof(f6884,plain,
! [X2,X0,X1] :
( ~ subclass(X0,restrict(X0,X1,X2))
| intersection(X0,cross_product(X1,X2)) = X0 ),
inference(superposition,[],[f3936,f28]) ).
fof(f6879,plain,
! [X0,X1] :
( singleton(X0) = intersection(singleton(X0),X1)
| not_subclass_element(singleton(X0),intersection(singleton(X0),X1)) = X0 ),
inference(resolution,[],[f3936,f652]) ).
fof(f3936,plain,
! [X0,X1] :
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[],[f3922,f7]) ).
fof(f6875,plain,
! [X0,X1] :
( ~ member(X1,symmetric_difference(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)))
| member(X1,successor(singleton(singleton(X0)))) ),
inference(superposition,[],[f6656,f4463]) ).
fof(f6874,plain,
! [X2,X0,X1] :
( member(apply(X0,X1),successor(X2))
| ~ subclass(universal_class,symmetric_difference(X2,singleton(X2)))
| ~ function(X0) ),
inference(resolution,[],[f6656,f3109]) ).
fof(f6873,plain,
! [X2,X0,X1] :
( member(image(X0,X1),successor(X2))
| ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(X2,singleton(X2)))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f6656,f554]) ).
fof(f6872,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),successor(X2))
| ~ subclass(universal_class,symmetric_difference(X2,singleton(X2))) ),
inference(resolution,[],[f6656,f697]) ).
fof(f6871,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),successor(X2))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,singleton(X2))))) ),
inference(resolution,[],[f6656,f787]) ).
fof(f6870,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),successor(X2))
| ~ subclass(universal_class,symmetric_difference(X2,singleton(X2))) ),
inference(resolution,[],[f6656,f161]) ).
fof(f6869,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),successor(X2))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,singleton(X2))))) ),
inference(resolution,[],[f6656,f471]) ).
fof(f6868,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),successor(X2))
| ~ subclass(X0,symmetric_difference(X2,singleton(X2)))
| subclass(X0,X1) ),
inference(resolution,[],[f6656,f160]) ).
fof(f6867,plain,
! [X0,X1] :
( member(regular(intersection(X0,symmetric_difference(X1,singleton(X1)))),successor(X1))
| null_class = intersection(X0,symmetric_difference(X1,singleton(X1))) ),
inference(resolution,[],[f6656,f132]) ).
fof(f6866,plain,
! [X0,X1] :
( member(regular(X0),successor(X1))
| ~ subclass(X0,symmetric_difference(X1,singleton(X1)))
| null_class = X0 ),
inference(resolution,[],[f6656,f159]) ).
fof(f6865,plain,
! [X0,X1] :
( member(power_class(X0),successor(X1))
| ~ subclass(universal_class,symmetric_difference(X1,singleton(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6656,f165]) ).
fof(f6864,plain,
! [X0,X1] :
( member(sum_class(X0),successor(X1))
| ~ subclass(universal_class,symmetric_difference(X1,singleton(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6656,f164]) ).
fof(f6863,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),successor(X1))
| ~ subclass(domain_relation,symmetric_difference(X1,singleton(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6656,f318]) ).
fof(f6862,plain,
! [X0,X1] :
( member(singleton(X0),successor(X1))
| ~ subclass(universal_class,symmetric_difference(X1,singleton(X1))) ),
inference(resolution,[],[f6656,f162]) ).
fof(f6861,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,symmetric_difference(X1,singleton(X1))),X2),successor(X1))
| subclass(intersection(X0,symmetric_difference(X1,singleton(X1))),X2) ),
inference(resolution,[],[f6656,f133]) ).
fof(f6860,plain,
! [X0] :
( member(apply(choice,symmetric_difference(X0,singleton(X0))),successor(X0))
| null_class = symmetric_difference(X0,singleton(X0))
| ~ member(symmetric_difference(X0,singleton(X0)),universal_class) ),
inference(resolution,[],[f6656,f70]) ).
fof(f6855,plain,
! [X0,X1] :
( member(regular(intersection(symmetric_difference(X0,singleton(X0)),X1)),successor(X0))
| null_class = intersection(symmetric_difference(X0,singleton(X0)),X1) ),
inference(resolution,[],[f6656,f127]) ).
fof(f6854,plain,
! [X0] :
( member(regular(symmetric_difference(X0,singleton(X0))),successor(X0))
| null_class = symmetric_difference(X0,singleton(X0)) ),
inference(resolution,[],[f6656,f66]) ).
fof(f6847,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(symmetric_difference(X0,singleton(X0)),X1),X2),successor(X0))
| subclass(intersection(symmetric_difference(X0,singleton(X0)),X1),X2) ),
inference(resolution,[],[f6656,f128]) ).
fof(f6846,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,singleton(X0)),X1),successor(X0))
| subclass(symmetric_difference(X0,singleton(X0)),X1) ),
inference(resolution,[],[f6656,f2]) ).
fof(f6656,plain,
! [X0,X1] :
( ~ member(X1,symmetric_difference(X0,singleton(X0)))
| member(X1,successor(X0)) ),
inference(superposition,[],[f22,f1658]) ).
fof(f215,plain,
! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) ),
inference(resolution,[],[f7,f57]) ).
fof(f6686,plain,
! [X0] : subclass(symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0)),complement(symmetric_difference(X0,singleton(X0)))),
inference(superposition,[],[f3947,f1658]) ).
fof(f6677,plain,
! [X0] :
( ~ member(null_class,symmetric_difference(X0,singleton(X0)))
| ~ inductive(symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0))) ),
inference(superposition,[],[f1693,f1658]) ).
fof(f6676,plain,
! [X0] :
( member(null_class,complement(symmetric_difference(X0,singleton(X0))))
| ~ inductive(symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0))) ),
inference(superposition,[],[f1662,f1658]) ).
fof(f6675,plain,
! [X0,X1] :
( member(X1,complement(symmetric_difference(X0,singleton(X0))))
| ~ member(X1,symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0))) ),
inference(superposition,[],[f1659,f1658]) ).
fof(f6674,plain,
! [X0] : symmetric_difference(complement(intersection(X0,singleton(X0))),successor(X0)) = intersection(complement(symmetric_difference(X0,singleton(X0))),union(complement(intersection(X0,singleton(X0))),successor(X0))),
inference(superposition,[],[f1614,f1658]) ).
fof(f6673,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(ordered_pair(X1,X2),complement(intersection(X0,singleton(X0)))) ),
inference(superposition,[],[f719,f1658]) ).
fof(f6672,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(ordered_pair(X1,X2),successor(X0)) ),
inference(superposition,[],[f718,f1658]) ).
fof(f6671,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(unordered_pair(X1,X2),complement(intersection(X0,singleton(X0)))) ),
inference(superposition,[],[f265,f1658]) ).
fof(f6670,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(unordered_pair(X1,X2),successor(X0)) ),
inference(superposition,[],[f264,f1658]) ).
fof(f6667,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(singleton(X1),complement(intersection(X0,singleton(X0)))) ),
inference(superposition,[],[f177,f1658]) ).
fof(f6666,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(singleton(X1),successor(X0)) ),
inference(superposition,[],[f176,f1658]) ).
fof(f6665,plain,
! [X0] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(omega,complement(intersection(X0,singleton(X0)))) ),
inference(superposition,[],[f173,f1658]) ).
fof(f6694,plain,
! [X0,X1] :
( subclass(symmetric_difference(X0,singleton(X0)),X1)
| member(not_subclass_element(symmetric_difference(X0,singleton(X0)),X1),successor(X0)) ),
inference(forward_demodulation,[],[f6663,f1658]) ).
fof(f6663,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,singleton(X0)),X1),successor(X0))
| subclass(intersection(complement(intersection(X0,singleton(X0))),successor(X0)),X1) ),
inference(superposition,[],[f133,f1658]) ).
fof(f6693,plain,
! [X0] :
( null_class = symmetric_difference(X0,singleton(X0))
| member(regular(symmetric_difference(X0,singleton(X0))),successor(X0)) ),
inference(forward_demodulation,[],[f6662,f1658]) ).
fof(f6662,plain,
! [X0] :
( member(regular(symmetric_difference(X0,singleton(X0))),successor(X0))
| null_class = intersection(complement(intersection(X0,singleton(X0))),successor(X0)) ),
inference(superposition,[],[f132,f1658]) ).
fof(f6692,plain,
! [X0,X1] :
( subclass(symmetric_difference(X0,singleton(X0)),X1)
| member(not_subclass_element(symmetric_difference(X0,singleton(X0)),X1),complement(intersection(X0,singleton(X0)))) ),
inference(forward_demodulation,[],[f6660,f1658]) ).
fof(f6660,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,singleton(X0)),X1),complement(intersection(X0,singleton(X0))))
| subclass(intersection(complement(intersection(X0,singleton(X0))),successor(X0)),X1) ),
inference(superposition,[],[f128,f1658]) ).
fof(f6691,plain,
! [X0] :
( null_class = symmetric_difference(X0,singleton(X0))
| member(regular(symmetric_difference(X0,singleton(X0))),complement(intersection(X0,singleton(X0)))) ),
inference(forward_demodulation,[],[f6659,f1658]) ).
fof(f6659,plain,
! [X0] :
( member(regular(symmetric_difference(X0,singleton(X0))),complement(intersection(X0,singleton(X0))))
| null_class = intersection(complement(intersection(X0,singleton(X0))),successor(X0)) ),
inference(superposition,[],[f127,f1658]) ).
fof(f6657,plain,
! [X0,X1] :
( member(X1,symmetric_difference(X0,singleton(X0)))
| ~ member(X1,successor(X0))
| ~ member(X1,complement(intersection(X0,singleton(X0)))) ),
inference(superposition,[],[f23,f1658]) ).
fof(f6654,plain,
symmetric_difference(universal_class,singleton(universal_class)) = intersection(complement(intersection(universal_class,singleton(universal_class))),complement(null_class)),
inference(superposition,[],[f1658,f4284]) ).
fof(f6653,plain,
symmetric_difference(null_class,singleton(null_class)) = intersection(complement(null_class),successor(null_class)),
inference(superposition,[],[f1658,f3938]) ).
fof(f6652,plain,
! [X0,X1] : symmetric_difference(cross_product(X0,X1),singleton(cross_product(X0,X1))) = intersection(complement(restrict(singleton(cross_product(X0,X1)),X0,X1)),successor(cross_product(X0,X1))),
inference(superposition,[],[f1658,f29]) ).
fof(f6648,plain,
! [X0] : symmetric_difference(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)) = intersection(complement(intersection(singleton(singleton(X0)),ordered_pair(singleton(X0),X0))),successor(singleton(singleton(X0)))),
inference(superposition,[],[f1658,f4463]) ).
fof(f1658,plain,
! [X0] : symmetric_difference(X0,singleton(X0)) = intersection(complement(intersection(X0,singleton(X0))),successor(X0)),
inference(superposition,[],[f1614,f43]) ).
fof(f6601,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(universal_class,X1)
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f6597,f69]) ).
fof(f6597,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(universal_class,X1)
| ~ function(choice)
| singleton(X0) = null_class ),
inference(superposition,[],[f3109,f890]) ).
fof(f6595,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| ~ function(X1)
| member(apply(X1,X2),range_of(X0)) ),
inference(resolution,[],[f3109,f6375]) ).
fof(f6594,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ function(X1)
| member(apply(X1,X2),domain_of(X0)) ),
inference(resolution,[],[f3109,f923]) ).
fof(f6592,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ function(X1)
| ~ member(apply(X1,X2),X0)
| null_class = X0 ),
inference(resolution,[],[f3109,f6160]) ).
fof(f6587,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,image(X0,image(X1,singleton(X2))))
| ~ function(X3)
| member(ordered_pair(X2,apply(X3,X4)),compose(X0,X1))
| ~ member(ordered_pair(X2,apply(X3,X4)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f3109,f59]) ).
fof(f6585,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ function(X1)
| ~ member(apply(X1,X2),power_class(X0)) ),
inference(resolution,[],[f3109,f152]) ).
fof(f6582,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ function(X1)
| ~ member(apply(X1,X2),diagonalise(X0)) ),
inference(resolution,[],[f3109,f155]) ).
fof(f6576,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| ~ function(X3)
| member(apply(X3,X4),X0) ),
inference(resolution,[],[f3109,f495]) ).
fof(f6575,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| ~ function(X3)
| member(apply(X3,X4),cross_product(X1,X2)) ),
inference(resolution,[],[f3109,f496]) ).
fof(f6574,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ function(X0)
| member(apply(X0,X1),complement(identity_relation)) ),
inference(resolution,[],[f3109,f3843]) ).
fof(f6573,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(null_class,X0))
| ~ function(X1)
| member(apply(X1,X2),complement(null_class)) ),
inference(resolution,[],[f3109,f3991]) ).
fof(f6572,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,null_class))
| ~ function(X1)
| member(apply(X1,X2),complement(null_class)) ),
inference(resolution,[],[f3109,f4123]) ).
fof(f6571,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| ~ function(X2)
| member(apply(X2,X3),union(X0,X1)) ),
inference(resolution,[],[f3109,f1660]) ).
fof(f6570,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| ~ function(X2)
| ~ member(apply(X2,X3),intersection(X0,X1)) ),
inference(resolution,[],[f3109,f3825]) ).
fof(f6568,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ function(X1)
| ~ member(apply(X1,X2),X0) ),
inference(resolution,[],[f3109,f24]) ).
fof(f6567,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(complement(X0),complement(X1)))
| ~ function(X2)
| ~ member(apply(X2,X3),union(X0,X1)) ),
inference(resolution,[],[f3109,f448]) ).
fof(f6566,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ function(X2)
| member(apply(X2,X3),X0) ),
inference(resolution,[],[f3109,f21]) ).
fof(f6565,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ function(X2)
| member(apply(X2,X3),X1) ),
inference(resolution,[],[f3109,f22]) ).
fof(f6564,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| ~ function(X2)
| apply(X2,X3) = ordered_pair(first(apply(X2,X3)),second(apply(X2,X3))) ),
inference(resolution,[],[f3109,f17]) ).
fof(f6563,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| ~ function(X1)
| apply(X1,X2) = X0 ),
inference(resolution,[],[f3109,f650]) ).
fof(f6562,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ function(X2)
| apply(X2,X3) = X0
| apply(X2,X3) = X1 ),
inference(resolution,[],[f3109,f8]) ).
fof(f6561,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ function(X1)
| ~ subclass(X0,X2)
| member(apply(X1,X3),X2) ),
inference(resolution,[],[f3109,f1]) ).
fof(f3109,plain,
! [X2,X0,X1] :
( member(apply(X0,X2),X1)
| ~ subclass(universal_class,X1)
| ~ function(X0) ),
inference(resolution,[],[f3108,f1]) ).
fof(f6551,plain,
! [X0,X1] :
( not_subclass_element(X0,X1) = ordered_pair(first(not_subclass_element(X0,X1)),second(not_subclass_element(X0,X1)))
| ~ subclass(X0,identity_relation)
| subclass(X0,X1) ),
inference(resolution,[],[f2428,f160]) ).
fof(f6550,plain,
! [X0] :
( regular(intersection(X0,identity_relation)) = ordered_pair(first(regular(intersection(X0,identity_relation))),second(regular(intersection(X0,identity_relation))))
| null_class = intersection(X0,identity_relation) ),
inference(resolution,[],[f2428,f132]) ).
fof(f6549,plain,
! [X0] :
( regular(X0) = ordered_pair(first(regular(X0)),second(regular(X0)))
| ~ subclass(X0,identity_relation)
| null_class = X0 ),
inference(resolution,[],[f2428,f159]) ).
fof(f6544,plain,
! [X0,X1] :
( not_subclass_element(intersection(X0,identity_relation),X1) = ordered_pair(first(not_subclass_element(intersection(X0,identity_relation),X1)),second(not_subclass_element(intersection(X0,identity_relation),X1)))
| subclass(intersection(X0,identity_relation),X1) ),
inference(resolution,[],[f2428,f133]) ).
fof(f6538,plain,
! [X0] :
( regular(intersection(identity_relation,X0)) = ordered_pair(first(regular(intersection(identity_relation,X0))),second(regular(intersection(identity_relation,X0))))
| null_class = intersection(identity_relation,X0) ),
inference(resolution,[],[f2428,f127]) ).
fof(f6532,plain,
! [X0,X1] :
( not_subclass_element(intersection(identity_relation,X0),X1) = ordered_pair(first(not_subclass_element(intersection(identity_relation,X0),X1)),second(not_subclass_element(intersection(identity_relation,X0),X1)))
| subclass(intersection(identity_relation,X0),X1) ),
inference(resolution,[],[f2428,f128]) ).
fof(f6531,plain,
! [X0] :
( not_subclass_element(identity_relation,X0) = ordered_pair(first(not_subclass_element(identity_relation,X0)),second(not_subclass_element(identity_relation,X0)))
| subclass(identity_relation,X0) ),
inference(resolution,[],[f2428,f2]) ).
fof(f2428,plain,
! [X0] :
( ~ member(X0,identity_relation)
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(resolution,[],[f2058,f134]) ).
fof(f6528,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(restrict(identity_relation,X0,X1)))
| ~ member(omega,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f956,f29]) ).
fof(f956,plain,
! [X0] :
( ~ subclass(universal_class,cantor(intersection(X0,identity_relation)))
| ~ member(omega,diagonalise(X0)) ),
inference(resolution,[],[f949,f155]) ).
fof(f6525,plain,
( ~ member(complement(null_class),universal_class)
| member(ordered_pair(universal_class,complement(null_class)),successor_relation)
| ~ member(universal_class,universal_class) ),
inference(forward_demodulation,[],[f6524,f4284]) ).
fof(f6524,plain,
( member(ordered_pair(universal_class,complement(null_class)),successor_relation)
| ~ member(successor(universal_class),universal_class)
| ~ member(universal_class,universal_class) ),
inference(superposition,[],[f1514,f4284]) ).
fof(f6523,plain,
! [X0,X1] :
( ~ member(successor(X0),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(successor_relation,X1)
| member(ordered_pair(X0,successor(X0)),X1) ),
inference(resolution,[],[f1514,f1]) ).
fof(f6522,plain,
! [X0] :
( ~ member(successor(X0),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(universal_class,complement(successor_relation)) ),
inference(resolution,[],[f1514,f698]) ).
fof(f1514,plain,
! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(successor(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f116,f16]) ).
fof(f6511,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| singleton(X0) = null_class
| ~ member(omega,singleton(X0)) ),
inference(duplicate_literal_removal,[],[f6510]) ).
fof(f6510,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| singleton(X0) = null_class
| ~ member(omega,singleton(X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f6249,f656]) ).
fof(f6249,plain,
! [X0] :
( ~ subclass(universal_class,regular(X0))
| null_class = X0
| ~ member(omega,X0) ),
inference(resolution,[],[f6160,f163]) ).
fof(f6499,plain,
! [X0] :
( ~ inductive(ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))))
| null_class = singleton(singleton(singleton(singleton(X0)))) ),
inference(superposition,[],[f4483,f4463]) ).
fof(f4483,plain,
! [X0] :
( ~ inductive(ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(X0)) ),
inference(duplicate_literal_removal,[],[f4481]) ).
fof(f4481,plain,
! [X0] :
( ~ inductive(ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(X0))
| null_class = singleton(singleton(X0)) ),
inference(superposition,[],[f643,f690]) ).
fof(f6498,plain,
! [X0,X1] :
( member(image(X0,X1),complement(identity_relation))
| ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f3843,f554]) ).
fof(f6497,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(resolution,[],[f3843,f697]) ).
fof(f6496,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),complement(identity_relation))
| ~ subclass(universal_class,complement(complement(symmetric_difference(inverse(subset_relation),subset_relation)))) ),
inference(resolution,[],[f3843,f787]) ).
fof(f6495,plain,
! [X0,X1] :
( member(unordered_pair(X0,X1),complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(resolution,[],[f3843,f161]) ).
fof(f6494,plain,
! [X0,X1] :
( member(unordered_pair(X0,X1),complement(identity_relation))
| ~ subclass(universal_class,complement(complement(symmetric_difference(inverse(subset_relation),subset_relation)))) ),
inference(resolution,[],[f3843,f471]) ).
fof(f6493,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),complement(identity_relation))
| ~ subclass(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| subclass(X0,X1) ),
inference(resolution,[],[f3843,f160]) ).
fof(f6492,plain,
! [X0] :
( member(regular(intersection(X0,symmetric_difference(inverse(subset_relation),subset_relation))),complement(identity_relation))
| null_class = intersection(X0,symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(resolution,[],[f3843,f132]) ).
fof(f6491,plain,
! [X0] :
( member(regular(X0),complement(identity_relation))
| ~ subclass(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| null_class = X0 ),
inference(resolution,[],[f3843,f159]) ).
fof(f6490,plain,
! [X0] :
( member(power_class(X0),complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3843,f165]) ).
fof(f6489,plain,
! [X0] :
( member(sum_class(X0),complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3843,f164]) ).
fof(f6488,plain,
! [X0] :
( member(ordered_pair(X0,domain_of(X0)),complement(identity_relation))
| ~ subclass(domain_relation,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3843,f318]) ).
fof(f6487,plain,
! [X0] :
( member(singleton(X0),complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(resolution,[],[f3843,f162]) ).
fof(f6486,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(X0,symmetric_difference(inverse(subset_relation),subset_relation)),X1),complement(identity_relation))
| subclass(intersection(X0,symmetric_difference(inverse(subset_relation),subset_relation)),X1) ),
inference(resolution,[],[f3843,f133]) ).
fof(f6485,plain,
( member(apply(choice,symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation))
| null_class = symmetric_difference(inverse(subset_relation),subset_relation)
| ~ member(symmetric_difference(inverse(subset_relation),subset_relation),universal_class) ),
inference(resolution,[],[f3843,f70]) ).
fof(f6480,plain,
! [X0] :
( member(regular(intersection(symmetric_difference(inverse(subset_relation),subset_relation),X0)),complement(identity_relation))
| null_class = intersection(symmetric_difference(inverse(subset_relation),subset_relation),X0) ),
inference(resolution,[],[f3843,f127]) ).
fof(f6479,plain,
( member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation))
| null_class = symmetric_difference(inverse(subset_relation),subset_relation) ),
inference(resolution,[],[f3843,f66]) ).
fof(f6478,plain,
( member(omega,complement(identity_relation))
| ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(resolution,[],[f3843,f163]) ).
fof(f6474,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(symmetric_difference(inverse(subset_relation),subset_relation),X0),X1),complement(identity_relation))
| subclass(intersection(symmetric_difference(inverse(subset_relation),subset_relation),X0),X1) ),
inference(resolution,[],[f3843,f128]) ).
fof(f6473,plain,
! [X0] :
( member(not_subclass_element(symmetric_difference(inverse(subset_relation),subset_relation),X0),complement(identity_relation))
| subclass(symmetric_difference(inverse(subset_relation),subset_relation),X0) ),
inference(resolution,[],[f3843,f2]) ).
fof(f3843,plain,
! [X0] :
( ~ member(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| member(X0,complement(identity_relation)) ),
inference(superposition,[],[f1659,f75]) ).
fof(f6472,plain,
! [X2,X3,X0,X1] :
( ~ member(image(X0,X1),intersection(X2,X3))
| ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(X2,X3))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f3825,f554]) ).
fof(f6471,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),intersection(X2,X3))
| ~ subclass(universal_class,symmetric_difference(X2,X3)) ),
inference(resolution,[],[f3825,f697]) ).
fof(f6470,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),intersection(X2,X3))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,X3)))) ),
inference(resolution,[],[f3825,f787]) ).
fof(f6469,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),intersection(X2,X3))
| ~ subclass(universal_class,symmetric_difference(X2,X3)) ),
inference(resolution,[],[f3825,f161]) ).
fof(f6468,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),intersection(X2,X3))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,X3)))) ),
inference(resolution,[],[f3825,f471]) ).
fof(f6467,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,X1),intersection(X2,X3))
| ~ subclass(X0,symmetric_difference(X2,X3))
| subclass(X0,X1) ),
inference(resolution,[],[f3825,f160]) ).
fof(f6466,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(X0,symmetric_difference(X1,X2))),intersection(X1,X2))
| null_class = intersection(X0,symmetric_difference(X1,X2)) ),
inference(resolution,[],[f3825,f132]) ).
fof(f6465,plain,
! [X2,X0,X1] :
( ~ member(regular(X0),intersection(X1,X2))
| ~ subclass(X0,symmetric_difference(X1,X2))
| null_class = X0 ),
inference(resolution,[],[f3825,f159]) ).
fof(f6464,plain,
! [X2,X0,X1] :
( ~ member(power_class(X0),intersection(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3825,f165]) ).
fof(f6463,plain,
! [X2,X0,X1] :
( ~ member(sum_class(X0),intersection(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3825,f164]) ).
fof(f6462,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,domain_of(X0)),intersection(X1,X2))
| ~ subclass(domain_relation,symmetric_difference(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3825,f318]) ).
fof(f6461,plain,
! [X2,X0,X1] :
( ~ member(singleton(X0),intersection(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2)) ),
inference(resolution,[],[f3825,f162]) ).
fof(f6460,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,symmetric_difference(X1,X2)),X3),intersection(X1,X2))
| subclass(intersection(X0,symmetric_difference(X1,X2)),X3) ),
inference(resolution,[],[f3825,f133]) ).
fof(f6459,plain,
! [X0,X1] :
( ~ member(apply(choice,symmetric_difference(X0,X1)),intersection(X0,X1))
| symmetric_difference(X0,X1) = null_class
| ~ member(symmetric_difference(X0,X1),universal_class) ),
inference(resolution,[],[f3825,f70]) ).
fof(f6454,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(symmetric_difference(X0,X1),X2)),intersection(X0,X1))
| null_class = intersection(symmetric_difference(X0,X1),X2) ),
inference(resolution,[],[f3825,f127]) ).
fof(f6453,plain,
! [X0,X1] :
( ~ member(regular(symmetric_difference(X0,X1)),intersection(X0,X1))
| symmetric_difference(X0,X1) = null_class ),
inference(resolution,[],[f3825,f66]) ).
fof(f6448,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(symmetric_difference(X0,X1),X2),X3),intersection(X0,X1))
| subclass(intersection(symmetric_difference(X0,X1),X2),X3) ),
inference(resolution,[],[f3825,f128]) ).
fof(f6447,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(symmetric_difference(X0,X1),X2),intersection(X0,X1))
| subclass(symmetric_difference(X0,X1),X2) ),
inference(resolution,[],[f3825,f2]) ).
fof(f3825,plain,
! [X2,X0,X1] :
( ~ member(X0,symmetric_difference(X1,X2))
| ~ member(X0,intersection(X1,X2)) ),
inference(resolution,[],[f1659,f24]) ).
fof(f6437,plain,
! [X2,X0,X1] :
( member(image(X0,X1),range_of(X2))
| ~ function(X0)
| ~ subclass(universal_class,cantor(inverse(X2)))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f6375,f554]) ).
fof(f6436,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),range_of(X2))
| ~ subclass(universal_class,cantor(inverse(X2))) ),
inference(resolution,[],[f6375,f697]) ).
fof(f6435,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),range_of(X2))
| ~ subclass(universal_class,complement(complement(cantor(inverse(X2))))) ),
inference(resolution,[],[f6375,f787]) ).
fof(f6434,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),range_of(X2))
| ~ subclass(universal_class,cantor(inverse(X2))) ),
inference(resolution,[],[f6375,f161]) ).
fof(f6433,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),range_of(X2))
| ~ subclass(universal_class,complement(complement(cantor(inverse(X2))))) ),
inference(resolution,[],[f6375,f471]) ).
fof(f6432,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),range_of(X2))
| ~ subclass(X0,cantor(inverse(X2)))
| subclass(X0,X1) ),
inference(resolution,[],[f6375,f160]) ).
fof(f6431,plain,
! [X0,X1] :
( member(regular(intersection(X0,cantor(inverse(X1)))),range_of(X1))
| null_class = intersection(X0,cantor(inverse(X1))) ),
inference(resolution,[],[f6375,f132]) ).
fof(f6430,plain,
! [X0,X1] :
( member(regular(X0),range_of(X1))
| ~ subclass(X0,cantor(inverse(X1)))
| null_class = X0 ),
inference(resolution,[],[f6375,f159]) ).
fof(f6429,plain,
! [X0,X1] :
( member(power_class(X0),range_of(X1))
| ~ subclass(universal_class,cantor(inverse(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6375,f165]) ).
fof(f6428,plain,
! [X0,X1] :
( member(sum_class(X0),range_of(X1))
| ~ subclass(universal_class,cantor(inverse(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6375,f164]) ).
fof(f6427,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),range_of(X1))
| ~ subclass(domain_relation,cantor(inverse(X1)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6375,f318]) ).
fof(f6425,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,cantor(inverse(X1))),X2),range_of(X1))
| subclass(intersection(X0,cantor(inverse(X1))),X2) ),
inference(resolution,[],[f6375,f133]) ).
fof(f6424,plain,
! [X0] :
( member(apply(choice,cantor(inverse(X0))),range_of(X0))
| null_class = cantor(inverse(X0))
| ~ member(cantor(inverse(X0)),universal_class) ),
inference(resolution,[],[f6375,f70]) ).
fof(f6419,plain,
! [X0,X1] :
( member(regular(intersection(cantor(inverse(X0)),X1)),range_of(X0))
| null_class = intersection(cantor(inverse(X0)),X1) ),
inference(resolution,[],[f6375,f127]) ).
fof(f6418,plain,
! [X0] :
( member(regular(cantor(inverse(X0))),range_of(X0))
| null_class = cantor(inverse(X0)) ),
inference(resolution,[],[f6375,f66]) ).
fof(f6413,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(cantor(inverse(X0)),X1),X2),range_of(X0))
| subclass(intersection(cantor(inverse(X0)),X1),X2) ),
inference(resolution,[],[f6375,f128]) ).
fof(f6412,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(inverse(X0)),X1),range_of(X0))
| subclass(cantor(inverse(X0)),X1) ),
inference(resolution,[],[f6375,f2]) ).
fof(f6375,plain,
! [X0,X1] :
( ~ member(X1,cantor(inverse(X0)))
| member(X1,range_of(X0)) ),
inference(superposition,[],[f21,f920]) ).
fof(f6406,plain,
! [X0] : subclass(symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))),complement(cantor(inverse(X0)))),
inference(superposition,[],[f3947,f920]) ).
fof(f6397,plain,
! [X0] :
( ~ member(null_class,cantor(inverse(X0)))
| ~ inductive(symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))) ),
inference(superposition,[],[f1693,f920]) ).
fof(f6396,plain,
! [X0] :
( member(null_class,complement(cantor(inverse(X0))))
| ~ inductive(symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))) ),
inference(superposition,[],[f1662,f920]) ).
fof(f6395,plain,
! [X0,X1] :
( member(X1,complement(cantor(inverse(X0))))
| ~ member(X1,symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))) ),
inference(superposition,[],[f1659,f920]) ).
fof(f6394,plain,
! [X0] : symmetric_difference(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) = intersection(complement(cantor(inverse(X0))),union(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0))))),
inference(superposition,[],[f1614,f920]) ).
fof(f6393,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(ordered_pair(X1,X2),range_of(X0)) ),
inference(superposition,[],[f719,f920]) ).
fof(f6392,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(ordered_pair(X1,X2),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f718,f920]) ).
fof(f6391,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(unordered_pair(X1,X2),range_of(X0)) ),
inference(superposition,[],[f265,f920]) ).
fof(f6390,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(unordered_pair(X1,X2),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f264,f920]) ).
fof(f6386,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(singleton(X1),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f176,f920]) ).
fof(f6384,plain,
! [X0] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(omega,diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f172,f920]) ).
fof(f6411,plain,
! [X0,X1] :
( subclass(cantor(inverse(X0)),X1)
| member(not_subclass_element(cantor(inverse(X0)),X1),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(forward_demodulation,[],[f6383,f920]) ).
fof(f6383,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(inverse(X0)),X1),diagonalise(compose(inverse(element_relation),inverse(X0))))
| subclass(intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))),X1) ),
inference(superposition,[],[f133,f920]) ).
fof(f6410,plain,
! [X0] :
( null_class = cantor(inverse(X0))
| member(regular(cantor(inverse(X0))),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(forward_demodulation,[],[f6382,f920]) ).
fof(f6382,plain,
! [X0] :
( member(regular(cantor(inverse(X0))),diagonalise(compose(inverse(element_relation),inverse(X0))))
| null_class = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f132,f920]) ).
fof(f6409,plain,
! [X0,X1] :
( subclass(cantor(inverse(X0)),X1)
| member(not_subclass_element(cantor(inverse(X0)),X1),range_of(X0)) ),
inference(forward_demodulation,[],[f6380,f920]) ).
fof(f6380,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(inverse(X0)),X1),range_of(X0))
| subclass(intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))),X1) ),
inference(superposition,[],[f128,f920]) ).
fof(f6408,plain,
! [X0] :
( null_class = cantor(inverse(X0))
| member(regular(cantor(inverse(X0))),range_of(X0)) ),
inference(forward_demodulation,[],[f6379,f920]) ).
fof(f6379,plain,
! [X0] :
( member(regular(cantor(inverse(X0))),range_of(X0))
| null_class = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) ),
inference(superposition,[],[f127,f920]) ).
fof(f6377,plain,
! [X0,X1] :
( member(X1,cantor(inverse(X0)))
| ~ member(X1,diagonalise(compose(inverse(element_relation),inverse(X0))))
| ~ member(X1,range_of(X0)) ),
inference(superposition,[],[f23,f920]) ).
fof(f6374,plain,
! [X0,X1] : cantor(inverse(restrict(X0,X1,universal_class))) = intersection(image(X0,X1),diagonalise(compose(inverse(element_relation),inverse(restrict(X0,X1,universal_class))))),
inference(superposition,[],[f920,f42]) ).
fof(f920,plain,
! [X0] : cantor(inverse(X0)) = intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))),
inference(superposition,[],[f77,f39]) ).
fof(f6248,plain,
! [X0] :
( ~ inductive(regular(X0))
| null_class = X0
| ~ member(null_class,X0) ),
inference(resolution,[],[f6160,f47]) ).
fof(f6271,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f6270]) ).
fof(f6270,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,singleton(X0))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f6160,f656]) ).
fof(f6269,plain,
! [X2,X0,X1] :
( ~ member(image(X0,X1),X2)
| null_class = X2
| ~ function(X0)
| ~ subclass(universal_class,regular(X2))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f6160,f554]) ).
fof(f6268,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,regular(X2)) ),
inference(resolution,[],[f6160,f697]) ).
fof(f6267,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,complement(complement(regular(X2)))) ),
inference(resolution,[],[f6160,f787]) ).
fof(f6266,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,regular(X2)) ),
inference(resolution,[],[f6160,f161]) ).
fof(f6265,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,complement(complement(regular(X2)))) ),
inference(resolution,[],[f6160,f471]) ).
fof(f6264,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| null_class = X2
| ~ subclass(X0,regular(X2))
| subclass(X0,X1) ),
inference(resolution,[],[f6160,f160]) ).
fof(f6263,plain,
! [X0,X1] :
( ~ member(regular(intersection(X0,regular(X1))),X1)
| null_class = X1
| null_class = intersection(X0,regular(X1)) ),
inference(resolution,[],[f6160,f132]) ).
fof(f6262,plain,
! [X0,X1] :
( ~ member(regular(X0),X1)
| null_class = X1
| ~ subclass(X0,regular(X1))
| null_class = X0 ),
inference(resolution,[],[f6160,f159]) ).
fof(f6261,plain,
! [X0,X1] :
( ~ member(power_class(X0),X1)
| null_class = X1
| ~ subclass(universal_class,regular(X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6160,f165]) ).
fof(f6260,plain,
! [X0,X1] :
( ~ member(sum_class(X0),X1)
| null_class = X1
| ~ subclass(universal_class,regular(X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6160,f164]) ).
fof(f6259,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,domain_of(X0)),X1)
| null_class = X1
| ~ subclass(domain_relation,regular(X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f6160,f318]) ).
fof(f6258,plain,
! [X0,X1] :
( ~ member(singleton(X0),X1)
| null_class = X1
| ~ subclass(universal_class,regular(X1)) ),
inference(resolution,[],[f6160,f162]) ).
fof(f6257,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| null_class = X1
| subclass(intersection(X0,regular(X1)),X2) ),
inference(resolution,[],[f6160,f133]) ).
fof(f6256,plain,
! [X0] :
( ~ member(apply(choice,regular(X0)),X0)
| null_class = X0
| null_class = regular(X0)
| ~ member(regular(X0),universal_class) ),
inference(resolution,[],[f6160,f70]) ).
fof(f6251,plain,
! [X0,X1] :
( ~ member(regular(intersection(regular(X0),X1)),X0)
| null_class = X0
| null_class = intersection(regular(X0),X1) ),
inference(resolution,[],[f6160,f127]) ).
fof(f6250,plain,
! [X0] :
( ~ member(regular(regular(X0)),X0)
| null_class = X0
| null_class = regular(X0) ),
inference(resolution,[],[f6160,f66]) ).
fof(f6245,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| null_class = X0
| subclass(intersection(regular(X0),X1),X2) ),
inference(resolution,[],[f6160,f128]) ).
fof(f6244,plain,
! [X0,X1] :
( ~ member(not_subclass_element(regular(X0),X1),X0)
| null_class = X0
| subclass(regular(X0),X1) ),
inference(resolution,[],[f6160,f2]) ).
fof(f6160,plain,
! [X0,X1] :
( ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ),
inference(subsumption_resolution,[],[f753,f4212]) ).
fof(f6067,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,cantor(X1))
| ~ member(X2,universal_class)
| member(image(X0,X2),domain_of(X1)) ),
inference(resolution,[],[f554,f923]) ).
fof(f6062,plain,
! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,image(X1,image(X2,singleton(X3))))
| ~ member(X4,universal_class)
| member(ordered_pair(X3,image(X0,X4)),compose(X1,X2))
| ~ member(ordered_pair(X3,image(X0,X4)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f554,f59]) ).
fof(f6060,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,image(element_relation,complement(X1)))
| ~ member(X2,universal_class)
| ~ member(image(X0,X2),power_class(X1)) ),
inference(resolution,[],[f554,f152]) ).
fof(f6057,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(intersection(X1,identity_relation)))
| ~ member(X2,universal_class)
| ~ member(image(X0,X2),diagonalise(X1)) ),
inference(resolution,[],[f554,f155]) ).
fof(f6051,plain,
! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,restrict(X1,X2,X3))
| ~ member(X4,universal_class)
| member(image(X0,X4),X1) ),
inference(resolution,[],[f554,f495]) ).
fof(f6050,plain,
! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,restrict(X1,X2,X3))
| ~ member(X4,universal_class)
| member(image(X0,X4),cross_product(X2,X3)) ),
inference(resolution,[],[f554,f496]) ).
fof(f6049,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(null_class,X1))
| ~ member(X2,universal_class)
| member(image(X0,X2),complement(null_class)) ),
inference(resolution,[],[f554,f3991]) ).
fof(f6048,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(X1,null_class))
| ~ member(X2,universal_class)
| member(image(X0,X2),complement(null_class)) ),
inference(resolution,[],[f554,f4123]) ).
fof(f6047,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,symmetric_difference(X1,X2))
| ~ member(X3,universal_class)
| member(image(X0,X3),union(X1,X2)) ),
inference(resolution,[],[f554,f1660]) ).
fof(f6046,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(image(X0,X2),X1) ),
inference(resolution,[],[f554,f24]) ).
fof(f6045,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(complement(X1),complement(X2)))
| ~ member(X3,universal_class)
| ~ member(image(X0,X3),union(X1,X2)) ),
inference(resolution,[],[f554,f448]) ).
fof(f6044,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(image(X0,X3),X1) ),
inference(resolution,[],[f554,f21]) ).
fof(f6043,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(image(X0,X3),X2) ),
inference(resolution,[],[f554,f22]) ).
fof(f6042,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,cross_product(X1,X2))
| ~ member(X3,universal_class)
| image(X0,X3) = ordered_pair(first(image(X0,X3)),second(image(X0,X3))) ),
inference(resolution,[],[f554,f17]) ).
fof(f6041,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,singleton(X1))
| ~ member(X2,universal_class)
| image(X0,X2) = X1 ),
inference(resolution,[],[f554,f650]) ).
fof(f6040,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,unordered_pair(X1,X2))
| ~ member(X3,universal_class)
| image(X0,X3) = X1
| image(X0,X3) = X2 ),
inference(resolution,[],[f554,f8]) ).
fof(f6039,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,X1)
| ~ member(X2,universal_class)
| ~ subclass(X1,X3)
| member(image(X0,X2),X3) ),
inference(resolution,[],[f554,f1]) ).
fof(f554,plain,
! [X2,X0,X1] :
( member(image(X1,X0),X2)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f65,f1]) ).
fof(f5886,plain,
! [X2,X3,X0,X1] : range(null_class,X0,X1) = range(null_class,X2,X3),
inference(superposition,[],[f4163,f4163]) ).
fof(f4163,plain,
! [X0,X1] : second(not_subclass_element(null_class,null_class)) = range(null_class,X0,X1),
inference(superposition,[],[f41,f4018]) ).
fof(f5882,plain,
! [X0,X1] : domain(null_class,X0,X1) = single_valued3(null_class),
inference(superposition,[],[f5880,f4161]) ).
fof(f5883,plain,
! [X0,X1] : domain(null_class,X0,X1) = single_valued3(null_class),
inference(superposition,[],[f4161,f5880]) ).
fof(f5880,plain,
first(not_subclass_element(null_class,null_class)) = single_valued3(null_class),
inference(superposition,[],[f4161,f103]) ).
fof(f5881,plain,
first(not_subclass_element(null_class,null_class)) = single_valued3(null_class),
inference(superposition,[],[f103,f4161]) ).
fof(f5879,plain,
! [X2,X3,X0,X1] : domain(null_class,X0,X1) = domain(null_class,X2,X3),
inference(superposition,[],[f4161,f4161]) ).
fof(f4161,plain,
! [X0,X1] : first(not_subclass_element(null_class,null_class)) = domain(null_class,X0,X1),
inference(superposition,[],[f40,f4018]) ).
fof(f5878,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),complement(null_class))
| ~ subclass(X0,symmetric_difference(X2,null_class))
| subclass(X0,X1) ),
inference(resolution,[],[f4123,f160]) ).
fof(f5877,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(X2,null_class)) ),
inference(resolution,[],[f4123,f697]) ).
fof(f5876,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,null_class)))) ),
inference(resolution,[],[f4123,f787]) ).
fof(f5875,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(X2,null_class)) ),
inference(resolution,[],[f4123,f161]) ).
fof(f5874,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,null_class)))) ),
inference(resolution,[],[f4123,f471]) ).
fof(f5873,plain,
! [X0,X1] :
( member(regular(intersection(X0,symmetric_difference(X1,null_class))),complement(null_class))
| null_class = intersection(X0,symmetric_difference(X1,null_class)) ),
inference(resolution,[],[f4123,f132]) ).
fof(f5872,plain,
! [X0,X1] :
( member(regular(X0),complement(null_class))
| ~ subclass(X0,symmetric_difference(X1,null_class))
| null_class = X0 ),
inference(resolution,[],[f4123,f159]) ).
fof(f5871,plain,
! [X0,X1] :
( member(power_class(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(X1,null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f4123,f165]) ).
fof(f5870,plain,
! [X0,X1] :
( member(sum_class(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(X1,null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f4123,f164]) ).
fof(f5869,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),complement(null_class))
| ~ subclass(domain_relation,symmetric_difference(X1,null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f4123,f318]) ).
fof(f5868,plain,
! [X0,X1] :
( member(singleton(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(X1,null_class)) ),
inference(resolution,[],[f4123,f162]) ).
fof(f5867,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,symmetric_difference(X1,null_class)),X2),complement(null_class))
| subclass(intersection(X0,symmetric_difference(X1,null_class)),X2) ),
inference(resolution,[],[f4123,f133]) ).
fof(f5866,plain,
! [X0] :
( member(apply(choice,symmetric_difference(X0,null_class)),complement(null_class))
| null_class = symmetric_difference(X0,null_class)
| ~ member(symmetric_difference(X0,null_class),universal_class) ),
inference(resolution,[],[f4123,f70]) ).
fof(f5861,plain,
! [X0,X1] :
( member(regular(intersection(symmetric_difference(X0,null_class),X1)),complement(null_class))
| null_class = intersection(symmetric_difference(X0,null_class),X1) ),
inference(resolution,[],[f4123,f127]) ).
fof(f5860,plain,
! [X0] :
( member(regular(symmetric_difference(X0,null_class)),complement(null_class))
| null_class = symmetric_difference(X0,null_class) ),
inference(resolution,[],[f4123,f66]) ).
fof(f5855,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(symmetric_difference(X0,null_class),X1),X2),complement(null_class))
| subclass(intersection(symmetric_difference(X0,null_class),X1),X2) ),
inference(resolution,[],[f4123,f128]) ).
fof(f5854,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,null_class),X1),complement(null_class))
| subclass(symmetric_difference(X0,null_class),X1) ),
inference(resolution,[],[f4123,f2]) ).
fof(f4123,plain,
! [X0,X1] :
( ~ member(X1,symmetric_difference(X0,null_class))
| member(X1,complement(null_class)) ),
inference(superposition,[],[f1659,f4080]) ).
fof(f5853,plain,
! [X2,X3,X0,X1] : range(cross_product(X0,X1),X2,X3) = second(not_subclass_element(restrict(cross_product(singleton(X2),X3),X0,X1),null_class)),
inference(superposition,[],[f41,f527]) ).
fof(f5852,plain,
! [X2,X0,X1] :
( null_class != restrict(cross_product(singleton(X2),universal_class),X0,X1)
| ~ member(X2,domain_of(cross_product(X0,X1))) ),
inference(superposition,[],[f30,f527]) ).
fof(f5851,plain,
! [X2,X3,X0,X1] : domain(cross_product(X0,X1),X2,X3) = first(not_subclass_element(restrict(cross_product(X2,singleton(X3)),X0,X1),null_class)),
inference(superposition,[],[f40,f527]) ).
fof(f5848,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(cross_product(X2,X3),X0,X1))
| member(singleton(X4),cross_product(X0,X1)) ),
inference(superposition,[],[f508,f527]) ).
fof(f5847,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(cross_product(X2,X3),X0,X1))
| member(omega,cross_product(X0,X1)) ),
inference(superposition,[],[f506,f527]) ).
fof(f5841,plain,
! [X2,X0,X1] : image(cross_product(X0,X1),X2) = range_of(restrict(cross_product(X2,universal_class),X0,X1)),
inference(superposition,[],[f42,f527]) ).
fof(f5840,plain,
! [X2,X3,X0,X1] : range(cross_product(X0,X1),X2,X3) = second(not_subclass_element(restrict(cross_product(singleton(X2),X3),X0,X1),null_class)),
inference(superposition,[],[f41,f527]) ).
fof(f5839,plain,
! [X2,X0,X1] :
( null_class != restrict(cross_product(singleton(X2),universal_class),X0,X1)
| ~ member(X2,domain_of(cross_product(X0,X1))) ),
inference(superposition,[],[f30,f527]) ).
fof(f5838,plain,
! [X2,X3,X0,X1] : domain(cross_product(X0,X1),X2,X3) = first(not_subclass_element(restrict(cross_product(X2,singleton(X3)),X0,X1),null_class)),
inference(superposition,[],[f40,f527]) ).
fof(f5835,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(cross_product(X2,X3),X0,X1))
| member(singleton(X4),cross_product(X0,X1)) ),
inference(superposition,[],[f508,f527]) ).
fof(f5834,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(cross_product(X2,X3),X0,X1))
| member(omega,cross_product(X0,X1)) ),
inference(superposition,[],[f506,f527]) ).
fof(f5828,plain,
! [X2,X0,X1] : image(cross_product(X0,X1),X2) = range_of(restrict(cross_product(X2,universal_class),X0,X1)),
inference(superposition,[],[f42,f527]) ).
fof(f527,plain,
! [X2,X3,X0,X1] : restrict(cross_product(X0,X1),X2,X3) = restrict(cross_product(X2,X3),X0,X1),
inference(superposition,[],[f29,f28]) ).
fof(f5825,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),complement(null_class))
| ~ subclass(X0,symmetric_difference(null_class,X2))
| subclass(X0,X1) ),
inference(resolution,[],[f3991,f160]) ).
fof(f5824,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(null_class,X2)) ),
inference(resolution,[],[f3991,f697]) ).
fof(f5823,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,complement(complement(symmetric_difference(null_class,X2)))) ),
inference(resolution,[],[f3991,f787]) ).
fof(f5822,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(null_class,X2)) ),
inference(resolution,[],[f3991,f161]) ).
fof(f5821,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),complement(null_class))
| ~ subclass(universal_class,complement(complement(symmetric_difference(null_class,X2)))) ),
inference(resolution,[],[f3991,f471]) ).
fof(f5820,plain,
! [X0,X1] :
( member(regular(intersection(X0,symmetric_difference(null_class,X1))),complement(null_class))
| null_class = intersection(X0,symmetric_difference(null_class,X1)) ),
inference(resolution,[],[f3991,f132]) ).
fof(f5819,plain,
! [X0,X1] :
( member(regular(X0),complement(null_class))
| ~ subclass(X0,symmetric_difference(null_class,X1))
| null_class = X0 ),
inference(resolution,[],[f3991,f159]) ).
fof(f5818,plain,
! [X0,X1] :
( member(power_class(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(null_class,X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3991,f165]) ).
fof(f5817,plain,
! [X0,X1] :
( member(sum_class(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(null_class,X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3991,f164]) ).
fof(f5816,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),complement(null_class))
| ~ subclass(domain_relation,symmetric_difference(null_class,X1))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f3991,f318]) ).
fof(f5815,plain,
! [X0,X1] :
( member(singleton(X0),complement(null_class))
| ~ subclass(universal_class,symmetric_difference(null_class,X1)) ),
inference(resolution,[],[f3991,f162]) ).
fof(f5814,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,symmetric_difference(null_class,X1)),X2),complement(null_class))
| subclass(intersection(X0,symmetric_difference(null_class,X1)),X2) ),
inference(resolution,[],[f3991,f133]) ).
fof(f5813,plain,
! [X0] :
( member(apply(choice,symmetric_difference(null_class,X0)),complement(null_class))
| null_class = symmetric_difference(null_class,X0)
| ~ member(symmetric_difference(null_class,X0),universal_class) ),
inference(resolution,[],[f3991,f70]) ).
fof(f5808,plain,
! [X0,X1] :
( member(regular(intersection(symmetric_difference(null_class,X0),X1)),complement(null_class))
| null_class = intersection(symmetric_difference(null_class,X0),X1) ),
inference(resolution,[],[f3991,f127]) ).
fof(f5807,plain,
! [X0] :
( member(regular(symmetric_difference(null_class,X0)),complement(null_class))
| null_class = symmetric_difference(null_class,X0) ),
inference(resolution,[],[f3991,f66]) ).
fof(f5802,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(symmetric_difference(null_class,X0),X1),X2),complement(null_class))
| subclass(intersection(symmetric_difference(null_class,X0),X1),X2) ),
inference(resolution,[],[f3991,f128]) ).
fof(f5801,plain,
! [X0,X1] :
( member(not_subclass_element(symmetric_difference(null_class,X0),X1),complement(null_class))
| subclass(symmetric_difference(null_class,X0),X1) ),
inference(resolution,[],[f3991,f2]) ).
fof(f3991,plain,
! [X0,X1] :
( ~ member(X1,symmetric_difference(null_class,X0))
| member(X1,complement(null_class)) ),
inference(superposition,[],[f1659,f3938]) ).
fof(f5779,plain,
! [X0] : subclass(symmetric_difference(complement(singleton(singleton(X0))),complement(ordered_pair(singleton(X0),X0))),successor(singleton(singleton(X0)))),
inference(superposition,[],[f5658,f4463]) ).
fof(f5778,plain,
subclass(symmetric_difference(power_class(image(element_relation,null_class)),complement(singleton(image(element_relation,power_class(universal_class))))),successor(image(element_relation,power_class(universal_class)))),
inference(superposition,[],[f5658,f664]) ).
fof(f5777,plain,
subclass(symmetric_difference(power_class(universal_class),complement(singleton(image(element_relation,null_class)))),successor(image(element_relation,null_class))),
inference(superposition,[],[f5658,f616]) ).
fof(f5776,plain,
! [X0] : subclass(symmetric_difference(power_class(X0),complement(singleton(image(element_relation,complement(X0))))),successor(image(element_relation,complement(X0)))),
inference(superposition,[],[f5658,f55]) ).
fof(f5775,plain,
! [X0,X1] : subclass(symmetric_difference(diagonalise(cross_product(X0,X1)),complement(singleton(domain_of(restrict(identity_relation,X0,X1))))),successor(domain_of(restrict(identity_relation,X0,X1)))),
inference(superposition,[],[f5658,f541]) ).
fof(f5774,plain,
! [X0] : subclass(symmetric_difference(diagonalise(X0),complement(singleton(domain_of(intersection(X0,identity_relation))))),successor(domain_of(intersection(X0,identity_relation)))),
inference(superposition,[],[f5658,f76]) ).
fof(f5773,plain,
! [X0,X1] : subclass(symmetric_difference(union(X0,domain_of(intersection(X1,identity_relation))),complement(singleton(intersection(complement(X0),diagonalise(X1))))),successor(intersection(complement(X0),diagonalise(X1)))),
inference(superposition,[],[f5658,f446]) ).
fof(f5772,plain,
! [X0,X1] : subclass(symmetric_difference(union(X0,image(element_relation,complement(X1))),complement(singleton(intersection(complement(X0),power_class(X1))))),successor(intersection(complement(X0),power_class(X1)))),
inference(superposition,[],[f5658,f445]) ).
fof(f5769,plain,
! [X0,X1] : subclass(symmetric_difference(union(domain_of(intersection(X0,identity_relation)),X1),complement(singleton(intersection(diagonalise(X0),complement(X1))))),successor(intersection(diagonalise(X0),complement(X1)))),
inference(superposition,[],[f5658,f443]) ).
fof(f5768,plain,
! [X0,X1] : subclass(symmetric_difference(union(image(element_relation,complement(X0)),X1),complement(singleton(intersection(power_class(X0),complement(X1))))),successor(intersection(power_class(X0),complement(X1)))),
inference(superposition,[],[f5658,f442]) ).
fof(f5766,plain,
! [X0,X1] : subclass(symmetric_difference(union(X0,X1),complement(singleton(intersection(complement(X0),complement(X1))))),successor(intersection(complement(X0),complement(X1)))),
inference(superposition,[],[f5658,f26]) ).
fof(f5764,plain,
! [X0] :
( member(null_class,successor(X0))
| ~ inductive(symmetric_difference(complement(X0),complement(singleton(X0)))) ),
inference(resolution,[],[f5658,f158]) ).
fof(f5763,plain,
! [X0] :
( ~ subclass(successor(X0),symmetric_difference(complement(X0),complement(singleton(X0))))
| successor(X0) = symmetric_difference(complement(X0),complement(singleton(X0))) ),
inference(resolution,[],[f5658,f7]) ).
fof(f5658,plain,
! [X0] : subclass(symmetric_difference(complement(X0),complement(singleton(X0))),successor(X0)),
inference(superposition,[],[f4681,f43]) ).
fof(f5716,plain,
! [X0,X1] :
( member(complement(image(element_relation,union(X0,X1))),universal_class)
| ~ member(intersection(complement(X0),complement(X1)),universal_class) ),
inference(superposition,[],[f56,f450]) ).
fof(f5715,plain,
! [X2,X0,X1] :
( member(complement(image(element_relation,union(X0,X1))),X2)
| ~ subclass(universal_class,X2)
| ~ member(intersection(complement(X0),complement(X1)),universal_class) ),
inference(superposition,[],[f165,f450]) ).
fof(f5712,plain,
! [X0] : complement(image(element_relation,union(X0,image(element_relation,power_class(universal_class))))) = power_class(intersection(complement(X0),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f450,f664]) ).
fof(f5711,plain,
! [X0] : complement(image(element_relation,union(X0,image(element_relation,null_class)))) = power_class(intersection(complement(X0),power_class(universal_class))),
inference(superposition,[],[f450,f616]) ).
fof(f5710,plain,
! [X0,X1] : complement(image(element_relation,union(X1,image(element_relation,complement(X0))))) = power_class(intersection(complement(X1),power_class(X0))),
inference(superposition,[],[f450,f55]) ).
fof(f5709,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,domain_of(restrict(identity_relation,X0,X1))))) = power_class(intersection(complement(X2),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f450,f541]) ).
fof(f5708,plain,
! [X0,X1] : complement(image(element_relation,union(X1,domain_of(intersection(X0,identity_relation))))) = power_class(intersection(complement(X1),diagonalise(X0))),
inference(superposition,[],[f450,f76]) ).
fof(f5707,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,intersection(complement(X0),diagonalise(X1))))) = power_class(intersection(complement(X2),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f450,f446]) ).
fof(f5706,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,intersection(complement(X0),power_class(X1))))) = power_class(intersection(complement(X2),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f450,f445]) ).
fof(f5703,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,intersection(diagonalise(X0),complement(X1))))) = power_class(intersection(complement(X2),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f450,f443]) ).
fof(f5702,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,intersection(power_class(X0),complement(X1))))) = power_class(intersection(complement(X2),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f450,f442]) ).
fof(f5700,plain,
! [X2,X0,X1] : complement(image(element_relation,union(X2,intersection(complement(X0),complement(X1))))) = power_class(intersection(complement(X2),union(X0,X1))),
inference(superposition,[],[f450,f26]) ).
fof(f5698,plain,
! [X0] : complement(image(element_relation,union(image(element_relation,power_class(universal_class)),X0))) = power_class(intersection(power_class(image(element_relation,null_class)),complement(X0))),
inference(superposition,[],[f450,f664]) ).
fof(f5697,plain,
! [X0] : complement(image(element_relation,union(image(element_relation,null_class),X0))) = power_class(intersection(power_class(universal_class),complement(X0))),
inference(superposition,[],[f450,f616]) ).
fof(f5696,plain,
! [X0,X1] : power_class(intersection(power_class(X0),complement(X1))) = complement(image(element_relation,union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f450,f55]) ).
fof(f5695,plain,
! [X2,X0,X1] : complement(image(element_relation,union(domain_of(restrict(identity_relation,X0,X1)),X2))) = power_class(intersection(diagonalise(cross_product(X0,X1)),complement(X2))),
inference(superposition,[],[f450,f541]) ).
fof(f5694,plain,
! [X0,X1] : power_class(intersection(diagonalise(X0),complement(X1))) = complement(image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f450,f76]) ).
fof(f5693,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(complement(X0),diagonalise(X1)),X2))) = power_class(intersection(union(X0,domain_of(intersection(X1,identity_relation))),complement(X2))),
inference(superposition,[],[f450,f446]) ).
fof(f5692,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(complement(X0),power_class(X1)),X2))) = power_class(intersection(union(X0,image(element_relation,complement(X1))),complement(X2))),
inference(superposition,[],[f450,f445]) ).
fof(f5689,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(diagonalise(X0),complement(X1)),X2))) = power_class(intersection(union(domain_of(intersection(X0,identity_relation)),X1),complement(X2))),
inference(superposition,[],[f450,f443]) ).
fof(f5688,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(power_class(X0),complement(X1)),X2))) = power_class(intersection(union(image(element_relation,complement(X0)),X1),complement(X2))),
inference(superposition,[],[f450,f442]) ).
fof(f5686,plain,
! [X2,X0,X1] : complement(image(element_relation,union(intersection(complement(X0),complement(X1)),X2))) = power_class(intersection(union(X0,X1),complement(X2))),
inference(superposition,[],[f450,f26]) ).
fof(f450,plain,
! [X0,X1] : power_class(intersection(complement(X0),complement(X1))) = complement(image(element_relation,union(X0,X1))),
inference(superposition,[],[f55,f26]) ).
fof(f5377,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),identity_relation)
| member(X0,universal_class) ),
inference(superposition,[],[f2076,f4463]) ).
fof(f5657,plain,
! [X0] : subclass(symmetric_difference(complement(X0),power_class(image(element_relation,null_class))),union(X0,image(element_relation,power_class(universal_class)))),
inference(superposition,[],[f4681,f664]) ).
fof(f5656,plain,
! [X0] : subclass(symmetric_difference(complement(X0),power_class(universal_class)),union(X0,image(element_relation,null_class))),
inference(superposition,[],[f4681,f616]) ).
fof(f5655,plain,
! [X0,X1] : subclass(symmetric_difference(complement(X1),power_class(X0)),union(X1,image(element_relation,complement(X0)))),
inference(superposition,[],[f4681,f55]) ).
fof(f5654,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),diagonalise(cross_product(X0,X1))),union(X2,domain_of(restrict(identity_relation,X0,X1)))),
inference(superposition,[],[f4681,f541]) ).
fof(f5653,plain,
! [X0,X1] : subclass(symmetric_difference(complement(X1),diagonalise(X0)),union(X1,domain_of(intersection(X0,identity_relation)))),
inference(superposition,[],[f4681,f76]) ).
fof(f5652,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),union(X0,domain_of(intersection(X1,identity_relation)))),union(X2,intersection(complement(X0),diagonalise(X1)))),
inference(superposition,[],[f4681,f446]) ).
fof(f5651,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),union(X0,image(element_relation,complement(X1)))),union(X2,intersection(complement(X0),power_class(X1)))),
inference(superposition,[],[f4681,f445]) ).
fof(f5648,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),union(domain_of(intersection(X0,identity_relation)),X1)),union(X2,intersection(diagonalise(X0),complement(X1)))),
inference(superposition,[],[f4681,f443]) ).
fof(f5647,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),union(image(element_relation,complement(X0)),X1)),union(X2,intersection(power_class(X0),complement(X1)))),
inference(superposition,[],[f4681,f442]) ).
fof(f5645,plain,
! [X2,X0,X1] : subclass(symmetric_difference(complement(X2),union(X0,X1)),union(X2,intersection(complement(X0),complement(X1)))),
inference(superposition,[],[f4681,f26]) ).
fof(f5643,plain,
! [X0] : subclass(symmetric_difference(power_class(image(element_relation,null_class)),complement(X0)),union(image(element_relation,power_class(universal_class)),X0)),
inference(superposition,[],[f4681,f664]) ).
fof(f5642,plain,
! [X0] : subclass(symmetric_difference(power_class(universal_class),complement(X0)),union(image(element_relation,null_class),X0)),
inference(superposition,[],[f4681,f616]) ).
fof(f5641,plain,
! [X0,X1] : subclass(symmetric_difference(power_class(X0),complement(X1)),union(image(element_relation,complement(X0)),X1)),
inference(superposition,[],[f4681,f55]) ).
fof(f5640,plain,
! [X2,X0,X1] : subclass(symmetric_difference(diagonalise(cross_product(X0,X1)),complement(X2)),union(domain_of(restrict(identity_relation,X0,X1)),X2)),
inference(superposition,[],[f4681,f541]) ).
fof(f5639,plain,
! [X0,X1] : subclass(symmetric_difference(diagonalise(X0),complement(X1)),union(domain_of(intersection(X0,identity_relation)),X1)),
inference(superposition,[],[f4681,f76]) ).
fof(f5638,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(X0,domain_of(intersection(X1,identity_relation))),complement(X2)),union(intersection(complement(X0),diagonalise(X1)),X2)),
inference(superposition,[],[f4681,f446]) ).
fof(f5637,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(X0,image(element_relation,complement(X1))),complement(X2)),union(intersection(complement(X0),power_class(X1)),X2)),
inference(superposition,[],[f4681,f445]) ).
fof(f5634,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(domain_of(intersection(X0,identity_relation)),X1),complement(X2)),union(intersection(diagonalise(X0),complement(X1)),X2)),
inference(superposition,[],[f4681,f443]) ).
fof(f5633,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(image(element_relation,complement(X0)),X1),complement(X2)),union(intersection(power_class(X0),complement(X1)),X2)),
inference(superposition,[],[f4681,f442]) ).
fof(f5631,plain,
! [X2,X0,X1] : subclass(symmetric_difference(union(X0,X1),complement(X2)),union(intersection(complement(X0),complement(X1)),X2)),
inference(superposition,[],[f4681,f26]) ).
fof(f5629,plain,
! [X0,X1] :
( member(null_class,union(X0,X1))
| ~ inductive(symmetric_difference(complement(X0),complement(X1))) ),
inference(resolution,[],[f4681,f158]) ).
fof(f5628,plain,
! [X0,X1] :
( ~ subclass(union(X0,X1),symmetric_difference(complement(X0),complement(X1)))
| union(X0,X1) = symmetric_difference(complement(X0),complement(X1)) ),
inference(resolution,[],[f4681,f7]) ).
fof(f4681,plain,
! [X0,X1] : subclass(symmetric_difference(complement(X0),complement(X1)),union(X0,X1)),
inference(superposition,[],[f3947,f26]) ).
fof(f5555,plain,
! [X0] :
( ~ subclass(singleton(singleton(singleton(X0))),identity_relation)
| member(singleton(singleton(X0)),subset_relation) ),
inference(superposition,[],[f3533,f4463]) ).
fof(f3533,plain,
! [X0,X1] :
( ~ subclass(ordered_pair(X0,X1),identity_relation)
| member(singleton(X0),subset_relation) ),
inference(resolution,[],[f2984,f706]) ).
fof(f5553,plain,
! [X2,X0,X1] :
( subclass(union(X0,domain_of(intersection(X1,identity_relation))),X2)
| ~ subclass(union(X0,domain_of(intersection(X1,identity_relation))),intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f5523,f446]) ).
fof(f5523,plain,
! [X2,X0,X1] :
( ~ subclass(union(X0,domain_of(intersection(X1,identity_relation))),intersection(complement(X0),diagonalise(X1)))
| subclass(complement(intersection(complement(X0),diagonalise(X1))),X2) ),
inference(superposition,[],[f2982,f446]) ).
fof(f5518,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f1358,f446]) ).
fof(f5546,plain,
! [X0,X1] :
( null_class = union(X0,domain_of(intersection(X1,identity_relation)))
| ~ subclass(union(X0,domain_of(intersection(X1,identity_relation))),intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f5513,f446]) ).
fof(f5513,plain,
! [X0,X1] :
( ~ subclass(union(X0,domain_of(intersection(X1,identity_relation))),intersection(complement(X0),diagonalise(X1)))
| null_class = complement(intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f600,f446]) ).
fof(f5512,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ member(omega,power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f567,f446]) ).
fof(f5511,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ member(null_class,power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f566,f446]) ).
fof(f5509,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ member(X2,union(X3,intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f448,f446]) ).
fof(f5508,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(union(X0,domain_of(intersection(X1,identity_relation))),complement(X3)))
| ~ member(X2,union(intersection(complement(X0),diagonalise(X1)),X3)) ),
inference(superposition,[],[f448,f446]) ).
fof(f5507,plain,
! [X2,X0,X1] : union(intersection(complement(X0),diagonalise(X1)),image(element_relation,complement(X2))) = complement(intersection(union(X0,domain_of(intersection(X1,identity_relation))),power_class(X2))),
inference(superposition,[],[f445,f446]) ).
fof(f5506,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),intersection(complement(X0),diagonalise(X1))) = complement(intersection(diagonalise(X2),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f443,f446]) ).
fof(f5505,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),intersection(complement(X0),diagonalise(X1))) = complement(intersection(power_class(X2),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f442,f446]) ).
fof(f5504,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(union(X0,domain_of(intersection(X1,identity_relation)))))
| member(singleton(X2),intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f426,f446]) ).
fof(f5503,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| member(X2,power_class(intersection(complement(X0),diagonalise(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f446]) ).
fof(f5502,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(X0,domain_of(intersection(X1,identity_relation))),X2)
| ~ member(X3,universal_class)
| member(X3,intersection(complement(X0),diagonalise(X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f446]) ).
fof(f5501,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ inductive(power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f402,f446]) ).
fof(f5499,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,domain_of(intersection(X1,identity_relation))))
| ~ subclass(universal_class,intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f276,f446]) ).
fof(f5496,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f179,f446]) ).
fof(f5495,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,domain_of(intersection(X1,identity_relation))))
| ~ member(omega,intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f171,f446]) ).
fof(f5494,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ member(X2,power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f152,f446]) ).
fof(f5493,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(X0,domain_of(intersection(X1,identity_relation)))))
| ~ inductive(power_class(intersection(complement(X0),diagonalise(X1)))) ),
inference(superposition,[],[f151,f446]) ).
fof(f5492,plain,
! [X0,X1] : complement(image(element_relation,power_class(intersection(complement(X0),diagonalise(X1))))) = power_class(image(element_relation,union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f150,f446]) ).
fof(f5545,plain,
! [X2,X0,X1] :
( subclass(union(X0,domain_of(intersection(X1,identity_relation))),X2)
| ~ member(not_subclass_element(union(X0,domain_of(intersection(X1,identity_relation))),X2),intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f5491,f446]) ).
fof(f5491,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(union(X0,domain_of(intersection(X1,identity_relation))),X2),intersection(complement(X0),diagonalise(X1)))
| subclass(complement(intersection(complement(X0),diagonalise(X1))),X2) ),
inference(superposition,[],[f121,f446]) ).
fof(f5544,plain,
! [X0,X1] :
( null_class = union(X0,domain_of(intersection(X1,identity_relation)))
| ~ member(regular(union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1))) ),
inference(forward_demodulation,[],[f5490,f446]) ).
fof(f5490,plain,
! [X0,X1] :
( ~ member(regular(union(X0,domain_of(intersection(X1,identity_relation)))),intersection(complement(X0),diagonalise(X1)))
| null_class = complement(intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f120,f446]) ).
fof(f5489,plain,
! [X0,X1] :
( ~ inductive(union(X0,domain_of(intersection(X1,identity_relation))))
| ~ member(null_class,intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f119,f446]) ).
fof(f5488,plain,
! [X0,X1] : power_class(intersection(complement(X0),diagonalise(X1))) = complement(image(element_relation,union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f55,f446]) ).
fof(f5487,plain,
! [X2,X0,X1] : union(X2,intersection(complement(X0),diagonalise(X1))) = complement(intersection(complement(X2),union(X0,domain_of(intersection(X1,identity_relation))))),
inference(superposition,[],[f26,f446]) ).
fof(f5486,plain,
! [X2,X0,X1] : union(intersection(complement(X0),diagonalise(X1)),X2) = complement(intersection(union(X0,domain_of(intersection(X1,identity_relation))),complement(X2))),
inference(superposition,[],[f26,f446]) ).
fof(f5485,plain,
! [X2,X0,X1] :
( member(X2,union(X0,domain_of(intersection(X1,identity_relation))))
| member(X2,intersection(complement(X0),diagonalise(X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f446]) ).
fof(f5484,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,domain_of(intersection(X1,identity_relation))))
| ~ member(X2,intersection(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f24,f446]) ).
fof(f5483,plain,
! [X0,X1] : symmetric_difference(complement(X0),diagonalise(X1)) = intersection(union(X0,domain_of(intersection(X1,identity_relation))),union(complement(X0),diagonalise(X1))),
inference(superposition,[],[f1614,f446]) ).
fof(f5482,plain,
! [X0,X1] :
( member(null_class,union(X0,domain_of(intersection(X1,identity_relation))))
| ~ inductive(symmetric_difference(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f1662,f446]) ).
fof(f5481,plain,
! [X2,X0,X1] :
( member(X2,union(X0,domain_of(intersection(X1,identity_relation))))
| ~ member(X2,symmetric_difference(complement(X0),diagonalise(X1))) ),
inference(superposition,[],[f1659,f446]) ).
fof(f5480,plain,
! [X0,X1] : subclass(symmetric_difference(complement(X0),diagonalise(X1)),union(X0,domain_of(intersection(X1,identity_relation)))),
inference(superposition,[],[f3947,f446]) ).
fof(f5478,plain,
! [X0] : union(image(element_relation,power_class(universal_class)),domain_of(intersection(X0,identity_relation))) = complement(intersection(power_class(image(element_relation,null_class)),diagonalise(X0))),
inference(superposition,[],[f446,f664]) ).
fof(f5477,plain,
! [X0] : union(image(element_relation,null_class),domain_of(intersection(X0,identity_relation))) = complement(intersection(power_class(universal_class),diagonalise(X0))),
inference(superposition,[],[f446,f616]) ).
fof(f5476,plain,
! [X0,X1] : union(image(element_relation,complement(X0)),domain_of(intersection(X1,identity_relation))) = complement(intersection(power_class(X0),diagonalise(X1))),
inference(superposition,[],[f446,f55]) ).
fof(f5475,plain,
! [X2,X0,X1] : union(domain_of(restrict(identity_relation,X0,X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(diagonalise(cross_product(X0,X1)),diagonalise(X2))),
inference(superposition,[],[f446,f541]) ).
fof(f5474,plain,
! [X0,X1] : union(domain_of(intersection(X0,identity_relation)),domain_of(intersection(X1,identity_relation))) = complement(intersection(diagonalise(X0),diagonalise(X1))),
inference(superposition,[],[f446,f76]) ).
fof(f5473,plain,
! [X2,X0,X1] : union(intersection(complement(X0),diagonalise(X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(union(X0,domain_of(intersection(X1,identity_relation))),diagonalise(X2))),
inference(superposition,[],[f446,f446]) ).
fof(f5472,plain,
! [X2,X0,X1] : union(intersection(complement(X0),power_class(X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(union(X0,image(element_relation,complement(X1))),diagonalise(X2))),
inference(superposition,[],[f446,f445]) ).
fof(f5469,plain,
! [X2,X0,X1] : union(intersection(diagonalise(X0),complement(X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(union(domain_of(intersection(X0,identity_relation)),X1),diagonalise(X2))),
inference(superposition,[],[f446,f443]) ).
fof(f5468,plain,
! [X2,X0,X1] : union(intersection(power_class(X0),complement(X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(union(image(element_relation,complement(X0)),X1),diagonalise(X2))),
inference(superposition,[],[f446,f442]) ).
fof(f5466,plain,
! [X2,X0,X1] : union(intersection(complement(X0),complement(X1)),domain_of(intersection(X2,identity_relation))) = complement(intersection(union(X0,X1),diagonalise(X2))),
inference(superposition,[],[f446,f26]) ).
fof(f446,plain,
! [X0,X1] : union(X1,domain_of(intersection(X0,identity_relation))) = complement(intersection(complement(X1),diagonalise(X0))),
inference(superposition,[],[f26,f76]) ).
fof(f5464,plain,
( ~ subclass(cross_product(universal_class,universal_class),identity_relation)
| cross_product(universal_class,universal_class) = subset_relation ),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f210,f211,f215,f216,f219,f221,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f421,f423,f194,f26,f444,f446,f447,f449,f450,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f526,f527,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f554,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f747,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f920,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f1514,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1658,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3109,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f956,f2428,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3530,f3531,f3532,f3533,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3825,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3843,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3922,f3936,f3921,f3953,f3945,f3957,f3948,f3959,f3938,f3964,f3971,f3973,f3990,f3991,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4063,f4078,f4084,f4087,f4062,f4097,f4080,f4102,f4103,f4122,f4123,f4131,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4154,f4161,f4163,f4164,f4167,f4170,f4172,f4173,f4174,f4176,f4179,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190,f4200,f4191,f4192,f4193,f4194,f4195,f4196,f4197,f4166,f4178,f208,f4204,f4205,f4168,f4212,f4175,f4240,f4242,f4180,f4270,f4271,f212,f4274,f218,f3967,f4290,f4294,f4284,f4296,f4297,f318,f4298,f4299,f4300,f4346,f4302,f4303,f4306,f4308,f4309,f4347,f4348,f4349,f4350,f4315,f4316,f4317,f4318,f4319,f4320,f4321,f4322,f4323,f4324,f4325,f4352,f4328,f4330,f4354,f4355,f4333,f4334,f4335,f4338,f4339,f4340,f4342,f4344,f4345,f4134,f4367,f448,f4373,f4374,f4375,f4377,f4378,f4379,f4380,f4385,f4386,f4387,f4388,f4389,f4390,f4391,f4392,f4394,f4396,f4397,f4399,f4403,f4404,f4405,f4406,f4407,f4409,f4413,f4414,f4415,f4416,f4417,f4152,f4435,f4436,f4439,f4440,f4235,f4450,f690,f4465,f4466,f4468,f4484,f4483,f4089,f4487,f4490,f4492,f4491,f4494,f4015,f4496,f4489,f4498,f1653,f4503,f4505,f4531,f4532,f4533,f4534,f4513,f4514,f4515,f4518,f4519,f4520,f4521,f4522,f4523,f4524,f4525,f4529,f4535,f4437,f4541,f4551,f4553,f4555,f4539,f4611,f4624,f4626,f4628,f4619,f4630,f4632,f4634,f4077,f4640,f4641,f420,f4645,f4646,f4647,f4649,f4653,f4654,f4655,f4656,f4657,f3944,f4664,f3947,f4667,f4669,f4670,f4672,f4673,f4674,f4676,f4677,f4679,f4681,f4686,f4687,f4688,f4671,f4689,f4678,f4691,f4091,f4693,f3961,f4696,f4698,f4699,f3962,f4700,f424,f4703,f4704,f4715,f4716,f4721,f4723,f4724,f425,f4796,f4797,f4819,f4831,f4810,f4833,f4835,f4836,f4837,f4841,f442,f4897,f4899,f4902,f4903,f4904,f4905,f4906,f4907,f4908,f4909,f4910,f4911,f4912,f4913,f4914,f4915,f4916,f4966,f4967,f4919,f4920,f4921,f4922,f4923,f4926,f4928,f4929,f4930,f4931,f4932,f4933,f4935,f4936,f4968,f4942,f4975,f443,f5073,f5075,f5076,f5079,f5080,f5081,f5082,f5083,f5084,f5085,f5086,f5087,f5088,f5089,f5090,f5091,f5092,f5093,f5146,f5147,f5096,f5097,f5098,f5099,f5100,f5103,f5105,f5106,f5107,f5108,f5109,f5110,f5111,f5113,f5114,f5148,f5120,f5155,f445,f5214,f5216,f5217,f5220,f5221,f5222,f5223,f5224,f5225,f5228,f5229,f5230,f5231,f5232,f5233,f5234,f5235,f5236,f5237,f5291,f5292,f5240,f5241,f5242,f5243,f5244,f5247,f5249,f5250,f5251,f5252,f5253,f5254,f5255,f5256,f5258,f5259,f5293,f5265,f5300,f3935,f5339,f4463,f5341,f5345,f5346,f5347,f5348,f5349,f5350,f5351,f5352,f5353,f5354,f5355,f5356,f5357,f5358,f5359,f5360,f5361,f5427,f5371,f5372,f5377,f5379,f5380,f5381,f5382,f5430,f5386,f5387,f5388,f5389,f5390,f5391,f5392,f5393,f5394,f5403,f5404,f5405,f5407,f5408,f5409,f5410,f5411,f5431,f5413,f5414,f5415,f5417,f5418,f5420,f5421,f5423,f5426,f5369,f5434,f5435,f5439,f3939,f5444,f4081,f5448,f5375,f5449,f3523,f5457,f5460]) ).
fof(f5460,plain,
( ~ subclass(cross_product(universal_class,universal_class),identity_relation)
| cross_product(universal_class,universal_class) = subset_relation
| ~ function(subset_relation) ),
inference(resolution,[],[f3523,f62]) ).
fof(f5457,plain,
( ~ subclass(cross_product(universal_class,universal_class),identity_relation)
| cross_product(universal_class,universal_class) = subset_relation ),
inference(resolution,[],[f3523,f3945]) ).
fof(f3523,plain,
! [X0] :
( ~ subclass(subset_relation,X0)
| ~ subclass(X0,identity_relation)
| subset_relation = X0 ),
inference(resolution,[],[f2984,f7]) ).
fof(f5449,plain,
! [X0] :
( member(X0,universal_class)
| ~ member(singleton(singleton(singleton(X0))),identity_relation) ),
inference(resolution,[],[f5375,f134]) ).
fof(f5375,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),subset_relation)
| member(X0,universal_class) ),
inference(superposition,[],[f2065,f4463]) ).
fof(f5448,plain,
! [X0,X1] :
( omega = restrict(omega,X0,X1)
| ~ inductive(restrict(omega,X0,X1)) ),
inference(forward_demodulation,[],[f5446,f29]) ).
fof(f5446,plain,
! [X0,X1] :
( ~ inductive(restrict(omega,X0,X1))
| omega = intersection(cross_product(X0,X1),omega) ),
inference(superposition,[],[f4081,f29]) ).
fof(f4081,plain,
! [X0] :
( ~ inductive(intersection(X0,omega))
| omega = intersection(X0,omega) ),
inference(resolution,[],[f4063,f214]) ).
fof(f5444,plain,
! [X0,X1] :
( omega = restrict(omega,X0,X1)
| ~ inductive(restrict(omega,X0,X1)) ),
inference(forward_demodulation,[],[f5442,f28]) ).
fof(f5442,plain,
! [X0,X1] :
( ~ inductive(restrict(omega,X0,X1))
| omega = intersection(omega,cross_product(X0,X1)) ),
inference(superposition,[],[f3939,f28]) ).
fof(f3939,plain,
! [X0] :
( ~ inductive(intersection(omega,X0))
| omega = intersection(omega,X0) ),
inference(resolution,[],[f3922,f214]) ).
fof(f5435,plain,
! [X0] : member(singleton(ordered_pair(singleton(X0),X0)),singleton(singleton(ordered_pair(singleton(X0),X0)))),
inference(superposition,[],[f5369,f4463]) ).
fof(f5434,plain,
! [X0,X1] :
( ~ subclass(singleton(singleton(singleton(X0))),X1)
| member(singleton(singleton(X0)),X1) ),
inference(resolution,[],[f5369,f1]) ).
fof(f5369,plain,
! [X0] : member(singleton(singleton(X0)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f702,f4463]) ).
fof(f5426,plain,
! [X0] : subclass(symmetric_difference(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)),successor(singleton(singleton(X0)))),
inference(superposition,[],[f4489,f4463]) ).
fof(f5423,plain,
! [X0] :
( ~ subclass(universal_class,symmetric_difference(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)))
| member(omega,successor(singleton(singleton(X0)))) ),
inference(superposition,[],[f1925,f4463]) ).
fof(f5421,plain,
! [X0] :
( ~ inductive(symmetric_difference(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)))
| member(null_class,successor(singleton(singleton(X0)))) ),
inference(superposition,[],[f1678,f4463]) ).
fof(f5420,plain,
! [X0,X1] :
( member(ordered_pair(singleton(X0),X0),range_of(X1))
| ~ subclass(universal_class,cantor(inverse(X1))) ),
inference(superposition,[],[f973,f4463]) ).
fof(f5418,plain,
! [X0] :
( singleton(singleton(X0)) = apply(choice,ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(singleton(X0))) ),
inference(superposition,[],[f890,f4463]) ).
fof(f5417,plain,
! [X0] :
( null_class = intersection(ordered_pair(singleton(X0),X0),singleton(singleton(X0)))
| null_class = singleton(singleton(singleton(X0))) ),
inference(superposition,[],[f767,f4463]) ).
fof(f5415,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,ordered_pair(singleton(X0),X0))
| ordered_pair(X1,X2) = singleton(singleton(X0)) ),
inference(superposition,[],[f717,f4463]) ).
fof(f5414,plain,
! [X0,X1] : member(unordered_pair(X1,ordered_pair(singleton(X0),X0)),ordered_pair(X1,singleton(singleton(X0)))),
inference(superposition,[],[f703,f4463]) ).
fof(f5431,plain,
! [X0] : ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))) = singleton(singleton(ordered_pair(singleton(X0),X0))),
inference(forward_demodulation,[],[f5412,f12]) ).
fof(f5412,plain,
! [X0] : ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(singleton(X0),X0)),singleton(ordered_pair(singleton(X0),X0))),
inference(superposition,[],[f690,f4463]) ).
fof(f5411,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,ordered_pair(singleton(X0),X0))
| unordered_pair(X1,X2) = singleton(singleton(X0)) ),
inference(superposition,[],[f659,f4463]) ).
fof(f5410,plain,
! [X0,X1] :
( ~ subclass(universal_class,ordered_pair(singleton(X0),X0))
| singleton(X1) = singleton(singleton(X0)) ),
inference(superposition,[],[f657,f4463]) ).
fof(f5409,plain,
! [X0] :
( singleton(singleton(X0)) = regular(ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(singleton(X0))) ),
inference(superposition,[],[f656,f4463]) ).
fof(f5408,plain,
! [X0] :
( ~ subclass(universal_class,ordered_pair(singleton(X0),X0))
| omega = singleton(singleton(X0)) ),
inference(superposition,[],[f655,f4463]) ).
fof(f5407,plain,
! [X0] :
( ~ inductive(ordered_pair(singleton(X0),X0))
| null_class = singleton(singleton(X0)) ),
inference(superposition,[],[f654,f4463]) ).
fof(f5405,plain,
! [X0,X1] :
( subclass(ordered_pair(singleton(X0),X0),X1)
| singleton(singleton(X0)) = not_subclass_element(singleton(singleton(singleton(X0))),X1) ),
inference(superposition,[],[f652,f4463]) ).
fof(f5404,plain,
! [X0,X1] :
( ~ member(X1,ordered_pair(singleton(X0),X0))
| singleton(singleton(X0)) = X1 ),
inference(superposition,[],[f650,f4463]) ).
fof(f5403,plain,
! [X0,X1] :
( ~ member(image(X1,ordered_pair(singleton(X0),X0)),universal_class)
| member(apply(X1,singleton(singleton(X0))),universal_class) ),
inference(superposition,[],[f316,f4463]) ).
fof(f5394,plain,
! [X0,X1] : apply(X1,singleton(singleton(X0))) = sum_class(image(X1,ordered_pair(singleton(X0),X0))),
inference(superposition,[],[f68,f4463]) ).
fof(f5393,plain,
! [X2,X3,X0,X1] :
( ~ member(X1,image(X2,image(X3,ordered_pair(singleton(X0),X0))))
| member(ordered_pair(singleton(singleton(X0)),X1),compose(X2,X3))
| ~ member(ordered_pair(singleton(singleton(X0)),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f59,f4463]) ).
fof(f5392,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,image(X3,ordered_pair(singleton(X0),X0))))
| ~ member(ordered_pair(singleton(singleton(X0)),X1),compose(X2,X3)) ),
inference(superposition,[],[f58,f4463]) ).
fof(f5391,plain,
! [X0] : successor(singleton(singleton(X0))) = union(singleton(singleton(X0)),ordered_pair(singleton(X0),X0)),
inference(superposition,[],[f43,f4463]) ).
fof(f5390,plain,
! [X2,X0,X1] : range(X1,singleton(singleton(X0)),X2) = second(not_subclass_element(restrict(X1,ordered_pair(singleton(X0),X0),X2),null_class)),
inference(superposition,[],[f41,f4463]) ).
fof(f5389,plain,
! [X2,X0,X1] : domain(X1,X2,singleton(singleton(X0))) = first(not_subclass_element(restrict(X1,X2,ordered_pair(singleton(X0),X0)),null_class)),
inference(superposition,[],[f40,f4463]) ).
fof(f5388,plain,
! [X0,X1] :
( null_class != restrict(X1,ordered_pair(singleton(X0),X0),universal_class)
| ~ member(singleton(singleton(X0)),domain_of(X1)) ),
inference(superposition,[],[f30,f4463]) ).
fof(f5387,plain,
! [X0,X1] : ordered_pair(X1,singleton(singleton(X0))) = unordered_pair(singleton(X1),unordered_pair(X1,ordered_pair(singleton(X0),X0))),
inference(superposition,[],[f13,f4463]) ).
fof(f5386,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),X1) = unordered_pair(ordered_pair(singleton(X0),X0),unordered_pair(singleton(singleton(X0)),singleton(X1))),
inference(superposition,[],[f13,f4463]) ).
fof(f5430,plain,
! [X0] : ordered_pair(singleton(singleton(X0)),singleton(X0)) = singleton(ordered_pair(singleton(X0),X0)),
inference(forward_demodulation,[],[f5384,f12]) ).
fof(f5384,plain,
! [X0] : ordered_pair(singleton(singleton(X0)),singleton(X0)) = unordered_pair(ordered_pair(singleton(X0),X0),ordered_pair(singleton(X0),X0)),
inference(superposition,[],[f690,f4463]) ).
fof(f5382,plain,
! [X0,X1] :
( ~ member(singleton(singleton(singleton(ordered_pair(X0,X1)))),application_function)
| member(X0,domain_of(singleton(ordered_pair(X0,X1)))) ),
inference(superposition,[],[f106,f4463]) ).
fof(f5381,plain,
! [X0,X1] :
( ~ member(singleton(singleton(singleton(ordered_pair(X0,X1)))),composition_function)
| compose(singleton(ordered_pair(X0,X1)),X0) = X1 ),
inference(superposition,[],[f96,f4463]) ).
fof(f5380,plain,
! [X0,X1] :
( ~ member(singleton(singleton(singleton(ordered_pair(X0,X1)))),application_function)
| apply(singleton(ordered_pair(X0,X1)),X0) = X1 ),
inference(superposition,[],[f107,f4463]) ).
fof(f5379,plain,
! [X0,X1] :
( ~ member(singleton(singleton(singleton(ordered_pair(X0,X1)))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| member(ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(X0,apply(singleton(ordered_pair(X0,X1)),X0))),application_function)
| ~ member(X0,domain_of(singleton(ordered_pair(X0,X1)))) ),
inference(superposition,[],[f108,f4463]) ).
fof(f5372,plain,
! [X0] :
( ~ function(singleton(singleton(singleton(X0))))
| member(singleton(singleton(X0)),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f775,f4463]) ).
fof(f5371,plain,
! [X0,X1] :
( ~ subclass(singleton(singleton(singleton(X0))),X1)
| member(singleton(singleton(X0)),X1) ),
inference(superposition,[],[f706,f4463]) ).
fof(f5427,plain,
! [X0] : member(singleton(singleton(X0)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f5370,f12]) ).
fof(f5370,plain,
! [X0] : member(unordered_pair(singleton(X0),singleton(X0)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f703,f4463]) ).
fof(f5361,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,singleton(singleton(singleton(X0)))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| member(ordered_pair(X1,ordered_pair(singleton(X0),apply(X1,singleton(X0)))),application_function)
| ~ member(singleton(X0),domain_of(X1)) ),
inference(superposition,[],[f108,f4463]) ).
fof(f5360,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,singleton(singleton(singleton(X0)))),application_function)
| apply(X1,singleton(X0)) = X0 ),
inference(superposition,[],[f107,f4463]) ).
fof(f5359,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,singleton(singleton(singleton(X0)))),application_function)
| member(singleton(X0),domain_of(X1)) ),
inference(superposition,[],[f106,f4463]) ).
fof(f5358,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),domain_relation)
| domain_of(singleton(X0)) = X0 ),
inference(superposition,[],[f99,f4463]) ).
fof(f5357,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,singleton(singleton(singleton(X0)))),composition_function)
| compose(X1,singleton(X0)) = X0 ),
inference(superposition,[],[f96,f4463]) ).
fof(f5356,plain,
! [X0,X1] :
( ~ member(singleton(singleton(singleton(X0))),compose_class(X1))
| compose(X1,singleton(X0)) = X0 ),
inference(superposition,[],[f93,f4463]) ).
fof(f5355,plain,
! [X2,X3,X0,X1] :
( ~ member(singleton(singleton(singleton(X0))),domain_of(X1))
| ~ homomorphism(X2,X1,X3)
| apply(X3,ordered_pair(apply(X2,singleton(X0)),apply(X2,X0))) = apply(X2,apply(X1,ordered_pair(singleton(X0),X0))) ),
inference(superposition,[],[f89,f4463]) ).
fof(f5354,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),successor_relation)
| successor(singleton(X0)) = X0 ),
inference(superposition,[],[f45,f4463]) ).
fof(f5353,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(singleton(singleton(singleton(X0))),X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(singleton(X0),X0),X1),flip(X2))
| ~ member(ordered_pair(ordered_pair(X0,singleton(X0)),X1),X2) ),
inference(superposition,[],[f37,f4463]) ).
fof(f5352,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(singleton(singleton(singleton(X0))),X1),flip(X2))
| member(ordered_pair(ordered_pair(X0,singleton(X0)),X1),X2) ),
inference(superposition,[],[f36,f4463]) ).
fof(f5351,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(singleton(singleton(singleton(X0))),X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(singleton(X0),X0),X1),rotate(X2))
| ~ member(ordered_pair(ordered_pair(X0,X1),singleton(X0)),X2) ),
inference(superposition,[],[f34,f4463]) ).
fof(f5350,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(singleton(singleton(singleton(X0))),X1),rotate(X2))
| member(ordered_pair(ordered_pair(X0,X1),singleton(X0)),X2) ),
inference(superposition,[],[f33,f4463]) ).
fof(f5349,plain,
! [X0] :
( ~ member(singleton(singleton(singleton(X0))),cross_product(universal_class,universal_class))
| member(ordered_pair(singleton(X0),X0),element_relation)
| ~ member(singleton(X0),X0) ),
inference(superposition,[],[f20,f4463]) ).
fof(f5347,plain,
! [X2,X0,X1] :
( member(singleton(singleton(singleton(X0))),cross_product(X1,X2))
| ~ member(X0,X2)
| ~ member(singleton(X0),X1) ),
inference(superposition,[],[f16,f4463]) ).
fof(f5346,plain,
! [X2,X0,X1] :
( ~ member(singleton(singleton(singleton(X0))),cross_product(X1,X2))
| member(X0,X2) ),
inference(superposition,[],[f15,f4463]) ).
fof(f5345,plain,
! [X2,X0,X1] :
( ~ member(singleton(singleton(singleton(X0))),cross_product(X1,X2))
| member(singleton(X0),X1) ),
inference(superposition,[],[f14,f4463]) ).
fof(f5341,plain,
! [X0] : ordered_pair(ordered_pair(singleton(X0),X0),singleton(singleton(X0))) = singleton(singleton(ordered_pair(singleton(X0),X0))),
inference(superposition,[],[f4463,f4463]) ).
fof(f4463,plain,
! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0))),
inference(superposition,[],[f690,f12]) ).
fof(f5339,plain,
! [X0,X1] :
( subclass(identity_relation,X0)
| ~ subclass(inverse(subset_relation),X1)
| member(not_subclass_element(identity_relation,X0),X1) ),
inference(resolution,[],[f3935,f1]) ).
fof(f3935,plain,
! [X0] :
( member(not_subclass_element(identity_relation,X0),inverse(subset_relation))
| subclass(identity_relation,X0) ),
inference(forward_demodulation,[],[f3919,f75]) ).
fof(f3919,plain,
! [X0] :
( member(not_subclass_element(identity_relation,X0),inverse(subset_relation))
| subclass(intersection(inverse(subset_relation),subset_relation),X0) ),
inference(superposition,[],[f128,f75]) ).
fof(f5300,plain,
! [X2,X0,X1] :
( subclass(union(X0,image(element_relation,complement(X1))),X2)
| ~ subclass(union(X0,image(element_relation,complement(X1))),intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f5270,f445]) ).
fof(f5270,plain,
! [X2,X0,X1] :
( ~ subclass(union(X0,image(element_relation,complement(X1))),intersection(complement(X0),power_class(X1)))
| subclass(complement(intersection(complement(X0),power_class(X1))),X2) ),
inference(superposition,[],[f2982,f445]) ).
fof(f5265,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f1358,f445]) ).
fof(f5293,plain,
! [X0,X1] :
( null_class = union(X0,image(element_relation,complement(X1)))
| ~ subclass(union(X0,image(element_relation,complement(X1))),intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f5260,f445]) ).
fof(f5260,plain,
! [X0,X1] :
( ~ subclass(union(X0,image(element_relation,complement(X1))),intersection(complement(X0),power_class(X1)))
| null_class = complement(intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f600,f445]) ).
fof(f5259,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ member(omega,power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f567,f445]) ).
fof(f5258,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ member(null_class,power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f566,f445]) ).
fof(f5256,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),union(X0,image(element_relation,complement(X1)))))
| ~ member(X2,union(X3,intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f448,f445]) ).
fof(f5255,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(union(X0,image(element_relation,complement(X1))),complement(X3)))
| ~ member(X2,union(intersection(complement(X0),power_class(X1)),X3)) ),
inference(superposition,[],[f448,f445]) ).
fof(f5254,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),intersection(complement(X0),power_class(X1))) = complement(intersection(diagonalise(X2),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f443,f445]) ).
fof(f5253,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),intersection(complement(X0),power_class(X1))) = complement(intersection(power_class(X2),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f442,f445]) ).
fof(f5252,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(union(X0,image(element_relation,complement(X1)))))
| member(singleton(X2),intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f426,f445]) ).
fof(f5251,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| member(X2,power_class(intersection(complement(X0),power_class(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f445]) ).
fof(f5250,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(X0,image(element_relation,complement(X1))),X2)
| ~ member(X3,universal_class)
| member(X3,intersection(complement(X0),power_class(X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f445]) ).
fof(f5249,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ inductive(power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f402,f445]) ).
fof(f5247,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,image(element_relation,complement(X1))))
| ~ subclass(universal_class,intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f276,f445]) ).
fof(f5244,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ subclass(universal_class,power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f179,f445]) ).
fof(f5243,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,image(element_relation,complement(X1))))
| ~ member(omega,intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f171,f445]) ).
fof(f5242,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ member(X2,power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f152,f445]) ).
fof(f5241,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(X0,image(element_relation,complement(X1)))))
| ~ inductive(power_class(intersection(complement(X0),power_class(X1)))) ),
inference(superposition,[],[f151,f445]) ).
fof(f5240,plain,
! [X0,X1] : complement(image(element_relation,power_class(intersection(complement(X0),power_class(X1))))) = power_class(image(element_relation,union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f150,f445]) ).
fof(f5292,plain,
! [X2,X0,X1] :
( subclass(union(X0,image(element_relation,complement(X1))),X2)
| ~ member(not_subclass_element(union(X0,image(element_relation,complement(X1))),X2),intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f5239,f445]) ).
fof(f5239,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(union(X0,image(element_relation,complement(X1))),X2),intersection(complement(X0),power_class(X1)))
| subclass(complement(intersection(complement(X0),power_class(X1))),X2) ),
inference(superposition,[],[f121,f445]) ).
fof(f5291,plain,
! [X0,X1] :
( null_class = union(X0,image(element_relation,complement(X1)))
| ~ member(regular(union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1))) ),
inference(forward_demodulation,[],[f5238,f445]) ).
fof(f5238,plain,
! [X0,X1] :
( ~ member(regular(union(X0,image(element_relation,complement(X1)))),intersection(complement(X0),power_class(X1)))
| null_class = complement(intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f120,f445]) ).
fof(f5237,plain,
! [X0,X1] :
( ~ inductive(union(X0,image(element_relation,complement(X1))))
| ~ member(null_class,intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f119,f445]) ).
fof(f5236,plain,
! [X0,X1] : power_class(intersection(complement(X0),power_class(X1))) = complement(image(element_relation,union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f55,f445]) ).
fof(f5235,plain,
! [X2,X0,X1] : union(X2,intersection(complement(X0),power_class(X1))) = complement(intersection(complement(X2),union(X0,image(element_relation,complement(X1))))),
inference(superposition,[],[f26,f445]) ).
fof(f5234,plain,
! [X2,X0,X1] : union(intersection(complement(X0),power_class(X1)),X2) = complement(intersection(union(X0,image(element_relation,complement(X1))),complement(X2))),
inference(superposition,[],[f26,f445]) ).
fof(f5233,plain,
! [X2,X0,X1] :
( member(X2,union(X0,image(element_relation,complement(X1))))
| member(X2,intersection(complement(X0),power_class(X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f445]) ).
fof(f5232,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,image(element_relation,complement(X1))))
| ~ member(X2,intersection(complement(X0),power_class(X1))) ),
inference(superposition,[],[f24,f445]) ).
fof(f5231,plain,
! [X0,X1] : symmetric_difference(complement(X0),power_class(X1)) = intersection(union(X0,image(element_relation,complement(X1))),union(complement(X0),power_class(X1))),
inference(superposition,[],[f1614,f445]) ).
fof(f5230,plain,
! [X0,X1] :
( member(null_class,union(X0,image(element_relation,complement(X1))))
| ~ inductive(symmetric_difference(complement(X0),power_class(X1))) ),
inference(superposition,[],[f1662,f445]) ).
fof(f5229,plain,
! [X2,X0,X1] :
( member(X2,union(X0,image(element_relation,complement(X1))))
| ~ member(X2,symmetric_difference(complement(X0),power_class(X1))) ),
inference(superposition,[],[f1659,f445]) ).
fof(f5228,plain,
! [X0,X1] : subclass(symmetric_difference(complement(X0),power_class(X1)),union(X0,image(element_relation,complement(X1)))),
inference(superposition,[],[f3947,f445]) ).
fof(f5225,plain,
! [X0] : union(image(element_relation,power_class(universal_class)),image(element_relation,complement(X0))) = complement(intersection(power_class(image(element_relation,null_class)),power_class(X0))),
inference(superposition,[],[f445,f664]) ).
fof(f5224,plain,
! [X0] : union(image(element_relation,null_class),image(element_relation,complement(X0))) = complement(intersection(power_class(universal_class),power_class(X0))),
inference(superposition,[],[f445,f616]) ).
fof(f5223,plain,
! [X0,X1] : union(image(element_relation,complement(X0)),image(element_relation,complement(X1))) = complement(intersection(power_class(X0),power_class(X1))),
inference(superposition,[],[f445,f55]) ).
fof(f5222,plain,
! [X2,X0,X1] : union(domain_of(restrict(identity_relation,X0,X1)),image(element_relation,complement(X2))) = complement(intersection(diagonalise(cross_product(X0,X1)),power_class(X2))),
inference(superposition,[],[f445,f541]) ).
fof(f5221,plain,
! [X0,X1] : union(domain_of(intersection(X0,identity_relation)),image(element_relation,complement(X1))) = complement(intersection(diagonalise(X0),power_class(X1))),
inference(superposition,[],[f445,f76]) ).
fof(f5220,plain,
! [X2,X0,X1] : union(intersection(complement(X0),power_class(X1)),image(element_relation,complement(X2))) = complement(intersection(union(X0,image(element_relation,complement(X1))),power_class(X2))),
inference(superposition,[],[f445,f445]) ).
fof(f5217,plain,
! [X2,X0,X1] : union(intersection(diagonalise(X0),complement(X1)),image(element_relation,complement(X2))) = complement(intersection(union(domain_of(intersection(X0,identity_relation)),X1),power_class(X2))),
inference(superposition,[],[f445,f443]) ).
fof(f5216,plain,
! [X2,X0,X1] : union(intersection(power_class(X0),complement(X1)),image(element_relation,complement(X2))) = complement(intersection(union(image(element_relation,complement(X0)),X1),power_class(X2))),
inference(superposition,[],[f445,f442]) ).
fof(f5214,plain,
! [X2,X0,X1] : union(intersection(complement(X0),complement(X1)),image(element_relation,complement(X2))) = complement(intersection(union(X0,X1),power_class(X2))),
inference(superposition,[],[f445,f26]) ).
fof(f445,plain,
! [X0,X1] : union(X1,image(element_relation,complement(X0))) = complement(intersection(complement(X1),power_class(X0))),
inference(superposition,[],[f26,f55]) ).
fof(f5155,plain,
! [X2,X0,X1] :
( subclass(union(domain_of(intersection(X0,identity_relation)),X1),X2)
| ~ subclass(union(domain_of(intersection(X0,identity_relation)),X1),intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f5125,f443]) ).
fof(f5125,plain,
! [X2,X0,X1] :
( ~ subclass(union(domain_of(intersection(X0,identity_relation)),X1),intersection(diagonalise(X0),complement(X1)))
| subclass(complement(intersection(diagonalise(X0),complement(X1))),X2) ),
inference(superposition,[],[f2982,f443]) ).
fof(f5120,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ subclass(universal_class,power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f1358,f443]) ).
fof(f5148,plain,
! [X0,X1] :
( null_class = union(domain_of(intersection(X0,identity_relation)),X1)
| ~ subclass(union(domain_of(intersection(X0,identity_relation)),X1),intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f5115,f443]) ).
fof(f5115,plain,
! [X0,X1] :
( ~ subclass(union(domain_of(intersection(X0,identity_relation)),X1),intersection(diagonalise(X0),complement(X1)))
| null_class = complement(intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f600,f443]) ).
fof(f5114,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ member(omega,power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f567,f443]) ).
fof(f5113,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ member(null_class,power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f566,f443]) ).
fof(f5111,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ member(X2,union(X3,intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f448,f443]) ).
fof(f5110,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(union(domain_of(intersection(X0,identity_relation)),X1),complement(X3)))
| ~ member(X2,union(intersection(diagonalise(X0),complement(X1)),X3)) ),
inference(superposition,[],[f448,f443]) ).
fof(f5109,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),intersection(diagonalise(X0),complement(X1))) = complement(intersection(power_class(X2),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f442,f443]) ).
fof(f5108,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(union(domain_of(intersection(X0,identity_relation)),X1)))
| member(singleton(X2),intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f426,f443]) ).
fof(f5107,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| member(X2,power_class(intersection(diagonalise(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f443]) ).
fof(f5106,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(domain_of(intersection(X0,identity_relation)),X1),X2)
| ~ member(X3,universal_class)
| member(X3,intersection(diagonalise(X0),complement(X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f443]) ).
fof(f5105,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ inductive(power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f402,f443]) ).
fof(f5103,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(domain_of(intersection(X0,identity_relation)),X1))
| ~ subclass(universal_class,intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f276,f443]) ).
fof(f5100,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ subclass(universal_class,power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f179,f443]) ).
fof(f5099,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(domain_of(intersection(X0,identity_relation)),X1))
| ~ member(omega,intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f171,f443]) ).
fof(f5098,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ member(X2,power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f152,f443]) ).
fof(f5097,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1)))
| ~ inductive(power_class(intersection(diagonalise(X0),complement(X1)))) ),
inference(superposition,[],[f151,f443]) ).
fof(f5096,plain,
! [X0,X1] : complement(image(element_relation,power_class(intersection(diagonalise(X0),complement(X1))))) = power_class(image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f150,f443]) ).
fof(f5147,plain,
! [X2,X0,X1] :
( subclass(union(domain_of(intersection(X0,identity_relation)),X1),X2)
| ~ member(not_subclass_element(union(domain_of(intersection(X0,identity_relation)),X1),X2),intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f5095,f443]) ).
fof(f5095,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(union(domain_of(intersection(X0,identity_relation)),X1),X2),intersection(diagonalise(X0),complement(X1)))
| subclass(complement(intersection(diagonalise(X0),complement(X1))),X2) ),
inference(superposition,[],[f121,f443]) ).
fof(f5146,plain,
! [X0,X1] :
( null_class = union(domain_of(intersection(X0,identity_relation)),X1)
| ~ member(regular(union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1))) ),
inference(forward_demodulation,[],[f5094,f443]) ).
fof(f5094,plain,
! [X0,X1] :
( ~ member(regular(union(domain_of(intersection(X0,identity_relation)),X1)),intersection(diagonalise(X0),complement(X1)))
| null_class = complement(intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f120,f443]) ).
fof(f5093,plain,
! [X0,X1] :
( ~ inductive(union(domain_of(intersection(X0,identity_relation)),X1))
| ~ member(null_class,intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f119,f443]) ).
fof(f5092,plain,
! [X0,X1] : power_class(intersection(diagonalise(X0),complement(X1))) = complement(image(element_relation,union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f55,f443]) ).
fof(f5091,plain,
! [X2,X0,X1] : union(X2,intersection(diagonalise(X0),complement(X1))) = complement(intersection(complement(X2),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f26,f443]) ).
fof(f5090,plain,
! [X2,X0,X1] : union(intersection(diagonalise(X0),complement(X1)),X2) = complement(intersection(union(domain_of(intersection(X0,identity_relation)),X1),complement(X2))),
inference(superposition,[],[f26,f443]) ).
fof(f5089,plain,
! [X2,X0,X1] :
( member(X2,union(domain_of(intersection(X0,identity_relation)),X1))
| member(X2,intersection(diagonalise(X0),complement(X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f443]) ).
fof(f5088,plain,
! [X2,X0,X1] :
( ~ member(X2,union(domain_of(intersection(X0,identity_relation)),X1))
| ~ member(X2,intersection(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f24,f443]) ).
fof(f5087,plain,
! [X0,X1] : symmetric_difference(diagonalise(X0),complement(X1)) = intersection(union(domain_of(intersection(X0,identity_relation)),X1),union(diagonalise(X0),complement(X1))),
inference(superposition,[],[f1614,f443]) ).
fof(f5086,plain,
! [X0,X1] :
( member(null_class,union(domain_of(intersection(X0,identity_relation)),X1))
| ~ inductive(symmetric_difference(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f1662,f443]) ).
fof(f5085,plain,
! [X2,X0,X1] :
( member(X2,union(domain_of(intersection(X0,identity_relation)),X1))
| ~ member(X2,symmetric_difference(diagonalise(X0),complement(X1))) ),
inference(superposition,[],[f1659,f443]) ).
fof(f5084,plain,
! [X0,X1] : subclass(symmetric_difference(diagonalise(X0),complement(X1)),union(domain_of(intersection(X0,identity_relation)),X1)),
inference(superposition,[],[f3947,f443]) ).
fof(f5083,plain,
! [X0] : union(domain_of(intersection(X0,identity_relation)),image(element_relation,power_class(universal_class))) = complement(intersection(diagonalise(X0),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f443,f664]) ).
fof(f5082,plain,
! [X0] : union(domain_of(intersection(X0,identity_relation)),image(element_relation,null_class)) = complement(intersection(diagonalise(X0),power_class(universal_class))),
inference(superposition,[],[f443,f616]) ).
fof(f5081,plain,
! [X0,X1] : union(domain_of(intersection(X1,identity_relation)),image(element_relation,complement(X0))) = complement(intersection(diagonalise(X1),power_class(X0))),
inference(superposition,[],[f443,f55]) ).
fof(f5080,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),domain_of(restrict(identity_relation,X0,X1))) = complement(intersection(diagonalise(X2),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f443,f541]) ).
fof(f5079,plain,
! [X0,X1] : union(domain_of(intersection(X1,identity_relation)),domain_of(intersection(X0,identity_relation))) = complement(intersection(diagonalise(X1),diagonalise(X0))),
inference(superposition,[],[f443,f76]) ).
fof(f5076,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),intersection(diagonalise(X0),complement(X1))) = complement(intersection(diagonalise(X2),union(domain_of(intersection(X0,identity_relation)),X1))),
inference(superposition,[],[f443,f443]) ).
fof(f5075,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),intersection(power_class(X0),complement(X1))) = complement(intersection(diagonalise(X2),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f443,f442]) ).
fof(f5073,plain,
! [X2,X0,X1] : union(domain_of(intersection(X2,identity_relation)),intersection(complement(X0),complement(X1))) = complement(intersection(diagonalise(X2),union(X0,X1))),
inference(superposition,[],[f443,f26]) ).
fof(f443,plain,
! [X0,X1] : union(domain_of(intersection(X0,identity_relation)),X1) = complement(intersection(diagonalise(X0),complement(X1))),
inference(superposition,[],[f26,f76]) ).
fof(f4975,plain,
! [X2,X0,X1] :
( subclass(union(image(element_relation,complement(X0)),X1),X2)
| ~ subclass(union(image(element_relation,complement(X0)),X1),intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f4947,f442]) ).
fof(f4947,plain,
! [X2,X0,X1] :
( ~ subclass(union(image(element_relation,complement(X0)),X1),intersection(power_class(X0),complement(X1)))
| subclass(complement(intersection(power_class(X0),complement(X1))),X2) ),
inference(superposition,[],[f2982,f442]) ).
fof(f4942,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ subclass(universal_class,power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f1358,f442]) ).
fof(f4968,plain,
! [X0,X1] :
( null_class = union(image(element_relation,complement(X0)),X1)
| ~ subclass(union(image(element_relation,complement(X0)),X1),intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f4937,f442]) ).
fof(f4937,plain,
! [X0,X1] :
( ~ subclass(union(image(element_relation,complement(X0)),X1),intersection(power_class(X0),complement(X1)))
| null_class = complement(intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f600,f442]) ).
fof(f4936,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ member(omega,power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f567,f442]) ).
fof(f4935,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ member(null_class,power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f566,f442]) ).
fof(f4933,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),union(image(element_relation,complement(X0)),X1)))
| ~ member(X2,union(X3,intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f448,f442]) ).
fof(f4932,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(union(image(element_relation,complement(X0)),X1),complement(X3)))
| ~ member(X2,union(intersection(power_class(X0),complement(X1)),X3)) ),
inference(superposition,[],[f448,f442]) ).
fof(f4931,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(union(image(element_relation,complement(X0)),X1)))
| member(singleton(X2),intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f426,f442]) ).
fof(f4930,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| member(X2,power_class(intersection(power_class(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f442]) ).
fof(f4929,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(image(element_relation,complement(X0)),X1),X2)
| ~ member(X3,universal_class)
| member(X3,intersection(power_class(X0),complement(X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f442]) ).
fof(f4928,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ inductive(power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f402,f442]) ).
fof(f4926,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(image(element_relation,complement(X0)),X1))
| ~ subclass(universal_class,intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f276,f442]) ).
fof(f4923,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ subclass(universal_class,power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f179,f442]) ).
fof(f4922,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(image(element_relation,complement(X0)),X1))
| ~ member(omega,intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f171,f442]) ).
fof(f4921,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ member(X2,power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f152,f442]) ).
fof(f4920,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(image(element_relation,complement(X0)),X1)))
| ~ inductive(power_class(intersection(power_class(X0),complement(X1)))) ),
inference(superposition,[],[f151,f442]) ).
fof(f4919,plain,
! [X0,X1] : complement(image(element_relation,power_class(intersection(power_class(X0),complement(X1))))) = power_class(image(element_relation,union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f150,f442]) ).
fof(f4967,plain,
! [X2,X0,X1] :
( subclass(union(image(element_relation,complement(X0)),X1),X2)
| ~ member(not_subclass_element(union(image(element_relation,complement(X0)),X1),X2),intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f4918,f442]) ).
fof(f4918,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(union(image(element_relation,complement(X0)),X1),X2),intersection(power_class(X0),complement(X1)))
| subclass(complement(intersection(power_class(X0),complement(X1))),X2) ),
inference(superposition,[],[f121,f442]) ).
fof(f4966,plain,
! [X0,X1] :
( null_class = union(image(element_relation,complement(X0)),X1)
| ~ member(regular(union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1))) ),
inference(forward_demodulation,[],[f4917,f442]) ).
fof(f4917,plain,
! [X0,X1] :
( ~ member(regular(union(image(element_relation,complement(X0)),X1)),intersection(power_class(X0),complement(X1)))
| null_class = complement(intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f120,f442]) ).
fof(f4916,plain,
! [X0,X1] :
( ~ inductive(union(image(element_relation,complement(X0)),X1))
| ~ member(null_class,intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f119,f442]) ).
fof(f4915,plain,
! [X0,X1] : power_class(intersection(power_class(X0),complement(X1))) = complement(image(element_relation,union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f55,f442]) ).
fof(f4914,plain,
! [X2,X0,X1] : union(X2,intersection(power_class(X0),complement(X1))) = complement(intersection(complement(X2),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f26,f442]) ).
fof(f4913,plain,
! [X2,X0,X1] : union(intersection(power_class(X0),complement(X1)),X2) = complement(intersection(union(image(element_relation,complement(X0)),X1),complement(X2))),
inference(superposition,[],[f26,f442]) ).
fof(f4912,plain,
! [X2,X0,X1] :
( member(X2,union(image(element_relation,complement(X0)),X1))
| member(X2,intersection(power_class(X0),complement(X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f442]) ).
fof(f4911,plain,
! [X2,X0,X1] :
( ~ member(X2,union(image(element_relation,complement(X0)),X1))
| ~ member(X2,intersection(power_class(X0),complement(X1))) ),
inference(superposition,[],[f24,f442]) ).
fof(f4910,plain,
! [X0,X1] : symmetric_difference(power_class(X0),complement(X1)) = intersection(union(image(element_relation,complement(X0)),X1),union(power_class(X0),complement(X1))),
inference(superposition,[],[f1614,f442]) ).
fof(f4909,plain,
! [X0,X1] :
( member(null_class,union(image(element_relation,complement(X0)),X1))
| ~ inductive(symmetric_difference(power_class(X0),complement(X1))) ),
inference(superposition,[],[f1662,f442]) ).
fof(f4908,plain,
! [X2,X0,X1] :
( member(X2,union(image(element_relation,complement(X0)),X1))
| ~ member(X2,symmetric_difference(power_class(X0),complement(X1))) ),
inference(superposition,[],[f1659,f442]) ).
fof(f4907,plain,
! [X0,X1] : subclass(symmetric_difference(power_class(X0),complement(X1)),union(image(element_relation,complement(X0)),X1)),
inference(superposition,[],[f3947,f442]) ).
fof(f4906,plain,
! [X0] : union(image(element_relation,complement(X0)),image(element_relation,power_class(universal_class))) = complement(intersection(power_class(X0),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f442,f664]) ).
fof(f4905,plain,
! [X0] : union(image(element_relation,complement(X0)),image(element_relation,null_class)) = complement(intersection(power_class(X0),power_class(universal_class))),
inference(superposition,[],[f442,f616]) ).
fof(f4904,plain,
! [X0,X1] : union(image(element_relation,complement(X1)),image(element_relation,complement(X0))) = complement(intersection(power_class(X1),power_class(X0))),
inference(superposition,[],[f442,f55]) ).
fof(f4903,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),domain_of(restrict(identity_relation,X0,X1))) = complement(intersection(power_class(X2),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f442,f541]) ).
fof(f4902,plain,
! [X0,X1] : union(image(element_relation,complement(X1)),domain_of(intersection(X0,identity_relation))) = complement(intersection(power_class(X1),diagonalise(X0))),
inference(superposition,[],[f442,f76]) ).
fof(f4899,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),intersection(power_class(X0),complement(X1))) = complement(intersection(power_class(X2),union(image(element_relation,complement(X0)),X1))),
inference(superposition,[],[f442,f442]) ).
fof(f4897,plain,
! [X2,X0,X1] : union(image(element_relation,complement(X2)),intersection(complement(X0),complement(X1))) = complement(intersection(power_class(X2),union(X0,X1))),
inference(superposition,[],[f442,f26]) ).
fof(f442,plain,
! [X0,X1] : union(image(element_relation,complement(X0)),X1) = complement(intersection(power_class(X0),complement(X1))),
inference(superposition,[],[f26,f55]) ).
fof(f4841,plain,
( ~ member(regular(complement(complement(null_class))),universal_class)
| null_class = complement(complement(null_class)) ),
inference(resolution,[],[f4833,f120]) ).
fof(f4837,plain,
! [X0] :
( ~ member(not_subclass_element(complement(complement(null_class)),X0),universal_class)
| subclass(complement(complement(null_class)),X0) ),
inference(resolution,[],[f4833,f121]) ).
fof(f4836,plain,
! [X0] :
( ~ member(not_subclass_element(X0,complement(null_class)),universal_class)
| subclass(X0,complement(null_class)) ),
inference(resolution,[],[f4833,f3]) ).
fof(f4835,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(complement(null_class),X1)
| member(X0,X1) ),
inference(resolution,[],[f4833,f1]) ).
fof(f4833,plain,
! [X0] :
( member(X0,complement(null_class))
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f4832,f4297]) ).
fof(f4832,plain,
! [X0] :
( member(X0,diagonalise(null_class))
| ~ member(X0,universal_class) ),
inference(subsumption_resolution,[],[f4811,f4164]) ).
fof(f4811,plain,
! [X0] :
( member(X0,domain_of(null_class))
| member(X0,diagonalise(null_class))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f425,f3938]) ).
fof(f4810,plain,
! [X2,X0,X1] :
( member(X2,domain_of(restrict(identity_relation,X0,X1)))
| member(X2,diagonalise(cross_product(X0,X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f425,f29]) ).
fof(f4831,plain,
! [X0] :
( member(X0,diagonalise(singleton(identity_relation)))
| ~ member(X0,universal_class)
| null_class = singleton(identity_relation) ),
inference(subsumption_resolution,[],[f4809,f4164]) ).
fof(f4809,plain,
! [X0] :
( member(X0,domain_of(null_class))
| member(X0,diagonalise(singleton(identity_relation)))
| ~ member(X0,universal_class)
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f425,f767]) ).
fof(f4819,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),diagonalise(X2))
| ~ homomorphism(X3,intersection(X2,identity_relation),X4)
| apply(X4,ordered_pair(apply(X3,X0),apply(X3,X1))) = apply(X3,apply(intersection(X2,identity_relation),ordered_pair(X0,X1))) ),
inference(subsumption_resolution,[],[f4801,f696]) ).
fof(f4801,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),diagonalise(X2))
| ~ member(ordered_pair(X0,X1),universal_class)
| ~ homomorphism(X3,intersection(X2,identity_relation),X4)
| apply(X4,ordered_pair(apply(X3,X0),apply(X3,X1))) = apply(X3,apply(intersection(X2,identity_relation),ordered_pair(X0,X1))) ),
inference(resolution,[],[f425,f89]) ).
fof(f4797,plain,
! [X0,X1] :
( member(not_subclass_element(X0,domain_of(intersection(X1,identity_relation))),diagonalise(X1))
| ~ member(not_subclass_element(X0,domain_of(intersection(X1,identity_relation))),universal_class)
| subclass(X0,domain_of(intersection(X1,identity_relation))) ),
inference(resolution,[],[f425,f3]) ).
fof(f4796,plain,
! [X2,X0,X1] :
( member(X0,diagonalise(X1))
| ~ member(X0,universal_class)
| ~ subclass(domain_of(intersection(X1,identity_relation)),X2)
| member(X0,X2) ),
inference(resolution,[],[f425,f1]) ).
fof(f425,plain,
! [X0,X1] :
( member(X1,domain_of(intersection(X0,identity_relation)))
| member(X1,diagonalise(X0))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f76]) ).
fof(f4724,plain,
! [X0] :
( member(X0,image(element_relation,power_class(image(element_relation,null_class))))
| member(X0,power_class(image(element_relation,power_class(universal_class))))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f424,f664]) ).
fof(f4723,plain,
! [X0] :
( member(X0,image(element_relation,power_class(universal_class)))
| member(X0,power_class(image(element_relation,null_class)))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f424,f616]) ).
fof(f4721,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,diagonalise(cross_product(X0,X1))))
| member(X2,power_class(domain_of(restrict(identity_relation,X0,X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f541]) ).
fof(f4716,plain,
! [X2,X0,X1] :
( member(X2,image(element_relation,union(X0,X1)))
| member(X2,power_class(intersection(complement(X0),complement(X1))))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f424,f26]) ).
fof(f4715,plain,
! [X0] :
( member(X0,image(element_relation,null_class))
| member(X0,power_class(universal_class))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f424,f603]) ).
fof(f4704,plain,
! [X0,X1] :
( member(not_subclass_element(X0,image(element_relation,complement(X1))),power_class(X1))
| ~ member(not_subclass_element(X0,image(element_relation,complement(X1))),universal_class)
| subclass(X0,image(element_relation,complement(X1))) ),
inference(resolution,[],[f424,f3]) ).
fof(f4703,plain,
! [X2,X0,X1] :
( member(X0,power_class(X1))
| ~ member(X0,universal_class)
| ~ subclass(image(element_relation,complement(X1)),X2)
| member(X0,X2) ),
inference(resolution,[],[f424,f1]) ).
fof(f424,plain,
! [X0,X1] :
( member(X1,image(element_relation,complement(X0)))
| member(X1,power_class(X0))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f55]) ).
fof(f4700,plain,
! [X0] :
( ~ subclass(inverse(X0),cantor(flip(cross_product(X0,universal_class))))
| inverse(X0) = cantor(flip(cross_product(X0,universal_class))) ),
inference(resolution,[],[f3962,f7]) ).
fof(f3962,plain,
! [X0] : subclass(cantor(flip(cross_product(X0,universal_class))),inverse(X0)),
inference(superposition,[],[f3948,f38]) ).
fof(f4699,plain,
! [X0] : subclass(cantor(restrict(element_relation,universal_class,range_of(null_class))),apply(null_class,X0)),
inference(superposition,[],[f3961,f4437]) ).
fof(f4698,plain,
! [X0,X1] : subclass(cantor(restrict(element_relation,universal_class,image(X0,singleton(X1)))),apply(X0,X1)),
inference(superposition,[],[f3961,f68]) ).
fof(f4696,plain,
! [X0] :
( ~ subclass(sum_class(X0),cantor(restrict(element_relation,universal_class,X0)))
| sum_class(X0) = cantor(restrict(element_relation,universal_class,X0)) ),
inference(resolution,[],[f3961,f7]) ).
fof(f3961,plain,
! [X0] : subclass(cantor(restrict(element_relation,universal_class,X0)),sum_class(X0)),
inference(superposition,[],[f3948,f53]) ).
fof(f4693,plain,
! [X0] :
( ~ subclass(diagonalise(compose(inverse(element_relation),X0)),cantor(X0))
| diagonalise(compose(inverse(element_relation),X0)) = cantor(X0) ),
inference(resolution,[],[f4091,f7]) ).
fof(f4091,plain,
! [X0] : subclass(cantor(X0),diagonalise(compose(inverse(element_relation),X0))),
inference(superposition,[],[f4063,f77]) ).
fof(f4691,plain,
! [X0] :
( ~ subclass(complement(null_class),symmetric_difference(null_class,X0))
| complement(null_class) = symmetric_difference(null_class,X0) ),
inference(resolution,[],[f4678,f7]) ).
fof(f4678,plain,
! [X0] : subclass(symmetric_difference(null_class,X0),complement(null_class)),
inference(superposition,[],[f3947,f3938]) ).
fof(f4689,plain,
! [X0] :
( ~ subclass(complement(null_class),symmetric_difference(X0,null_class))
| complement(null_class) = symmetric_difference(X0,null_class) ),
inference(resolution,[],[f4671,f7]) ).
fof(f4671,plain,
! [X0] : subclass(symmetric_difference(X0,null_class),complement(null_class)),
inference(superposition,[],[f3947,f4080]) ).
fof(f4688,plain,
! [X0] : subclass(symmetric_difference(complement(X0),null_class),complement(null_class)),
inference(forward_demodulation,[],[f4684,f4134]) ).
fof(f4684,plain,
! [X0] : subclass(symmetric_difference(complement(X0),null_class),union(X0,universal_class)),
inference(superposition,[],[f3947,f615]) ).
fof(f4687,plain,
subclass(symmetric_difference(null_class,null_class),complement(null_class)),
inference(forward_demodulation,[],[f4683,f4134]) ).
fof(f4683,plain,
subclass(symmetric_difference(null_class,null_class),union(universal_class,universal_class)),
inference(superposition,[],[f3947,f796]) ).
fof(f4686,plain,
! [X0] : subclass(symmetric_difference(null_class,complement(X0)),complement(null_class)),
inference(forward_demodulation,[],[f4682,f3967]) ).
fof(f4682,plain,
! [X0] : subclass(symmetric_difference(null_class,complement(X0)),union(universal_class,X0)),
inference(superposition,[],[f3947,f614]) ).
fof(f4679,plain,
! [X0] : subclass(symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))),complement(cantor(X0))),
inference(superposition,[],[f3947,f77]) ).
fof(f4677,plain,
subclass(symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation)),complement(symmetric_difference(inverse(subset_relation),subset_relation))),
inference(superposition,[],[f3947,f1653]) ).
fof(f4676,plain,
! [X0,X1] : subclass(symmetric_difference(complement(intersection(X0,X1)),union(X0,X1)),complement(symmetric_difference(X0,X1))),
inference(superposition,[],[f3947,f1614]) ).
fof(f4674,plain,
subclass(symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),complement(subset_relation)),
inference(superposition,[],[f3947,f1933]) ).
fof(f4673,plain,
! [X2,X0,X1] : subclass(symmetric_difference(cross_product(X0,X1),X2),complement(restrict(X2,X0,X1))),
inference(superposition,[],[f3947,f29]) ).
fof(f4672,plain,
! [X0] :
( subclass(symmetric_difference(singleton(X0),X0),complement(null_class))
| singleton(X0) = null_class ),
inference(superposition,[],[f3947,f767]) ).
fof(f4670,plain,
! [X2,X0,X1] : subclass(symmetric_difference(X0,cross_product(X1,X2)),complement(restrict(X0,X1,X2))),
inference(superposition,[],[f3947,f28]) ).
fof(f4667,plain,
! [X0,X1] :
( ~ subclass(complement(intersection(X0,X1)),symmetric_difference(X0,X1))
| complement(intersection(X0,X1)) = symmetric_difference(X0,X1) ),
inference(resolution,[],[f3947,f7]) ).
fof(f3947,plain,
! [X0,X1] : subclass(symmetric_difference(X0,X1),complement(intersection(X0,X1))),
inference(superposition,[],[f3922,f1614]) ).
fof(f4664,plain,
! [X2,X0,X1] :
( ~ subclass(cross_product(X0,X1),restrict(X2,X0,X1))
| cross_product(X0,X1) = restrict(X2,X0,X1) ),
inference(resolution,[],[f3944,f7]) ).
fof(f3944,plain,
! [X2,X0,X1] : subclass(restrict(X2,X0,X1),cross_product(X0,X1)),
inference(superposition,[],[f3922,f29]) ).
fof(f4657,plain,
! [X0,X1] :
( ~ subclass(power_class(image(element_relation,null_class)),X0)
| ~ member(X1,universal_class)
| member(X1,image(element_relation,power_class(universal_class)))
| member(X1,X0) ),
inference(superposition,[],[f420,f664]) ).
fof(f4656,plain,
! [X0,X1] :
( ~ subclass(power_class(universal_class),X0)
| ~ member(X1,universal_class)
| member(X1,image(element_relation,null_class))
| member(X1,X0) ),
inference(superposition,[],[f420,f616]) ).
fof(f4655,plain,
! [X2,X0,X1] :
( ~ subclass(power_class(X0),X1)
| ~ member(X2,universal_class)
| member(X2,image(element_relation,complement(X0)))
| member(X2,X1) ),
inference(superposition,[],[f420,f55]) ).
fof(f4654,plain,
! [X2,X3,X0,X1] :
( ~ subclass(diagonalise(cross_product(X0,X1)),X2)
| ~ member(X3,universal_class)
| member(X3,domain_of(restrict(identity_relation,X0,X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f541]) ).
fof(f4653,plain,
! [X2,X0,X1] :
( ~ subclass(diagonalise(X0),X1)
| ~ member(X2,universal_class)
| member(X2,domain_of(intersection(X0,identity_relation)))
| member(X2,X1) ),
inference(superposition,[],[f420,f76]) ).
fof(f4649,plain,
! [X2,X3,X0,X1] :
( ~ subclass(union(X0,X1),X2)
| ~ member(X3,universal_class)
| member(X3,intersection(complement(X0),complement(X1)))
| member(X3,X2) ),
inference(superposition,[],[f420,f26]) ).
fof(f4647,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,subset_relation)
| ~ subclass(complement(X1),identity_relation) ),
inference(resolution,[],[f420,f2984]) ).
fof(f4646,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,inverse(subset_relation))
| ~ subclass(complement(X1),identity_relation) ),
inference(resolution,[],[f420,f2983]) ).
fof(f4645,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) ),
inference(resolution,[],[f420,f62]) ).
fof(f420,plain,
! [X2,X0,X1] :
( ~ subclass(complement(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,X2) ),
inference(resolution,[],[f25,f1]) ).
fof(f4641,plain,
! [X0,X1] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(not_subclass_element(identity_relation,X0),X1) ),
inference(resolution,[],[f4077,f1]) ).
fof(f4640,plain,
! [X0] :
( subclass(identity_relation,X0)
| not_subclass_element(identity_relation,X0) = ordered_pair(first(not_subclass_element(identity_relation,X0)),second(not_subclass_element(identity_relation,X0))) ),
inference(resolution,[],[f4077,f2058]) ).
fof(f4077,plain,
! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) ),
inference(forward_demodulation,[],[f4060,f75]) ).
fof(f4060,plain,
! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(intersection(inverse(subset_relation),subset_relation),X0) ),
inference(superposition,[],[f133,f75]) ).
fof(f4634,plain,
! [X2,X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(sum_class(range_of(null_class)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4633,f4437]) ).
fof(f4633,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(sum_class(range_of(null_class)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4622,f4437]) ).
fof(f4622,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4632,plain,
! [X2,X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(apply(null_class,X2),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4631,f4437]) ).
fof(f4631,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,X2),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4621,f4437]) ).
fof(f4621,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,X2),apply(null_class,not_homomorphism2(null_class,X0,X1))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4630,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4629,f4437]) ).
fof(f4629,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),sum_class(range_of(null_class)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4620,f4437]) ).
fof(f4620,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),apply(null_class,not_homomorphism2(null_class,X0,X1)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4619,plain,
! [X2,X0,X1] :
( apply(X0,apply(X1,ordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism2(X0,X1,null_class)))) != apply(null_class,X2)
| ~ operation(null_class)
| ~ compatible(X0,X1,null_class)
| homomorphism(X0,X1,null_class)
| ~ operation(X1) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4628,plain,
! [X2,X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(sum_class(range_of(null_class)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4627,f4437]) ).
fof(f4627,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(sum_class(range_of(null_class)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4614,f4437]) ).
fof(f4614,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),apply(null_class,X2)))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4626,plain,
! [X2,X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(apply(null_class,X2),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4625,f4437]) ).
fof(f4625,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,X2),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4613,f4437]) ).
fof(f4613,plain,
! [X2,X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,X2),apply(null_class,not_homomorphism2(null_class,X0,X1))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4624,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4623,f4437]) ).
fof(f4623,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),sum_class(range_of(null_class)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4612,f4437]) ).
fof(f4612,plain,
! [X2,X0,X1] :
( apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),apply(null_class,not_homomorphism2(null_class,X0,X1)))) != apply(null_class,X2)
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4611,plain,
! [X2,X0,X1] :
( apply(X0,apply(X1,ordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism2(X0,X1,null_class)))) != apply(null_class,X2)
| ~ operation(null_class)
| ~ compatible(X0,X1,null_class)
| homomorphism(X0,X1,null_class)
| ~ operation(X1) ),
inference(superposition,[],[f91,f4539]) ).
fof(f4539,plain,
! [X0,X1] : apply(null_class,X0) = apply(null_class,X1),
inference(superposition,[],[f4437,f4437]) ).
fof(f4555,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4554,f4437]) ).
fof(f4554,plain,
! [X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4544,f4437]) ).
fof(f4544,plain,
! [X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4437]) ).
fof(f4553,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4552,f4437]) ).
fof(f4552,plain,
! [X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4543,f4437]) ).
fof(f4543,plain,
! [X0,X1] :
( apply(null_class,apply(X0,ordered_pair(not_homomorphism1(null_class,X0,X1),not_homomorphism2(null_class,X0,X1)))) != apply(X1,ordered_pair(sum_class(range_of(null_class)),apply(null_class,not_homomorphism2(null_class,X0,X1))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4437]) ).
fof(f4551,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(sum_class(range_of(null_class)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4550,f4437]) ).
fof(f4550,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),sum_class(range_of(null_class))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(forward_demodulation,[],[f4542,f4437]) ).
fof(f4542,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X1,ordered_pair(apply(null_class,not_homomorphism1(null_class,X0,X1)),apply(null_class,not_homomorphism2(null_class,X0,X1))))
| ~ operation(X1)
| ~ compatible(null_class,X0,X1)
| homomorphism(null_class,X0,X1)
| ~ operation(X0) ),
inference(superposition,[],[f91,f4437]) ).
fof(f4541,plain,
! [X0,X1] :
( sum_class(range_of(null_class)) != apply(X0,apply(X1,ordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism2(X0,X1,null_class))))
| ~ operation(null_class)
| ~ compatible(X0,X1,null_class)
| homomorphism(X0,X1,null_class)
| ~ operation(X1) ),
inference(superposition,[],[f91,f4437]) ).
fof(f4437,plain,
! [X0] : apply(null_class,X0) = sum_class(range_of(null_class)),
inference(superposition,[],[f68,f4152]) ).
fof(f4535,plain,
( ~ subclass(complement(identity_relation),symmetric_difference(inverse(subset_relation),subset_relation))
| complement(identity_relation) = symmetric_difference(inverse(subset_relation),subset_relation) ),
inference(resolution,[],[f4529,f7]) ).
fof(f4529,plain,
subclass(symmetric_difference(inverse(subset_relation),subset_relation),complement(identity_relation)),
inference(superposition,[],[f3922,f1653]) ).
fof(f4525,plain,
( ~ member(null_class,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ inductive(symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation))) ),
inference(superposition,[],[f1693,f1653]) ).
fof(f4524,plain,
( member(null_class,complement(symmetric_difference(inverse(subset_relation),subset_relation)))
| ~ inductive(symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation))) ),
inference(superposition,[],[f1662,f1653]) ).
fof(f4523,plain,
! [X0] :
( member(X0,complement(symmetric_difference(inverse(subset_relation),subset_relation)))
| ~ member(X0,symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation))) ),
inference(superposition,[],[f1659,f1653]) ).
fof(f4522,plain,
symmetric_difference(complement(identity_relation),union(inverse(subset_relation),subset_relation)) = intersection(complement(symmetric_difference(inverse(subset_relation),subset_relation)),union(complement(identity_relation),union(inverse(subset_relation),subset_relation))),
inference(superposition,[],[f1614,f1653]) ).
fof(f4521,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(ordered_pair(X0,X1),complement(identity_relation)) ),
inference(superposition,[],[f719,f1653]) ).
fof(f4520,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(ordered_pair(X0,X1),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f718,f1653]) ).
fof(f4519,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(unordered_pair(X0,X1),complement(identity_relation)) ),
inference(superposition,[],[f265,f1653]) ).
fof(f4518,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(unordered_pair(X0,X1),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f264,f1653]) ).
fof(f4515,plain,
! [X0] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(singleton(X0),complement(identity_relation)) ),
inference(superposition,[],[f177,f1653]) ).
fof(f4514,plain,
! [X0] :
( ~ subclass(universal_class,symmetric_difference(inverse(subset_relation),subset_relation))
| member(singleton(X0),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f176,f1653]) ).
fof(f4534,plain,
! [X0] :
( subclass(symmetric_difference(inverse(subset_relation),subset_relation),X0)
| member(not_subclass_element(symmetric_difference(inverse(subset_relation),subset_relation),X0),union(inverse(subset_relation),subset_relation)) ),
inference(forward_demodulation,[],[f4511,f1653]) ).
fof(f4511,plain,
! [X0] :
( member(not_subclass_element(symmetric_difference(inverse(subset_relation),subset_relation),X0),union(inverse(subset_relation),subset_relation))
| subclass(intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)),X0) ),
inference(superposition,[],[f133,f1653]) ).
fof(f4533,plain,
( null_class = symmetric_difference(inverse(subset_relation),subset_relation)
| member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),union(inverse(subset_relation),subset_relation)) ),
inference(forward_demodulation,[],[f4510,f1653]) ).
fof(f4510,plain,
( member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),union(inverse(subset_relation),subset_relation))
| null_class = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f132,f1653]) ).
fof(f4532,plain,
! [X0] :
( subclass(symmetric_difference(inverse(subset_relation),subset_relation),X0)
| member(not_subclass_element(symmetric_difference(inverse(subset_relation),subset_relation),X0),complement(identity_relation)) ),
inference(forward_demodulation,[],[f4508,f1653]) ).
fof(f4508,plain,
! [X0] :
( member(not_subclass_element(symmetric_difference(inverse(subset_relation),subset_relation),X0),complement(identity_relation))
| subclass(intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)),X0) ),
inference(superposition,[],[f128,f1653]) ).
fof(f4531,plain,
( null_class = symmetric_difference(inverse(subset_relation),subset_relation)
| member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation)) ),
inference(forward_demodulation,[],[f4507,f1653]) ).
fof(f4507,plain,
( member(regular(symmetric_difference(inverse(subset_relation),subset_relation)),complement(identity_relation))
| null_class = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f127,f1653]) ).
fof(f4505,plain,
! [X0] :
( member(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| ~ member(X0,union(inverse(subset_relation),subset_relation))
| ~ member(X0,complement(identity_relation)) ),
inference(superposition,[],[f23,f1653]) ).
fof(f4503,plain,
! [X0] :
( ~ member(X0,symmetric_difference(inverse(subset_relation),subset_relation))
| member(X0,complement(identity_relation)) ),
inference(superposition,[],[f21,f1653]) ).
fof(f1653,plain,
symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)),
inference(superposition,[],[f1614,f75]) ).
fof(f4498,plain,
! [X0] :
( ~ subclass(successor(X0),symmetric_difference(X0,singleton(X0)))
| successor(X0) = symmetric_difference(X0,singleton(X0)) ),
inference(resolution,[],[f4489,f7]) ).
fof(f4489,plain,
! [X0] : subclass(symmetric_difference(X0,singleton(X0)),successor(X0)),
inference(superposition,[],[f4089,f43]) ).
fof(f4496,plain,
! [X0,X1] :
( ~ subclass(inverse(subset_relation),restrict(identity_relation,X0,X1))
| inverse(subset_relation) = restrict(identity_relation,X0,X1) ),
inference(resolution,[],[f4015,f7]) ).
fof(f4015,plain,
! [X0,X1] : subclass(restrict(identity_relation,X0,X1),inverse(subset_relation)),
inference(superposition,[],[f3920,f28]) ).
fof(f4494,plain,
! [X0] :
( ~ subclass(complement(null_class),symmetric_difference(universal_class,X0))
| complement(null_class) = symmetric_difference(universal_class,X0) ),
inference(resolution,[],[f4491,f7]) ).
fof(f4491,plain,
! [X0] : subclass(symmetric_difference(universal_class,X0),complement(null_class)),
inference(superposition,[],[f4089,f3967]) ).
fof(f4492,plain,
! [X0] :
( ~ subclass(complement(null_class),symmetric_difference(X0,universal_class))
| complement(null_class) = symmetric_difference(X0,universal_class) ),
inference(resolution,[],[f4490,f7]) ).
fof(f4490,plain,
! [X0] : subclass(symmetric_difference(X0,universal_class),complement(null_class)),
inference(superposition,[],[f4089,f4134]) ).
fof(f4487,plain,
! [X0,X1] :
( ~ subclass(union(X0,X1),symmetric_difference(X0,X1))
| union(X0,X1) = symmetric_difference(X0,X1) ),
inference(resolution,[],[f4089,f7]) ).
fof(f4089,plain,
! [X0,X1] : subclass(symmetric_difference(X0,X1),union(X0,X1)),
inference(superposition,[],[f4063,f1614]) ).
fof(f4484,plain,
! [X0,X1] :
( ~ member(X1,ordered_pair(singleton(X0),X0))
| singleton(singleton(X0)) = X1 ),
inference(duplicate_literal_removal,[],[f4469]) ).
fof(f4469,plain,
! [X0,X1] :
( ~ member(X1,ordered_pair(singleton(X0),X0))
| singleton(singleton(X0)) = X1
| singleton(singleton(X0)) = X1 ),
inference(superposition,[],[f8,f690]) ).
fof(f4468,plain,
! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0))),
inference(superposition,[],[f12,f690]) ).
fof(f4466,plain,
! [X0] : ordered_pair(singleton(singleton(X0)),singleton(X0)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),X0)),
inference(superposition,[],[f13,f690]) ).
fof(f4465,plain,
! [X0] : member(ordered_pair(singleton(X0),X0),ordered_pair(singleton(singleton(X0)),singleton(X0))),
inference(superposition,[],[f703,f690]) ).
fof(f690,plain,
! [X0] : ordered_pair(singleton(X0),X0) = unordered_pair(singleton(singleton(X0)),singleton(singleton(X0))),
inference(superposition,[],[f13,f12]) ).
fof(f4450,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),null_class) = X0 ),
inference(resolution,[],[f4235,f652]) ).
fof(f4235,plain,
! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ),
inference(resolution,[],[f4212,f160]) ).
fof(f4440,plain,
! [X2,X0,X1] :
( member(X2,range_of(null_class))
| ~ member(ordered_pair(X1,X2),compose(null_class,X0)) ),
inference(superposition,[],[f58,f4152]) ).
fof(f4439,plain,
! [X2,X0,X1] :
( ~ member(X2,range_of(null_class))
| member(ordered_pair(X1,X2),compose(null_class,X0))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f59,f4152]) ).
fof(f4436,plain,
! [X2,X0,X1] :
( member(X1,image(X2,range_of(null_class)))
| ~ member(ordered_pair(X0,X1),compose(X2,null_class)) ),
inference(superposition,[],[f58,f4152]) ).
fof(f4435,plain,
! [X2,X0,X1] :
( ~ member(X1,image(X2,range_of(null_class)))
| member(ordered_pair(X0,X1),compose(X2,null_class))
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f59,f4152]) ).
fof(f4152,plain,
! [X0] : image(null_class,X0) = range_of(null_class),
inference(superposition,[],[f42,f4018]) ).
fof(f4417,plain,
! [X0,X1] :
( ~ member(X0,intersection(complement(X1),power_class(image(element_relation,null_class))))
| ~ member(X0,union(X1,image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f448,f664]) ).
fof(f4416,plain,
! [X0,X1] :
( ~ member(X0,intersection(complement(X1),power_class(universal_class)))
| ~ member(X0,union(X1,image(element_relation,null_class))) ),
inference(superposition,[],[f448,f616]) ).
fof(f4415,plain,
! [X2,X0,X1] :
( ~ member(X1,intersection(complement(X2),power_class(X0)))
| ~ member(X1,union(X2,image(element_relation,complement(X0)))) ),
inference(superposition,[],[f448,f55]) ).
fof(f4414,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),diagonalise(cross_product(X0,X1))))
| ~ member(X2,union(X3,domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f448,f541]) ).
fof(f4413,plain,
! [X2,X0,X1] :
( ~ member(X1,intersection(complement(X2),diagonalise(X0)))
| ~ member(X1,union(X2,domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f448,f76]) ).
fof(f4409,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(complement(X3),union(X0,X1)))
| ~ member(X2,union(X3,intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f448,f26]) ).
fof(f4407,plain,
! [X0,X1] :
( ~ member(X0,intersection(power_class(image(element_relation,null_class)),complement(X1)))
| ~ member(X0,union(image(element_relation,power_class(universal_class)),X1)) ),
inference(superposition,[],[f448,f664]) ).
fof(f4406,plain,
! [X0,X1] :
( ~ member(X0,intersection(power_class(universal_class),complement(X1)))
| ~ member(X0,union(image(element_relation,null_class),X1)) ),
inference(superposition,[],[f448,f616]) ).
fof(f4405,plain,
! [X2,X0,X1] :
( ~ member(X1,intersection(power_class(X0),complement(X2)))
| ~ member(X1,union(image(element_relation,complement(X0)),X2)) ),
inference(superposition,[],[f448,f55]) ).
fof(f4404,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(diagonalise(cross_product(X0,X1)),complement(X3)))
| ~ member(X2,union(domain_of(restrict(identity_relation,X0,X1)),X3)) ),
inference(superposition,[],[f448,f541]) ).
fof(f4403,plain,
! [X2,X0,X1] :
( ~ member(X1,intersection(diagonalise(X0),complement(X2)))
| ~ member(X1,union(domain_of(intersection(X0,identity_relation)),X2)) ),
inference(superposition,[],[f448,f76]) ).
fof(f4399,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,intersection(union(X0,X1),complement(X3)))
| ~ member(X2,union(intersection(complement(X0),complement(X1)),X3)) ),
inference(superposition,[],[f448,f26]) ).
fof(f4397,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,X1),union(X2,X3))
| ~ subclass(X0,intersection(complement(X2),complement(X3)))
| subclass(X0,X1) ),
inference(resolution,[],[f448,f160]) ).
fof(f4396,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,intersection(complement(X2),complement(X3))) ),
inference(resolution,[],[f448,f697]) ).
fof(f4394,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,intersection(complement(X2),complement(X3))) ),
inference(resolution,[],[f448,f161]) ).
fof(f4392,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(X0,intersection(complement(X1),complement(X2)))),union(X1,X2))
| null_class = intersection(X0,intersection(complement(X1),complement(X2))) ),
inference(resolution,[],[f448,f132]) ).
fof(f4391,plain,
! [X2,X0,X1] :
( ~ member(regular(X0),union(X1,X2))
| ~ subclass(X0,intersection(complement(X1),complement(X2)))
| null_class = X0 ),
inference(resolution,[],[f448,f159]) ).
fof(f4390,plain,
! [X2,X0,X1] :
( ~ member(power_class(X0),union(X1,X2))
| ~ subclass(universal_class,intersection(complement(X1),complement(X2)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f448,f165]) ).
fof(f4389,plain,
! [X2,X0,X1] :
( ~ member(sum_class(X0),union(X1,X2))
| ~ subclass(universal_class,intersection(complement(X1),complement(X2)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f448,f164]) ).
fof(f4388,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,domain_of(X0)),union(X1,X2))
| ~ subclass(domain_relation,intersection(complement(X1),complement(X2)))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f448,f318]) ).
fof(f4387,plain,
! [X2,X0,X1] :
( ~ member(singleton(X0),union(X1,X2))
| ~ subclass(universal_class,intersection(complement(X1),complement(X2))) ),
inference(resolution,[],[f448,f162]) ).
fof(f4386,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,intersection(complement(X1),complement(X2))),X3),union(X1,X2))
| subclass(intersection(X0,intersection(complement(X1),complement(X2))),X3) ),
inference(resolution,[],[f448,f133]) ).
fof(f4385,plain,
! [X0,X1] :
( ~ member(apply(choice,intersection(complement(X0),complement(X1))),union(X0,X1))
| intersection(complement(X0),complement(X1)) = null_class
| ~ member(intersection(complement(X0),complement(X1)),universal_class) ),
inference(resolution,[],[f448,f70]) ).
fof(f4380,plain,
! [X2,X0,X1] :
( ~ member(regular(intersection(intersection(complement(X0),complement(X1)),X2)),union(X0,X1))
| null_class = intersection(intersection(complement(X0),complement(X1)),X2) ),
inference(resolution,[],[f448,f127]) ).
fof(f4379,plain,
! [X0,X1] :
( ~ member(regular(intersection(complement(X0),complement(X1))),union(X0,X1))
| intersection(complement(X0),complement(X1)) = null_class ),
inference(resolution,[],[f448,f66]) ).
fof(f4378,plain,
! [X0,X1] :
( ~ member(omega,union(X0,X1))
| ~ subclass(universal_class,intersection(complement(X0),complement(X1))) ),
inference(resolution,[],[f448,f163]) ).
fof(f4377,plain,
! [X0,X1] :
( ~ member(null_class,union(X0,X1))
| ~ inductive(intersection(complement(X0),complement(X1))) ),
inference(resolution,[],[f448,f47]) ).
fof(f4375,plain,
! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(intersection(intersection(complement(X0),complement(X1)),X2),X3),union(X0,X1))
| subclass(intersection(intersection(complement(X0),complement(X1)),X2),X3) ),
inference(resolution,[],[f448,f128]) ).
fof(f4374,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(complement(X0),complement(X1)),X2),union(X0,X1))
| subclass(intersection(complement(X0),complement(X1)),X2) ),
inference(resolution,[],[f448,f2]) ).
fof(f4373,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| ~ member(X0,complement(X2))
| ~ member(X0,complement(X1)) ),
inference(resolution,[],[f448,f23]) ).
fof(f448,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,union(X0,X1)) ),
inference(superposition,[],[f24,f26]) ).
fof(f4367,plain,
! [X0] : symmetric_difference(X0,universal_class) = intersection(complement(intersection(X0,universal_class)),complement(null_class)),
inference(superposition,[],[f1614,f4134]) ).
fof(f4134,plain,
! [X0] : complement(null_class) = union(X0,universal_class),
inference(superposition,[],[f615,f4080]) ).
fof(f4345,plain,
! [X0,X1] :
( member(ordered_pair(inverse(X0),range_of(X0)),X1)
| ~ subclass(domain_relation,X1)
| ~ member(inverse(X0),universal_class) ),
inference(superposition,[],[f318,f39]) ).
fof(f4344,plain,
! [X0,X1] :
( member(ordered_pair(flip(cross_product(X0,universal_class)),inverse(X0)),X1)
| ~ subclass(domain_relation,X1)
| ~ member(flip(cross_product(X0,universal_class)),universal_class) ),
inference(superposition,[],[f318,f38]) ).
fof(f4342,plain,
! [X0,X1] :
( member(ordered_pair(restrict(element_relation,universal_class,X0),sum_class(X0)),X1)
| ~ subclass(domain_relation,X1)
| ~ member(restrict(element_relation,universal_class,X0),universal_class) ),
inference(superposition,[],[f318,f53]) ).
fof(f4340,plain,
! [X0,X1] :
( ~ subclass(domain_relation,cantor(X0))
| ~ member(X1,universal_class)
| member(ordered_pair(X1,domain_of(X1)),domain_of(X0)) ),
inference(resolution,[],[f318,f923]) ).
fof(f4339,plain,
! [X0] :
( ~ subclass(domain_relation,subset_relation)
| ~ member(X0,universal_class)
| ordered_pair(X0,domain_of(X0)) = ordered_pair(first(ordered_pair(X0,domain_of(X0))),second(ordered_pair(X0,domain_of(X0)))) ),
inference(resolution,[],[f318,f2058]) ).
fof(f4338,plain,
! [X0,X1] :
( ~ subclass(domain_relation,identity_relation)
| ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),X1)
| ~ subclass(subset_relation,X1) ),
inference(resolution,[],[f318,f170]) ).
fof(f4335,plain,
! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,image(X0,image(X1,singleton(X2))))
| ~ member(X3,universal_class)
| member(ordered_pair(X2,ordered_pair(X3,domain_of(X3))),compose(X0,X1))
| ~ member(ordered_pair(X2,ordered_pair(X3,domain_of(X3))),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f318,f59]) ).
fof(f4334,plain,
! [X0] :
( ~ subclass(domain_relation,image(element_relation,null_class))
| ~ member(X0,universal_class)
| ~ member(ordered_pair(X0,domain_of(X0)),power_class(universal_class)) ),
inference(resolution,[],[f318,f621]) ).
fof(f4333,plain,
! [X0,X1] :
( ~ subclass(domain_relation,image(element_relation,complement(X0)))
| ~ member(X1,universal_class)
| ~ member(ordered_pair(X1,domain_of(X1)),power_class(X0)) ),
inference(resolution,[],[f318,f152]) ).
fof(f4355,plain,
! [X0] :
( ~ subclass(domain_relation,inverse(subset_relation))
| ~ member(ordered_pair(X0,domain_of(X0)),subset_relation)
| member(ordered_pair(X0,domain_of(X0)),identity_relation) ),
inference(subsumption_resolution,[],[f4332,f2066]) ).
fof(f4332,plain,
! [X0] :
( ~ subclass(domain_relation,inverse(subset_relation))
| ~ member(X0,universal_class)
| ~ member(ordered_pair(X0,domain_of(X0)),subset_relation)
| member(ordered_pair(X0,domain_of(X0)),identity_relation) ),
inference(resolution,[],[f318,f757]) ).
fof(f4354,plain,
! [X0] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f4331,f4180]) ).
fof(f4331,plain,
! [X0] :
( ~ subclass(domain_relation,domain_of(null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f318,f4164]) ).
fof(f4330,plain,
! [X0,X1] :
( ~ subclass(domain_relation,domain_of(intersection(X0,identity_relation)))
| ~ member(X1,universal_class)
| ~ member(ordered_pair(X1,domain_of(X1)),diagonalise(X0)) ),
inference(resolution,[],[f318,f155]) ).
fof(f4328,plain,
! [X0,X1] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),X1)
| null_class = X1 ),
inference(resolution,[],[f318,f291]) ).
fof(f4352,plain,
! [X0] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class) ),
inference(subsumption_resolution,[],[f4327,f696]) ).
fof(f4327,plain,
! [X0] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class)
| ~ member(ordered_pair(X0,domain_of(X0)),universal_class) ),
inference(resolution,[],[f318,f612]) ).
fof(f4325,plain,
! [X0] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f318,f4212]) ).
fof(f4324,plain,
! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,restrict(X0,X1,X2))
| ~ member(X3,universal_class)
| member(ordered_pair(X3,domain_of(X3)),X0) ),
inference(resolution,[],[f318,f495]) ).
fof(f4323,plain,
! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,restrict(X0,X1,X2))
| ~ member(X3,universal_class)
| member(ordered_pair(X3,domain_of(X3)),cross_product(X1,X2)) ),
inference(resolution,[],[f318,f496]) ).
fof(f4322,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,symmetric_difference(X0,X1))
| ~ member(X2,universal_class)
| member(ordered_pair(X2,domain_of(X2)),union(X0,X1)) ),
inference(resolution,[],[f318,f1660]) ).
fof(f4321,plain,
! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(ordered_pair(X1,domain_of(X1)),X0) ),
inference(resolution,[],[f318,f24]) ).
fof(f4320,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(ordered_pair(X2,domain_of(X2)),X0) ),
inference(resolution,[],[f318,f21]) ).
fof(f4319,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(ordered_pair(X2,domain_of(X2)),X1) ),
inference(resolution,[],[f318,f22]) ).
fof(f4318,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| ordered_pair(X2,domain_of(X2)) = ordered_pair(first(ordered_pair(X2,domain_of(X2))),second(ordered_pair(X2,domain_of(X2)))) ),
inference(resolution,[],[f318,f17]) ).
fof(f4317,plain,
! [X0,X1] :
( ~ subclass(domain_relation,singleton(X0))
| ~ member(X1,universal_class)
| ordered_pair(X1,domain_of(X1)) = X0 ),
inference(resolution,[],[f318,f650]) ).
fof(f4316,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| ordered_pair(X2,domain_of(X2)) = X0
| ordered_pair(X2,domain_of(X2)) = X1 ),
inference(resolution,[],[f318,f8]) ).
fof(f4315,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(ordered_pair(X1,domain_of(X1)),X2) ),
inference(resolution,[],[f318,f1]) ).
fof(f4350,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X0,X1),domain_of(ordered_pair(X0,X1))),rotate(X2))
| ~ member(ordered_pair(ordered_pair(X1,domain_of(ordered_pair(X0,X1))),X0),X2) ),
inference(subsumption_resolution,[],[f4314,f696]) ).
fof(f4314,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(X0,X1),universal_class)
| member(ordered_pair(ordered_pair(X0,X1),domain_of(ordered_pair(X0,X1))),rotate(X2))
| ~ member(ordered_pair(ordered_pair(X1,domain_of(ordered_pair(X0,X1))),X0),X2) ),
inference(resolution,[],[f318,f34]) ).
fof(f4349,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X0,X1),domain_of(ordered_pair(X0,X1))),flip(X2))
| ~ member(ordered_pair(ordered_pair(X1,X0),domain_of(ordered_pair(X0,X1))),X2) ),
inference(subsumption_resolution,[],[f4313,f696]) ).
fof(f4313,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(X0,X1),universal_class)
| member(ordered_pair(ordered_pair(X0,X1),domain_of(ordered_pair(X0,X1))),flip(X2))
| ~ member(ordered_pair(ordered_pair(X1,X0),domain_of(ordered_pair(X0,X1))),X2) ),
inference(resolution,[],[f318,f37]) ).
fof(f4348,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| member(ordered_pair(ordered_pair(X2,X1),domain_of(ordered_pair(X1,X2))),X0) ),
inference(subsumption_resolution,[],[f4312,f696]) ).
fof(f4312,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(ordered_pair(X1,X2),universal_class)
| member(ordered_pair(ordered_pair(X2,X1),domain_of(ordered_pair(X1,X2))),X0) ),
inference(resolution,[],[f318,f36]) ).
fof(f4347,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| member(ordered_pair(ordered_pair(X2,domain_of(ordered_pair(X1,X2))),X1),X0) ),
inference(subsumption_resolution,[],[f4311,f696]) ).
fof(f4311,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(ordered_pair(X1,X2),universal_class)
| member(ordered_pair(ordered_pair(X2,domain_of(ordered_pair(X1,X2))),X1),X0) ),
inference(resolution,[],[f318,f33]) ).
fof(f4309,plain,
! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) ),
inference(resolution,[],[f318,f93]) ).
fof(f4306,plain,
! [X0] :
( ~ subclass(domain_relation,identity_relation)
| ~ member(X0,universal_class)
| member(domain_of(X0),universal_class) ),
inference(resolution,[],[f318,f2076]) ).
fof(f4303,plain,
! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| apply(X3,ordered_pair(apply(X2,X1),apply(X2,domain_of(X1)))) = apply(X2,apply(X0,ordered_pair(X1,domain_of(X1)))) ),
inference(resolution,[],[f318,f89]) ).
fof(f4302,plain,
! [X0] :
( ~ subclass(domain_relation,element_relation)
| ~ member(X0,universal_class)
| member(X0,domain_of(X0)) ),
inference(resolution,[],[f318,f19]) ).
fof(f4346,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),element_relation)
| ~ member(X0,domain_of(X0)) ),
inference(subsumption_resolution,[],[f4301,f98]) ).
fof(f4301,plain,
! [X0] :
( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),element_relation)
| ~ member(X0,domain_of(X0)) ),
inference(resolution,[],[f318,f20]) ).
fof(f4300,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) ),
inference(resolution,[],[f318,f14]) ).
fof(f4299,plain,
! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) ),
inference(resolution,[],[f318,f15]) ).
fof(f4298,plain,
! [X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(universal_class,complement(X0)) ),
inference(resolution,[],[f318,f698]) ).
fof(f318,plain,
! [X0,X1] :
( member(ordered_pair(X0,domain_of(X0)),X1)
| ~ subclass(domain_relation,X1)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f100,f1]) ).
fof(f4297,plain,
complement(null_class) = diagonalise(null_class),
inference(forward_demodulation,[],[f3999,f4180]) ).
fof(f4296,plain,
( member(ordered_pair(universal_class,complement(null_class)),successor_relation)
| ~ member(ordered_pair(universal_class,complement(null_class)),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[],[f4295,f4284]) ).
fof(f4295,plain,
( ~ member(ordered_pair(universal_class,complement(null_class)),cross_product(universal_class,universal_class))
| member(ordered_pair(universal_class,successor(universal_class)),successor_relation) ),
inference(superposition,[],[f116,f4284]) ).
fof(f4284,plain,
complement(null_class) = successor(universal_class),
inference(superposition,[],[f3967,f43]) ).
fof(f4294,plain,
! [X0] : symmetric_difference(universal_class,X0) = intersection(complement(intersection(universal_class,X0)),complement(null_class)),
inference(superposition,[],[f1614,f3967]) ).
fof(f4290,plain,
complement(null_class) = successor(universal_class),
inference(superposition,[],[f43,f3967]) ).
fof(f3967,plain,
! [X0] : complement(null_class) = union(universal_class,X0),
inference(superposition,[],[f614,f3938]) ).
fof(f218,plain,
! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) ),
inference(resolution,[],[f7,f92]) ).
fof(f4274,plain,
! [X0] :
( singleton(X0) = image(successor_relation,singleton(X0))
| ~ inductive(singleton(X0))
| not_subclass_element(singleton(X0),image(successor_relation,singleton(X0))) = X0 ),
inference(resolution,[],[f212,f652]) ).
fof(f212,plain,
! [X0] :
( ~ subclass(X0,image(successor_relation,X0))
| image(successor_relation,X0) = X0
| ~ inductive(X0) ),
inference(resolution,[],[f7,f48]) ).
fof(f4271,plain,
! [X0,X1] :
( ~ operation(X1)
| ~ compatible(X0,null_class,X1)
| homomorphism(X0,null_class,X1)
| ~ operation(null_class) ),
inference(subsumption_resolution,[],[f4254,f4212]) ).
fof(f4254,plain,
! [X0,X1] :
( member(ordered_pair(not_homomorphism1(X0,null_class,X1),not_homomorphism2(X0,null_class,X1)),null_class)
| ~ operation(X1)
| ~ compatible(X0,null_class,X1)
| homomorphism(X0,null_class,X1)
| ~ operation(null_class) ),
inference(superposition,[],[f90,f4180]) ).
fof(f4270,plain,
! [X0,X1] :
( ~ subclass(range_of(X0),null_class)
| compatible(X0,X1,null_class)
| domain_of(X0) != domain_of(domain_of(X1))
| ~ function(X0) ),
inference(forward_demodulation,[],[f4252,f4180]) ).
fof(f4252,plain,
! [X0,X1] :
( ~ subclass(range_of(X0),domain_of(null_class))
| compatible(X0,X1,null_class)
| domain_of(X0) != domain_of(domain_of(X1))
| ~ function(X0) ),
inference(superposition,[],[f85,f4180]) ).
fof(f4180,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f4164,f66]) ).
fof(f4242,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f4175,f3484]) ).
fof(f4240,plain,
! [X0] :
( ~ subclass(X0,domain_of(null_class))
| domain_of(null_class) = X0 ),
inference(resolution,[],[f4175,f7]) ).
fof(f4175,plain,
! [X0] : subclass(domain_of(null_class),X0),
inference(resolution,[],[f4164,f2]) ).
fof(f4212,plain,
! [X0] : ~ member(X0,null_class),
inference(subsumption_resolution,[],[f4211,f4164]) ).
fof(f4211,plain,
! [X0] :
( ~ member(X0,null_class)
| member(X0,domain_of(null_class)) ),
inference(superposition,[],[f923,f4168]) ).
fof(f4168,plain,
null_class = cantor(null_class),
inference(resolution,[],[f4164,f950]) ).
fof(f4205,plain,
( cross_product(universal_class,universal_class) = subset_relation
| ~ function(subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),identity_relation) ),
inference(resolution,[],[f208,f2984]) ).
fof(f4204,plain,
( cross_product(universal_class,universal_class) = inverse(subset_relation)
| ~ function(inverse(subset_relation))
| ~ subclass(cross_product(universal_class,universal_class),identity_relation) ),
inference(resolution,[],[f208,f2983]) ).
fof(f208,plain,
! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ),
inference(resolution,[],[f7,f62]) ).
fof(f4178,plain,
~ inductive(domain_of(null_class)),
inference(resolution,[],[f4164,f47]) ).
fof(f4166,plain,
~ inductive(cantor(null_class)),
inference(resolution,[],[f4164,f926]) ).
fof(f4197,plain,
! [X0,X1] :
( ~ subclass(X0,domain_of(null_class))
| subclass(X0,X1) ),
inference(resolution,[],[f4164,f160]) ).
fof(f4196,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(resolution,[],[f4164,f697]) ).
fof(f4195,plain,
~ subclass(universal_class,complement(complement(domain_of(null_class)))),
inference(resolution,[],[f4164,f787]) ).
fof(f4194,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(resolution,[],[f4164,f161]) ).
fof(f4193,plain,
~ subclass(universal_class,complement(complement(domain_of(null_class)))),
inference(resolution,[],[f4164,f471]) ).
fof(f4192,plain,
! [X0] : null_class = intersection(X0,domain_of(null_class)),
inference(resolution,[],[f4164,f132]) ).
fof(f4191,plain,
! [X0] :
( ~ subclass(X0,domain_of(null_class))
| null_class = X0 ),
inference(resolution,[],[f4164,f159]) ).
fof(f4200,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f208,f210,f211,f215,f216,f218,f219,f221,f212,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f318,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f420,f421,f423,f424,f425,f194,f26,f442,f443,f444,f445,f446,f447,f448,f449,f450,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f526,f527,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f554,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f690,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f747,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f920,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f1514,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1658,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1653,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3109,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f956,f2428,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3523,f3530,f3531,f3532,f3533,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3825,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3843,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3935,f3922,f3936,f3939,f3944,f3947,f3921,f3953,f3945,f3957,f3948,f3959,f3961,f3962,f3938,f3964,f3967,f3971,f3973,f3990,f3991,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f4015,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4077,f4063,f4078,f4081,f4084,f4087,f4089,f4091,f4062,f4097,f4080,f4102,f4103,f4122,f4123,f4131,f4134,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4152,f4154,f4161,f4163,f4164,f4166,f4167,f4168,f4170,f4172,f4173,f4174,f4175,f4176,f4178,f4179,f4180,f4181,f4186,f4198,f4187,f4188,f4189,f4199,f4190]) ).
fof(f4190,plain,
! [X0] :
( ~ subclass(universal_class,domain_of(null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f4164,f165]) ).
fof(f4199,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f208,f210,f211,f215,f216,f218,f219,f221,f212,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f318,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f420,f421,f423,f424,f425,f194,f26,f442,f443,f444,f445,f446,f447,f448,f449,f450,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f526,f527,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f554,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f690,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f747,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f920,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f1514,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1658,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1653,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3109,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f956,f2428,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3523,f3530,f3531,f3532,f3533,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3825,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3843,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3935,f3922,f3936,f3939,f3944,f3947,f3921,f3953,f3945,f3957,f3948,f3959,f3961,f3962,f3938,f3964,f3967,f3971,f3973,f3990,f3991,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f4015,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4077,f4063,f4078,f4081,f4084,f4087,f4089,f4091,f4062,f4097,f4080,f4102,f4103,f4122,f4123,f4131,f4134,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4152,f4154,f4161,f4163,f4164,f4166,f4167,f4168,f4170,f4172,f4173,f4174,f4175,f4176,f4178,f4179,f4180,f4181,f4186,f4198,f4187,f4188,f4189]) ).
fof(f4189,plain,
! [X0] :
( ~ subclass(universal_class,domain_of(null_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f4164,f164]) ).
fof(f4188,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(resolution,[],[f4164,f162]) ).
fof(f4187,plain,
! [X0,X1] : subclass(intersection(X0,domain_of(null_class)),X1),
inference(resolution,[],[f4164,f133]) ).
fof(f4198,plain,
null_class = domain_of(null_class),
inference(global_subsumption,[],[f27,f74,f115,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f126,f22,f134,f130,f129,f131,f32,f35,f38,f53,f55,f63,f76,f135,f157,f1,f163,f162,f171,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f208,f210,f211,f215,f216,f218,f219,f221,f212,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f283,f284,f290,f282,f68,f99,f100,f318,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f174,f25,f420,f421,f423,f424,f425,f194,f26,f442,f443,f444,f445,f446,f447,f448,f449,f450,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f499,f500,f497,f495,f503,f507,f509,f506,f176,f512,f177,f516,f281,f29,f526,f527,f528,f530,f533,f534,f535,f538,f539,f540,f542,f426,f547,f548,f549,f49,f65,f554,f101,f102,f121,f555,f556,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f665,f678,f679,f668,f669,f672,f675,f676,f626,f657,f13,f690,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f720,f721,f725,f726,f713,f714,f23,f747,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f30,f766,f770,f659,f706,f698,f782,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f920,f921,f922,f925,f928,f929,f930,f931,f926,f923,f946,f951,f953,f949,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f974,f975,f958,f962,f970,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1151,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381,f1390,f1393,f1395,f508,f718,f1409,f1410,f1413,f719,f1416,f1417,f1420,f767,f1422,f1438,f775,f942,f1479,f1480,f1481,f31,f1484,f1485,f1486,f1497,f1498,f1499,f1492,f1493,f1494,f1495,f944,f945,f955,f1508,f1509,f1510,f1511,f116,f1514,f787,f1536,f1537,f1540,f1542,f1544,f1545,f1546,f1547,f1548,f1549,f1550,f1551,f1552,f1553,f1565,f1538,f20,f1582,f1583,f1539,f1541,f1543,f973,f1600,f1601,f1602,f1358,f1605,f1606,f1607,f1608,f1611,f1612,f1614,f1645,f1646,f1647,f1648,f1651,f1652,f1654,f1655,f1656,f1657,f1658,f1661,f1664,f1665,f1666,f1667,f1670,f1671,f1672,f1673,f1663,f1677,f1678,f1660,f1679,f1683,f1684,f1685,f1686,f1687,f1688,f1689,f1690,f1691,f1692,f1662,f1694,f1695,f1696,f1697,f1698,f1701,f1702,f1704,f1705,f1707,f1693,f1715,f1717,f1720,f1721,f1713,f1703,f1653,f1609,f1564,f1559,f1507,f1483,f1455,f1454,f1453,f1452,f1450,f1449,f1448,f1425,f1389,f1384,f1364,f1346,f1338,f1324,f1716,f1714,f64,f33,f1778,f1779,f1146,f1802,f36,f1844,f1845,f1706,f557,f58,f1888,f1889,f1890,f1891,f1892,f1893,f1894,f580,f1896,f1897,f1682,f1924,f180,f1931,f1929,f1930,f1933,f2004,f2005,f2007,f2008,f2010,f2011,f2012,f2013,f2014,f2017,f2018,f2019,f2020,f2021,f2022,f2023,f97,f2046,f2047,f2006,f2059,f2060,f2061,f2062,f2064,f2067,f2068,f2070,f2065,f2066,f2080,f2076,f2079,f117,f2095,f2096,f2097,f85,f2184,f2185,f2188,f2187,f81,f2195,f2198,f2199,f59,f2207,f2209,f2210,f2211,f2213,f2214,f2215,f2216,f2217,f2218,f2219,f2220,f2221,f2077,f90,f2299,f2301,f2302,f2303,f2304,f108,f2347,f2348,f34,f2388,f2389,f2058,f2429,f2433,f2436,f2440,f37,f2447,f2448,f1925,f1711,f89,f2459,f2467,f2461,f2462,f2463,f2464,f2465,f2466,f2063,f664,f2484,f2485,f2486,f2487,f2488,f2489,f2512,f2513,f2492,f2493,f2494,f2495,f2498,f2500,f2501,f2503,f2504,f2514,f2506,f2507,f2508,f674,f91,f680,f807,f2538,f2539,f2540,f2541,f2544,f2545,f2546,f2536,f2549,f2550,f2551,f2552,f2555,f2556,f2557,f858,f2563,f2564,f2565,f2566,f2569,f2570,f2571,f2561,f2574,f2575,f2576,f2577,f2580,f2581,f2582,f976,f127,f2585,f2586,f2587,f2620,f2589,f2590,f2591,f2592,f2593,f2596,f2600,f2601,f2602,f2606,f2607,f2635,f2636,f2637,f2641,f132,f2745,f2746,f2747,f2782,f2749,f2750,f2751,f2752,f2753,f2756,f2761,f2762,f2763,f2767,f2768,f2797,f2798,f2799,f2803,f2804,f150,f2847,f2850,f2854,f2855,f2856,f2857,f160,f2955,f2956,f2957,f2958,f2959,f2960,f2961,f2962,f2963,f2966,f2971,f2972,f2973,f2977,f2978,f166,f3012,f167,f3033,f3036,f2982,f3066,f3080,f3104,f3105,f316,f3108,f3109,f3114,f3115,f3122,f319,f3227,f3228,f496,f3279,f3282,f3283,f3284,f3287,f3288,f3289,f3290,f3291,f3292,f3293,f3294,f3295,f3296,f3297,f3118,f3127,f3468,f3469,f3470,f3471,f3473,f2976,f2975,f2970,f2968,f2965,f3474,f2851,f2849,f2848,f3475,f2766,f2765,f2760,f2758,f2755,f3477,f2605,f2604,f2599,f2598,f2595,f2578,f2567,f2553,f2542,f637,f293,f1928,f1926,f1424,f1155,f1070,f956,f2428,f2300,f2084,f413,f3077,f153,f3499,f3500,f3501,f3502,f2984,f3523,f3530,f3531,f3532,f3533,f541,f3543,f3544,f3545,f3546,f3547,f3548,f3549,f3577,f3578,f3552,f3553,f3554,f3555,f3556,f3559,f3561,f3562,f3564,f3565,f3579,f3567,f3568,f3569,f3570,f3571,f3574,f3575,f3580,f3484,f3588,f2983,f3592,f3599,f3600,f3601,f3602,f3603,f3604,f924,f3689,f3690,f3691,f3692,f3693,f3694,f3695,f1052,f1659,f3825,f3826,f3827,f3828,f3829,f3830,f3831,f3832,f3835,f3836,f3837,f3838,f3839,f3841,f3842,f3843,f3844,f3845,f3846,f3847,f2082,f128,f3886,f3887,f3888,f3924,f3890,f3891,f3892,f3893,f3894,f3895,f3897,f3898,f3900,f3901,f3902,f3903,f3904,f3906,f3907,f3908,f3909,f3911,f3927,f3913,f3928,f3929,f3933,f3934,f3935,f3922,f3936,f3939,f3944,f3947,f3921,f3953,f3945,f3957,f3948,f3959,f3961,f3962,f3938,f3964,f3967,f3971,f3973,f3990,f3991,f3998,f3999,f4000,f4001,f4002,f4003,f4005,f4006,f4007,f4008,f4009,f3920,f4012,f4015,f3942,f4016,f4019,f3956,f4021,f133,f4026,f4027,f4028,f4065,f4030,f4031,f4032,f4033,f4034,f4035,f4037,f4038,f4040,f4041,f4042,f4043,f4044,f4046,f4047,f4048,f4049,f4051,f4068,f4053,f4069,f4070,f4074,f4076,f4077,f4063,f4078,f4081,f4084,f4087,f4089,f4091,f4062,f4097,f4080,f4102,f4103,f4122,f4123,f4131,f4134,f4138,f4061,f4144,f4147,f3963,f4149,f4151,f4018,f4152,f4154,f4161,f4163,f4164,f4166,f4167,f4168,f4170,f4172,f4173,f4174,f4175,f4176,f4178,f4179,f4180,f4181,f4186]) ).
fof(f4186,plain,
( null_class = domain_of(null_class)
| ~ member(domain_of(null_class),universal_class) ),
inference(resolution,[],[f4164,f70]) ).
fof(f4181,plain,
! [X0] : null_class = intersection(domain_of(null_class),X0),
inference(resolution,[],[f4164,f127]) ).
fof(f4179,plain,
~ subclass(universal_class,domain_of(null_class)),
inference(resolution,[],[f4164,f163]) ).
fof(f4176,plain,
! [X0,X1] : subclass(intersection(domain_of(null_class),X0),X1),
inference(resolution,[],[f4164,f128]) ).
fof(f4174,plain,
~ subclass(universal_class,cantor(null_class)),
inference(resolution,[],[f4164,f955]) ).
fof(f4173,plain,
~ subclass(universal_class,cantor(null_class)),
inference(resolution,[],[f4164,f954]) ).
fof(f4172,plain,
! [X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,null_class,X0)
| homomorphism(X1,null_class,X0)
| ~ operation(null_class) ),
inference(resolution,[],[f4164,f90]) ).
fof(f4170,plain,
~ subclass(universal_class,cantor(null_class)),
inference(resolution,[],[f4164,f952]) ).
fof(f4167,plain,
~ subclass(universal_class,cantor(null_class)),
inference(resolution,[],[f4164,f949]) ).
fof(f4164,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f4162]) ).
fof(f4162,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f30,f4018]) ).
fof(f4154,plain,
! [X2,X0,X1] :
( ~ member(X2,null_class)
| member(X2,cross_product(X0,X1)) ),
inference(superposition,[],[f496,f4018]) ).
fof(f4018,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(resolution,[],[f3942,f3484]) ).
fof(f4149,plain,
! [X0] :
( ~ subclass(range_of(X0),cantor(inverse(X0)))
| range_of(X0) = cantor(inverse(X0)) ),
inference(resolution,[],[f3963,f7]) ).
fof(f3963,plain,
! [X0] : subclass(cantor(inverse(X0)),range_of(X0)),
inference(superposition,[],[f3948,f39]) ).
fof(f4147,plain,
! [X0,X1] : subclass(restrict(identity_relation,X0,X1),inverse(subset_relation)),
inference(superposition,[],[f4061,f29]) ).
fof(f4144,plain,
! [X0] :
( ~ subclass(inverse(subset_relation),intersection(X0,identity_relation))
| inverse(subset_relation) = intersection(X0,identity_relation) ),
inference(resolution,[],[f4061,f7]) ).
fof(f4061,plain,
! [X0] : subclass(intersection(X0,identity_relation),inverse(subset_relation)),
inference(duplicate_literal_removal,[],[f4025]) ).
fof(f4025,plain,
! [X0] :
( subclass(intersection(X0,identity_relation),inverse(subset_relation))
| subclass(intersection(X0,identity_relation),inverse(subset_relation)) ),
inference(resolution,[],[f133,f146]) ).
fof(f4138,plain,
complement(null_class) = union(universal_class,universal_class),
inference(superposition,[],[f796,f4080]) ).
fof(f4131,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(superposition,[],[f29,f4080]) ).
fof(f4122,plain,
! [X0] : symmetric_difference(X0,null_class) = intersection(complement(null_class),union(X0,null_class)),
inference(superposition,[],[f1614,f4080]) ).
fof(f4103,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0) ),
inference(superposition,[],[f21,f4080]) ).
fof(f4102,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(superposition,[],[f4080,f29]) ).
fof(f4080,plain,
! [X0] : null_class = intersection(X0,null_class),
inference(resolution,[],[f4063,f3484]) ).
fof(f4062,plain,
! [X0] : subclass(intersection(X0,identity_relation),subset_relation),
inference(duplicate_literal_removal,[],[f4024]) ).
fof(f4024,plain,
! [X0] :
( subclass(intersection(X0,identity_relation),subset_relation)
| subclass(intersection(X0,identity_relation),subset_relation) ),
inference(resolution,[],[f133,f135]) ).
fof(f4087,plain,
subclass(subset_relation,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),
inference(superposition,[],[f4063,f1933]) ).
fof(f4084,plain,
! [X2,X0,X1] : subclass(restrict(X0,X1,X2),cross_product(X1,X2)),
inference(superposition,[],[f4063,f28]) ).
fof(f4063,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literal_removal,[],[f4023]) ).
fof(f4023,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[],[f133,f3]) ).
fof(f4076,plain,
! [X0,X1] :
( subclass(cantor(X0),X1)
| member(not_subclass_element(cantor(X0),X1),diagonalise(compose(inverse(element_relation),X0))) ),
inference(forward_demodulation,[],[f4059,f77]) ).
fof(f4059,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(X0),X1),diagonalise(compose(inverse(element_relation),X0)))
| subclass(intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))),X1) ),
inference(superposition,[],[f133,f77]) ).
fof(f4074,plain,
! [X2,X0,X1] :
( subclass(symmetric_difference(X0,X1),X2)
| member(not_subclass_element(symmetric_difference(X0,X1),X2),union(X0,X1)) ),
inference(forward_demodulation,[],[f4057,f1614]) ).
fof(f4057,plain,
! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,X1),X2),union(X0,X1))
| subclass(intersection(complement(intersection(X0,X1)),union(X0,X1)),X2) ),
inference(superposition,[],[f133,f1614]) ).
fof(f4070,plain,
! [X0] :
( subclass(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),X0)
| member(not_subclass_element(subset_relation,X0),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(forward_demodulation,[],[f4055,f29]) ).
fof(f4055,plain,
! [X0] :
( member(not_subclass_element(subset_relation,X0),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| subclass(intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),X0) ),
inference(superposition,[],[f133,f1933]) ).
fof(f4069,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X2,X0,X1),X3)
| member(not_subclass_element(restrict(X2,X0,X1),X3),X2) ),
inference(forward_demodulation,[],[f4054,f29]) ).
fof(f4054,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X2,X0,X1),X3),X2)
| subclass(intersection(cross_product(X0,X1),X2),X3) ),
inference(superposition,[],[f133,f29]) ).
fof(f4053,plain,
! [X0,X1] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(singleton(X0),X0),X1)
| singleton(X0) = null_class ),
inference(superposition,[],[f133,f767]) ).
fof(f4068,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X0,X1,X2),X3)
| member(not_subclass_element(restrict(X0,X1,X2),X3),cross_product(X1,X2)) ),
inference(forward_demodulation,[],[f4052,f28]) ).
fof(f4052,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),cross_product(X1,X2))
| subclass(intersection(X0,cross_product(X1,X2)),X3) ),
inference(superposition,[],[f133,f28]) ).
fof(f4051,plain,
! [X0,X1] :
( member(not_subclass_element(null_class,X1),regular(X0))
| subclass(intersection(X0,regular(X0)),X1)
| null_class = X0 ),
inference(superposition,[],[f133,f67]) ).
fof(f4049,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,cantor(X1)),X2)
| member(not_subclass_element(intersection(X0,cantor(X1)),X2),domain_of(X1)) ),
inference(resolution,[],[f133,f923]) ).
fof(f4048,plain,
! [X0,X1] :
( subclass(intersection(X0,subset_relation),X1)
| not_subclass_element(intersection(X0,subset_relation),X1) = ordered_pair(first(not_subclass_element(intersection(X0,subset_relation),X1)),second(not_subclass_element(intersection(X0,subset_relation),X1))) ),
inference(resolution,[],[f133,f2058]) ).
fof(f4047,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),X2)
| ~ subclass(subset_relation,X2) ),
inference(resolution,[],[f133,f170]) ).
fof(f4046,plain,
! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),universal_class) ),
inference(resolution,[],[f133,f1143]) ).
fof(f4044,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,image(X1,image(X2,singleton(X3)))),X4)
| member(ordered_pair(X3,not_subclass_element(intersection(X0,image(X1,image(X2,singleton(X3)))),X4)),compose(X1,X2))
| ~ member(ordered_pair(X3,not_subclass_element(intersection(X0,image(X1,image(X2,singleton(X3)))),X4)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f133,f59]) ).
fof(f4043,plain,
! [X0,X1] :
( subclass(intersection(X0,image(element_relation,null_class)),X1)
| ~ member(not_subclass_element(intersection(X0,image(element_relation,null_class)),X1),power_class(universal_class)) ),
inference(resolution,[],[f133,f621]) ).
fof(f4042,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,image(element_relation,complement(X1))),X2)
| ~ member(not_subclass_element(intersection(X0,image(element_relation,complement(X1))),X2),power_class(X1)) ),
inference(resolution,[],[f133,f152]) ).
fof(f4041,plain,
! [X0,X1] :
( subclass(intersection(X0,inverse(subset_relation)),X1)
| ~ member(not_subclass_element(intersection(X0,inverse(subset_relation)),X1),subset_relation)
| member(not_subclass_element(intersection(X0,inverse(subset_relation)),X1),identity_relation) ),
inference(resolution,[],[f133,f757]) ).
fof(f4040,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,domain_of(intersection(X1,identity_relation))),X2)
| ~ member(not_subclass_element(intersection(X0,domain_of(intersection(X1,identity_relation))),X2),diagonalise(X1)) ),
inference(resolution,[],[f133,f155]) ).
fof(f4038,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,null_class),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X2)
| null_class = X2 ),
inference(resolution,[],[f133,f291]) ).
fof(f4037,plain,
! [X0,X1] :
( subclass(intersection(X0,null_class),X1)
| ~ member(not_subclass_element(intersection(X0,null_class),X1),universal_class) ),
inference(resolution,[],[f133,f612]) ).
fof(f4035,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,restrict(X1,X2,X3)),X4)
| member(not_subclass_element(intersection(X0,restrict(X1,X2,X3)),X4),X1) ),
inference(resolution,[],[f133,f495]) ).
fof(f4034,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,restrict(X1,X2,X3)),X4)
| member(not_subclass_element(intersection(X0,restrict(X1,X2,X3)),X4),cross_product(X2,X3)) ),
inference(resolution,[],[f133,f496]) ).
fof(f4033,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,symmetric_difference(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,symmetric_difference(X1,X2)),X3),union(X1,X2)) ),
inference(resolution,[],[f133,f1660]) ).
fof(f4032,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ),
inference(resolution,[],[f133,f24]) ).
fof(f4031,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ),
inference(resolution,[],[f133,f21]) ).
fof(f4030,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ),
inference(resolution,[],[f133,f22]) ).
fof(f4065,plain,
! [X2,X3,X0,X1] :
( not_subclass_element(restrict(X0,X1,X2),X3) = ordered_pair(first(not_subclass_element(restrict(X0,X1,X2),X3)),second(not_subclass_element(restrict(X0,X1,X2),X3)))
| subclass(restrict(X0,X1,X2),X3) ),
inference(forward_demodulation,[],[f4064,f28]) ).
fof(f4064,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X0,X1,X2),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = ordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))) ),
inference(forward_demodulation,[],[f4029,f28]) ).
fof(f4029,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = ordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))) ),
inference(resolution,[],[f133,f17]) ).
fof(f4028,plain,
! [X2,X0,X1] :
( subclass(intersection(X0,singleton(X1)),X2)
| not_subclass_element(intersection(X0,singleton(X1)),X2) = X1 ),
inference(resolution,[],[f133,f650]) ).
fof(f4027,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 ),
inference(resolution,[],[f133,f8]) ).
fof(f4026,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ),
inference(resolution,[],[f133,f1]) ).
fof(f133,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f22,f2]) ).
fof(f4021,plain,
! [X0,X1] :
( ~ subclass(subset_relation,restrict(identity_relation,X0,X1))
| subset_relation = restrict(identity_relation,X0,X1) ),
inference(resolution,[],[f3956,f7]) ).
fof(f3956,plain,
! [X0,X1] : subclass(restrict(identity_relation,X0,X1),subset_relation),
inference(superposition,[],[f3921,f28]) ).
fof(f4019,plain,
! [X0,X1] :
( omega = restrict(omega,X0,X1)
| ~ inductive(restrict(omega,X0,X1)) ),
inference(resolution,[],[f3942,f214]) ).
fof(f4016,plain,
! [X2,X0,X1] :
( ~ subclass(X0,restrict(X0,X1,X2))
| restrict(X0,X1,X2) = X0 ),
inference(resolution,[],[f3942,f7]) ).
fof(f3942,plain,
! [X2,X0,X1] : subclass(restrict(X0,X1,X2),X0),
inference(superposition,[],[f3922,f28]) ).
fof(f4012,plain,
! [X0] :
( ~ subclass(inverse(subset_relation),intersection(identity_relation,X0))
| inverse(subset_relation) = intersection(identity_relation,X0) ),
inference(resolution,[],[f3920,f7]) ).
fof(f3920,plain,
! [X0] : subclass(intersection(identity_relation,X0),inverse(subset_relation)),
inference(duplicate_literal_removal,[],[f3885]) ).
fof(f3885,plain,
! [X0] :
( subclass(intersection(identity_relation,X0),inverse(subset_relation))
| subclass(intersection(identity_relation,X0),inverse(subset_relation)) ),
inference(resolution,[],[f128,f146]) ).
fof(f4009,plain,
( ~ inductive(cantor(null_class))
| ~ member(null_class,diagonalise(null_class)) ),
inference(superposition,[],[f941,f3938]) ).
fof(f4008,plain,
( ~ inductive(cantor(null_class))
| ~ inductive(diagonalise(null_class)) ),
inference(superposition,[],[f940,f3938]) ).
fof(f4007,plain,
( ~ subclass(universal_class,domain_of(null_class))
| ~ member(omega,diagonalise(null_class)) ),
inference(superposition,[],[f580,f3938]) ).
fof(f4006,plain,
( ~ inductive(domain_of(null_class))
| ~ member(null_class,diagonalise(null_class)) ),
inference(superposition,[],[f579,f3938]) ).
fof(f4005,plain,
( ~ inductive(domain_of(null_class))
| ~ inductive(diagonalise(null_class)) ),
inference(superposition,[],[f408,f3938]) ).
fof(f4003,plain,
( ~ member(omega,domain_of(null_class))
| ~ subclass(universal_class,diagonalise(null_class)) ),
inference(superposition,[],[f180,f3938]) ).
fof(f4002,plain,
! [X0] :
( ~ member(X0,domain_of(null_class))
| ~ member(X0,diagonalise(null_class)) ),
inference(superposition,[],[f155,f3938]) ).
fof(f4001,plain,
( ~ member(null_class,domain_of(null_class))
| ~ inductive(diagonalise(null_class)) ),
inference(superposition,[],[f154,f3938]) ).
fof(f4000,plain,
power_class(domain_of(null_class)) = complement(image(element_relation,diagonalise(null_class))),
inference(superposition,[],[f153,f3938]) ).
fof(f3999,plain,
complement(domain_of(null_class)) = diagonalise(null_class),
inference(superposition,[],[f76,f3938]) ).
fof(f3998,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(superposition,[],[f28,f3938]) ).
fof(f3990,plain,
! [X0] : symmetric_difference(null_class,X0) = intersection(complement(null_class),union(null_class,X0)),
inference(superposition,[],[f1614,f3938]) ).
fof(f3973,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0) ),
inference(superposition,[],[f22,f3938]) ).
fof(f3971,plain,
complement(null_class) = union(universal_class,universal_class),
inference(superposition,[],[f796,f3938]) ).
fof(f3964,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(superposition,[],[f3938,f28]) ).
fof(f3938,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f3922,f3484]) ).
fof(f3948,plain,
! [X0] : subclass(cantor(X0),domain_of(X0)),
inference(superposition,[],[f3922,f77]) ).
fof(f3945,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(superposition,[],[f3922,f1933]) ).
fof(f3921,plain,
! [X0] : subclass(intersection(identity_relation,X0),subset_relation),
inference(duplicate_literal_removal,[],[f3884]) ).
fof(f3884,plain,
! [X0] :
( subclass(intersection(identity_relation,X0),subset_relation)
| subclass(intersection(identity_relation,X0),subset_relation) ),
inference(resolution,[],[f128,f135]) ).
fof(f3922,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f3883]) ).
fof(f3883,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f128,f3]) ).
fof(f3934,plain,
! [X0,X1] :
( subclass(cantor(X0),X1)
| member(not_subclass_element(cantor(X0),X1),domain_of(X0)) ),
inference(forward_demodulation,[],[f3918,f77]) ).
fof(f3918,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(X0),X1),domain_of(X0))
| subclass(intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))),X1) ),
inference(superposition,[],[f128,f77]) ).
fof(f3933,plain,
! [X2,X0,X1] :
( subclass(symmetric_difference(X0,X1),X2)
| member(not_subclass_element(symmetric_difference(X0,X1),X2),complement(intersection(X0,X1))) ),
inference(forward_demodulation,[],[f3917,f1614]) ).
fof(f3917,plain,
! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,X1),X2),complement(intersection(X0,X1)))
| subclass(intersection(complement(intersection(X0,X1)),union(X0,X1)),X2) ),
inference(superposition,[],[f128,f1614]) ).
fof(f3929,plain,
! [X0] :
( subclass(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),X0)
| member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[],[f3915,f29]) ).
fof(f3915,plain,
! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),X0) ),
inference(superposition,[],[f128,f1933]) ).
fof(f3928,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X2,X0,X1),X3)
| member(not_subclass_element(restrict(X2,X0,X1),X3),cross_product(X0,X1)) ),
inference(forward_demodulation,[],[f3914,f29]) ).
fof(f3914,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X2,X0,X1),X3),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),X2),X3) ),
inference(superposition,[],[f128,f29]) ).
fof(f3913,plain,
! [X0,X1] :
( member(not_subclass_element(null_class,X1),singleton(X0))
| subclass(intersection(singleton(X0),X0),X1)
| singleton(X0) = null_class ),
inference(superposition,[],[f128,f767]) ).
fof(f3927,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X0,X1,X2),X3)
| member(not_subclass_element(restrict(X0,X1,X2),X3),X0) ),
inference(forward_demodulation,[],[f3912,f28]) ).
fof(f3912,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(intersection(X0,cross_product(X1,X2)),X3) ),
inference(superposition,[],[f128,f28]) ).
fof(f3911,plain,
! [X0,X1] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(X0,regular(X0)),X1)
| null_class = X0 ),
inference(superposition,[],[f128,f67]) ).
fof(f3909,plain,
! [X2,X0,X1] :
( subclass(intersection(cantor(X0),X1),X2)
| member(not_subclass_element(intersection(cantor(X0),X1),X2),domain_of(X0)) ),
inference(resolution,[],[f128,f923]) ).
fof(f3908,plain,
! [X0,X1] :
( subclass(intersection(subset_relation,X0),X1)
| not_subclass_element(intersection(subset_relation,X0),X1) = ordered_pair(first(not_subclass_element(intersection(subset_relation,X0),X1)),second(not_subclass_element(intersection(subset_relation,X0),X1))) ),
inference(resolution,[],[f128,f2058]) ).
fof(f3907,plain,
! [X2,X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),X2)
| ~ subclass(subset_relation,X2) ),
inference(resolution,[],[f128,f170]) ).
fof(f3906,plain,
! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),universal_class) ),
inference(resolution,[],[f128,f1143]) ).
fof(f3904,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(image(X0,image(X1,singleton(X2))),X3),X4)
| member(ordered_pair(X2,not_subclass_element(intersection(image(X0,image(X1,singleton(X2))),X3),X4)),compose(X0,X1))
| ~ member(ordered_pair(X2,not_subclass_element(intersection(image(X0,image(X1,singleton(X2))),X3),X4)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f128,f59]) ).
fof(f3903,plain,
! [X0,X1] :
( subclass(intersection(image(element_relation,null_class),X0),X1)
| ~ member(not_subclass_element(intersection(image(element_relation,null_class),X0),X1),power_class(universal_class)) ),
inference(resolution,[],[f128,f621]) ).
fof(f3902,plain,
! [X2,X0,X1] :
( subclass(intersection(image(element_relation,complement(X0)),X1),X2)
| ~ member(not_subclass_element(intersection(image(element_relation,complement(X0)),X1),X2),power_class(X0)) ),
inference(resolution,[],[f128,f152]) ).
fof(f3901,plain,
! [X0,X1] :
( subclass(intersection(inverse(subset_relation),X0),X1)
| ~ member(not_subclass_element(intersection(inverse(subset_relation),X0),X1),subset_relation)
| member(not_subclass_element(intersection(inverse(subset_relation),X0),X1),identity_relation) ),
inference(resolution,[],[f128,f757]) ).
fof(f3900,plain,
! [X2,X0,X1] :
( subclass(intersection(domain_of(intersection(X0,identity_relation)),X1),X2)
| ~ member(not_subclass_element(intersection(domain_of(intersection(X0,identity_relation)),X1),X2),diagonalise(X0)) ),
inference(resolution,[],[f128,f155]) ).
fof(f3898,plain,
! [X2,X0,X1] :
( subclass(intersection(null_class,X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),X2)
| null_class = X2 ),
inference(resolution,[],[f128,f291]) ).
fof(f3897,plain,
! [X0,X1] :
( subclass(intersection(null_class,X0),X1)
| ~ member(not_subclass_element(intersection(null_class,X0),X1),universal_class) ),
inference(resolution,[],[f128,f612]) ).
fof(f3895,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(restrict(X0,X1,X2),X3),X4)
| member(not_subclass_element(intersection(restrict(X0,X1,X2),X3),X4),X0) ),
inference(resolution,[],[f128,f495]) ).
fof(f3894,plain,
! [X2,X3,X0,X1,X4] :
( subclass(intersection(restrict(X0,X1,X2),X3),X4)
| member(not_subclass_element(intersection(restrict(X0,X1,X2),X3),X4),cross_product(X1,X2)) ),
inference(resolution,[],[f128,f496]) ).
fof(f3893,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(symmetric_difference(X0,X1),X2),X3)
| member(not_subclass_element(intersection(symmetric_difference(X0,X1),X2),X3),union(X0,X1)) ),
inference(resolution,[],[f128,f1660]) ).
fof(f3892,plain,
! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ),
inference(resolution,[],[f128,f24]) ).
fof(f3891,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ),
inference(resolution,[],[f128,f21]) ).
fof(f3890,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ),
inference(resolution,[],[f128,f22]) ).
fof(f3924,plain,
! [X2,X3,X0,X1] :
( not_subclass_element(restrict(X2,X0,X1),X3) = ordered_pair(first(not_subclass_element(restrict(X2,X0,X1),X3)),second(not_subclass_element(restrict(X2,X0,X1),X3)))
| subclass(restrict(X2,X0,X1),X3) ),
inference(forward_demodulation,[],[f3923,f29]) ).
fof(f3923,plain,
! [X2,X3,X0,X1] :
( subclass(restrict(X2,X0,X1),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = ordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))) ),
inference(forward_demodulation,[],[f3889,f29]) ).
fof(f3889,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = ordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))) ),
inference(resolution,[],[f128,f17]) ).
fof(f3888,plain,
! [X2,X0,X1] :
( subclass(intersection(singleton(X0),X1),X2)
| not_subclass_element(intersection(singleton(X0),X1),X2) = X0 ),
inference(resolution,[],[f128,f650]) ).
fof(f3887,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 ),
inference(resolution,[],[f128,f8]) ).
fof(f3886,plain,
! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ),
inference(resolution,[],[f128,f1]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f2082,plain,
! [X0] :
( member(X0,universal_class)
| ~ subclass(universal_class,complement(complement(identity_relation))) ),
inference(resolution,[],[f2076,f787]) ).
fof(f3847,plain,
! [X0,X1] :
( member(X1,union(X0,universal_class))
| ~ member(X1,symmetric_difference(complement(X0),null_class)) ),
inference(superposition,[],[f1659,f615]) ).
fof(f3846,plain,
! [X0] :
( member(X0,union(universal_class,universal_class))
| ~ member(X0,symmetric_difference(null_class,null_class)) ),
inference(superposition,[],[f1659,f796]) ).
fof(f3845,plain,
! [X0,X1] :
( member(X1,union(universal_class,X0))
| ~ member(X1,symmetric_difference(null_class,complement(X0))) ),
inference(superposition,[],[f1659,f614]) ).
fof(f3844,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,symmetric_difference(complement(X0),complement(X1))) ),
inference(superposition,[],[f1659,f26]) ).
fof(f3842,plain,
! [X0,X1] :
( member(X1,complement(cantor(X0)))
| ~ member(X1,symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))) ),
inference(superposition,[],[f1659,f77]) ).
fof(f3841,plain,
! [X2,X0,X1] :
( member(X2,complement(symmetric_difference(X0,X1)))
| ~ member(X2,symmetric_difference(complement(intersection(X0,X1)),union(X0,X1))) ),
inference(superposition,[],[f1659,f1614]) ).
fof(f3839,plain,
! [X0] :
( member(X0,complement(subset_relation))
| ~ member(X0,symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(superposition,[],[f1659,f1933]) ).
fof(f3838,plain,
! [X2,X3,X0,X1] :
( member(X3,complement(restrict(X2,X0,X1)))
| ~ member(X3,symmetric_difference(cross_product(X0,X1),X2)) ),
inference(superposition,[],[f1659,f29]) ).
fof(f3837,plain,
! [X0,X1] :
( member(X1,complement(null_class))
| ~ member(X1,symmetric_difference(singleton(X0),X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f1659,f767]) ).
fof(f3836,plain,
! [X2,X3,X0,X1] :
( member(X3,complement(restrict(X0,X1,X2)))
| ~ member(X3,symmetric_difference(X0,cross_product(X1,X2))) ),
inference(superposition,[],[f1659,f28]) ).
fof(f3835,plain,
! [X0,X1] :
( member(X1,complement(null_class))
| ~ member(X1,symmetric_difference(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f1659,f67]) ).
fof(f3832,plain,
! [X0,X1] :
( ~ member(regular(complement(complement(intersection(X0,X1)))),symmetric_difference(X0,X1))
| null_class = complement(complement(intersection(X0,X1))) ),
inference(resolution,[],[f1659,f120]) ).
fof(f3831,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),symmetric_difference(X2,X3))
| ~ subclass(universal_class,complement(complement(intersection(X2,X3)))) ),
inference(resolution,[],[f1659,f698]) ).
fof(f3830,plain,
! [X2,X0,X1] :
( ~ member(singleton(X0),symmetric_difference(X1,X2))
| ~ subclass(universal_class,complement(complement(intersection(X1,X2)))) ),
inference(resolution,[],[f1659,f175]) ).
fof(f3829,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),symmetric_difference(X2,X3))
| ~ subclass(universal_class,complement(complement(intersection(X2,X3)))) ),
inference(resolution,[],[f1659,f263]) ).
fof(f3828,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(complement(complement(intersection(X0,X1))),X2),symmetric_difference(X0,X1))
| subclass(complement(complement(intersection(X0,X1))),X2) ),
inference(resolution,[],[f1659,f121]) ).
fof(f3827,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,complement(intersection(X1,X2))),symmetric_difference(X1,X2))
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[],[f1659,f3]) ).
fof(f3826,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,symmetric_difference(X1,X2))
| ~ subclass(complement(intersection(X1,X2)),X3)
| member(X0,X3) ),
inference(resolution,[],[f1659,f1]) ).
fof(f1659,plain,
! [X2,X0,X1] :
( member(X2,complement(intersection(X0,X1)))
| ~ member(X2,symmetric_difference(X0,X1)) ),
inference(superposition,[],[f21,f1614]) ).
fof(f1052,plain,
! [X0,X1] :
( null_class = ordered_pair(first(null_class),second(null_class))
| ~ inductive(cross_product(X0,X1)) ),
inference(resolution,[],[f17,f47]) ).
fof(f3695,plain,
! [X0] :
( ~ member(regular(complement(diagonalise(compose(inverse(element_relation),X0)))),cantor(X0))
| null_class = complement(diagonalise(compose(inverse(element_relation),X0))) ),
inference(resolution,[],[f924,f120]) ).
fof(f3694,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),cantor(X2))
| ~ subclass(universal_class,complement(diagonalise(compose(inverse(element_relation),X2)))) ),
inference(resolution,[],[f924,f698]) ).
fof(f3693,plain,
! [X0,X1] :
( ~ member(singleton(X0),cantor(X1))
| ~ subclass(universal_class,complement(diagonalise(compose(inverse(element_relation),X1)))) ),
inference(resolution,[],[f924,f175]) ).
fof(f3692,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),cantor(X2))
| ~ subclass(universal_class,complement(diagonalise(compose(inverse(element_relation),X2)))) ),
inference(resolution,[],[f924,f263]) ).
fof(f3691,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(diagonalise(compose(inverse(element_relation),X0))),X1),cantor(X0))
| subclass(complement(diagonalise(compose(inverse(element_relation),X0))),X1) ),
inference(resolution,[],[f924,f121]) ).
fof(f3690,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,diagonalise(compose(inverse(element_relation),X1))),cantor(X1))
| subclass(X0,diagonalise(compose(inverse(element_relation),X1))) ),
inference(resolution,[],[f924,f3]) ).
fof(f3689,plain,
! [X2,X0,X1] :
( ~ member(X0,cantor(X1))
| ~ subclass(diagonalise(compose(inverse(element_relation),X1)),X2)
| member(X0,X2) ),
inference(resolution,[],[f924,f1]) ).
fof(f924,plain,
! [X0,X1] :
( member(X1,diagonalise(compose(inverse(element_relation),X0)))
| ~ member(X1,cantor(X0)) ),
inference(superposition,[],[f22,f77]) ).
fof(f3604,plain,
( ~ subclass(complement(inverse(subset_relation)),identity_relation)
| null_class = complement(inverse(subset_relation)) ),
inference(resolution,[],[f2983,f600]) ).
fof(f3601,plain,
! [X0] :
( ~ subclass(singleton(X0),identity_relation)
| member(X0,inverse(subset_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f2983,f168]) ).
fof(f3600,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X1),identity_relation)
| member(X0,inverse(subset_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f2983,f166]) ).
fof(f3599,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X1),identity_relation)
| member(X1,inverse(subset_relation))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f2983,f167]) ).
fof(f3592,plain,
! [X0] :
( ~ subclass(X0,identity_relation)
| ~ subclass(inverse(subset_relation),X0)
| inverse(subset_relation) = X0 ),
inference(resolution,[],[f2983,f7]) ).
fof(f2983,plain,
! [X0] :
( subclass(X0,inverse(subset_relation))
| ~ subclass(X0,identity_relation) ),
inference(duplicate_literal_removal,[],[f2951]) ).
fof(f2951,plain,
! [X0] :
( ~ subclass(X0,identity_relation)
| subclass(X0,inverse(subset_relation))
| subclass(X0,inverse(subset_relation)) ),
inference(resolution,[],[f160,f146]) ).
fof(f3484,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f3077,f7]) ).
fof(f3580,plain,
! [X2,X0,X1] :
( subclass(diagonalise(cross_product(X0,X1)),X2)
| ~ subclass(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f3576,f541]) ).
fof(f3576,plain,
! [X2,X0,X1] :
( ~ subclass(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1)))
| subclass(complement(domain_of(restrict(identity_relation,X0,X1))),X2) ),
inference(superposition,[],[f2982,f541]) ).
fof(f3575,plain,
! [X0,X1] :
( ~ inductive(intersection(diagonalise(cross_product(X0,X1)),null_class))
| ~ inductive(union(domain_of(restrict(identity_relation,X0,X1)),universal_class)) ),
inference(superposition,[],[f2561,f541]) ).
fof(f3574,plain,
! [X0,X1] :
( ~ inductive(intersection(null_class,diagonalise(cross_product(X0,X1))))
| ~ inductive(union(universal_class,domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f2536,f541]) ).
fof(f3571,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ subclass(universal_class,power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f1358,f541]) ).
fof(f3570,plain,
! [X0,X1] :
( ~ member(null_class,intersection(diagonalise(cross_product(X0,X1)),null_class))
| ~ inductive(union(domain_of(restrict(identity_relation,X0,X1)),universal_class)) ),
inference(superposition,[],[f858,f541]) ).
fof(f3569,plain,
! [X0,X1] :
( ~ member(null_class,intersection(null_class,diagonalise(cross_product(X0,X1))))
| ~ inductive(union(universal_class,domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f807,f541]) ).
fof(f3568,plain,
! [X0,X1] : union(domain_of(restrict(identity_relation,X0,X1)),universal_class) = complement(intersection(diagonalise(cross_product(X0,X1)),null_class)),
inference(superposition,[],[f615,f541]) ).
fof(f3567,plain,
! [X0,X1] : union(universal_class,domain_of(restrict(identity_relation,X0,X1))) = complement(intersection(null_class,diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f614,f541]) ).
fof(f3579,plain,
! [X0,X1] :
( null_class = diagonalise(cross_product(X0,X1))
| ~ subclass(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f3566,f541]) ).
fof(f3566,plain,
! [X0,X1] :
( ~ subclass(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1)))
| null_class = complement(domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f600,f541]) ).
fof(f3565,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ member(omega,power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f567,f541]) ).
fof(f3564,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ member(null_class,power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f566,f541]) ).
fof(f3562,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(diagonalise(cross_product(X0,X1))))
| member(singleton(X2),domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f426,f541]) ).
fof(f3561,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ inductive(power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f402,f541]) ).
fof(f3559,plain,
! [X0,X1] :
( ~ subclass(universal_class,diagonalise(cross_product(X0,X1)))
| ~ subclass(universal_class,domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f276,f541]) ).
fof(f3556,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ subclass(universal_class,power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f179,f541]) ).
fof(f3555,plain,
! [X0,X1] :
( ~ subclass(universal_class,diagonalise(cross_product(X0,X1)))
| ~ member(omega,domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f171,f541]) ).
fof(f3554,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ member(X2,power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f152,f541]) ).
fof(f3553,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,diagonalise(cross_product(X0,X1))))
| ~ inductive(power_class(domain_of(restrict(identity_relation,X0,X1)))) ),
inference(superposition,[],[f151,f541]) ).
fof(f3552,plain,
! [X0,X1] : complement(image(element_relation,power_class(domain_of(restrict(identity_relation,X0,X1))))) = power_class(image(element_relation,diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f150,f541]) ).
fof(f3578,plain,
! [X2,X0,X1] :
( subclass(diagonalise(cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(diagonalise(cross_product(X0,X1)),X2),domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f3551,f541]) ).
fof(f3551,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(diagonalise(cross_product(X0,X1)),X2),domain_of(restrict(identity_relation,X0,X1)))
| subclass(complement(domain_of(restrict(identity_relation,X0,X1))),X2) ),
inference(superposition,[],[f121,f541]) ).
fof(f3577,plain,
! [X0,X1] :
( null_class = diagonalise(cross_product(X0,X1))
| ~ member(regular(diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1))) ),
inference(forward_demodulation,[],[f3550,f541]) ).
fof(f3550,plain,
! [X0,X1] :
( ~ member(regular(diagonalise(cross_product(X0,X1))),domain_of(restrict(identity_relation,X0,X1)))
| null_class = complement(domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f120,f541]) ).
fof(f3549,plain,
! [X0,X1] :
( ~ inductive(diagonalise(cross_product(X0,X1)))
| ~ member(null_class,domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f119,f541]) ).
fof(f3548,plain,
! [X0,X1] : complement(image(element_relation,diagonalise(cross_product(X0,X1)))) = power_class(domain_of(restrict(identity_relation,X0,X1))),
inference(superposition,[],[f55,f541]) ).
fof(f3547,plain,
! [X2,X0,X1] : union(X2,domain_of(restrict(identity_relation,X0,X1))) = complement(intersection(complement(X2),diagonalise(cross_product(X0,X1)))),
inference(superposition,[],[f26,f541]) ).
fof(f3546,plain,
! [X2,X0,X1] : union(domain_of(restrict(identity_relation,X0,X1)),X2) = complement(intersection(diagonalise(cross_product(X0,X1)),complement(X2))),
inference(superposition,[],[f26,f541]) ).
fof(f3545,plain,
! [X2,X0,X1] :
( member(X2,diagonalise(cross_product(X0,X1)))
| member(X2,domain_of(restrict(identity_relation,X0,X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f541]) ).
fof(f3544,plain,
! [X2,X0,X1] :
( ~ member(X2,diagonalise(cross_product(X0,X1)))
| ~ member(X2,domain_of(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f24,f541]) ).
fof(f3543,plain,
! [X0,X1] :
( ~ subclass(universal_class,diagonalise(cross_product(X0,X1)))
| ~ subclass(universal_class,cantor(restrict(identity_relation,X0,X1))) ),
inference(superposition,[],[f970,f541]) ).
fof(f541,plain,
! [X0,X1] : diagonalise(cross_product(X0,X1)) = complement(domain_of(restrict(identity_relation,X0,X1))),
inference(superposition,[],[f76,f29]) ).
fof(f3531,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X1),identity_relation)
| member(X0,subset_relation)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f2984,f166]) ).
fof(f3530,plain,
! [X0,X1] :
( ~ subclass(unordered_pair(X0,X1),identity_relation)
| member(X1,subset_relation)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f2984,f167]) ).
fof(f2984,plain,
! [X0] :
( subclass(X0,subset_relation)
| ~ subclass(X0,identity_relation) ),
inference(duplicate_literal_removal,[],[f2950]) ).
fof(f2950,plain,
! [X0] :
( ~ subclass(X0,identity_relation)
| subclass(X0,subset_relation)
| subclass(X0,subset_relation) ),
inference(resolution,[],[f160,f135]) ).
fof(f3502,plain,
! [X0] :
( member(complement(image(element_relation,diagonalise(X0))),universal_class)
| ~ member(domain_of(intersection(X0,identity_relation)),universal_class) ),
inference(superposition,[],[f56,f153]) ).
fof(f3501,plain,
! [X0,X1] :
( member(complement(image(element_relation,diagonalise(X0))),X1)
| ~ subclass(universal_class,X1)
| ~ member(domain_of(intersection(X0,identity_relation)),universal_class) ),
inference(superposition,[],[f165,f153]) ).
fof(f3500,plain,
! [X0,X1] : complement(image(element_relation,diagonalise(cross_product(X0,X1)))) = power_class(domain_of(restrict(identity_relation,X0,X1))),
inference(superposition,[],[f153,f29]) ).
fof(f3499,plain,
( power_class(domain_of(null_class)) = complement(image(element_relation,diagonalise(singleton(identity_relation))))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f153,f767]) ).
fof(f153,plain,
! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0))),
inference(superposition,[],[f55,f76]) ).
fof(f3077,plain,
! [X0] : subclass(null_class,X0),
inference(forward_demodulation,[],[f3065,f603]) ).
fof(f3065,plain,
! [X0] : subclass(complement(universal_class),X0),
inference(resolution,[],[f2982,f4]) ).
fof(f413,plain,
! [X0] :
( member(regular(identity_relation),X0)
| ~ subclass(subset_relation,X0)
| null_class = identity_relation ),
inference(resolution,[],[f170,f66]) ).
fof(f2084,plain,
! [X0] :
( member(X0,universal_class)
| ~ subclass(universal_class,complement(complement(identity_relation))) ),
inference(resolution,[],[f2079,f787]) ).
fof(f2300,plain,
! [X2,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,intersection(X2,identity_relation),X0)
| homomorphism(X1,intersection(X2,identity_relation),X0)
| ~ operation(intersection(X2,identity_relation))
| ~ member(ordered_pair(not_homomorphism1(X1,intersection(X2,identity_relation),X0),not_homomorphism2(X1,intersection(X2,identity_relation),X0)),diagonalise(X2)) ),
inference(resolution,[],[f90,f155]) ).
fof(f1070,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,null_class)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f1069]) ).
fof(f1069,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,null_class)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f289,f656]) ).
fof(f1155,plain,
! [X0] :
( member(regular(X0),universal_class)
| ~ subclass(X0,identity_relation)
| null_class = X0 ),
inference(resolution,[],[f1143,f159]) ).
fof(f1424,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| singleton(X0) = null_class ),
inference(superposition,[],[f22,f767]) ).
fof(f293,plain,
! [X0] :
( ~ subclass(universal_class,diagonalise(X0))
| ~ subclass(universal_class,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f276,f76]) ).
fof(f637,plain,
! [X0] :
( ~ member(regular(X0),universal_class)
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f612,f159]) ).
fof(f2542,plain,
! [X0] :
( ~ member(null_class,intersection(null_class,diagonalise(X0)))
| ~ inductive(union(universal_class,domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f807,f76]) ).
fof(f2553,plain,
! [X0] :
( ~ inductive(intersection(null_class,diagonalise(X0)))
| ~ inductive(union(universal_class,domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f2536,f76]) ).
fof(f2567,plain,
! [X0] :
( ~ member(null_class,intersection(diagonalise(X0),null_class))
| ~ inductive(union(domain_of(intersection(X0,identity_relation)),universal_class)) ),
inference(superposition,[],[f858,f76]) ).
fof(f2578,plain,
! [X0] :
( ~ inductive(intersection(diagonalise(X0),null_class))
| ~ inductive(union(domain_of(intersection(X0,identity_relation)),universal_class)) ),
inference(superposition,[],[f2561,f76]) ).
fof(f2595,plain,
! [X0] :
( null_class = intersection(null_class,X0)
| ~ member(regular(intersection(null_class,X0)),universal_class) ),
inference(resolution,[],[f127,f612]) ).
fof(f2598,plain,
! [X0,X1] :
( null_class = intersection(domain_of(intersection(X0,identity_relation)),X1)
| ~ member(regular(intersection(domain_of(intersection(X0,identity_relation)),X1)),diagonalise(X0)) ),
inference(resolution,[],[f127,f155]) ).
fof(f2599,plain,
! [X0] :
( null_class = intersection(inverse(subset_relation),X0)
| ~ member(regular(intersection(inverse(subset_relation),X0)),subset_relation)
| member(regular(intersection(inverse(subset_relation),X0)),identity_relation) ),
inference(resolution,[],[f127,f757]) ).
fof(f2604,plain,
! [X0] :
( null_class = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),universal_class) ),
inference(resolution,[],[f127,f1143]) ).
fof(f2605,plain,
! [X0,X1] :
( null_class = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),X1)
| ~ subclass(subset_relation,X1) ),
inference(resolution,[],[f127,f170]) ).
fof(f3477,plain,
( null_class = identity_relation
| member(regular(identity_relation),inverse(subset_relation)) ),
inference(forward_demodulation,[],[f2618,f75]) ).
fof(f2618,plain,
( member(regular(identity_relation),inverse(subset_relation))
| null_class = intersection(inverse(subset_relation),subset_relation) ),
inference(superposition,[],[f127,f75]) ).
fof(f2755,plain,
! [X0] :
( null_class = intersection(X0,null_class)
| ~ member(regular(intersection(X0,null_class)),universal_class) ),
inference(resolution,[],[f132,f612]) ).
fof(f2758,plain,
! [X0,X1] :
( null_class = intersection(X0,domain_of(intersection(X1,identity_relation)))
| ~ member(regular(intersection(X0,domain_of(intersection(X1,identity_relation)))),diagonalise(X1)) ),
inference(resolution,[],[f132,f155]) ).
fof(f2760,plain,
! [X0] :
( null_class = intersection(X0,inverse(subset_relation))
| ~ member(regular(intersection(X0,inverse(subset_relation))),subset_relation)
| member(regular(intersection(X0,inverse(subset_relation))),identity_relation) ),
inference(resolution,[],[f132,f757]) ).
fof(f2765,plain,
! [X0] :
( null_class = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),universal_class) ),
inference(resolution,[],[f132,f1143]) ).
fof(f2766,plain,
! [X0,X1] :
( null_class = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),X1)
| ~ subclass(subset_relation,X1) ),
inference(resolution,[],[f132,f170]) ).
fof(f3475,plain,
( null_class = identity_relation
| member(regular(identity_relation),subset_relation) ),
inference(forward_demodulation,[],[f2780,f75]) ).
fof(f2780,plain,
( member(regular(identity_relation),subset_relation)
| null_class = intersection(inverse(subset_relation),subset_relation) ),
inference(superposition,[],[f132,f75]) ).
fof(f2848,plain,
! [X0] : complement(image(element_relation,power_class(intersection(null_class,complement(X0))))) = power_class(image(element_relation,union(universal_class,X0))),
inference(superposition,[],[f150,f614]) ).
fof(f2849,plain,
complement(image(element_relation,power_class(intersection(null_class,null_class)))) = power_class(image(element_relation,union(universal_class,universal_class))),
inference(superposition,[],[f150,f796]) ).
fof(f2851,plain,
! [X0] : complement(image(element_relation,power_class(domain_of(intersection(X0,identity_relation))))) = power_class(image(element_relation,diagonalise(X0))),
inference(superposition,[],[f150,f76]) ).
fof(f3474,plain,
! [X0] : subclass(null_class,X0),
inference(subsumption_resolution,[],[f2980,f4]) ).
fof(f2980,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X0) ),
inference(duplicate_literal_removal,[],[f2954]) ).
fof(f2954,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X0)
| subclass(null_class,X0) ),
inference(resolution,[],[f160,f630]) ).
fof(f2965,plain,
! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[],[f160,f612]) ).
fof(f2968,plain,
! [X2,X0,X1] :
( ~ subclass(X0,domain_of(intersection(X1,identity_relation)))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),diagonalise(X1)) ),
inference(resolution,[],[f160,f155]) ).
fof(f2970,plain,
! [X0,X1] :
( ~ subclass(X0,inverse(subset_relation))
| subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation) ),
inference(resolution,[],[f160,f757]) ).
fof(f2975,plain,
! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[],[f160,f1143]) ).
fof(f2976,plain,
! [X2,X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| ~ subclass(subset_relation,X2) ),
inference(resolution,[],[f160,f170]) ).
fof(f3473,plain,
! [X0] : subclass(null_class,X0),
inference(forward_demodulation,[],[f3472,f603]) ).
fof(f3472,plain,
! [X0] : subclass(complement(universal_class),X0),
inference(subsumption_resolution,[],[f3067,f4]) ).
fof(f3067,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(complement(universal_class),X0) ),
inference(superposition,[],[f2982,f603]) ).
fof(f3471,plain,
! [X0,X1] :
( subclass(union(universal_class,X0),X1)
| ~ subclass(union(universal_class,X0),intersection(null_class,complement(X0))) ),
inference(forward_demodulation,[],[f3069,f614]) ).
fof(f3069,plain,
! [X0,X1] :
( ~ subclass(union(universal_class,X0),intersection(null_class,complement(X0)))
| subclass(complement(intersection(null_class,complement(X0))),X1) ),
inference(superposition,[],[f2982,f614]) ).
fof(f3470,plain,
! [X0] :
( subclass(union(universal_class,universal_class),X0)
| ~ subclass(union(universal_class,universal_class),intersection(null_class,null_class)) ),
inference(forward_demodulation,[],[f3070,f796]) ).
fof(f3070,plain,
! [X0] :
( ~ subclass(union(universal_class,universal_class),intersection(null_class,null_class))
| subclass(complement(intersection(null_class,null_class)),X0) ),
inference(superposition,[],[f2982,f796]) ).
fof(f3469,plain,
! [X0,X1] :
( subclass(union(X0,universal_class),X1)
| ~ subclass(union(X0,universal_class),intersection(complement(X0),null_class)) ),
inference(forward_demodulation,[],[f3071,f615]) ).
fof(f3071,plain,
! [X0,X1] :
( ~ subclass(union(X0,universal_class),intersection(complement(X0),null_class))
| subclass(complement(intersection(complement(X0),null_class)),X1) ),
inference(superposition,[],[f2982,f615]) ).
fof(f3468,plain,
! [X0,X1] :
( subclass(diagonalise(X0),X1)
| ~ subclass(diagonalise(X0),domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f3072,f76]) ).
fof(f3072,plain,
! [X0,X1] :
( ~ subclass(diagonalise(X0),domain_of(intersection(X0,identity_relation)))
| subclass(complement(domain_of(intersection(X0,identity_relation))),X1) ),
inference(superposition,[],[f2982,f76]) ).
fof(f3127,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = singleton(not_subclass_element(null_class,X0)) ),
inference(forward_demodulation,[],[f3126,f603]) ).
fof(f3126,plain,
! [X0] :
( null_class = singleton(not_subclass_element(null_class,X0))
| subclass(complement(universal_class),X0) ),
inference(forward_demodulation,[],[f3117,f603]) ).
fof(f3117,plain,
! [X0] :
( null_class = singleton(not_subclass_element(complement(universal_class),X0))
| subclass(complement(universal_class),X0) ),
inference(resolution,[],[f3114,f121]) ).
fof(f3118,plain,
! [X0] :
( null_class = singleton(not_subclass_element(null_class,X0))
| subclass(null_class,X0) ),
inference(resolution,[],[f3114,f630]) ).
fof(f3297,plain,
! [X2,X3,X0,X1,X4] :
( member(not_subclass_element(X0,X1),cross_product(X2,X3))
| ~ subclass(X0,restrict(X4,X2,X3))
| subclass(X0,X1) ),
inference(resolution,[],[f496,f160]) ).
fof(f3296,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ subclass(universal_class,restrict(X4,X2,X3)) ),
inference(resolution,[],[f496,f697]) ).
fof(f3295,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ subclass(universal_class,complement(complement(restrict(X4,X2,X3)))) ),
inference(resolution,[],[f496,f787]) ).
fof(f3294,plain,
! [X2,X3,X0,X1,X4] :
( member(unordered_pair(X0,X1),cross_product(X2,X3))
| ~ subclass(universal_class,restrict(X4,X2,X3)) ),
inference(resolution,[],[f496,f161]) ).
fof(f3293,plain,
! [X2,X3,X0,X1,X4] :
( member(unordered_pair(X0,X1),cross_product(X2,X3))
| ~ subclass(universal_class,complement(complement(restrict(X4,X2,X3)))) ),
inference(resolution,[],[f496,f471]) ).
fof(f3292,plain,
! [X2,X3,X0,X1] :
( member(regular(intersection(X0,restrict(X1,X2,X3))),cross_product(X2,X3))
| null_class = intersection(X0,restrict(X1,X2,X3)) ),
inference(resolution,[],[f496,f132]) ).
fof(f3291,plain,
! [X2,X3,X0,X1] :
( member(regular(X0),cross_product(X1,X2))
| ~ subclass(X0,restrict(X3,X1,X2))
| null_class = X0 ),
inference(resolution,[],[f496,f159]) ).
fof(f3290,plain,
! [X2,X3,X0,X1] :
( member(power_class(X0),cross_product(X1,X2))
| ~ subclass(universal_class,restrict(X3,X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f496,f165]) ).
fof(f3289,plain,
! [X2,X3,X0,X1] :
( member(sum_class(X0),cross_product(X1,X2))
| ~ subclass(universal_class,restrict(X3,X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f496,f164]) ).
fof(f3288,plain,
! [X2,X3,X0,X1] :
( member(singleton(X0),cross_product(X1,X2))
| ~ subclass(universal_class,restrict(X3,X1,X2)) ),
inference(resolution,[],[f496,f162]) ).
fof(f3287,plain,
! [X2,X0,X1] :
( member(apply(choice,restrict(X0,X1,X2)),cross_product(X1,X2))
| null_class = restrict(X0,X1,X2)
| ~ member(restrict(X0,X1,X2),universal_class) ),
inference(resolution,[],[f496,f70]) ).
fof(f3284,plain,
! [X2,X3,X0,X1] :
( member(regular(intersection(restrict(X0,X1,X2),X3)),cross_product(X1,X2))
| null_class = intersection(restrict(X0,X1,X2),X3) ),
inference(resolution,[],[f496,f127]) ).
fof(f3283,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
| null_class = restrict(X0,X1,X2) ),
inference(resolution,[],[f496,f66]) ).
fof(f3282,plain,
! [X2,X0,X1] :
( member(omega,cross_product(X0,X1))
| ~ subclass(universal_class,restrict(X2,X0,X1)) ),
inference(resolution,[],[f496,f163]) ).
fof(f3279,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),cross_product(X1,X2))
| subclass(restrict(X0,X1,X2),X3) ),
inference(resolution,[],[f496,f2]) ).
fof(f496,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) ),
inference(superposition,[],[f22,f28]) ).
fof(f3228,plain,
! [X0,X1] :
( member(ordered_pair(inverse(restrict(X0,X1,universal_class)),image(X0,X1)),domain_relation)
| ~ member(inverse(restrict(X0,X1,universal_class)),universal_class) ),
inference(superposition,[],[f319,f42]) ).
fof(f3227,plain,
! [X0,X1] :
( ~ member(inverse(X0),universal_class)
| ~ subclass(domain_relation,X1)
| member(ordered_pair(inverse(X0),range_of(X0)),X1) ),
inference(resolution,[],[f319,f1]) ).
fof(f319,plain,
! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) ),
inference(superposition,[],[f100,f39]) ).
fof(f3122,plain,
! [X0,X1] :
( null_class = singleton(image(X0,singleton(X1)))
| member(apply(X0,X1),universal_class) ),
inference(resolution,[],[f3114,f316]) ).
fof(f3114,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f3110,f69]) ).
fof(f3110,plain,
! [X0] :
( member(X0,universal_class)
| ~ function(choice)
| singleton(X0) = null_class ),
inference(superposition,[],[f3108,f890]) ).
fof(f3108,plain,
! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ function(X0) ),
inference(subsumption_resolution,[],[f3106,f118]) ).
fof(f3106,plain,
! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(singleton(X1),universal_class)
| ~ function(X0) ),
inference(resolution,[],[f316,f65]) ).
fof(f316,plain,
! [X0,X1] :
( ~ member(image(X0,singleton(X1)),universal_class)
| member(apply(X0,X1),universal_class) ),
inference(superposition,[],[f54,f68]) ).
fof(f3105,plain,
! [X0] :
( subclass(power_class(image(element_relation,null_class)),X0)
| ~ subclass(power_class(image(element_relation,null_class)),image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f3076,f664]) ).
fof(f3076,plain,
! [X0] :
( ~ subclass(power_class(image(element_relation,null_class)),image(element_relation,power_class(universal_class)))
| subclass(complement(image(element_relation,power_class(universal_class))),X0) ),
inference(superposition,[],[f2982,f664]) ).
fof(f3104,plain,
! [X0,X1] :
( subclass(power_class(X0),X1)
| ~ subclass(power_class(X0),image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f3074,f55]) ).
fof(f3074,plain,
! [X0,X1] :
( ~ subclass(power_class(X0),image(element_relation,complement(X0)))
| subclass(complement(image(element_relation,complement(X0))),X1) ),
inference(superposition,[],[f2982,f55]) ).
fof(f3080,plain,
! [X2,X0,X1] :
( subclass(union(X0,X1),X2)
| ~ subclass(union(X0,X1),intersection(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f3068,f26]) ).
fof(f3068,plain,
! [X2,X0,X1] :
( ~ subclass(union(X0,X1),intersection(complement(X0),complement(X1)))
| subclass(complement(intersection(complement(X0),complement(X1))),X2) ),
inference(superposition,[],[f2982,f26]) ).
fof(f3066,plain,
! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ function(complement(cross_product(universal_class,universal_class))) ),
inference(resolution,[],[f2982,f62]) ).
fof(f2982,plain,
! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ),
inference(duplicate_literal_removal,[],[f2952]) ).
fof(f2952,plain,
! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f160,f121]) ).
fof(f3036,plain,
! [X2,X0,X1] :
( ~ subclass(ordered_pair(X0,X1),X2)
| member(unordered_pair(X0,singleton(X1)),X2) ),
inference(subsumption_resolution,[],[f3035,f11]) ).
fof(f3035,plain,
! [X2,X0,X1] :
( ~ subclass(ordered_pair(X0,X1),X2)
| member(unordered_pair(X0,singleton(X1)),X2)
| ~ member(unordered_pair(X0,singleton(X1)),universal_class) ),
inference(superposition,[],[f167,f13]) ).
fof(f3033,plain,
! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) ),
inference(resolution,[],[f167,f62]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f10]) ).
fof(f3012,plain,
! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) ),
inference(resolution,[],[f166,f62]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1,f9]) ).
fof(f2978,plain,
! [X2,X0,X1] :
( ~ subclass(X0,cantor(X1))
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),domain_of(X1)) ),
inference(resolution,[],[f160,f923]) ).
fof(f2977,plain,
! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(X0,X1)
| not_subclass_element(X0,X1) = ordered_pair(first(not_subclass_element(X0,X1)),second(not_subclass_element(X0,X1))) ),
inference(resolution,[],[f160,f2058]) ).
fof(f2973,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(X0,image(X1,image(X2,singleton(X3))))
| subclass(X0,X4)
| member(ordered_pair(X3,not_subclass_element(X0,X4)),compose(X1,X2))
| ~ member(ordered_pair(X3,not_subclass_element(X0,X4)),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f160,f59]) ).
fof(f2972,plain,
! [X0,X1] :
( ~ subclass(X0,image(element_relation,null_class))
| subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),power_class(universal_class)) ),
inference(resolution,[],[f160,f621]) ).
fof(f2971,plain,
! [X2,X0,X1] :
( ~ subclass(X0,image(element_relation,complement(X1)))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),power_class(X1)) ),
inference(resolution,[],[f160,f152]) ).
fof(f2966,plain,
! [X2,X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| null_class = X2 ),
inference(resolution,[],[f160,f291]) ).
fof(f2963,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(X0,restrict(X1,X2,X3))
| subclass(X0,X4)
| member(not_subclass_element(X0,X4),X1) ),
inference(resolution,[],[f160,f495]) ).
fof(f2962,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,symmetric_difference(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),union(X1,X2)) ),
inference(resolution,[],[f160,f1660]) ).
fof(f2961,plain,
! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) ),
inference(resolution,[],[f160,f24]) ).
fof(f2960,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) ),
inference(resolution,[],[f160,f21]) ).
fof(f2959,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) ),
inference(resolution,[],[f160,f22]) ).
fof(f2958,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = ordered_pair(first(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))) ),
inference(resolution,[],[f160,f17]) ).
fof(f2957,plain,
! [X2,X0,X1] :
( ~ subclass(X0,singleton(X1))
| subclass(X0,X2)
| not_subclass_element(X0,X2) = X1 ),
inference(resolution,[],[f160,f650]) ).
fof(f2956,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = X1
| not_subclass_element(X0,X3) = X2 ),
inference(resolution,[],[f160,f8]) ).
fof(f2955,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) ),
inference(resolution,[],[f160,f1]) ).
fof(f160,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f2857,plain,
! [X0] :
( member(complement(image(element_relation,power_class(X0))),universal_class)
| ~ member(image(element_relation,complement(X0)),universal_class) ),
inference(superposition,[],[f56,f150]) ).
fof(f2856,plain,
! [X0,X1] :
( member(complement(image(element_relation,power_class(X0))),X1)
| ~ subclass(universal_class,X1)
| ~ member(image(element_relation,complement(X0)),universal_class) ),
inference(superposition,[],[f165,f150]) ).
fof(f2855,plain,
complement(image(element_relation,power_class(image(element_relation,power_class(universal_class))))) = power_class(image(element_relation,power_class(image(element_relation,null_class)))),
inference(superposition,[],[f150,f664]) ).
fof(f2854,plain,
power_class(image(element_relation,power_class(universal_class))) = complement(image(element_relation,power_class(image(element_relation,null_class)))),
inference(superposition,[],[f150,f616]) ).
fof(f2850,plain,
! [X0] : complement(image(element_relation,power_class(intersection(complement(X0),null_class)))) = power_class(image(element_relation,union(X0,universal_class))),
inference(superposition,[],[f150,f615]) ).
fof(f2847,plain,
! [X0,X1] : complement(image(element_relation,power_class(intersection(complement(X0),complement(X1))))) = power_class(image(element_relation,union(X0,X1))),
inference(superposition,[],[f150,f26]) ).
fof(f150,plain,
! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0))),
inference(superposition,[],[f55,f55]) ).
fof(f2804,plain,
! [X0] :
( null_class = cantor(X0)
| member(regular(cantor(X0)),diagonalise(compose(inverse(element_relation),X0))) ),
inference(forward_demodulation,[],[f2779,f77]) ).
fof(f2779,plain,
! [X0] :
( member(regular(cantor(X0)),diagonalise(compose(inverse(element_relation),X0)))
| null_class = intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f132,f77]) ).
fof(f2803,plain,
! [X0,X1] :
( symmetric_difference(X0,X1) = null_class
| member(regular(symmetric_difference(X0,X1)),union(X0,X1)) ),
inference(forward_demodulation,[],[f2777,f1614]) ).
fof(f2777,plain,
! [X0,X1] :
( member(regular(symmetric_difference(X0,X1)),union(X0,X1))
| null_class = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
inference(superposition,[],[f132,f1614]) ).
fof(f2799,plain,
( null_class = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| member(regular(subset_relation),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(forward_demodulation,[],[f2774,f29]) ).
fof(f2774,plain,
( member(regular(subset_relation),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| null_class = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f132,f1933]) ).
fof(f2798,plain,
! [X2,X0,X1] :
( null_class = restrict(X2,X0,X1)
| member(regular(restrict(X2,X0,X1)),X2) ),
inference(forward_demodulation,[],[f2773,f29]) ).
fof(f2773,plain,
! [X2,X0,X1] :
( member(regular(restrict(X2,X0,X1)),X2)
| null_class = intersection(cross_product(X0,X1),X2) ),
inference(superposition,[],[f132,f29]) ).
fof(f2797,plain,
! [X2,X0,X1] :
( null_class = restrict(X0,X1,X2)
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(forward_demodulation,[],[f2771,f28]) ).
fof(f2771,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
| null_class = intersection(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f132,f28]) ).
fof(f2768,plain,
! [X0,X1] :
( null_class = intersection(X0,cantor(X1))
| member(regular(intersection(X0,cantor(X1))),domain_of(X1)) ),
inference(resolution,[],[f132,f923]) ).
fof(f2767,plain,
! [X0] :
( null_class = intersection(X0,subset_relation)
| regular(intersection(X0,subset_relation)) = ordered_pair(first(regular(intersection(X0,subset_relation))),second(regular(intersection(X0,subset_relation)))) ),
inference(resolution,[],[f132,f2058]) ).
fof(f2763,plain,
! [X2,X3,X0,X1] :
( null_class = intersection(X0,image(X1,image(X2,singleton(X3))))
| member(ordered_pair(X3,regular(intersection(X0,image(X1,image(X2,singleton(X3)))))),compose(X1,X2))
| ~ member(ordered_pair(X3,regular(intersection(X0,image(X1,image(X2,singleton(X3)))))),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f132,f59]) ).
fof(f2762,plain,
! [X0] :
( null_class = intersection(X0,image(element_relation,null_class))
| ~ member(regular(intersection(X0,image(element_relation,null_class))),power_class(universal_class)) ),
inference(resolution,[],[f132,f621]) ).
fof(f2761,plain,
! [X0,X1] :
( null_class = intersection(X0,image(element_relation,complement(X1)))
| ~ member(regular(intersection(X0,image(element_relation,complement(X1)))),power_class(X1)) ),
inference(resolution,[],[f132,f152]) ).
fof(f2756,plain,
! [X0,X1] :
( null_class = intersection(X0,null_class)
| member(regular(intersection(X0,null_class)),X1)
| null_class = X1 ),
inference(resolution,[],[f132,f291]) ).
fof(f2753,plain,
! [X2,X3,X0,X1] :
( null_class = intersection(X0,restrict(X1,X2,X3))
| member(regular(intersection(X0,restrict(X1,X2,X3))),X1) ),
inference(resolution,[],[f132,f495]) ).
fof(f2752,plain,
! [X2,X0,X1] :
( null_class = intersection(X0,symmetric_difference(X1,X2))
| member(regular(intersection(X0,symmetric_difference(X1,X2))),union(X1,X2)) ),
inference(resolution,[],[f132,f1660]) ).
fof(f2751,plain,
! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) ),
inference(resolution,[],[f132,f24]) ).
fof(f2750,plain,
! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) ),
inference(resolution,[],[f132,f21]) ).
fof(f2749,plain,
! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) ),
inference(resolution,[],[f132,f22]) ).
fof(f2782,plain,
! [X2,X0,X1] :
( regular(restrict(X0,X1,X2)) = ordered_pair(first(regular(restrict(X0,X1,X2))),second(regular(restrict(X0,X1,X2))))
| null_class = restrict(X0,X1,X2) ),
inference(forward_demodulation,[],[f2781,f28]) ).
fof(f2781,plain,
! [X2,X0,X1] :
( null_class = restrict(X0,X1,X2)
| regular(intersection(X0,cross_product(X1,X2))) = ordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))) ),
inference(forward_demodulation,[],[f2748,f28]) ).
fof(f2748,plain,
! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = ordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))) ),
inference(resolution,[],[f132,f17]) ).
fof(f2747,plain,
! [X0,X1] :
( null_class = intersection(X0,singleton(X1))
| regular(intersection(X0,singleton(X1))) = X1 ),
inference(resolution,[],[f132,f650]) ).
fof(f2746,plain,
! [X2,X0,X1] :
( null_class = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 ),
inference(resolution,[],[f132,f8]) ).
fof(f2745,plain,
! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) ),
inference(resolution,[],[f132,f1]) ).
fof(f132,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f22,f66]) ).
fof(f2641,plain,
! [X0,X1] :
( symmetric_difference(X0,X1) = null_class
| member(regular(symmetric_difference(X0,X1)),complement(intersection(X0,X1))) ),
inference(forward_demodulation,[],[f2616,f1614]) ).
fof(f2616,plain,
! [X0,X1] :
( member(regular(symmetric_difference(X0,X1)),complement(intersection(X0,X1)))
| null_class = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
inference(superposition,[],[f127,f1614]) ).
fof(f2637,plain,
( null_class = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[],[f2613,f29]) ).
fof(f2613,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| null_class = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f127,f1933]) ).
fof(f2636,plain,
! [X2,X0,X1] :
( null_class = restrict(X2,X0,X1)
| member(regular(restrict(X2,X0,X1)),cross_product(X0,X1)) ),
inference(forward_demodulation,[],[f2612,f29]) ).
fof(f2612,plain,
! [X2,X0,X1] :
( member(regular(restrict(X2,X0,X1)),cross_product(X0,X1))
| null_class = intersection(cross_product(X0,X1),X2) ),
inference(superposition,[],[f127,f29]) ).
fof(f2635,plain,
! [X2,X0,X1] :
( null_class = restrict(X0,X1,X2)
| member(regular(restrict(X0,X1,X2)),X0) ),
inference(forward_demodulation,[],[f2610,f28]) ).
fof(f2610,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),X0)
| null_class = intersection(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f127,f28]) ).
fof(f2607,plain,
! [X0,X1] :
( null_class = intersection(cantor(X0),X1)
| member(regular(intersection(cantor(X0),X1)),domain_of(X0)) ),
inference(resolution,[],[f127,f923]) ).
fof(f2606,plain,
! [X0] :
( null_class = intersection(subset_relation,X0)
| regular(intersection(subset_relation,X0)) = ordered_pair(first(regular(intersection(subset_relation,X0))),second(regular(intersection(subset_relation,X0)))) ),
inference(resolution,[],[f127,f2058]) ).
fof(f2602,plain,
! [X2,X3,X0,X1] :
( null_class = intersection(image(X0,image(X1,singleton(X2))),X3)
| member(ordered_pair(X2,regular(intersection(image(X0,image(X1,singleton(X2))),X3))),compose(X0,X1))
| ~ member(ordered_pair(X2,regular(intersection(image(X0,image(X1,singleton(X2))),X3))),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f127,f59]) ).
fof(f2601,plain,
! [X0] :
( null_class = intersection(image(element_relation,null_class),X0)
| ~ member(regular(intersection(image(element_relation,null_class),X0)),power_class(universal_class)) ),
inference(resolution,[],[f127,f621]) ).
fof(f2600,plain,
! [X0,X1] :
( null_class = intersection(image(element_relation,complement(X0)),X1)
| ~ member(regular(intersection(image(element_relation,complement(X0)),X1)),power_class(X0)) ),
inference(resolution,[],[f127,f152]) ).
fof(f2596,plain,
! [X0,X1] :
( null_class = intersection(null_class,X0)
| member(regular(intersection(null_class,X0)),X1)
| null_class = X1 ),
inference(resolution,[],[f127,f291]) ).
fof(f2593,plain,
! [X2,X3,X0,X1] :
( null_class = intersection(restrict(X0,X1,X2),X3)
| member(regular(intersection(restrict(X0,X1,X2),X3)),X0) ),
inference(resolution,[],[f127,f495]) ).
fof(f2592,plain,
! [X2,X0,X1] :
( null_class = intersection(symmetric_difference(X0,X1),X2)
| member(regular(intersection(symmetric_difference(X0,X1),X2)),union(X0,X1)) ),
inference(resolution,[],[f127,f1660]) ).
fof(f2591,plain,
! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) ),
inference(resolution,[],[f127,f24]) ).
fof(f2590,plain,
! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) ),
inference(resolution,[],[f127,f21]) ).
fof(f2589,plain,
! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) ),
inference(resolution,[],[f127,f22]) ).
fof(f2620,plain,
! [X2,X0,X1] :
( regular(restrict(X2,X0,X1)) = ordered_pair(first(regular(restrict(X2,X0,X1))),second(regular(restrict(X2,X0,X1))))
| null_class = restrict(X2,X0,X1) ),
inference(forward_demodulation,[],[f2619,f29]) ).
fof(f2619,plain,
! [X2,X0,X1] :
( null_class = restrict(X2,X0,X1)
| regular(intersection(cross_product(X0,X1),X2)) = ordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))) ),
inference(forward_demodulation,[],[f2588,f29]) ).
fof(f2588,plain,
! [X2,X0,X1] :
( null_class = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = ordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))) ),
inference(resolution,[],[f127,f17]) ).
fof(f2587,plain,
! [X0,X1] :
( null_class = intersection(singleton(X0),X1)
| regular(intersection(singleton(X0),X1)) = X0 ),
inference(resolution,[],[f127,f650]) ).
fof(f2586,plain,
! [X2,X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 ),
inference(resolution,[],[f127,f8]) ).
fof(f2585,plain,
! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) ),
inference(resolution,[],[f127,f1]) ).
fof(f127,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f21,f66]) ).
fof(f976,plain,
! [X0] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| ~ subclass(universal_class,complement(range_of(X0))) ),
inference(superposition,[],[f970,f39]) ).
fof(f2582,plain,
( ~ inductive(intersection(power_class(image(element_relation,null_class)),null_class))
| ~ inductive(union(image(element_relation,power_class(universal_class)),universal_class)) ),
inference(superposition,[],[f2561,f664]) ).
fof(f2581,plain,
( ~ inductive(intersection(power_class(universal_class),null_class))
| ~ inductive(union(image(element_relation,null_class),universal_class)) ),
inference(superposition,[],[f2561,f616]) ).
fof(f2580,plain,
! [X0] :
( ~ inductive(intersection(power_class(X0),null_class))
| ~ inductive(union(image(element_relation,complement(X0)),universal_class)) ),
inference(superposition,[],[f2561,f55]) ).
fof(f2577,plain,
! [X0] :
( ~ inductive(intersection(union(X0,universal_class),null_class))
| ~ inductive(union(intersection(complement(X0),null_class),universal_class)) ),
inference(superposition,[],[f2561,f615]) ).
fof(f2576,plain,
( ~ inductive(intersection(union(universal_class,universal_class),null_class))
| ~ inductive(union(intersection(null_class,null_class),universal_class)) ),
inference(superposition,[],[f2561,f796]) ).
fof(f2575,plain,
! [X0] :
( ~ inductive(intersection(union(universal_class,X0),null_class))
| ~ inductive(union(intersection(null_class,complement(X0)),universal_class)) ),
inference(superposition,[],[f2561,f614]) ).
fof(f2574,plain,
! [X0,X1] :
( ~ inductive(intersection(union(X0,X1),null_class))
| ~ inductive(union(intersection(complement(X0),complement(X1)),universal_class)) ),
inference(superposition,[],[f2561,f26]) ).
fof(f2561,plain,
! [X0] :
( ~ inductive(intersection(complement(X0),null_class))
| ~ inductive(union(X0,universal_class)) ),
inference(resolution,[],[f858,f47]) ).
fof(f2571,plain,
( ~ member(null_class,intersection(power_class(image(element_relation,null_class)),null_class))
| ~ inductive(union(image(element_relation,power_class(universal_class)),universal_class)) ),
inference(superposition,[],[f858,f664]) ).
fof(f2570,plain,
( ~ member(null_class,intersection(power_class(universal_class),null_class))
| ~ inductive(union(image(element_relation,null_class),universal_class)) ),
inference(superposition,[],[f858,f616]) ).
fof(f2569,plain,
! [X0] :
( ~ member(null_class,intersection(power_class(X0),null_class))
| ~ inductive(union(image(element_relation,complement(X0)),universal_class)) ),
inference(superposition,[],[f858,f55]) ).
fof(f2566,plain,
! [X0] :
( ~ member(null_class,intersection(union(X0,universal_class),null_class))
| ~ inductive(union(intersection(complement(X0),null_class),universal_class)) ),
inference(superposition,[],[f858,f615]) ).
fof(f2565,plain,
( ~ member(null_class,intersection(union(universal_class,universal_class),null_class))
| ~ inductive(union(intersection(null_class,null_class),universal_class)) ),
inference(superposition,[],[f858,f796]) ).
fof(f2564,plain,
! [X0] :
( ~ member(null_class,intersection(union(universal_class,X0),null_class))
| ~ inductive(union(intersection(null_class,complement(X0)),universal_class)) ),
inference(superposition,[],[f858,f614]) ).
fof(f2563,plain,
! [X0,X1] :
( ~ member(null_class,intersection(union(X0,X1),null_class))
| ~ inductive(union(intersection(complement(X0),complement(X1)),universal_class)) ),
inference(superposition,[],[f858,f26]) ).
fof(f858,plain,
! [X0] :
( ~ member(null_class,intersection(complement(X0),null_class))
| ~ inductive(union(X0,universal_class)) ),
inference(superposition,[],[f119,f615]) ).
fof(f2557,plain,
( ~ inductive(intersection(null_class,power_class(image(element_relation,null_class))))
| ~ inductive(union(universal_class,image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f2536,f664]) ).
fof(f2556,plain,
( ~ inductive(intersection(null_class,power_class(universal_class)))
| ~ inductive(union(universal_class,image(element_relation,null_class))) ),
inference(superposition,[],[f2536,f616]) ).
fof(f2555,plain,
! [X0] :
( ~ inductive(intersection(null_class,power_class(X0)))
| ~ inductive(union(universal_class,image(element_relation,complement(X0)))) ),
inference(superposition,[],[f2536,f55]) ).
fof(f2552,plain,
! [X0] :
( ~ inductive(intersection(null_class,union(X0,universal_class)))
| ~ inductive(union(universal_class,intersection(complement(X0),null_class))) ),
inference(superposition,[],[f2536,f615]) ).
fof(f2551,plain,
( ~ inductive(intersection(null_class,union(universal_class,universal_class)))
| ~ inductive(union(universal_class,intersection(null_class,null_class))) ),
inference(superposition,[],[f2536,f796]) ).
fof(f2550,plain,
! [X0] :
( ~ inductive(intersection(null_class,union(universal_class,X0)))
| ~ inductive(union(universal_class,intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f2536,f614]) ).
fof(f2549,plain,
! [X0,X1] :
( ~ inductive(intersection(null_class,union(X0,X1)))
| ~ inductive(union(universal_class,intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f2536,f26]) ).
fof(f2536,plain,
! [X0] :
( ~ inductive(intersection(null_class,complement(X0)))
| ~ inductive(union(universal_class,X0)) ),
inference(resolution,[],[f807,f47]) ).
fof(f2546,plain,
( ~ member(null_class,intersection(null_class,power_class(image(element_relation,null_class))))
| ~ inductive(union(universal_class,image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f807,f664]) ).
fof(f2545,plain,
( ~ member(null_class,intersection(null_class,power_class(universal_class)))
| ~ inductive(union(universal_class,image(element_relation,null_class))) ),
inference(superposition,[],[f807,f616]) ).
fof(f2544,plain,
! [X0] :
( ~ member(null_class,intersection(null_class,power_class(X0)))
| ~ inductive(union(universal_class,image(element_relation,complement(X0)))) ),
inference(superposition,[],[f807,f55]) ).
fof(f2541,plain,
! [X0] :
( ~ member(null_class,intersection(null_class,union(X0,universal_class)))
| ~ inductive(union(universal_class,intersection(complement(X0),null_class))) ),
inference(superposition,[],[f807,f615]) ).
fof(f2540,plain,
( ~ member(null_class,intersection(null_class,union(universal_class,universal_class)))
| ~ inductive(union(universal_class,intersection(null_class,null_class))) ),
inference(superposition,[],[f807,f796]) ).
fof(f2539,plain,
! [X0] :
( ~ member(null_class,intersection(null_class,union(universal_class,X0)))
| ~ inductive(union(universal_class,intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f807,f614]) ).
fof(f2538,plain,
! [X0,X1] :
( ~ member(null_class,intersection(null_class,union(X0,X1)))
| ~ inductive(union(universal_class,intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f807,f26]) ).
fof(f807,plain,
! [X0] :
( ~ member(null_class,intersection(null_class,complement(X0)))
| ~ inductive(union(universal_class,X0)) ),
inference(superposition,[],[f119,f614]) ).
fof(f680,plain,
( null_class = power_class(universal_class)
| ~ subclass(power_class(universal_class),image(element_relation,null_class)) ),
inference(forward_demodulation,[],[f677,f616]) ).
fof(f677,plain,
( ~ subclass(power_class(universal_class),image(element_relation,null_class))
| null_class = complement(image(element_relation,null_class)) ),
inference(superposition,[],[f600,f616]) ).
fof(f91,axiom,
! [X10,X11,X9] :
( apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11))))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
fof(f674,plain,
( ~ inductive(image(element_relation,power_class(universal_class)))
| ~ inductive(power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f402,f616]) ).
fof(f2508,plain,
( ~ subclass(universal_class,image(element_relation,power_class(image(element_relation,null_class))))
| ~ subclass(universal_class,power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f1358,f664]) ).
fof(f2507,plain,
union(image(element_relation,power_class(universal_class)),universal_class) = complement(intersection(power_class(image(element_relation,null_class)),null_class)),
inference(superposition,[],[f615,f664]) ).
fof(f2506,plain,
union(universal_class,image(element_relation,power_class(universal_class))) = complement(intersection(null_class,power_class(image(element_relation,null_class)))),
inference(superposition,[],[f614,f664]) ).
fof(f2514,plain,
( null_class = power_class(image(element_relation,null_class))
| ~ subclass(power_class(image(element_relation,null_class)),image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f2505,f664]) ).
fof(f2505,plain,
( ~ subclass(power_class(image(element_relation,null_class)),image(element_relation,power_class(universal_class)))
| null_class = complement(image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f600,f664]) ).
fof(f2504,plain,
( ~ subclass(universal_class,image(element_relation,power_class(image(element_relation,null_class))))
| ~ member(omega,power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f567,f664]) ).
fof(f2503,plain,
( ~ inductive(image(element_relation,power_class(image(element_relation,null_class))))
| ~ member(null_class,power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f566,f664]) ).
fof(f2501,plain,
! [X0] :
( ~ subclass(universal_class,complement(power_class(image(element_relation,null_class))))
| member(singleton(X0),image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f426,f664]) ).
fof(f2500,plain,
( ~ inductive(image(element_relation,power_class(image(element_relation,null_class))))
| ~ inductive(power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f402,f664]) ).
fof(f2498,plain,
( ~ subclass(universal_class,power_class(image(element_relation,null_class)))
| ~ subclass(universal_class,image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f276,f664]) ).
fof(f2495,plain,
( ~ member(omega,image(element_relation,power_class(image(element_relation,null_class))))
| ~ subclass(universal_class,power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f179,f664]) ).
fof(f2494,plain,
( ~ subclass(universal_class,power_class(image(element_relation,null_class)))
| ~ member(omega,image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f171,f664]) ).
fof(f2493,plain,
! [X0] :
( ~ member(X0,image(element_relation,power_class(image(element_relation,null_class))))
| ~ member(X0,power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f152,f664]) ).
fof(f2492,plain,
( ~ member(null_class,image(element_relation,power_class(image(element_relation,null_class))))
| ~ inductive(power_class(image(element_relation,power_class(universal_class)))) ),
inference(superposition,[],[f151,f664]) ).
fof(f2513,plain,
! [X0] :
( subclass(power_class(image(element_relation,null_class)),X0)
| ~ member(not_subclass_element(power_class(image(element_relation,null_class)),X0),image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f2491,f664]) ).
fof(f2491,plain,
! [X0] :
( ~ member(not_subclass_element(power_class(image(element_relation,null_class)),X0),image(element_relation,power_class(universal_class)))
| subclass(complement(image(element_relation,power_class(universal_class))),X0) ),
inference(superposition,[],[f121,f664]) ).
fof(f2512,plain,
( null_class = power_class(image(element_relation,null_class))
| ~ member(regular(power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class))) ),
inference(forward_demodulation,[],[f2490,f664]) ).
fof(f2490,plain,
( ~ member(regular(power_class(image(element_relation,null_class))),image(element_relation,power_class(universal_class)))
| null_class = complement(image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f120,f664]) ).
fof(f2489,plain,
( ~ inductive(power_class(image(element_relation,null_class)))
| ~ member(null_class,image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f119,f664]) ).
fof(f2488,plain,
power_class(image(element_relation,power_class(universal_class))) = complement(image(element_relation,power_class(image(element_relation,null_class)))),
inference(superposition,[],[f55,f664]) ).
fof(f2487,plain,
! [X0] : union(X0,image(element_relation,power_class(universal_class))) = complement(intersection(complement(X0),power_class(image(element_relation,null_class)))),
inference(superposition,[],[f26,f664]) ).
fof(f2486,plain,
! [X0] : union(image(element_relation,power_class(universal_class)),X0) = complement(intersection(power_class(image(element_relation,null_class)),complement(X0))),
inference(superposition,[],[f26,f664]) ).
fof(f2485,plain,
! [X0] :
( member(X0,power_class(image(element_relation,null_class)))
| member(X0,image(element_relation,power_class(universal_class)))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f25,f664]) ).
fof(f2484,plain,
! [X0] :
( ~ member(X0,power_class(image(element_relation,null_class)))
| ~ member(X0,image(element_relation,power_class(universal_class))) ),
inference(superposition,[],[f24,f664]) ).
fof(f664,plain,
power_class(image(element_relation,null_class)) = complement(image(element_relation,power_class(universal_class))),
inference(superposition,[],[f55,f616]) ).
fof(f2063,plain,
! [X0] :
( ~ member(singleton(X0),subset_relation)
| ~ subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
inference(resolution,[],[f2006,f175]) ).
fof(f2466,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X1,X2),sum_class(X0))
| ~ homomorphism(X3,restrict(element_relation,universal_class,X0),X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(restrict(element_relation,universal_class,X0),ordered_pair(X1,X2))) ),
inference(superposition,[],[f89,f53]) ).
fof(f2465,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X1,X2),inverse(X0))
| ~ homomorphism(X3,flip(cross_product(X0,universal_class)),X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(flip(cross_product(X0,universal_class)),ordered_pair(X1,X2))) ),
inference(superposition,[],[f89,f38]) ).
fof(f2464,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X1,X2),range_of(X0))
| ~ homomorphism(X3,inverse(X0),X4)
| apply(X4,ordered_pair(apply(X3,X1),apply(X3,X2))) = apply(X3,apply(inverse(X0),ordered_pair(X1,X2))) ),
inference(superposition,[],[f89,f39]) ).
fof(f2463,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| ~ subclass(universal_class,domain_of(X1)) ),
inference(resolution,[],[f89,f697]) ).
fof(f2462,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| ~ subclass(universal_class,complement(complement(domain_of(X1)))) ),
inference(resolution,[],[f89,f787]) ).
fof(f2461,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| ~ subclass(universal_class,cantor(X1)) ),
inference(resolution,[],[f89,f955]) ).
fof(f2467,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| null_class = restrict(X1,singleton(ordered_pair(X3,X4)),universal_class) ),
inference(subsumption_resolution,[],[f2460,f696]) ).
fof(f2460,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),universal_class)
| null_class = restrict(X1,singleton(ordered_pair(X3,X4)),universal_class) ),
inference(resolution,[],[f89,f31]) ).
fof(f2459,plain,
! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| apply(X2,ordered_pair(apply(X0,not_homomorphism1(X3,X1,X4)),apply(X0,not_homomorphism2(X3,X1,X4)))) = apply(X0,apply(X1,ordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism2(X3,X1,X4))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) ),
inference(resolution,[],[f89,f90]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ member(ordered_pair(X0,X1),domain_of(X10))
| ~ homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
fof(f1711,plain,
! [X0,X1] :
( ~ inductive(symmetric_difference(X0,X1))
| ~ member(null_class,X1)
| ~ member(null_class,X0) ),
inference(resolution,[],[f1693,f23]) ).
fof(f1925,plain,
! [X0] :
( ~ subclass(universal_class,symmetric_difference(X0,singleton(X0)))
| member(omega,successor(X0)) ),
inference(superposition,[],[f1682,f43]) ).
fof(f2448,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ subclass(universal_class,complement(complement(cross_product(cross_product(universal_class,universal_class),universal_class)))) ),
inference(resolution,[],[f37,f787]) ).
fof(f2447,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f37,f16]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
fof(f2440,plain,
! [X0] :
( regular(X0) = ordered_pair(first(regular(X0)),second(regular(X0)))
| ~ subclass(X0,subset_relation)
| null_class = X0 ),
inference(resolution,[],[f2058,f159]) ).
fof(f2436,plain,
( apply(choice,subset_relation) = ordered_pair(first(apply(choice,subset_relation)),second(apply(choice,subset_relation)))
| null_class = subset_relation
| ~ member(subset_relation,universal_class) ),
inference(resolution,[],[f2058,f70]) ).
fof(f2433,plain,
( regular(subset_relation) = ordered_pair(first(regular(subset_relation)),second(regular(subset_relation)))
| null_class = subset_relation ),
inference(resolution,[],[f2058,f66]) ).
fof(f2429,plain,
! [X0] :
( not_subclass_element(subset_relation,X0) = ordered_pair(first(not_subclass_element(subset_relation,X0)),second(not_subclass_element(subset_relation,X0)))
| subclass(subset_relation,X0) ),
inference(resolution,[],[f2058,f2]) ).
fof(f2058,plain,
! [X0] :
( ~ member(X0,subset_relation)
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(resolution,[],[f2006,f17]) ).
fof(f2389,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))
| ~ member(ordered_pair(ordered_pair(X1,X2),X0),X3)
| ~ subclass(universal_class,complement(complement(cross_product(cross_product(universal_class,universal_class),universal_class)))) ),
inference(resolution,[],[f34,f787]) ).
fof(f2388,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))
| ~ member(ordered_pair(ordered_pair(X1,X2),X0),X3)
| ~ member(X2,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f34,f16]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
fof(f2348,plain,
! [X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0))
| ~ subclass(universal_class,complement(complement(cross_product(universal_class,cross_product(universal_class,universal_class))))) ),
inference(resolution,[],[f108,f787]) ).
fof(f2347,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f108,f16]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).
fof(f2304,plain,
! [X2,X0,X1] :
( member(ordered_pair(not_homomorphism1(X1,restrict(element_relation,universal_class,X0),X2),not_homomorphism2(X1,restrict(element_relation,universal_class,X0),X2)),sum_class(X0))
| ~ operation(X2)
| ~ compatible(X1,restrict(element_relation,universal_class,X0),X2)
| homomorphism(X1,restrict(element_relation,universal_class,X0),X2)
| ~ operation(restrict(element_relation,universal_class,X0)) ),
inference(superposition,[],[f90,f53]) ).
fof(f2303,plain,
! [X2,X0,X1] :
( member(ordered_pair(not_homomorphism1(X1,flip(cross_product(X0,universal_class)),X2),not_homomorphism2(X1,flip(cross_product(X0,universal_class)),X2)),inverse(X0))
| ~ operation(X2)
| ~ compatible(X1,flip(cross_product(X0,universal_class)),X2)
| homomorphism(X1,flip(cross_product(X0,universal_class)),X2)
| ~ operation(flip(cross_product(X0,universal_class))) ),
inference(superposition,[],[f90,f38]) ).
fof(f2302,plain,
! [X2,X0,X1] :
( member(ordered_pair(not_homomorphism1(X1,inverse(X0),X2),not_homomorphism2(X1,inverse(X0),X2)),range_of(X0))
| ~ operation(X2)
| ~ compatible(X1,inverse(X0),X2)
| homomorphism(X1,inverse(X0),X2)
| ~ operation(inverse(X0)) ),
inference(superposition,[],[f90,f39]) ).
fof(f2301,plain,
! [X2,X3,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism2(X1,X2,X0)),X3) ),
inference(resolution,[],[f90,f1]) ).
fof(f2299,plain,
! [X2,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(universal_class,complement(domain_of(X2))) ),
inference(resolution,[],[f90,f698]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
fof(f2077,plain,
! [X0] :
( member(X0,universal_class)
| ~ subclass(universal_class,complement(complement(subset_relation))) ),
inference(resolution,[],[f2065,f787]) ).
fof(f2221,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,ordered_pair(X1,X2)),compose(X3,X4))
| ~ member(ordered_pair(X0,ordered_pair(X1,X2)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X3,image(X4,singleton(X0)))) ),
inference(resolution,[],[f59,f697]) ).
fof(f2220,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,ordered_pair(X1,X2)),compose(X3,X4))
| ~ member(ordered_pair(X0,ordered_pair(X1,X2)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,complement(complement(image(X3,image(X4,singleton(X0)))))) ),
inference(resolution,[],[f59,f787]) ).
fof(f2219,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,unordered_pair(X1,X2)),compose(X3,X4))
| ~ member(ordered_pair(X0,unordered_pair(X1,X2)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X3,image(X4,singleton(X0)))) ),
inference(resolution,[],[f59,f161]) ).
fof(f2218,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,unordered_pair(X1,X2)),compose(X3,X4))
| ~ member(ordered_pair(X0,unordered_pair(X1,X2)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,complement(complement(image(X3,image(X4,singleton(X0)))))) ),
inference(resolution,[],[f59,f471]) ).
fof(f2217,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,regular(X1)),compose(X2,X3))
| ~ member(ordered_pair(X0,regular(X1)),cross_product(universal_class,universal_class))
| ~ subclass(X1,image(X2,image(X3,singleton(X0))))
| null_class = X1 ),
inference(resolution,[],[f59,f159]) ).
fof(f2216,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,power_class(X1)),compose(X2,X3))
| ~ member(ordered_pair(X0,power_class(X1)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X2,image(X3,singleton(X0))))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f59,f165]) ).
fof(f2215,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sum_class(X1)),compose(X2,X3))
| ~ member(ordered_pair(X0,sum_class(X1)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X2,image(X3,singleton(X0))))
| ~ member(X1,universal_class) ),
inference(resolution,[],[f59,f164]) ).
fof(f2214,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,singleton(X1)),compose(X2,X3))
| ~ member(ordered_pair(X0,singleton(X1)),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X2,image(X3,singleton(X0)))) ),
inference(resolution,[],[f59,f162]) ).
fof(f2213,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,apply(choice,image(X1,image(X2,singleton(X0))))),compose(X1,X2))
| ~ member(ordered_pair(X0,apply(choice,image(X1,image(X2,singleton(X0))))),cross_product(universal_class,universal_class))
| null_class = image(X1,image(X2,singleton(X0)))
| ~ member(image(X1,image(X2,singleton(X0))),universal_class) ),
inference(resolution,[],[f59,f70]) ).
fof(f2211,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,regular(image(X1,image(X2,singleton(X0))))),compose(X1,X2))
| ~ member(ordered_pair(X0,regular(image(X1,image(X2,singleton(X0))))),cross_product(universal_class,universal_class))
| null_class = image(X1,image(X2,singleton(X0))) ),
inference(resolution,[],[f59,f66]) ).
fof(f2210,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,omega),compose(X1,X2))
| ~ member(ordered_pair(X0,omega),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,image(X1,image(X2,singleton(X0)))) ),
inference(resolution,[],[f59,f163]) ).
fof(f2209,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,null_class),compose(X1,X2))
| ~ member(ordered_pair(X0,null_class),cross_product(universal_class,universal_class))
| ~ inductive(image(X1,image(X2,singleton(X0)))) ),
inference(resolution,[],[f59,f47]) ).
fof(f2207,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),compose(X1,X2))
| ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),cross_product(universal_class,universal_class))
| subclass(image(X1,image(X2,singleton(X0))),X3) ),
inference(resolution,[],[f59,f2]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(X4,image(X7,image(X5,singleton(X1))))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
fof(f2199,plain,
! [X0] :
( ~ subclass(range_of(restrict(element_relation,universal_class,X0)),domain_of(sum_class(X0)))
| sum_class(X0) != cross_product(domain_of(sum_class(X0)),domain_of(sum_class(X0)))
| operation(restrict(element_relation,universal_class,X0))
| ~ function(restrict(element_relation,universal_class,X0)) ),
inference(forward_demodulation,[],[f2194,f53]) ).
fof(f2194,plain,
! [X0] :
( sum_class(X0) != cross_product(domain_of(sum_class(X0)),domain_of(sum_class(X0)))
| operation(restrict(element_relation,universal_class,X0))
| ~ subclass(range_of(restrict(element_relation,universal_class,X0)),domain_of(domain_of(restrict(element_relation,universal_class,X0))))
| ~ function(restrict(element_relation,universal_class,X0)) ),
inference(superposition,[],[f81,f53]) ).
fof(f2198,plain,
! [X0] :
( ~ subclass(range_of(flip(cross_product(X0,universal_class))),range_of(X0))
| inverse(X0) != cross_product(range_of(X0),range_of(X0))
| operation(flip(cross_product(X0,universal_class)))
| ~ function(flip(cross_product(X0,universal_class))) ),
inference(forward_demodulation,[],[f2197,f39]) ).
fof(f2197,plain,
! [X0] :
( ~ subclass(range_of(flip(cross_product(X0,universal_class))),domain_of(inverse(X0)))
| inverse(X0) != cross_product(range_of(X0),range_of(X0))
| operation(flip(cross_product(X0,universal_class)))
| ~ function(flip(cross_product(X0,universal_class))) ),
inference(forward_demodulation,[],[f2196,f38]) ).
fof(f2196,plain,
! [X0] :
( inverse(X0) != cross_product(range_of(X0),range_of(X0))
| operation(flip(cross_product(X0,universal_class)))
| ~ subclass(range_of(flip(cross_product(X0,universal_class))),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(flip(cross_product(X0,universal_class))) ),
inference(forward_demodulation,[],[f2193,f39]) ).
fof(f2193,plain,
! [X0] :
( inverse(X0) != cross_product(domain_of(inverse(X0)),domain_of(inverse(X0)))
| operation(flip(cross_product(X0,universal_class)))
| ~ subclass(range_of(flip(cross_product(X0,universal_class))),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(flip(cross_product(X0,universal_class))) ),
inference(superposition,[],[f81,f38]) ).
fof(f2195,plain,
! [X0] :
( ~ subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| range_of(X0) != cross_product(domain_of(range_of(X0)),domain_of(range_of(X0)))
| operation(inverse(X0))
| ~ function(inverse(X0)) ),
inference(forward_demodulation,[],[f2192,f39]) ).
fof(f2192,plain,
! [X0] :
( range_of(X0) != cross_product(domain_of(range_of(X0)),domain_of(range_of(X0)))
| operation(inverse(X0))
| ~ subclass(range_of(inverse(X0)),domain_of(domain_of(inverse(X0))))
| ~ function(inverse(X0)) ),
inference(superposition,[],[f81,f39]) ).
fof(f81,axiom,
! [X8] :
( domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8)))
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| ~ function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
fof(f2187,plain,
! [X2,X0,X1] :
( ~ subclass(range_of(X1),domain_of(sum_class(X0)))
| compatible(X1,X2,restrict(element_relation,universal_class,X0))
| domain_of(X1) != domain_of(domain_of(X2))
| ~ function(X1) ),
inference(superposition,[],[f85,f53]) ).
fof(f2188,plain,
! [X2,X0,X1] :
( ~ subclass(range_of(X1),range_of(X0))
| compatible(X1,X2,flip(cross_product(X0,universal_class)))
| domain_of(X1) != domain_of(domain_of(X2))
| ~ function(X1) ),
inference(forward_demodulation,[],[f2186,f39]) ).
fof(f2186,plain,
! [X2,X0,X1] :
( ~ subclass(range_of(X1),domain_of(inverse(X0)))
| compatible(X1,X2,flip(cross_product(X0,universal_class)))
| domain_of(X1) != domain_of(domain_of(X2))
| ~ function(X1) ),
inference(superposition,[],[f85,f38]) ).
fof(f2185,plain,
! [X2,X0,X1] :
( ~ subclass(range_of(X1),domain_of(range_of(X0)))
| compatible(X1,X2,inverse(X0))
| domain_of(X1) != domain_of(domain_of(X2))
| ~ function(X1) ),
inference(superposition,[],[f85,f39]) ).
fof(f2184,plain,
! [X2,X3,X0,X1] :
( ~ subclass(image(X0,X1),domain_of(domain_of(X2)))
| compatible(restrict(X0,X1,universal_class),X3,X2)
| domain_of(domain_of(X3)) != domain_of(restrict(X0,X1,universal_class))
| ~ function(restrict(X0,X1,universal_class)) ),
inference(superposition,[],[f85,f42]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ subclass(range_of(X9),domain_of(domain_of(X11)))
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ function(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
fof(f2097,plain,
! [X0,X1] :
( member(ordered_pair(X0,compose(X1,X0)),compose_class(X1))
| ~ subclass(universal_class,complement(complement(cross_product(universal_class,universal_class)))) ),
inference(resolution,[],[f117,f787]) ).
fof(f2096,plain,
! [X0,X1] :
( member(ordered_pair(X0,compose(X1,X0)),compose_class(X1))
| ~ member(ordered_pair(X0,compose(X1,X0)),subset_relation) ),
inference(resolution,[],[f117,f2006]) ).
fof(f2095,plain,
! [X0,X1] :
( member(ordered_pair(X0,compose(X1,X0)),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f117,f16]) ).
fof(f117,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,compose(X0,X1)),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,compose(X0,X1)),compose_class(X0)) ),
inference(equality_resolution,[],[f94]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).
fof(f2079,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),identity_relation)
| member(X0,universal_class) ),
inference(resolution,[],[f2066,f134]) ).
fof(f2076,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),identity_relation)
| member(X0,universal_class) ),
inference(resolution,[],[f2065,f134]) ).
fof(f2080,plain,
! [X0] :
( member(X0,universal_class)
| ~ subclass(universal_class,complement(complement(subset_relation))) ),
inference(resolution,[],[f2066,f787]) ).
fof(f2066,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),subset_relation)
| member(X0,universal_class) ),
inference(resolution,[],[f2006,f14]) ).
fof(f2065,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),subset_relation)
| member(X1,universal_class) ),
inference(resolution,[],[f2006,f15]) ).
fof(f2070,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| null_class = complement(cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f2006,f120]) ).
fof(f2068,plain,
! [X0] :
( ~ member(ordered_pair(X0,successor(X0)),subset_relation)
| member(ordered_pair(X0,successor(X0)),successor_relation) ),
inference(resolution,[],[f2006,f116]) ).
fof(f2067,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),subset_relation)
| ~ subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
inference(resolution,[],[f2006,f698]) ).
fof(f2064,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),subset_relation)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1) ),
inference(resolution,[],[f2006,f20]) ).
fof(f2062,plain,
! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| ~ subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
inference(resolution,[],[f2006,f263]) ).
fof(f2061,plain,
! [X0] :
( ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation)
| subclass(complement(cross_product(universal_class,universal_class)),X0) ),
inference(resolution,[],[f2006,f121]) ).
fof(f2060,plain,
! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f2006,f3]) ).
fof(f2059,plain,
! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) ),
inference(resolution,[],[f2006,f1]) ).
fof(f2006,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) ),
inference(superposition,[],[f21,f1933]) ).
fof(f2047,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X2)
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),X2) ),
inference(resolution,[],[f97,f1]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,complement(composition_function)) ),
inference(resolution,[],[f97,f698]) ).
fof(f97,axiom,
! [X0,X1] :
( member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).
fof(f2023,plain,
( ~ member(null_class,subset_relation)
| ~ inductive(symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(superposition,[],[f1693,f1933]) ).
fof(f2022,plain,
( member(null_class,complement(subset_relation))
| ~ inductive(symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(superposition,[],[f1662,f1933]) ).
fof(f2021,plain,
symmetric_difference(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) = intersection(complement(subset_relation),union(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),
inference(superposition,[],[f1614,f1933]) ).
fof(f2020,plain,
! [X0,X1] :
( ~ subclass(universal_class,subset_relation)
| member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f719,f1933]) ).
fof(f2019,plain,
! [X0,X1] :
( ~ subclass(universal_class,subset_relation)
| member(ordered_pair(X0,X1),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f718,f1933]) ).
fof(f2018,plain,
! [X0,X1] :
( ~ subclass(universal_class,subset_relation)
| member(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f265,f1933]) ).
fof(f2017,plain,
! [X0,X1] :
( ~ subclass(universal_class,subset_relation)
| member(unordered_pair(X0,X1),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f264,f1933]) ).
fof(f2014,plain,
! [X0] :
( ~ subclass(universal_class,subset_relation)
| member(singleton(X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f177,f1933]) ).
fof(f2013,plain,
! [X0] :
( ~ subclass(universal_class,subset_relation)
| member(singleton(X0),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f176,f1933]) ).
fof(f2012,plain,
( ~ subclass(universal_class,subset_relation)
| member(omega,cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f173,f1933]) ).
fof(f2011,plain,
( ~ subclass(universal_class,subset_relation)
| member(omega,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f172,f1933]) ).
fof(f2010,plain,
( ~ inductive(subset_relation)
| member(null_class,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
inference(superposition,[],[f131,f1933]) ).
fof(f2008,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ member(X0,cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f23,f1933]) ).
fof(f2005,plain,
subset_relation = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),
inference(superposition,[],[f29,f1933]) ).
fof(f1933,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),
inference(forward_demodulation,[],[f74,f29]) ).
fof(f1930,plain,
! [X0,X1] :
( ~ member(omega,domain_of(restrict(identity_relation,X0,X1)))
| ~ subclass(universal_class,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f180,f29]) ).
fof(f1929,plain,
( ~ member(omega,domain_of(null_class))
| ~ subclass(universal_class,diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f180,f767]) ).
fof(f1931,plain,
! [X0] :
( ~ subclass(universal_class,diagonalise(X0))
| null_class = restrict(intersection(X0,identity_relation),singleton(omega),universal_class) ),
inference(subsumption_resolution,[],[f1927,f52]) ).
fof(f1927,plain,
! [X0] :
( ~ subclass(universal_class,diagonalise(X0))
| ~ member(omega,universal_class)
| null_class = restrict(intersection(X0,identity_relation),singleton(omega),universal_class) ),
inference(resolution,[],[f180,f31]) ).
fof(f180,plain,
! [X0] :
( ~ member(omega,domain_of(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(superposition,[],[f171,f76]) ).
fof(f1924,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| ~ subclass(union(X0,X1),X2)
| member(omega,X2) ),
inference(resolution,[],[f1682,f1]) ).
fof(f1682,plain,
! [X0,X1] :
( member(omega,union(X0,X1))
| ~ subclass(universal_class,symmetric_difference(X0,X1)) ),
inference(resolution,[],[f1660,f163]) ).
fof(f1897,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_of(restrict(identity_relation,X0,X1)))
| ~ member(omega,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f580,f29]) ).
fof(f1896,plain,
( ~ subclass(universal_class,domain_of(null_class))
| ~ member(omega,diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f580,f767]) ).
fof(f580,plain,
! [X0] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ member(omega,diagonalise(X0)) ),
inference(resolution,[],[f155,f163]) ).
fof(f1894,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,regular(complement(image(X1,image(X2,singleton(X0)))))),compose(X1,X2))
| null_class = complement(image(X1,image(X2,singleton(X0)))) ),
inference(resolution,[],[f58,f120]) ).
fof(f1893,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X2)),compose(X3,X4))
| ~ subclass(universal_class,complement(image(X3,image(X4,singleton(X0))))) ),
inference(resolution,[],[f58,f698]) ).
fof(f1892,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,singleton(X1)),compose(X2,X3))
| ~ subclass(universal_class,complement(image(X2,image(X3,singleton(X0))))) ),
inference(resolution,[],[f58,f175]) ).
fof(f1891,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,unordered_pair(X1,X2)),compose(X3,X4))
| ~ subclass(universal_class,complement(image(X3,image(X4,singleton(X0))))) ),
inference(resolution,[],[f58,f263]) ).
fof(f1890,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,not_subclass_element(complement(image(X1,image(X2,singleton(X0)))),X3)),compose(X1,X2))
| subclass(complement(image(X1,image(X2,singleton(X0)))),X3) ),
inference(resolution,[],[f58,f121]) ).
fof(f1889,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,not_subclass_element(X1,image(X2,image(X3,singleton(X0))))),compose(X2,X3))
| subclass(X1,image(X2,image(X3,singleton(X0)))) ),
inference(resolution,[],[f58,f3]) ).
fof(f1888,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ subclass(image(X2,image(X3,singleton(X0))),X4)
| member(X1,X4) ),
inference(resolution,[],[f58,f1]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( member(X4,image(X7,image(X5,singleton(X1))))
| ~ member(ordered_pair(X1,X4),compose(X7,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
fof(f557,plain,
! [X0] :
( ~ member(not_subclass_element(complement(subset_relation),X0),identity_relation)
| subclass(complement(subset_relation),X0) ),
inference(resolution,[],[f121,f134]) ).
fof(f1706,plain,
( member(null_class,union(universal_class,universal_class))
| ~ inductive(symmetric_difference(null_class,null_class)) ),
inference(superposition,[],[f1662,f796]) ).
fof(f1845,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,flip(X3)) ),
inference(resolution,[],[f36,f697]) ).
fof(f1844,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,complement(complement(flip(X3)))) ),
inference(resolution,[],[f36,f787]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| member(ordered_pair(ordered_pair(X3,X2),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
fof(f1802,plain,
! [X0,X1] :
( subclass(identity_relation,X0)
| ~ subclass(universal_class,X1)
| member(not_subclass_element(identity_relation,X0),X1) ),
inference(resolution,[],[f1146,f1]) ).
fof(f1146,plain,
! [X0] :
( member(not_subclass_element(identity_relation,X0),universal_class)
| subclass(identity_relation,X0) ),
inference(resolution,[],[f1143,f2]) ).
fof(f1779,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,rotate(X3)) ),
inference(resolution,[],[f33,f697]) ).
fof(f1778,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,complement(complement(rotate(X3)))) ),
inference(resolution,[],[f33,f787]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| member(ordered_pair(ordered_pair(X3,X6),X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
fof(f64,axiom,
! [X8] :
( ~ subclass(compose(X8,inverse(X8)),identity_relation)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
fof(f1714,plain,
! [X0] :
( ~ member(null_class,null_class)
| ~ inductive(symmetric_difference(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f1693,f67]) ).
fof(f1716,plain,
! [X0] :
( ~ member(null_class,null_class)
| ~ inductive(symmetric_difference(singleton(X0),X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f1693,f767]) ).
fof(f1324,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,diagonalise(X0)))
| ~ member(omega,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f567,f76]) ).
fof(f1338,plain,
! [X0] :
( null_class = cantor(intersection(X0,identity_relation))
| ~ member(regular(cantor(intersection(X0,identity_relation))),diagonalise(X0)) ),
inference(resolution,[],[f950,f155]) ).
fof(f1346,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(intersection(X0,identity_relation)))
| ~ member(unordered_pair(X1,X2),diagonalise(X0)) ),
inference(resolution,[],[f954,f155]) ).
fof(f1364,plain,
! [X0] :
( ~ member(omega,image(element_relation,diagonalise(X0)))
| ~ subclass(universal_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f179,f76]) ).
fof(f1384,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(inverse(subset_relation))))
| ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation) ),
inference(resolution,[],[f471,f757]) ).
fof(f1389,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(identity_relation)))
| member(unordered_pair(X0,X1),X2)
| ~ subclass(subset_relation,X2) ),
inference(resolution,[],[f471,f170]) ).
fof(f1425,plain,
! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,X0)
| ~ member(X1,singleton(X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f23,f767]) ).
fof(f1448,plain,
( complement(domain_of(null_class)) = diagonalise(singleton(identity_relation))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f76,f767]) ).
fof(f1449,plain,
( ~ member(null_class,domain_of(null_class))
| ~ inductive(diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f154,f767]) ).
fof(f1450,plain,
! [X0] :
( ~ member(X0,domain_of(null_class))
| ~ member(X0,diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f155,f767]) ).
fof(f1452,plain,
( ~ inductive(domain_of(null_class))
| ~ inductive(diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f408,f767]) ).
fof(f1453,plain,
( ~ inductive(domain_of(null_class))
| ~ member(null_class,diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f579,f767]) ).
fof(f1454,plain,
( ~ inductive(cantor(null_class))
| ~ inductive(diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f940,f767]) ).
fof(f1455,plain,
( ~ inductive(cantor(null_class))
| ~ member(null_class,diagonalise(singleton(identity_relation)))
| null_class = singleton(identity_relation) ),
inference(superposition,[],[f941,f767]) ).
fof(f1483,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(intersection(X1,identity_relation),singleton(X0),universal_class)
| ~ member(X0,diagonalise(X1)) ),
inference(resolution,[],[f31,f155]) ).
fof(f1507,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(intersection(X0,identity_relation)))
| ~ member(ordered_pair(X1,X2),diagonalise(X0)) ),
inference(resolution,[],[f955,f155]) ).
fof(f1559,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(inverse(subset_relation))))
| ~ member(ordered_pair(X0,X1),subset_relation)
| member(ordered_pair(X0,X1),identity_relation) ),
inference(resolution,[],[f787,f757]) ).
fof(f1564,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(identity_relation)))
| member(ordered_pair(X0,X1),X2)
| ~ subclass(subset_relation,X2) ),
inference(resolution,[],[f787,f170]) ).
fof(f1609,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,diagonalise(X0)))
| ~ subclass(universal_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f1358,f76]) ).
fof(f1703,plain,
( member(null_class,complement(identity_relation))
| ~ inductive(symmetric_difference(inverse(subset_relation),subset_relation)) ),
inference(superposition,[],[f1662,f75]) ).
fof(f1713,plain,
! [X0,X1] :
( ~ inductive(symmetric_difference(X0,X1))
| ~ inductive(intersection(X0,X1)) ),
inference(resolution,[],[f1693,f47]) ).
fof(f1721,plain,
! [X0] :
( ~ member(null_class,cantor(X0))
| ~ inductive(symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))) ),
inference(superposition,[],[f1693,f77]) ).
fof(f1720,plain,
! [X0,X1] :
( ~ member(null_class,symmetric_difference(X0,X1))
| ~ inductive(symmetric_difference(complement(intersection(X0,X1)),union(X0,X1))) ),
inference(superposition,[],[f1693,f1614]) ).
fof(f1717,plain,
! [X2,X0,X1] :
( ~ member(null_class,restrict(X2,X0,X1))
| ~ inductive(symmetric_difference(cross_product(X0,X1),X2)) ),
inference(superposition,[],[f1693,f29]) ).
fof(f1715,plain,
! [X2,X0,X1] :
( ~ member(null_class,restrict(X0,X1,X2))
| ~ inductive(symmetric_difference(X0,cross_product(X1,X2))) ),
inference(superposition,[],[f1693,f28]) ).
fof(f1693,plain,
! [X0,X1] :
( ~ member(null_class,intersection(X0,X1))
| ~ inductive(symmetric_difference(X0,X1)) ),
inference(resolution,[],[f1662,f24]) ).
fof(f1707,plain,
! [X0] :
( member(null_class,union(X0,universal_class))
| ~ inductive(symmetric_difference(complement(X0),null_class)) ),
inference(superposition,[],[f1662,f615]) ).
fof(f1705,plain,
! [X0] :
( member(null_class,union(universal_class,X0))
| ~ inductive(symmetric_difference(null_class,complement(X0))) ),
inference(superposition,[],[f1662,f614]) ).
fof(f1704,plain,
! [X0,X1] :
( member(null_class,union(X0,X1))
| ~ inductive(symmetric_difference(complement(X0),complement(X1))) ),
inference(superposition,[],[f1662,f26]) ).
fof(f1702,plain,
! [X0] :
( member(null_class,complement(cantor(X0)))
| ~ inductive(symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))) ),
inference(superposition,[],[f1662,f77]) ).
fof(f1701,plain,
! [X0,X1] :
( member(null_class,complement(symmetric_difference(X0,X1)))
| ~ inductive(symmetric_difference(complement(intersection(X0,X1)),union(X0,X1))) ),
inference(superposition,[],[f1662,f1614]) ).
fof(f1698,plain,
! [X2,X0,X1] :
( member(null_class,complement(restrict(X2,X0,X1)))
| ~ inductive(symmetric_difference(cross_product(X0,X1),X2)) ),
inference(superposition,[],[f1662,f29]) ).
fof(f1697,plain,
! [X0] :
( member(null_class,complement(null_class))
| ~ inductive(symmetric_difference(singleton(X0),X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f1662,f767]) ).
fof(f1696,plain,
! [X2,X0,X1] :
( member(null_class,complement(restrict(X0,X1,X2)))
| ~ inductive(symmetric_difference(X0,cross_product(X1,X2))) ),
inference(superposition,[],[f1662,f28]) ).
fof(f1695,plain,
! [X0] :
( member(null_class,complement(null_class))
| ~ inductive(symmetric_difference(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f1662,f67]) ).
fof(f1694,plain,
! [X2,X0,X1] :
( ~ inductive(symmetric_difference(X0,X1))
| ~ subclass(complement(intersection(X0,X1)),X2)
| member(null_class,X2) ),
inference(resolution,[],[f1662,f1]) ).
fof(f1662,plain,
! [X0,X1] :
( member(null_class,complement(intersection(X0,X1)))
| ~ inductive(symmetric_difference(X0,X1)) ),
inference(superposition,[],[f126,f1614]) ).
fof(f1692,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,symmetric_difference(X2,X3)) ),
inference(resolution,[],[f1660,f697]) ).
fof(f1691,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,X3)))) ),
inference(resolution,[],[f1660,f787]) ).
fof(f1690,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,symmetric_difference(X2,X3)) ),
inference(resolution,[],[f1660,f161]) ).
fof(f1689,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),union(X2,X3))
| ~ subclass(universal_class,complement(complement(symmetric_difference(X2,X3)))) ),
inference(resolution,[],[f1660,f471]) ).
fof(f1688,plain,
! [X2,X0,X1] :
( member(regular(X0),union(X1,X2))
| ~ subclass(X0,symmetric_difference(X1,X2))
| null_class = X0 ),
inference(resolution,[],[f1660,f159]) ).
fof(f1687,plain,
! [X2,X0,X1] :
( member(power_class(X0),union(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1660,f165]) ).
fof(f1686,plain,
! [X2,X0,X1] :
( member(sum_class(X0),union(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1660,f164]) ).
fof(f1685,plain,
! [X2,X0,X1] :
( member(singleton(X0),union(X1,X2))
| ~ subclass(universal_class,symmetric_difference(X1,X2)) ),
inference(resolution,[],[f1660,f162]) ).
fof(f1684,plain,
! [X0,X1] :
( member(apply(choice,symmetric_difference(X0,X1)),union(X0,X1))
| symmetric_difference(X0,X1) = null_class
| ~ member(symmetric_difference(X0,X1),universal_class) ),
inference(resolution,[],[f1660,f70]) ).
fof(f1683,plain,
! [X0,X1] :
( member(regular(symmetric_difference(X0,X1)),union(X0,X1))
| symmetric_difference(X0,X1) = null_class ),
inference(resolution,[],[f1660,f66]) ).
fof(f1679,plain,
! [X2,X0,X1] :
( member(not_subclass_element(symmetric_difference(X0,X1),X2),union(X0,X1))
| subclass(symmetric_difference(X0,X1),X2) ),
inference(resolution,[],[f1660,f2]) ).
fof(f1660,plain,
! [X2,X0,X1] :
( ~ member(X2,symmetric_difference(X0,X1))
| member(X2,union(X0,X1)) ),
inference(superposition,[],[f22,f1614]) ).
fof(f1678,plain,
! [X0] :
( ~ inductive(symmetric_difference(X0,singleton(X0)))
| member(null_class,successor(X0)) ),
inference(superposition,[],[f1663,f43]) ).
fof(f1677,plain,
! [X2,X0,X1] :
( ~ inductive(symmetric_difference(X0,X1))
| ~ subclass(union(X0,X1),X2)
| member(null_class,X2) ),
inference(resolution,[],[f1663,f1]) ).
fof(f1663,plain,
! [X0,X1] :
( member(null_class,union(X0,X1))
| ~ inductive(symmetric_difference(X0,X1)) ),
inference(superposition,[],[f131,f1614]) ).
fof(f1673,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(ordered_pair(X2,X3),complement(intersection(X0,X1))) ),
inference(superposition,[],[f719,f1614]) ).
fof(f1672,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(ordered_pair(X2,X3),union(X0,X1)) ),
inference(superposition,[],[f718,f1614]) ).
fof(f1671,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(unordered_pair(X2,X3),complement(intersection(X0,X1))) ),
inference(superposition,[],[f265,f1614]) ).
fof(f1670,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(unordered_pair(X2,X3),union(X0,X1)) ),
inference(superposition,[],[f264,f1614]) ).
fof(f1667,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(singleton(X2),complement(intersection(X0,X1))) ),
inference(superposition,[],[f177,f1614]) ).
fof(f1666,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(singleton(X2),union(X0,X1)) ),
inference(superposition,[],[f176,f1614]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(omega,complement(intersection(X0,X1))) ),
inference(superposition,[],[f173,f1614]) ).
fof(f1664,plain,
! [X0,X1] :
( ~ subclass(universal_class,symmetric_difference(X0,X1))
| member(omega,union(X0,X1)) ),
inference(superposition,[],[f172,f1614]) ).
fof(f1661,plain,
! [X2,X0,X1] :
( member(X2,symmetric_difference(X0,X1))
| ~ member(X2,union(X0,X1))
| ~ member(X2,complement(intersection(X0,X1))) ),
inference(superposition,[],[f23,f1614]) ).
fof(f1657,plain,
! [X0] : symmetric_difference(complement(X0),null_class) = intersection(union(X0,universal_class),union(complement(X0),null_class)),
inference(superposition,[],[f1614,f615]) ).
fof(f1656,plain,
symmetric_difference(null_class,null_class) = intersection(union(universal_class,universal_class),union(null_class,null_class)),
inference(superposition,[],[f1614,f796]) ).
fof(f1655,plain,
! [X0] : symmetric_difference(null_class,complement(X0)) = intersection(union(universal_class,X0),union(null_class,complement(X0))),
inference(superposition,[],[f1614,f614]) ).
fof(f1652,plain,
! [X0] : symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = intersection(complement(cantor(X0)),union(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))),
inference(superposition,[],[f1614,f77]) ).
fof(f1651,plain,
! [X0,X1] : symmetric_difference(complement(intersection(X0,X1)),union(X0,X1)) = intersection(complement(symmetric_difference(X0,X1)),union(complement(intersection(X0,X1)),union(X0,X1))),
inference(superposition,[],[f1614,f1614]) ).
fof(f1648,plain,
! [X2,X0,X1] : symmetric_difference(cross_product(X0,X1),X2) = intersection(complement(restrict(X2,X0,X1)),union(cross_product(X0,X1),X2)),
inference(superposition,[],[f1614,f29]) ).
fof(f1647,plain,
! [X0] :
( symmetric_difference(singleton(X0),X0) = intersection(complement(null_class),union(singleton(X0),X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f1614,f767]) ).
fof(f1646,plain,
! [X2,X0,X1] : symmetric_difference(X0,cross_product(X1,X2)) = intersection(complement(restrict(X0,X1,X2)),union(X0,cross_product(X1,X2))),
inference(superposition,[],[f1614,f28]) ).
fof(f1614,plain,
! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f1612,plain,
( ~ subclass(universal_class,image(element_relation,power_class(universal_class)))
| ~ subclass(universal_class,power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f1358,f616]) ).
fof(f1611,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,power_class(X0)))
| ~ subclass(universal_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f1358,f55]) ).
fof(f1608,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,union(X0,universal_class)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f1358,f615]) ).
fof(f1607,plain,
( ~ subclass(universal_class,image(element_relation,union(universal_class,universal_class)))
| ~ subclass(universal_class,power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f1358,f796]) ).
fof(f1606,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,union(universal_class,X0)))
| ~ subclass(universal_class,power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f1358,f614]) ).
fof(f1605,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,X1)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f1358,f26]) ).
fof(f1358,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ subclass(universal_class,power_class(X0)) ),
inference(resolution,[],[f179,f163]) ).
fof(f1602,plain,
! [X2,X0,X1] :
( member(singleton(X2),image(X0,X1))
| ~ subclass(universal_class,cantor(inverse(restrict(X0,X1,universal_class)))) ),
inference(superposition,[],[f973,f42]) ).
fof(f1601,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| ~ subclass(range_of(X0),X1)
| member(singleton(X2),X1) ),
inference(resolution,[],[f973,f1]) ).
fof(f1600,plain,
! [X0] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| ~ subclass(universal_class,complement(range_of(X0))) ),
inference(resolution,[],[f973,f175]) ).
fof(f973,plain,
! [X0,X1] :
( member(singleton(X1),range_of(X0))
| ~ subclass(universal_class,cantor(inverse(X0))) ),
inference(superposition,[],[f952,f39]) ).
fof(f1543,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(application_function)))
| member(X0,domain_of(X1)) ),
inference(resolution,[],[f787,f106]) ).
fof(f1541,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(domain_relation)))
| domain_of(X0) = X1 ),
inference(resolution,[],[f787,f99]) ).
fof(f1539,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(successor_relation)))
| successor(X0) = X1 ),
inference(resolution,[],[f787,f45]) ).
fof(f1583,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ subclass(universal_class,complement(complement(cross_product(universal_class,universal_class)))) ),
inference(resolution,[],[f20,f787]) ).
fof(f1582,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f20,f16]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
fof(f1538,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(element_relation)))
| member(X0,X1) ),
inference(resolution,[],[f787,f19]) ).
fof(f1565,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(cantor(X0))))
| member(ordered_pair(X1,X2),domain_of(X0)) ),
inference(resolution,[],[f787,f923]) ).
fof(f1553,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,complement(complement(restrict(X0,X1,X2))))
| member(ordered_pair(X3,X4),X0) ),
inference(resolution,[],[f787,f495]) ).
fof(f1552,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(complement(X0))))
| ~ member(ordered_pair(X1,X2),X0) ),
inference(resolution,[],[f787,f24]) ).
fof(f1551,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(intersection(X0,X1))))
| member(ordered_pair(X2,X3),X0) ),
inference(resolution,[],[f787,f21]) ).
fof(f1550,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(intersection(X0,X1))))
| member(ordered_pair(X2,X3),X1) ),
inference(resolution,[],[f787,f22]) ).
fof(f1549,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(cross_product(X0,X1))))
| ordered_pair(X2,X3) = ordered_pair(first(ordered_pair(X2,X3)),second(ordered_pair(X2,X3))) ),
inference(resolution,[],[f787,f17]) ).
fof(f1548,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(singleton(X0))))
| ordered_pair(X1,X2) = X0 ),
inference(resolution,[],[f787,f650]) ).
fof(f1547,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(unordered_pair(X0,X1))))
| ordered_pair(X2,X3) = X0
| ordered_pair(X2,X3) = X1 ),
inference(resolution,[],[f787,f8]) ).
fof(f1546,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(X0)))
| ~ subclass(X0,X1)
| member(ordered_pair(X2,X3),X1) ),
inference(resolution,[],[f787,f1]) ).
fof(f1545,plain,
! [X0] :
( ~ subclass(universal_class,complement(complement(cross_product(universal_class,universal_class))))
| member(ordered_pair(X0,successor(X0)),successor_relation) ),
inference(resolution,[],[f787,f116]) ).
fof(f1542,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(application_function)))
| apply(X0,X1) = X2 ),
inference(resolution,[],[f787,f107]) ).
fof(f1540,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(compose_class(X0))))
| compose(X0,X1) = X2 ),
inference(resolution,[],[f787,f93]) ).
fof(f787,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(complement(X0))) ),
inference(subsumption_resolution,[],[f783,f696]) ).
fof(f783,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(X0)))
| member(ordered_pair(X1,X2),X0)
| ~ member(ordered_pair(X1,X2),universal_class) ),
inference(resolution,[],[f698,f25]) ).
fof(f116,plain,
! [X0] :
( ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,successor(X0)),successor_relation) ),
inference(equality_resolution,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
fof(f1511,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X2),sum_class(X0))
| ~ subclass(universal_class,cantor(restrict(element_relation,universal_class,X0))) ),
inference(superposition,[],[f955,f53]) ).
fof(f1510,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X2),inverse(X0))
| ~ subclass(universal_class,cantor(flip(cross_product(X0,universal_class)))) ),
inference(superposition,[],[f955,f38]) ).
fof(f1509,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X2),range_of(X0))
| ~ subclass(universal_class,cantor(inverse(X0))) ),
inference(superposition,[],[f955,f39]) ).
fof(f1508,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ subclass(domain_of(X0),X1)
| member(ordered_pair(X2,X3),X1) ),
inference(resolution,[],[f955,f1]) ).
fof(f955,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,cantor(X2)) ),
inference(resolution,[],[f923,f697]) ).
fof(f945,plain,
! [X0] :
( ~ inductive(cantor(restrict(element_relation,universal_class,X0)))
| member(null_class,sum_class(X0)) ),
inference(superposition,[],[f926,f53]) ).
fof(f944,plain,
! [X0] :
( ~ inductive(cantor(flip(cross_product(X0,universal_class))))
| member(null_class,inverse(X0)) ),
inference(superposition,[],[f926,f38]) ).
fof(f1495,plain,
! [X0,X1] :
( member(X1,sum_class(X0))
| ~ member(X1,universal_class)
| null_class = restrict(restrict(element_relation,universal_class,X0),singleton(X1),universal_class) ),
inference(superposition,[],[f31,f53]) ).
fof(f1494,plain,
! [X0,X1] :
( member(X1,inverse(X0))
| ~ member(X1,universal_class)
| null_class = restrict(flip(cross_product(X0,universal_class)),singleton(X1),universal_class) ),
inference(superposition,[],[f31,f38]) ).
fof(f1492,plain,
! [X0] :
( ~ member(regular(complement(domain_of(X0))),universal_class)
| null_class = restrict(X0,singleton(regular(complement(domain_of(X0)))),universal_class)
| null_class = complement(domain_of(X0)) ),
inference(resolution,[],[f31,f120]) ).
fof(f1499,plain,
! [X2,X0,X1] :
( null_class = restrict(X2,singleton(ordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X2))) ),
inference(subsumption_resolution,[],[f1489,f696]) ).
fof(f1489,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),universal_class)
| null_class = restrict(X2,singleton(ordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X2))) ),
inference(resolution,[],[f31,f698]) ).
fof(f1498,plain,
! [X0,X1] :
( null_class = restrict(X1,singleton(singleton(X0)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X1))) ),
inference(subsumption_resolution,[],[f1488,f118]) ).
fof(f1488,plain,
! [X0,X1] :
( ~ member(singleton(X0),universal_class)
| null_class = restrict(X1,singleton(singleton(X0)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X1))) ),
inference(resolution,[],[f31,f175]) ).
fof(f1497,plain,
! [X2,X0,X1] :
( null_class = restrict(X2,singleton(unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X2))) ),
inference(subsumption_resolution,[],[f1487,f11]) ).
fof(f1487,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| null_class = restrict(X2,singleton(unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,complement(domain_of(X2))) ),
inference(resolution,[],[f31,f263]) ).
fof(f1486,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
| null_class = restrict(X0,singleton(not_subclass_element(complement(domain_of(X0)),X1)),universal_class)
| subclass(complement(domain_of(X0)),X1) ),
inference(resolution,[],[f31,f121]) ).
fof(f1485,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| null_class = restrict(X1,singleton(not_subclass_element(X0,domain_of(X1))),universal_class)
| subclass(X0,domain_of(X1)) ),
inference(resolution,[],[f31,f3]) ).
fof(f1484,plain,
! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| ~ subclass(domain_of(X1),X2)
| member(X0,X2) ),
inference(resolution,[],[f31,f1]) ).
fof(f31,axiom,
! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f1481,plain,
! [X0,X1] :
( ~ subclass(sum_class(X0),X1)
| ~ inductive(cantor(restrict(element_relation,universal_class,X0)))
| member(null_class,X1) ),
inference(superposition,[],[f942,f53]) ).
fof(f1480,plain,
! [X0,X1] :
( ~ subclass(inverse(X0),X1)
| ~ inductive(cantor(flip(cross_product(X0,universal_class))))
| member(null_class,X1) ),
inference(superposition,[],[f942,f38]) ).
fof(f1479,plain,
! [X0,X1] :
( ~ subclass(range_of(X0),X1)
| ~ inductive(cantor(inverse(X0)))
| member(null_class,X1) ),
inference(superposition,[],[f942,f39]) ).
fof(f942,plain,
! [X0,X1] :
( ~ subclass(domain_of(X0),X1)
| ~ inductive(cantor(X0))
| member(null_class,X1) ),
inference(resolution,[],[f926,f1]) ).
fof(f775,plain,
! [X0,X1] :
( ~ function(ordered_pair(X0,X1))
| member(singleton(X0),cross_product(universal_class,universal_class)) ),
inference(resolution,[],[f706,f62]) ).
fof(f1438,plain,
! [X0,X1] :
( null_class = restrict(singleton(cross_product(X0,X1)),X0,X1)
| null_class = singleton(cross_product(X0,X1)) ),
inference(superposition,[],[f28,f767]) ).
fof(f1422,plain,
! [X0,X1] :
( null_class = restrict(singleton(cross_product(X0,X1)),X0,X1)
| null_class = singleton(cross_product(X0,X1)) ),
inference(superposition,[],[f767,f28]) ).
fof(f767,plain,
! [X0] :
( null_class = intersection(singleton(X0),X0)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f764]) ).
fof(f764,plain,
! [X0] :
( null_class = intersection(singleton(X0),X0)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f67,f656]) ).
fof(f1420,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(ordered_pair(X1,X2),domain_of(X0)) ),
inference(superposition,[],[f719,f77]) ).
fof(f1417,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(ordered_pair(X3,X4),cross_product(X0,X1)) ),
inference(superposition,[],[f719,f29]) ).
fof(f1416,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(ordered_pair(X3,X4),X0) ),
inference(superposition,[],[f719,f28]) ).
fof(f719,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(ordered_pair(X2,X3),X0) ),
inference(resolution,[],[f697,f21]) ).
fof(f1413,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(ordered_pair(X1,X2),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f718,f77]) ).
fof(f1410,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(ordered_pair(X3,X4),X2) ),
inference(superposition,[],[f718,f29]) ).
fof(f1409,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(ordered_pair(X3,X4),cross_product(X1,X2)) ),
inference(superposition,[],[f718,f28]) ).
fof(f718,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(ordered_pair(X2,X3),X1) ),
inference(resolution,[],[f697,f22]) ).
fof(f508,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X1,X2,X3))
| member(singleton(X0),X1) ),
inference(resolution,[],[f495,f162]) ).
fof(f1395,plain,
~ subclass(universal_class,complement(complement(null_class))),
inference(global_subsumption,[],[f27,f74,f115,f97,f58,f33,f36,f64,f20,f31,f116,f108,f89,f117,f59,f34,f37,f81,f85,f90,f91,f50,f69,f4,f52,f114,f113,f11,f18,f44,f47,f51,f98,f12,f118,f39,f75,f92,f24,f119,f43,f48,f54,f56,f57,f62,f66,f95,f105,f2,f3,f9,f124,f10,f19,f21,f127,f128,f126,f22,f132,f133,f134,f130,f129,f131,f32,f35,f38,f53,f55,f150,f63,f76,f153,f135,f157,f1,f160,f166,f167,f163,f162,f171,f180,f158,f183,f186,f188,f190,f193,f195,f196,f181,f7,f208,f210,f211,f215,f216,f218,f219,f221,f212,f206,f231,f217,f42,f184,f45,f161,f266,f214,f172,f173,f175,f277,f285,f67,f286,f287,f288,f276,f292,f293,f283,f284,f290,f282,f68,f316,f99,f100,f318,f319,f320,f321,f104,f322,f324,f326,f327,f325,f323,f341,f344,f346,f347,f14,f345,f15,f120,f388,f392,f393,f291,f394,f151,f403,f404,f402,f405,f406,f154,f408,f170,f409,f413,f174,f25,f420,f421,f423,f424,f425,f194,f26,f442,f443,f444,f445,f446,f447,f448,f449,f450,f451,f458,f453,f454,f456,f457,f263,f465,f470,f468,f469,f272,f389,f28,f496,f499,f500,f497,f495,f503,f507,f508,f509,f506,f176,f512,f177,f516,f281,f29,f526,f527,f528,f530,f533,f534,f535,f538,f539,f540,f541,f542,f426,f547,f548,f549,f49,f65,f554,f101,f102,f121,f555,f556,f557,f561,f562,f563,f152,f564,f568,f569,f570,f571,f572,f573,f566,f574,f575,f576,f155,f577,f580,f581,f582,f583,f584,f579,f585,f159,f589,f590,f591,f592,f593,f594,f596,f597,f598,f600,f604,f608,f609,f610,f603,f620,f628,f612,f631,f637,f8,f641,f644,f645,f646,f647,f648,f650,f658,f654,f655,f616,f660,f661,f662,f663,f664,f665,f678,f679,f668,f669,f672,f674,f675,f676,f680,f626,f657,f13,f690,f691,f693,f696,f704,f702,f705,f692,f701,f703,f708,f697,f715,f716,f718,f719,f720,f721,f725,f726,f713,f714,f23,f747,f748,f749,f750,f751,f752,f753,f754,f755,f710,f711,f630,f699,f700,f656,f768,f767,f30,f766,f770,f659,f706,f775,f698,f782,f787,f786,f717,f614,f797,f798,f799,f800,f801,f802,f803,f804,f805,f806,f807,f820,f821,f810,f811,f812,f814,f816,f817,f818,f822,f796,f823,f824,f825,f826,f827,f842,f843,f831,f832,f833,f835,f837,f838,f839,f844,f841,f615,f846,f847,f848,f849,f850,f851,f852,f853,f854,f855,f856,f857,f858,f872,f873,f861,f862,f863,f865,f867,f868,f869,f874,f871,f70,f875,f889,f878,f879,f880,f881,f885,f886,f887,f621,f891,f894,f895,f896,f897,f898,f899,f900,f670,f828,f77,f920,f921,f922,f924,f925,f928,f929,f930,f931,f926,f942,f944,f945,f923,f946,f951,f953,f955,f949,f956,f957,f959,f960,f940,f961,f943,f93,f941,f969,f952,f971,f972,f973,f974,f975,f958,f962,f970,f976,f977,f978,f979,f164,f981,f982,f983,f984,f985,f986,f987,f991,f992,f995,f997,f106,f998,f165,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1017,f1018,f1021,f209,f213,f220,f17,f1050,f1052,f1053,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f289,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1070,f643,f1073,f757,f1076,f1080,f1081,f1085,f146,f96,f1119,f1120,f1121,f168,f1142,f169,f1145,f1143,f1146,f1151,f1155,f1150,f107,f16,f1221,f1222,f1223,f40,f41,f185,f264,f1304,f1305,f1308,f265,f1312,f1313,f1316,f498,f567,f1320,f1321,f1322,f1323,f1326,f1327,f652,f1330,f1331,f1332,f1333,f890,f927,f1337,f950,f1339,f1340,f1341,f1342,f103,f954,f1347,f1349,f1350,f1351,f1352,f178,f179,f1358,f1360,f1361,f1362,f1363,f1366,f1367,f471,f1371,f1372,f1373,f1374,f1375,f1376,f1377,f1378,f1394,f1381]) ).
fof(f1393,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),X2)
| ~ subclass(universal_class,complement(complement(X2))) ),
inference(superposition,[],[f471,f13]) ).
fof(f1390,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(cantor(X0))))
| member(unordered_pair(X1,X2),domain_of(X0)) ),
inference(resolution,[],[f471,f923]) ).
fof(f1381,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(null_class)))
| member(unordered_pair(X0,X1),X2)
| null_class = X2 ),
inference(resolution,[],[f471,f291]) ).
fof(f1394,plain,
~ subclass(universal_class,complement(complement(null_class))),
inference(subsumption_resolution,[],[f1380,f11]) ).
fof(f1380,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(null_class)))
| ~ member(unordered_pair(X0,X1),universal_class) ),
inference(resolution,[],[f471,f612]) ).
fof(f1378,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,complement(complement(restrict(X0,X1,X2))))
| member(unordered_pair(X3,X4),X0) ),
inference(resolution,[],[f471,f495]) ).
fof(f1377,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(complement(X0))))
| ~ member(unordered_pair(X1,X2),X0) ),
inference(resolution,[],[f471,f24]) ).
fof(f1376,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(intersection(X0,X1))))
| member(unordered_pair(X2,X3),X0) ),
inference(resolution,[],[f471,f21]) ).
fof(f1375,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(intersection(X0,X1))))
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f471,f22]) ).
fof(f1374,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(cross_product(X0,X1))))
| unordered_pair(X2,X3) = ordered_pair(first(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))) ),
inference(resolution,[],[f471,f17]) ).
fof(f1373,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(singleton(X0))))
| unordered_pair(X1,X2) = X0 ),
inference(resolution,[],[f471,f650]) ).
fof(f1372,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(unordered_pair(X0,X1))))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 ),
inference(resolution,[],[f471,f8]) ).
fof(f1371,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(complement(X0)))
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f471,f1]) ).
fof(f471,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(complement(X0))) ),
inference(subsumption_resolution,[],[f464,f11]) ).
fof(f464,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(complement(X0)))
| member(unordered_pair(X1,X2),X0)
| ~ member(unordered_pair(X1,X2),universal_class) ),
inference(resolution,[],[f263,f25]) ).
fof(f1367,plain,
( ~ member(omega,image(element_relation,power_class(universal_class)))
| ~ subclass(universal_class,power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f179,f616]) ).
fof(f1366,plain,
! [X0] :
( ~ member(omega,image(element_relation,power_class(X0)))
| ~ subclass(universal_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f179,f55]) ).
fof(f1363,plain,
! [X0] :
( ~ member(omega,image(element_relation,union(X0,universal_class)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f179,f615]) ).
fof(f1362,plain,
( ~ member(omega,image(element_relation,union(universal_class,universal_class)))
| ~ subclass(universal_class,power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f179,f796]) ).
fof(f1361,plain,
! [X0] :
( ~ member(omega,image(element_relation,union(universal_class,X0)))
| ~ subclass(universal_class,power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f179,f614]) ).
fof(f1360,plain,
! [X0,X1] :
( ~ member(omega,image(element_relation,union(X0,X1)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f179,f26]) ).
fof(f179,plain,
! [X0] :
( ~ member(omega,image(element_relation,complement(X0)))
| ~ subclass(universal_class,power_class(X0)) ),
inference(superposition,[],[f171,f55]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(singleton(X2),X1) ),
inference(resolution,[],[f162,f1]) ).
fof(f1352,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),sum_class(X0))
| ~ subclass(universal_class,cantor(restrict(element_relation,universal_class,X0))) ),
inference(superposition,[],[f954,f53]) ).
fof(f1351,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),inverse(X0))
| ~ subclass(universal_class,cantor(flip(cross_product(X0,universal_class)))) ),
inference(superposition,[],[f954,f38]) ).
fof(f1350,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),range_of(X0))
| ~ subclass(universal_class,cantor(inverse(X0))) ),
inference(superposition,[],[f954,f39]) ).
fof(f1349,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,cantor(X2)) ),
inference(superposition,[],[f954,f13]) ).
fof(f1347,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ subclass(domain_of(X0),X1)
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f954,f1]) ).
fof(f954,plain,
! [X2,X0,X1] :
( member(unordered_pair(X0,X1),domain_of(X2))
| ~ subclass(universal_class,cantor(X2)) ),
inference(resolution,[],[f923,f161]) ).
fof(f103,axiom,
! [X0] : domain(X0,image(inverse(X0),singleton(single_valued1(X0))),single_valued2(X0)) = single_valued3(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn3) ).
fof(f1342,plain,
! [X0] :
( member(regular(cantor(restrict(element_relation,universal_class,X0))),sum_class(X0))
| null_class = cantor(restrict(element_relation,universal_class,X0)) ),
inference(superposition,[],[f950,f53]) ).
fof(f1341,plain,
! [X0] :
( member(regular(cantor(flip(cross_product(X0,universal_class)))),inverse(X0))
| null_class = cantor(flip(cross_product(X0,universal_class))) ),
inference(superposition,[],[f950,f38]) ).
fof(f1340,plain,
! [X0] :
( member(regular(cantor(inverse(X0))),range_of(X0))
| null_class = cantor(inverse(X0)) ),
inference(superposition,[],[f950,f39]) ).
fof(f1339,plain,
! [X0,X1] :
( null_class = cantor(X0)
| ~ subclass(domain_of(X0),X1)
| member(regular(cantor(X0)),X1) ),
inference(resolution,[],[f950,f1]) ).
fof(f950,plain,
! [X0] :
( member(regular(cantor(X0)),domain_of(X0))
| null_class = cantor(X0) ),
inference(resolution,[],[f923,f66]) ).
fof(f1337,plain,
! [X0,X1] :
( ~ inductive(cantor(X0))
| ~ subclass(diagonalise(compose(inverse(element_relation),X0)),X1)
| member(null_class,X1) ),
inference(resolution,[],[f927,f1]) ).
fof(f927,plain,
! [X0] :
( member(null_class,diagonalise(compose(inverse(element_relation),X0)))
| ~ inductive(cantor(X0)) ),
inference(superposition,[],[f131,f77]) ).
fof(f890,plain,
! [X0] :
( apply(choice,singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(subsumption_resolution,[],[f877,f118]) ).
fof(f877,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(singleton(X0),universal_class)
| apply(choice,singleton(X0)) = X0 ),
inference(resolution,[],[f70,f650]) ).
fof(f1333,plain,
! [X0] :
( not_subclass_element(singleton(X0),omega) = X0
| singleton(X0) = omega
| ~ inductive(singleton(X0)) ),
inference(resolution,[],[f652,f214]) ).
fof(f1332,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),X1) = X0
| member(null_class,X1)
| ~ inductive(singleton(X0)) ),
inference(resolution,[],[f652,f158]) ).
fof(f1331,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),X1) = X0
| ~ subclass(X1,singleton(X0))
| singleton(X0) = X1 ),
inference(resolution,[],[f652,f7]) ).
fof(f1330,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),X1) = X0
| member(X0,X1)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f652,f168]) ).
fof(f652,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[],[f650,f2]) ).
fof(f1327,plain,
( ~ subclass(universal_class,image(element_relation,power_class(universal_class)))
| ~ member(omega,power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f567,f616]) ).
fof(f1326,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,power_class(X0)))
| ~ member(omega,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f567,f55]) ).
fof(f1323,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,union(X0,universal_class)))
| ~ member(omega,power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f567,f615]) ).
fof(f1322,plain,
( ~ subclass(universal_class,image(element_relation,union(universal_class,universal_class)))
| ~ member(omega,power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f567,f796]) ).
fof(f1321,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,union(universal_class,X0)))
| ~ member(omega,power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f567,f614]) ).
fof(f1320,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,X1)))
| ~ member(omega,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f567,f26]) ).
fof(f567,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ member(omega,power_class(X0)) ),
inference(resolution,[],[f152,f163]) ).
fof(f498,plain,
! [X2,X0,X1] :
( ~ inductive(restrict(X0,X1,X2))
| member(null_class,cross_product(X1,X2)) ),
inference(superposition,[],[f131,f28]) ).
fof(f1316,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(unordered_pair(X1,X2),domain_of(X0)) ),
inference(superposition,[],[f265,f77]) ).
fof(f1313,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(unordered_pair(X3,X4),cross_product(X0,X1)) ),
inference(superposition,[],[f265,f29]) ).
fof(f1312,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(unordered_pair(X3,X4),X0) ),
inference(superposition,[],[f265,f28]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ),
inference(resolution,[],[f161,f21]) ).
fof(f1308,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(unordered_pair(X1,X2),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f264,f77]) ).
fof(f1305,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(unordered_pair(X3,X4),X2) ),
inference(superposition,[],[f264,f29]) ).
fof(f1304,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(unordered_pair(X3,X4),cross_product(X1,X2)) ),
inference(superposition,[],[f264,f28]) ).
fof(f264,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f161,f22]) ).
fof(f185,plain,
! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) ),
inference(resolution,[],[f158,f32]) ).
fof(f41,axiom,
! [X0,X1,X4] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range) ).
fof(f40,axiom,
! [X0,X1,X4] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain) ).
fof(f1223,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(cross_product(X3,X1),X4)
| member(ordered_pair(X2,X0),X4) ),
inference(resolution,[],[f16,f1]) ).
fof(f1222,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ordered_pair(X2,X0) = ordered_pair(first(ordered_pair(X2,X0)),second(ordered_pair(X2,X0))) ),
inference(resolution,[],[f16,f17]) ).
fof(f1221,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(universal_class,complement(cross_product(X3,X1))) ),
inference(resolution,[],[f16,f698]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f107,axiom,
! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function)
| apply(X0,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).
fof(f1150,plain,
( member(regular(identity_relation),universal_class)
| null_class = identity_relation ),
inference(resolution,[],[f1143,f66]) ).
fof(f1151,plain,
( member(apply(choice,identity_relation),universal_class)
| null_class = identity_relation
| ~ member(identity_relation,universal_class) ),
inference(resolution,[],[f1143,f70]) ).
fof(f1143,plain,
! [X0] :
( ~ member(X0,identity_relation)
| member(X0,universal_class) ),
inference(resolution,[],[f169,f4]) ).
fof(f1145,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,identity_relation)
| ~ function(inverse(subset_relation)) ),
inference(resolution,[],[f169,f62]) ).
fof(f169,plain,
! [X0,X1] :
( ~ subclass(inverse(subset_relation),X0)
| member(X1,X0)
| ~ member(X1,identity_relation) ),
inference(resolution,[],[f1,f129]) ).
fof(f1142,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(singleton(X0)) ),
inference(resolution,[],[f168,f62]) ).
fof(f168,plain,
! [X0,X1] :
( ~ subclass(singleton(X0),X1)
| member(X0,X1)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1,f124]) ).
fof(f1121,plain,
( ~ subclass(inverse(subset_relation),identity_relation)
| identity_relation = inverse(subset_relation) ),
inference(resolution,[],[f1119,f7]) ).
fof(f1120,plain,
! [X2,X0,X1] :
( compose(X0,X1) = X2
| ~ subclass(universal_class,composition_function) ),
inference(resolution,[],[f96,f697]) ).
fof(f1119,plain,
subclass(identity_relation,inverse(subset_relation)),
inference(duplicate_literal_removal,[],[f1118]) ).
fof(f1118,plain,
( subclass(identity_relation,inverse(subset_relation))
| subclass(identity_relation,inverse(subset_relation)) ),
inference(resolution,[],[f146,f2]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function)
| compose(X0,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).
fof(f146,plain,
! [X0] :
( ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
| subclass(X0,inverse(subset_relation)) ),
inference(resolution,[],[f129,f3]) ).
fof(f1085,plain,
! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,inverse(subset_relation))
| null_class = X0 ),
inference(resolution,[],[f757,f159]) ).
fof(f1081,plain,
( ~ member(apply(choice,inverse(subset_relation)),subset_relation)
| member(apply(choice,inverse(subset_relation)),identity_relation)
| null_class = inverse(subset_relation)
| ~ member(inverse(subset_relation),universal_class) ),
inference(resolution,[],[f757,f70]) ).
fof(f1080,plain,
( ~ member(regular(inverse(subset_relation)),subset_relation)
| member(regular(inverse(subset_relation)),identity_relation)
| null_class = inverse(subset_relation) ),
inference(resolution,[],[f757,f66]) ).
fof(f1076,plain,
! [X0] :
( ~ member(not_subclass_element(inverse(subset_relation),X0),subset_relation)
| member(not_subclass_element(inverse(subset_relation),X0),identity_relation)
| subclass(inverse(subset_relation),X0) ),
inference(resolution,[],[f757,f2]) ).
fof(f757,plain,
! [X0] :
( ~ member(X0,inverse(subset_relation))
| ~ member(X0,subset_relation)
| member(X0,identity_relation) ),
inference(superposition,[],[f23,f75]) ).
fof(f1073,plain,
! [X0,X1] :
( ~ inductive(ordered_pair(X0,X1))
| unordered_pair(X0,singleton(X1)) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f643,f13]) ).
fof(f643,plain,
! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| null_class = X1
| null_class = X0 ),
inference(resolution,[],[f8,f47]) ).
fof(f1068,plain,
! [X0] :
( ~ member(regular(complement(regular(X0))),null_class)
| null_class = X0
| null_class = complement(regular(X0)) ),
inference(resolution,[],[f289,f120]) ).
fof(f1067,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),null_class)
| null_class = X2
| ~ subclass(universal_class,complement(regular(X2))) ),
inference(resolution,[],[f289,f698]) ).
fof(f1066,plain,
! [X0,X1] :
( ~ member(singleton(X0),null_class)
| null_class = X1
| ~ subclass(universal_class,complement(regular(X1))) ),
inference(resolution,[],[f289,f175]) ).
fof(f1065,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),null_class)
| null_class = X2
| ~ subclass(universal_class,complement(regular(X2))) ),
inference(resolution,[],[f289,f263]) ).
fof(f1064,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
| null_class = X0
| subclass(complement(regular(X0)),X1) ),
inference(resolution,[],[f289,f121]) ).
fof(f1063,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),null_class)
| null_class = X1
| subclass(X0,regular(X1)) ),
inference(resolution,[],[f289,f3]) ).
fof(f1062,plain,
! [X2,X0,X1] :
( ~ member(X0,null_class)
| null_class = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) ),
inference(resolution,[],[f289,f1]) ).
fof(f289,plain,
! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,null_class)
| null_class = X0 ),
inference(superposition,[],[f22,f67]) ).
fof(f1061,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) = ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1)))
| ~ subclass(universal_class,cross_product(X2,X3)) ),
inference(resolution,[],[f17,f697]) ).
fof(f1060,plain,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) = ordered_pair(first(unordered_pair(X0,X1)),second(unordered_pair(X0,X1)))
| ~ subclass(universal_class,cross_product(X2,X3)) ),
inference(resolution,[],[f17,f161]) ).
fof(f1059,plain,
! [X2,X0,X1] :
( regular(X0) = ordered_pair(first(regular(X0)),second(regular(X0)))
| ~ subclass(X0,cross_product(X1,X2))
| null_class = X0 ),
inference(resolution,[],[f17,f159]) ).
fof(f1058,plain,
! [X2,X0,X1] :
( power_class(X0) = ordered_pair(first(power_class(X0)),second(power_class(X0)))
| ~ subclass(universal_class,cross_product(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f17,f165]) ).
fof(f1057,plain,
! [X2,X0,X1] :
( sum_class(X0) = ordered_pair(first(sum_class(X0)),second(sum_class(X0)))
| ~ subclass(universal_class,cross_product(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f17,f164]) ).
fof(f1056,plain,
! [X2,X0,X1] :
( singleton(X0) = ordered_pair(first(singleton(X0)),second(singleton(X0)))
| ~ subclass(universal_class,cross_product(X1,X2)) ),
inference(resolution,[],[f17,f162]) ).
fof(f1055,plain,
! [X0,X1] :
( apply(choice,cross_product(X0,X1)) = ordered_pair(first(apply(choice,cross_product(X0,X1))),second(apply(choice,cross_product(X0,X1))))
| cross_product(X0,X1) = null_class
| ~ member(cross_product(X0,X1),universal_class) ),
inference(resolution,[],[f17,f70]) ).
fof(f1054,plain,
! [X0,X1] :
( regular(cross_product(X0,X1)) = ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ),
inference(resolution,[],[f17,f66]) ).
fof(f1053,plain,
! [X0,X1] :
( omega = ordered_pair(first(omega),second(omega))
| ~ subclass(universal_class,cross_product(X0,X1)) ),
inference(resolution,[],[f17,f163]) ).
fof(f1050,plain,
! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))
| subclass(cross_product(X0,X1),X2) ),
inference(resolution,[],[f17,f2]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f220,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation ),
inference(resolution,[],[f7,f98]) ).
fof(f213,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation ),
inference(resolution,[],[f7,f44]) ).
fof(f209,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class) ),
inference(resolution,[],[f7,f18]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ member(X1,universal_class)
| member(power_class(X1),domain_of(X0)) ),
inference(resolution,[],[f165,f923]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),power_class(X0)) ),
inference(resolution,[],[f165,f152]) ).
fof(f1017,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),diagonalise(X0)) ),
inference(resolution,[],[f165,f155]) ).
fof(f1013,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| ~ member(X3,universal_class)
| member(power_class(X3),X0) ),
inference(resolution,[],[f165,f495]) ).
fof(f1012,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0) ),
inference(resolution,[],[f165,f24]) ).
fof(f1011,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X0) ),
inference(resolution,[],[f165,f21]) ).
fof(f1010,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X1) ),
inference(resolution,[],[f165,f22]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| ~ member(X1,universal_class)
| power_class(X1) = X0 ),
inference(resolution,[],[f165,f650]) ).
fof(f1008,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| power_class(X2) = X0
| power_class(X2) = X1 ),
inference(resolution,[],[f165,f8]) ).
fof(f1007,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(power_class(X1),X2) ),
inference(resolution,[],[f165,f1]) ).
fof(f165,plain,
! [X0,X1] :
( member(power_class(X1),X0)
| ~ subclass(universal_class,X0)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f56]) ).
fof(f998,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| ~ subclass(universal_class,application_function) ),
inference(resolution,[],[f106,f697]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function)
| member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).
fof(f997,plain,
! [X2,X0,X1] :
( member(apply(X0,X1),X2)
| ~ subclass(universal_class,X2)
| ~ member(image(X0,singleton(X1)),universal_class) ),
inference(superposition,[],[f164,f68]) ).
fof(f995,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ member(X1,universal_class)
| member(sum_class(X1),domain_of(X0)) ),
inference(resolution,[],[f164,f923]) ).
fof(f992,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),power_class(X0)) ),
inference(resolution,[],[f164,f152]) ).
fof(f991,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),diagonalise(X0)) ),
inference(resolution,[],[f164,f155]) ).
fof(f987,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| ~ member(X3,universal_class)
| member(sum_class(X3),X0) ),
inference(resolution,[],[f164,f495]) ).
fof(f986,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0) ),
inference(resolution,[],[f164,f24]) ).
fof(f985,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X0) ),
inference(resolution,[],[f164,f21]) ).
fof(f984,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X1) ),
inference(resolution,[],[f164,f22]) ).
fof(f983,plain,
! [X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| ~ member(X1,universal_class)
| sum_class(X1) = X0 ),
inference(resolution,[],[f164,f650]) ).
fof(f982,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| sum_class(X2) = X0
| sum_class(X2) = X1 ),
inference(resolution,[],[f164,f8]) ).
fof(f981,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(sum_class(X1),X2) ),
inference(resolution,[],[f164,f1]) ).
fof(f164,plain,
! [X0,X1] :
( member(sum_class(X1),X0)
| ~ subclass(universal_class,X0)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f54]) ).
fof(f979,plain,
! [X0] :
( ~ subclass(universal_class,diagonalise(X0))
| ~ subclass(universal_class,cantor(intersection(X0,identity_relation))) ),
inference(superposition,[],[f970,f76]) ).
fof(f978,plain,
! [X0] :
( ~ subclass(universal_class,complement(sum_class(X0)))
| ~ subclass(universal_class,cantor(restrict(element_relation,universal_class,X0))) ),
inference(superposition,[],[f970,f53]) ).
fof(f977,plain,
! [X0] :
( ~ subclass(universal_class,complement(inverse(X0)))
| ~ subclass(universal_class,cantor(flip(cross_product(X0,universal_class)))) ),
inference(superposition,[],[f970,f38]) ).
fof(f970,plain,
! [X0] :
( ~ subclass(universal_class,complement(domain_of(X0)))
| ~ subclass(universal_class,cantor(X0)) ),
inference(resolution,[],[f952,f175]) ).
fof(f962,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 ),
inference(resolution,[],[f93,f697]) ).
fof(f958,plain,
! [X0] :
( ~ subclass(universal_class,cantor(inverse(X0)))
| member(omega,range_of(X0)) ),
inference(superposition,[],[f949,f39]) ).
fof(f975,plain,
! [X0,X1] :
( member(singleton(X1),sum_class(X0))
| ~ subclass(universal_class,cantor(restrict(element_relation,universal_class,X0))) ),
inference(superposition,[],[f952,f53]) ).
fof(f974,plain,
! [X0,X1] :
( member(singleton(X1),inverse(X0))
| ~ subclass(universal_class,cantor(flip(cross_product(X0,universal_class)))) ),
inference(superposition,[],[f952,f38]) ).
fof(f972,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ subclass(domain_of(X0),X1)
| member(singleton(X2),X1) ),
inference(resolution,[],[f952,f1]) ).
fof(f971,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(intersection(X0,identity_relation)))
| ~ member(singleton(X1),diagonalise(X0)) ),
inference(resolution,[],[f952,f155]) ).
fof(f952,plain,
! [X0,X1] :
( member(singleton(X0),domain_of(X1))
| ~ subclass(universal_class,cantor(X1)) ),
inference(resolution,[],[f923,f162]) ).
fof(f969,plain,
! [X0,X1] :
( ~ inductive(cantor(restrict(identity_relation,X0,X1)))
| ~ member(null_class,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f941,f29]) ).
fof(f941,plain,
! [X0] :
( ~ inductive(cantor(intersection(X0,identity_relation)))
| ~ member(null_class,diagonalise(X0)) ),
inference(resolution,[],[f926,f155]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( ~ member(ordered_pair(X1,X4),compose_class(X0))
| compose(X0,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).
fof(f943,plain,
! [X0] :
( ~ inductive(cantor(inverse(X0)))
| member(null_class,range_of(X0)) ),
inference(superposition,[],[f926,f39]) ).
fof(f961,plain,
! [X0,X1] :
( ~ inductive(cantor(restrict(identity_relation,X0,X1)))
| ~ inductive(diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f940,f29]) ).
fof(f940,plain,
! [X0] :
( ~ inductive(cantor(intersection(X0,identity_relation)))
| ~ inductive(diagonalise(X0)) ),
inference(resolution,[],[f926,f154]) ).
fof(f960,plain,
! [X0] :
( member(omega,sum_class(X0))
| ~ subclass(universal_class,cantor(restrict(element_relation,universal_class,X0))) ),
inference(superposition,[],[f949,f53]) ).
fof(f959,plain,
! [X0] :
( member(omega,inverse(X0))
| ~ subclass(universal_class,cantor(flip(cross_product(X0,universal_class)))) ),
inference(superposition,[],[f949,f38]) ).
fof(f957,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| ~ subclass(domain_of(X0),X1)
| member(omega,X1) ),
inference(resolution,[],[f949,f1]) ).
fof(f949,plain,
! [X0] :
( member(omega,domain_of(X0))
| ~ subclass(universal_class,cantor(X0)) ),
inference(resolution,[],[f923,f163]) ).
fof(f953,plain,
! [X0,X1] :
( member(regular(X0),domain_of(X1))
| ~ subclass(X0,cantor(X1))
| null_class = X0 ),
inference(resolution,[],[f923,f159]) ).
fof(f951,plain,
! [X0] :
( member(apply(choice,cantor(X0)),domain_of(X0))
| null_class = cantor(X0)
| ~ member(cantor(X0),universal_class) ),
inference(resolution,[],[f923,f70]) ).
fof(f946,plain,
! [X0,X1] :
( member(not_subclass_element(cantor(X0),X1),domain_of(X0))
| subclass(cantor(X0),X1) ),
inference(resolution,[],[f923,f2]) ).
fof(f923,plain,
! [X0,X1] :
( ~ member(X1,cantor(X0))
| member(X1,domain_of(X0)) ),
inference(superposition,[],[f21,f77]) ).
fof(f926,plain,
! [X0] :
( member(null_class,domain_of(X0))
| ~ inductive(cantor(X0)) ),
inference(superposition,[],[f126,f77]) ).
fof(f931,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(singleton(X1),domain_of(X0)) ),
inference(superposition,[],[f177,f77]) ).
fof(f930,plain,
! [X0,X1] :
( ~ subclass(universal_class,cantor(X0))
| member(singleton(X1),diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f176,f77]) ).
fof(f929,plain,
! [X0] :
( ~ subclass(universal_class,cantor(X0))
| member(omega,domain_of(X0)) ),
inference(superposition,[],[f173,f77]) ).
fof(f928,plain,
! [X0] :
( ~ subclass(universal_class,cantor(X0))
| member(omega,diagonalise(compose(inverse(element_relation),X0))) ),
inference(superposition,[],[f172,f77]) ).
fof(f922,plain,
! [X0] : cantor(restrict(element_relation,universal_class,X0)) = intersection(sum_class(X0),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,X0)))),
inference(superposition,[],[f77,f53]) ).
fof(f921,plain,
! [X0] : cantor(flip(cross_product(X0,universal_class))) = intersection(inverse(X0),diagonalise(compose(inverse(element_relation),flip(cross_product(X0,universal_class))))),
inference(superposition,[],[f77,f38]) ).
fof(f77,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_class) ).
fof(f828,plain,
( ~ inductive(union(universal_class,universal_class))
| ~ member(null_class,intersection(null_class,null_class)) ),
inference(superposition,[],[f119,f796]) ).
fof(f670,plain,
( ~ subclass(universal_class,power_class(universal_class))
| ~ member(omega,image(element_relation,null_class)) ),
inference(superposition,[],[f171,f616]) ).
fof(f900,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),power_class(universal_class))
| ~ subclass(universal_class,image(element_relation,null_class)) ),
inference(resolution,[],[f621,f697]) ).
fof(f899,plain,
! [X0,X1] :
( ~ member(unordered_pair(X0,X1),power_class(universal_class))
| ~ subclass(universal_class,image(element_relation,null_class)) ),
inference(resolution,[],[f621,f161]) ).
fof(f898,plain,
! [X0] :
( ~ member(regular(X0),power_class(universal_class))
| ~ subclass(X0,image(element_relation,null_class))
| null_class = X0 ),
inference(resolution,[],[f621,f159]) ).
fof(f897,plain,
! [X0] :
( ~ member(singleton(X0),power_class(universal_class))
| ~ subclass(universal_class,image(element_relation,null_class)) ),
inference(resolution,[],[f621,f162]) ).
fof(f896,plain,
( ~ member(apply(choice,image(element_relation,null_class)),power_class(universal_class))
| null_class = image(element_relation,null_class)
| ~ member(image(element_relation,null_class),universal_class) ),
inference(resolution,[],[f621,f70]) ).
fof(f895,plain,
( ~ member(regular(image(element_relation,null_class)),power_class(universal_class))
| null_class = image(element_relation,null_class) ),
inference(resolution,[],[f621,f66]) ).
fof(f894,plain,
( ~ member(omega,power_class(universal_class))
| ~ subclass(universal_class,image(element_relation,null_class)) ),
inference(resolution,[],[f621,f163]) ).
fof(f891,plain,
! [X0] :
( ~ member(not_subclass_element(image(element_relation,null_class),X0),power_class(universal_class))
| subclass(image(element_relation,null_class),X0) ),
inference(resolution,[],[f621,f2]) ).
fof(f621,plain,
! [X0] :
( ~ member(X0,image(element_relation,null_class))
| ~ member(X0,power_class(universal_class)) ),
inference(superposition,[],[f152,f603]) ).
fof(f887,plain,
! [X0] :
( null_class = identity_relation
| ~ member(identity_relation,universal_class)
| member(apply(choice,identity_relation),X0)
| ~ subclass(subset_relation,X0) ),
inference(resolution,[],[f70,f170]) ).
fof(f886,plain,
! [X0] :
( null_class = image(element_relation,complement(X0))
| ~ member(image(element_relation,complement(X0)),universal_class)
| ~ member(apply(choice,image(element_relation,complement(X0))),power_class(X0)) ),
inference(resolution,[],[f70,f152]) ).
fof(f885,plain,
! [X0] :
( null_class = domain_of(intersection(X0,identity_relation))
| ~ member(domain_of(intersection(X0,identity_relation)),universal_class)
| ~ member(apply(choice,domain_of(intersection(X0,identity_relation))),diagonalise(X0)) ),
inference(resolution,[],[f70,f155]) ).
fof(f881,plain,
! [X2,X0,X1] :
( null_class = restrict(X0,X1,X2)
| ~ member(restrict(X0,X1,X2),universal_class)
| member(apply(choice,restrict(X0,X1,X2)),X0) ),
inference(resolution,[],[f70,f495]) ).
fof(f879,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(apply(choice,intersection(X0,X1)),X0) ),
inference(resolution,[],[f70,f21]) ).
fof(f878,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(apply(choice,intersection(X0,X1)),X1) ),
inference(resolution,[],[f70,f22]) ).
fof(f889,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| apply(choice,unordered_pair(X0,X1)) = X0
| apply(choice,unordered_pair(X0,X1)) = X1 ),
inference(subsumption_resolution,[],[f876,f11]) ).
fof(f876,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| apply(choice,unordered_pair(X0,X1)) = X0
| apply(choice,unordered_pair(X0,X1)) = X1 ),
inference(resolution,[],[f70,f8]) ).
fof(f70,axiom,
! [X1] :
( member(apply(choice,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
fof(f871,plain,
! [X0] : union(universal_class,intersection(complement(X0),null_class)) = complement(intersection(null_class,union(X0,universal_class))),
inference(superposition,[],[f614,f615]) ).
fof(f874,plain,
! [X0] :
( null_class = union(X0,universal_class)
| ~ subclass(union(X0,universal_class),intersection(complement(X0),null_class)) ),
inference(forward_demodulation,[],[f870,f615]) ).
fof(f870,plain,
! [X0] :
( ~ subclass(union(X0,universal_class),intersection(complement(X0),null_class))
| null_class = complement(intersection(complement(X0),null_class)) ),
inference(superposition,[],[f600,f615]) ).
fof(f869,plain,
! [X0] :
( ~ inductive(image(element_relation,union(X0,universal_class)))
| ~ member(null_class,power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f566,f615]) ).
fof(f868,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(union(X0,universal_class)))
| member(singleton(X1),intersection(complement(X0),null_class)) ),
inference(superposition,[],[f426,f615]) ).
fof(f867,plain,
! [X0] :
( ~ inductive(image(element_relation,union(X0,universal_class)))
| ~ inductive(power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f402,f615]) ).
fof(f865,plain,
! [X0] :
( ~ subclass(universal_class,union(X0,universal_class))
| ~ subclass(universal_class,intersection(complement(X0),null_class)) ),
inference(superposition,[],[f276,f615]) ).
fof(f863,plain,
! [X0] :
( ~ subclass(universal_class,union(X0,universal_class))
| ~ member(omega,intersection(complement(X0),null_class)) ),
inference(superposition,[],[f171,f615]) ).
fof(f862,plain,
! [X0,X1] :
( ~ member(X1,image(element_relation,union(X0,universal_class)))
| ~ member(X1,power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f152,f615]) ).
fof(f861,plain,
! [X0] :
( ~ member(null_class,image(element_relation,union(X0,universal_class)))
| ~ inductive(power_class(intersection(complement(X0),null_class))) ),
inference(superposition,[],[f151,f615]) ).
fof(f873,plain,
! [X0,X1] :
( subclass(union(X0,universal_class),X1)
| ~ member(not_subclass_element(union(X0,universal_class),X1),intersection(complement(X0),null_class)) ),
inference(forward_demodulation,[],[f860,f615]) ).
fof(f860,plain,
! [X0,X1] :
( ~ member(not_subclass_element(union(X0,universal_class),X1),intersection(complement(X0),null_class))
| subclass(complement(intersection(complement(X0),null_class)),X1) ),
inference(superposition,[],[f121,f615]) ).
fof(f872,plain,
! [X0] :
( null_class = union(X0,universal_class)
| ~ member(regular(union(X0,universal_class)),intersection(complement(X0),null_class)) ),
inference(forward_demodulation,[],[f859,f615]) ).
fof(f859,plain,
! [X0] :
( ~ member(regular(union(X0,universal_class)),intersection(complement(X0),null_class))
| null_class = complement(intersection(complement(X0),null_class)) ),
inference(superposition,[],[f120,f615]) ).
fof(f857,plain,
! [X0] : power_class(intersection(complement(X0),null_class)) = complement(image(element_relation,union(X0,universal_class))),
inference(superposition,[],[f55,f615]) ).
fof(f856,plain,
! [X0,X1] : union(X1,intersection(complement(X0),null_class)) = complement(intersection(complement(X1),union(X0,universal_class))),
inference(superposition,[],[f26,f615]) ).
fof(f855,plain,
! [X0,X1] : union(intersection(complement(X0),null_class),X1) = complement(intersection(union(X0,universal_class),complement(X1))),
inference(superposition,[],[f26,f615]) ).
fof(f854,plain,
! [X0,X1] :
( member(X1,union(X0,universal_class))
| member(X1,intersection(complement(X0),null_class))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f615]) ).
fof(f853,plain,
! [X0,X1] :
( ~ member(X1,union(X0,universal_class))
| ~ member(X1,intersection(complement(X0),null_class)) ),
inference(superposition,[],[f24,f615]) ).
fof(f852,plain,
union(image(element_relation,null_class),universal_class) = complement(intersection(power_class(universal_class),null_class)),
inference(superposition,[],[f615,f616]) ).
fof(f851,plain,
! [X0] : union(image(element_relation,complement(X0)),universal_class) = complement(intersection(power_class(X0),null_class)),
inference(superposition,[],[f615,f55]) ).
fof(f850,plain,
! [X0] : union(domain_of(intersection(X0,identity_relation)),universal_class) = complement(intersection(diagonalise(X0),null_class)),
inference(superposition,[],[f615,f76]) ).
fof(f849,plain,
! [X0] : union(intersection(complement(X0),null_class),universal_class) = complement(intersection(union(X0,universal_class),null_class)),
inference(superposition,[],[f615,f615]) ).
fof(f848,plain,
union(intersection(null_class,null_class),universal_class) = complement(intersection(union(universal_class,universal_class),null_class)),
inference(superposition,[],[f615,f796]) ).
fof(f847,plain,
! [X0] : union(intersection(null_class,complement(X0)),universal_class) = complement(intersection(union(universal_class,X0),null_class)),
inference(superposition,[],[f615,f614]) ).
fof(f846,plain,
! [X0,X1] : union(intersection(complement(X0),complement(X1)),universal_class) = complement(intersection(union(X0,X1),null_class)),
inference(superposition,[],[f615,f26]) ).
fof(f615,plain,
! [X0] : union(X0,universal_class) = complement(intersection(complement(X0),null_class)),
inference(superposition,[],[f26,f603]) ).
fof(f841,plain,
union(universal_class,intersection(null_class,null_class)) = complement(intersection(null_class,union(universal_class,universal_class))),
inference(superposition,[],[f614,f796]) ).
fof(f844,plain,
( null_class = union(universal_class,universal_class)
| ~ subclass(union(universal_class,universal_class),intersection(null_class,null_class)) ),
inference(forward_demodulation,[],[f840,f796]) ).
fof(f840,plain,
( ~ subclass(union(universal_class,universal_class),intersection(null_class,null_class))
| null_class = complement(intersection(null_class,null_class)) ),
inference(superposition,[],[f600,f796]) ).
fof(f839,plain,
( ~ inductive(image(element_relation,union(universal_class,universal_class)))
| ~ member(null_class,power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f566,f796]) ).
fof(f838,plain,
! [X0] :
( ~ subclass(universal_class,complement(union(universal_class,universal_class)))
| member(singleton(X0),intersection(null_class,null_class)) ),
inference(superposition,[],[f426,f796]) ).
fof(f837,plain,
( ~ inductive(image(element_relation,union(universal_class,universal_class)))
| ~ inductive(power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f402,f796]) ).
fof(f835,plain,
( ~ subclass(universal_class,union(universal_class,universal_class))
| ~ subclass(universal_class,intersection(null_class,null_class)) ),
inference(superposition,[],[f276,f796]) ).
fof(f833,plain,
( ~ subclass(universal_class,union(universal_class,universal_class))
| ~ member(omega,intersection(null_class,null_class)) ),
inference(superposition,[],[f171,f796]) ).
fof(f832,plain,
! [X0] :
( ~ member(X0,image(element_relation,union(universal_class,universal_class)))
| ~ member(X0,power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f152,f796]) ).
fof(f831,plain,
( ~ member(null_class,image(element_relation,union(universal_class,universal_class)))
| ~ inductive(power_class(intersection(null_class,null_class))) ),
inference(superposition,[],[f151,f796]) ).
fof(f843,plain,
! [X0] :
( subclass(union(universal_class,universal_class),X0)
| ~ member(not_subclass_element(union(universal_class,universal_class),X0),intersection(null_class,null_class)) ),
inference(forward_demodulation,[],[f830,f796]) ).
fof(f830,plain,
! [X0] :
( ~ member(not_subclass_element(union(universal_class,universal_class),X0),intersection(null_class,null_class))
| subclass(complement(intersection(null_class,null_class)),X0) ),
inference(superposition,[],[f121,f796]) ).
fof(f842,plain,
( null_class = union(universal_class,universal_class)
| ~ member(regular(union(universal_class,universal_class)),intersection(null_class,null_class)) ),
inference(forward_demodulation,[],[f829,f796]) ).
fof(f829,plain,
( ~ member(regular(union(universal_class,universal_class)),intersection(null_class,null_class))
| null_class = complement(intersection(null_class,null_class)) ),
inference(superposition,[],[f120,f796]) ).
fof(f827,plain,
power_class(intersection(null_class,null_class)) = complement(image(element_relation,union(universal_class,universal_class))),
inference(superposition,[],[f55,f796]) ).
fof(f826,plain,
! [X0] : union(X0,intersection(null_class,null_class)) = complement(intersection(complement(X0),union(universal_class,universal_class))),
inference(superposition,[],[f26,f796]) ).
fof(f825,plain,
! [X0] : union(intersection(null_class,null_class),X0) = complement(intersection(union(universal_class,universal_class),complement(X0))),
inference(superposition,[],[f26,f796]) ).
fof(f824,plain,
! [X0] :
( member(X0,union(universal_class,universal_class))
| member(X0,intersection(null_class,null_class))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f25,f796]) ).
fof(f823,plain,
! [X0] :
( ~ member(X0,union(universal_class,universal_class))
| ~ member(X0,intersection(null_class,null_class)) ),
inference(superposition,[],[f24,f796]) ).
fof(f796,plain,
union(universal_class,universal_class) = complement(intersection(null_class,null_class)),
inference(superposition,[],[f614,f603]) ).
fof(f822,plain,
! [X0] :
( null_class = union(universal_class,X0)
| ~ subclass(union(universal_class,X0),intersection(null_class,complement(X0))) ),
inference(forward_demodulation,[],[f819,f614]) ).
fof(f819,plain,
! [X0] :
( ~ subclass(union(universal_class,X0),intersection(null_class,complement(X0)))
| null_class = complement(intersection(null_class,complement(X0))) ),
inference(superposition,[],[f600,f614]) ).
fof(f818,plain,
! [X0] :
( ~ inductive(image(element_relation,union(universal_class,X0)))
| ~ member(null_class,power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f566,f614]) ).
fof(f817,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(union(universal_class,X0)))
| member(singleton(X1),intersection(null_class,complement(X0))) ),
inference(superposition,[],[f426,f614]) ).
fof(f816,plain,
! [X0] :
( ~ inductive(image(element_relation,union(universal_class,X0)))
| ~ inductive(power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f402,f614]) ).
fof(f814,plain,
! [X0] :
( ~ subclass(universal_class,union(universal_class,X0))
| ~ subclass(universal_class,intersection(null_class,complement(X0))) ),
inference(superposition,[],[f276,f614]) ).
fof(f812,plain,
! [X0] :
( ~ subclass(universal_class,union(universal_class,X0))
| ~ member(omega,intersection(null_class,complement(X0))) ),
inference(superposition,[],[f171,f614]) ).
fof(f811,plain,
! [X0,X1] :
( ~ member(X1,image(element_relation,union(universal_class,X0)))
| ~ member(X1,power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f152,f614]) ).
fof(f810,plain,
! [X0] :
( ~ member(null_class,image(element_relation,union(universal_class,X0)))
| ~ inductive(power_class(intersection(null_class,complement(X0)))) ),
inference(superposition,[],[f151,f614]) ).
fof(f821,plain,
! [X0,X1] :
( subclass(union(universal_class,X0),X1)
| ~ member(not_subclass_element(union(universal_class,X0),X1),intersection(null_class,complement(X0))) ),
inference(forward_demodulation,[],[f809,f614]) ).
fof(f809,plain,
! [X0,X1] :
( ~ member(not_subclass_element(union(universal_class,X0),X1),intersection(null_class,complement(X0)))
| subclass(complement(intersection(null_class,complement(X0))),X1) ),
inference(superposition,[],[f121,f614]) ).
fof(f820,plain,
! [X0] :
( null_class = union(universal_class,X0)
| ~ member(regular(union(universal_class,X0)),intersection(null_class,complement(X0))) ),
inference(forward_demodulation,[],[f808,f614]) ).
fof(f808,plain,
! [X0] :
( ~ member(regular(union(universal_class,X0)),intersection(null_class,complement(X0)))
| null_class = complement(intersection(null_class,complement(X0))) ),
inference(superposition,[],[f120,f614]) ).
fof(f806,plain,
! [X0] : power_class(intersection(null_class,complement(X0))) = complement(image(element_relation,union(universal_class,X0))),
inference(superposition,[],[f55,f614]) ).
fof(f805,plain,
! [X0,X1] : union(X1,intersection(null_class,complement(X0))) = complement(intersection(complement(X1),union(universal_class,X0))),
inference(superposition,[],[f26,f614]) ).
fof(f804,plain,
! [X0,X1] : union(intersection(null_class,complement(X0)),X1) = complement(intersection(union(universal_class,X0),complement(X1))),
inference(superposition,[],[f26,f614]) ).
fof(f803,plain,
! [X0,X1] :
( member(X1,union(universal_class,X0))
| member(X1,intersection(null_class,complement(X0)))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f614]) ).
fof(f802,plain,
! [X0,X1] :
( ~ member(X1,union(universal_class,X0))
| ~ member(X1,intersection(null_class,complement(X0))) ),
inference(superposition,[],[f24,f614]) ).
fof(f801,plain,
union(universal_class,image(element_relation,null_class)) = complement(intersection(null_class,power_class(universal_class))),
inference(superposition,[],[f614,f616]) ).
fof(f800,plain,
! [X0] : union(universal_class,image(element_relation,complement(X0))) = complement(intersection(null_class,power_class(X0))),
inference(superposition,[],[f614,f55]) ).
fof(f799,plain,
! [X0] : union(universal_class,domain_of(intersection(X0,identity_relation))) = complement(intersection(null_class,diagonalise(X0))),
inference(superposition,[],[f614,f76]) ).
fof(f798,plain,
! [X0] : union(universal_class,intersection(null_class,complement(X0))) = complement(intersection(null_class,union(universal_class,X0))),
inference(superposition,[],[f614,f614]) ).
fof(f797,plain,
! [X0,X1] : union(universal_class,intersection(complement(X0),complement(X1))) = complement(intersection(null_class,union(X0,X1))),
inference(superposition,[],[f614,f26]) ).
fof(f614,plain,
! [X0] : union(universal_class,X0) = complement(intersection(null_class,complement(X0))),
inference(superposition,[],[f26,f603]) ).
fof(f717,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| ordered_pair(X1,X2) = X0 ),
inference(resolution,[],[f697,f650]) ).
fof(f786,plain,
! [X0] :
( ~ subclass(universal_class,complement(domain_relation))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f698,f100]) ).
fof(f782,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,complement(intersection(X0,X1)))
| ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) ),
inference(resolution,[],[f698,f23]) ).
fof(f698,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| ~ subclass(universal_class,complement(X2)) ),
inference(superposition,[],[f263,f13]) ).
fof(f706,plain,
! [X2,X0,X1] :
( ~ subclass(ordered_pair(X0,X1),X2)
| member(singleton(X0),X2) ),
inference(resolution,[],[f702,f1]) ).
fof(f659,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| unordered_pair(X1,X2) = X0 ),
inference(resolution,[],[f650,f161]) ).
fof(f770,plain,
! [X0,X1] :
( singleton(X0) = null_class
| ~ subclass(singleton(X0),X1)
| member(X0,X1) ),
inference(resolution,[],[f766,f1]) ).
fof(f766,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f765]) ).
fof(f765,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f66,f656]) ).
fof(f30,axiom,
! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f768,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f763]) ).
fof(f763,plain,
! [X0,X1] :
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f159,f656]) ).
fof(f656,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f650,f66]) ).
fof(f700,plain,
! [X2,X0,X1] : ~ subclass(universal_class,complement(unordered_pair(X2,ordered_pair(X0,X1)))),
inference(superposition,[],[f469,f13]) ).
fof(f699,plain,
! [X2,X0,X1] : ~ subclass(universal_class,complement(unordered_pair(ordered_pair(X0,X1),X2))),
inference(superposition,[],[f468,f13]) ).
fof(f630,plain,
! [X0] :
( ~ member(not_subclass_element(null_class,X0),universal_class)
| subclass(null_class,X0) ),
inference(forward_demodulation,[],[f619,f603]) ).
fof(f619,plain,
! [X0] :
( ~ member(not_subclass_element(null_class,X0),universal_class)
| subclass(complement(universal_class),X0) ),
inference(superposition,[],[f121,f603]) ).
fof(f711,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ),
inference(resolution,[],[f697,f14]) ).
fof(f710,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ),
inference(resolution,[],[f697,f15]) ).
fof(f755,plain,
! [X2,X3,X0,X1] :
( member(X3,restrict(X2,X0,X1))
| ~ member(X3,X2)
| ~ member(X3,cross_product(X0,X1)) ),
inference(superposition,[],[f23,f29]) ).
fof(f753,plain,
! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ),
inference(superposition,[],[f23,f67]) ).
fof(f752,plain,
! [X0,X1] :
( ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0)
| complement(intersection(X0,X1)) = null_class ),
inference(resolution,[],[f23,f120]) ).
fof(f751,plain,
! [X2,X0,X1] :
( ~ member(singleton(X0),X1)
| ~ member(singleton(X0),X2)
| ~ subclass(universal_class,complement(intersection(X2,X1))) ),
inference(resolution,[],[f23,f175]) ).
fof(f750,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| ~ member(unordered_pair(X0,X1),X3)
| ~ subclass(universal_class,complement(intersection(X3,X2))) ),
inference(resolution,[],[f23,f263]) ).
fof(f749,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0)
| subclass(complement(intersection(X0,X1)),X2) ),
inference(resolution,[],[f23,f121]) ).
fof(f748,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[],[f23,f3]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f714,plain,
! [X0,X1] :
( ~ subclass(universal_class,domain_relation)
| domain_of(X0) = X1 ),
inference(resolution,[],[f697,f99]) ).
fof(f713,plain,
! [X0,X1] :
( ~ subclass(universal_class,successor_relation)
| successor(X0) = X1 ),
inference(resolution,[],[f697,f45]) ).
fof(f726,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ member(ordered_pair(X1,X2),power_class(X0)) ),
inference(resolution,[],[f697,f152]) ).
fof(f725,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ member(ordered_pair(X1,X2),diagonalise(X0)) ),
inference(resolution,[],[f697,f155]) ).
fof(f721,plain,
! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(ordered_pair(X3,X4),X0) ),
inference(resolution,[],[f697,f495]) ).
fof(f720,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(ordered_pair(X1,X2),X0) ),
inference(resolution,[],[f697,f24]) ).
fof(f716,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ordered_pair(X2,X3) = X0
| ordered_pair(X2,X3) = X1 ),
inference(resolution,[],[f697,f8]) ).
fof(f715,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(ordered_pair(X2,X3),X1) ),
inference(resolution,[],[f697,f1]) ).
fof(f697,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) ),
inference(superposition,[],[f161,f13]) ).
fof(f708,plain,
! [X2,X0,X1] :
( ~ subclass(ordered_pair(X0,X1),X2)
| member(unordered_pair(X0,singleton(X1)),X2) ),
inference(resolution,[],[f703,f1]) ).
fof(f703,plain,
! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
inference(subsumption_resolution,[],[f695,f11]) ).
fof(f695,plain,
! [X0,X1] :
( member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1))
| ~ member(unordered_pair(X0,singleton(X1)),universal_class) ),
inference(superposition,[],[f10,f13]) ).
fof(f701,plain,
! [X0,X1] : ~ subclass(universal_class,complement(singleton(ordered_pair(X0,X1)))),
inference(superposition,[],[f470,f13]) ).
fof(f692,plain,
! [X0,X1] : ~ subclass(universal_class,complement(ordered_pair(X0,X1))),
inference(superposition,[],[f469,f13]) ).
fof(f705,plain,
! [X0,X1] : ~ subclass(universal_class,complement(ordered_pair(X0,X1))),
inference(resolution,[],[f702,f175]) ).
fof(f702,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(subsumption_resolution,[],[f694,f118]) ).
fof(f694,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(superposition,[],[f9,f13]) ).
fof(f704,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(ordered_pair(X1,X2),X0) ),
inference(resolution,[],[f696,f1]) ).
fof(f696,plain,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(superposition,[],[f11,f13]) ).
fof(f691,plain,
! [X0,X1] : ~ subclass(universal_class,complement(ordered_pair(X0,X1))),
inference(superposition,[],[f283,f13]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f657,plain,
! [X0,X1] :
( ~ subclass(universal_class,singleton(X0))
| singleton(X1) = X0 ),
inference(resolution,[],[f650,f162]) ).
fof(f626,plain,
( ~ inductive(image(element_relation,null_class))
| ~ inductive(power_class(universal_class)) ),
inference(superposition,[],[f402,f603]) ).
fof(f676,plain,
( ~ inductive(image(element_relation,power_class(universal_class)))
| ~ member(null_class,power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f566,f616]) ).
fof(f675,plain,
! [X0] :
( ~ subclass(universal_class,complement(power_class(universal_class)))
| member(singleton(X0),image(element_relation,null_class)) ),
inference(superposition,[],[f426,f616]) ).
fof(f672,plain,
( ~ subclass(universal_class,power_class(universal_class))
| ~ subclass(universal_class,image(element_relation,null_class)) ),
inference(superposition,[],[f276,f616]) ).
fof(f669,plain,
! [X0] :
( ~ member(X0,image(element_relation,power_class(universal_class)))
| ~ member(X0,power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f152,f616]) ).
fof(f668,plain,
( ~ member(null_class,image(element_relation,power_class(universal_class)))
| ~ inductive(power_class(image(element_relation,null_class))) ),
inference(superposition,[],[f151,f616]) ).
fof(f679,plain,
! [X0] :
( subclass(power_class(universal_class),X0)
| ~ member(not_subclass_element(power_class(universal_class),X0),image(element_relation,null_class)) ),
inference(forward_demodulation,[],[f667,f616]) ).
fof(f667,plain,
! [X0] :
( ~ member(not_subclass_element(power_class(universal_class),X0),image(element_relation,null_class))
| subclass(complement(image(element_relation,null_class)),X0) ),
inference(superposition,[],[f121,f616]) ).
fof(f678,plain,
( null_class = power_class(universal_class)
| ~ member(regular(power_class(universal_class)),image(element_relation,null_class)) ),
inference(forward_demodulation,[],[f666,f616]) ).
fof(f666,plain,
( ~ member(regular(power_class(universal_class)),image(element_relation,null_class))
| null_class = complement(image(element_relation,null_class)) ),
inference(superposition,[],[f120,f616]) ).
fof(f665,plain,
( ~ inductive(power_class(universal_class))
| ~ member(null_class,image(element_relation,null_class)) ),
inference(superposition,[],[f119,f616]) ).
fof(f663,plain,
! [X0] : union(X0,image(element_relation,null_class)) = complement(intersection(complement(X0),power_class(universal_class))),
inference(superposition,[],[f26,f616]) ).
fof(f662,plain,
! [X0] : union(image(element_relation,null_class),X0) = complement(intersection(power_class(universal_class),complement(X0))),
inference(superposition,[],[f26,f616]) ).
fof(f661,plain,
! [X0] :
( member(X0,power_class(universal_class))
| member(X0,image(element_relation,null_class))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f25,f616]) ).
fof(f660,plain,
! [X0] :
( ~ member(X0,power_class(universal_class))
| ~ member(X0,image(element_relation,null_class)) ),
inference(superposition,[],[f24,f616]) ).
fof(f616,plain,
power_class(universal_class) = complement(image(element_relation,null_class)),
inference(superposition,[],[f55,f603]) ).
fof(f655,plain,
! [X0] :
( ~ subclass(universal_class,singleton(X0))
| omega = X0 ),
inference(resolution,[],[f650,f163]) ).
fof(f654,plain,
! [X0] :
( ~ inductive(singleton(X0))
| null_class = X0 ),
inference(resolution,[],[f650,f47]) ).
fof(f658,plain,
! [X0,X1] :
( regular(X1) = X0
| ~ subclass(X1,singleton(X0))
| null_class = X1 ),
inference(resolution,[],[f650,f159]) ).
fof(f650,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f649]) ).
fof(f649,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f648,plain,
! [X2,X3,X0,X1] :
( unordered_pair(X1,X2) = X0
| unordered_pair(X1,X2) = X3
| ~ subclass(universal_class,unordered_pair(X0,X3)) ),
inference(resolution,[],[f8,f161]) ).
fof(f647,plain,
! [X2,X0,X1] :
( regular(X1) = X0
| regular(X1) = X2
| ~ subclass(X1,unordered_pair(X0,X2))
| null_class = X1 ),
inference(resolution,[],[f8,f159]) ).
fof(f646,plain,
! [X2,X0,X1] :
( singleton(X1) = X0
| singleton(X1) = X2
| ~ subclass(universal_class,unordered_pair(X0,X2)) ),
inference(resolution,[],[f8,f162]) ).
fof(f645,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f8,f66]) ).
fof(f644,plain,
! [X0,X1] :
( omega = X0
| omega = X1
| ~ subclass(universal_class,unordered_pair(X0,X1)) ),
inference(resolution,[],[f8,f163]) ).
fof(f641,plain,
! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X0
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ),
inference(resolution,[],[f8,f2]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f631,plain,
! [X0] :
( ~ member(not_subclass_element(null_class,X0),universal_class)
| subclass(null_class,X0) ),
inference(resolution,[],[f612,f2]) ).
fof(f612,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f603]) ).
fof(f628,plain,
( ~ inductive(image(element_relation,null_class))
| ~ member(null_class,power_class(universal_class)) ),
inference(superposition,[],[f566,f603]) ).
fof(f620,plain,
( ~ member(null_class,image(element_relation,null_class))
| ~ inductive(power_class(universal_class)) ),
inference(superposition,[],[f151,f603]) ).
fof(f603,plain,
null_class = complement(universal_class),
inference(resolution,[],[f600,f4]) ).
fof(f610,plain,
! [X0,X1] :
( union(X0,X1) = null_class
| ~ subclass(union(X0,X1),intersection(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f607,f26]) ).
fof(f607,plain,
! [X0,X1] :
( ~ subclass(union(X0,X1),intersection(complement(X0),complement(X1)))
| complement(intersection(complement(X0),complement(X1))) = null_class ),
inference(superposition,[],[f600,f26]) ).
fof(f609,plain,
! [X0] :
( null_class = diagonalise(X0)
| ~ subclass(diagonalise(X0),domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f606,f76]) ).
fof(f606,plain,
! [X0] :
( ~ subclass(diagonalise(X0),domain_of(intersection(X0,identity_relation)))
| null_class = complement(domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f600,f76]) ).
fof(f608,plain,
! [X0] :
( null_class = power_class(X0)
| ~ subclass(power_class(X0),image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f605,f55]) ).
fof(f605,plain,
! [X0] :
( ~ subclass(power_class(X0),image(element_relation,complement(X0)))
| null_class = complement(image(element_relation,complement(X0))) ),
inference(superposition,[],[f600,f55]) ).
fof(f604,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ function(complement(cross_product(universal_class,universal_class))) ),
inference(resolution,[],[f600,f62]) ).
fof(f600,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f587]) ).
fof(f587,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f159,f120]) ).
fof(f598,plain,
! [X0,X1] :
( ~ subclass(X0,identity_relation)
| null_class = X0
| member(regular(X0),X1)
| ~ subclass(subset_relation,X1) ),
inference(resolution,[],[f159,f170]) ).
fof(f597,plain,
! [X0,X1] :
( ~ subclass(X0,image(element_relation,complement(X1)))
| null_class = X0
| ~ member(regular(X0),power_class(X1)) ),
inference(resolution,[],[f159,f152]) ).
fof(f596,plain,
! [X0,X1] :
( ~ subclass(X0,domain_of(intersection(X1,identity_relation)))
| null_class = X0
| ~ member(regular(X0),diagonalise(X1)) ),
inference(resolution,[],[f159,f155]) ).
fof(f594,plain,
! [X0,X1] :
( ~ subclass(X0,null_class)
| null_class = X0
| member(regular(X0),X1)
| null_class = X1 ),
inference(resolution,[],[f159,f291]) ).
fof(f593,plain,
! [X2,X3,X0,X1] :
( ~ subclass(X0,restrict(X1,X2,X3))
| null_class = X0
| member(regular(X0),X1) ),
inference(resolution,[],[f159,f495]) ).
fof(f592,plain,
! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(regular(X0),X1) ),
inference(resolution,[],[f159,f24]) ).
fof(f591,plain,
! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X1) ),
inference(resolution,[],[f159,f21]) ).
fof(f590,plain,
! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X2) ),
inference(resolution,[],[f159,f22]) ).
fof(f589,plain,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) ),
inference(resolution,[],[f159,f1]) ).
fof(f159,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f1,f66]) ).
fof(f585,plain,
! [X0,X1] :
( ~ inductive(domain_of(restrict(identity_relation,X0,X1)))
| ~ member(null_class,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f579,f29]) ).
fof(f579,plain,
! [X0] :
( ~ inductive(domain_of(intersection(X0,identity_relation)))
| ~ member(null_class,diagonalise(X0)) ),
inference(resolution,[],[f155,f47]) ).
fof(f584,plain,
! [X2,X0,X1] :
( ~ member(X2,domain_of(restrict(identity_relation,X0,X1)))
| ~ member(X2,diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f155,f29]) ).
fof(f583,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),diagonalise(X2))
| ~ subclass(universal_class,domain_of(intersection(X2,identity_relation))) ),
inference(resolution,[],[f155,f161]) ).
fof(f582,plain,
! [X0,X1] :
( ~ member(singleton(X0),diagonalise(X1))
| ~ subclass(universal_class,domain_of(intersection(X1,identity_relation))) ),
inference(resolution,[],[f155,f162]) ).
fof(f581,plain,
! [X0] :
( ~ member(regular(domain_of(intersection(X0,identity_relation))),diagonalise(X0))
| null_class = domain_of(intersection(X0,identity_relation)) ),
inference(resolution,[],[f155,f66]) ).
fof(f577,plain,
! [X0,X1] :
( ~ member(not_subclass_element(domain_of(intersection(X0,identity_relation)),X1),diagonalise(X0))
| subclass(domain_of(intersection(X0,identity_relation)),X1) ),
inference(resolution,[],[f155,f2]) ).
fof(f155,plain,
! [X0,X1] :
( ~ member(X1,domain_of(intersection(X0,identity_relation)))
| ~ member(X1,diagonalise(X0)) ),
inference(superposition,[],[f24,f76]) ).
fof(f576,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,X1)))
| ~ member(null_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f566,f26]) ).
fof(f575,plain,
! [X0] :
( ~ inductive(image(element_relation,diagonalise(X0)))
| ~ member(null_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f566,f76]) ).
fof(f574,plain,
! [X0] :
( ~ inductive(image(element_relation,power_class(X0)))
| ~ member(null_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f566,f55]) ).
fof(f566,plain,
! [X0] :
( ~ inductive(image(element_relation,complement(X0)))
| ~ member(null_class,power_class(X0)) ),
inference(resolution,[],[f152,f47]) ).
fof(f573,plain,
! [X2,X0,X1] :
( ~ member(X2,image(element_relation,union(X0,X1)))
| ~ member(X2,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f152,f26]) ).
fof(f572,plain,
! [X0,X1] :
( ~ member(X1,image(element_relation,diagonalise(X0)))
| ~ member(X1,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f152,f76]) ).
fof(f571,plain,
! [X0,X1] :
( ~ member(X1,image(element_relation,power_class(X0)))
| ~ member(X1,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f152,f55]) ).
fof(f570,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),power_class(X2))
| ~ subclass(universal_class,image(element_relation,complement(X2))) ),
inference(resolution,[],[f152,f161]) ).
fof(f569,plain,
! [X0,X1] :
( ~ member(singleton(X0),power_class(X1))
| ~ subclass(universal_class,image(element_relation,complement(X1))) ),
inference(resolution,[],[f152,f162]) ).
fof(f568,plain,
! [X0] :
( ~ member(regular(image(element_relation,complement(X0))),power_class(X0))
| null_class = image(element_relation,complement(X0)) ),
inference(resolution,[],[f152,f66]) ).
fof(f564,plain,
! [X0,X1] :
( ~ member(not_subclass_element(image(element_relation,complement(X0)),X1),power_class(X0))
| subclass(image(element_relation,complement(X0)),X1) ),
inference(resolution,[],[f152,f2]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,image(element_relation,complement(X0)))
| ~ member(X1,power_class(X0)) ),
inference(superposition,[],[f24,f55]) ).
fof(f563,plain,
! [X2,X0,X1] :
( subclass(union(X0,X1),X2)
| ~ member(not_subclass_element(union(X0,X1),X2),intersection(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f560,f26]) ).
fof(f560,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(union(X0,X1),X2),intersection(complement(X0),complement(X1)))
| subclass(complement(intersection(complement(X0),complement(X1))),X2) ),
inference(superposition,[],[f121,f26]) ).
fof(f562,plain,
! [X0,X1] :
( subclass(diagonalise(X0),X1)
| ~ member(not_subclass_element(diagonalise(X0),X1),domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f559,f76]) ).
fof(f559,plain,
! [X0,X1] :
( ~ member(not_subclass_element(diagonalise(X0),X1),domain_of(intersection(X0,identity_relation)))
| subclass(complement(domain_of(intersection(X0,identity_relation))),X1) ),
inference(superposition,[],[f121,f76]) ).
fof(f561,plain,
! [X0,X1] :
( subclass(power_class(X0),X1)
| ~ member(not_subclass_element(power_class(X0),X1),image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f558,f55]) ).
fof(f558,plain,
! [X0,X1] :
( ~ member(not_subclass_element(power_class(X0),X1),image(element_relation,complement(X0)))
| subclass(complement(image(element_relation,complement(X0))),X1) ),
inference(superposition,[],[f121,f55]) ).
fof(f556,plain,
! [X0] :
( subclass(complement(inverse(subset_relation)),X0)
| ~ member(not_subclass_element(complement(inverse(subset_relation)),X0),identity_relation) ),
inference(resolution,[],[f121,f129]) ).
fof(f555,plain,
! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ),
inference(resolution,[],[f121,f25]) ).
fof(f121,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f2,f24]) ).
fof(f102,axiom,
! [X0] : second(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued2(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn2) ).
fof(f101,axiom,
! [X0] : first(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued1(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn1) ).
fof(f65,axiom,
! [X0,X8] :
( member(image(X8,X0),universal_class)
| ~ member(X0,universal_class)
| ~ function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f49,axiom,
! [X0] :
( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
fof(f549,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(union(X0,X1)))
| member(singleton(X2),intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f426,f26]) ).
fof(f548,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(diagonalise(X0)))
| member(singleton(X1),domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f426,f76]) ).
fof(f547,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(power_class(X0)))
| member(singleton(X1),image(element_relation,complement(X0))) ),
inference(superposition,[],[f426,f55]) ).
fof(f426,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(complement(X1)))
| member(singleton(X0),X1) ),
inference(subsumption_resolution,[],[f422,f118]) ).
fof(f422,plain,
! [X0,X1] :
( member(singleton(X0),X1)
| ~ member(singleton(X0),universal_class)
| ~ subclass(universal_class,complement(complement(X1))) ),
inference(resolution,[],[f25,f175]) ).
fof(f542,plain,
! [X0,X1] :
( null_class = restrict(regular(cross_product(X0,X1)),X0,X1)
| cross_product(X0,X1) = null_class ),
inference(superposition,[],[f67,f29]) ).
fof(f540,plain,
! [X0,X1] :
( ~ member(null_class,domain_of(restrict(identity_relation,X0,X1)))
| ~ inductive(diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f154,f29]) ).
fof(f539,plain,
! [X0,X1] :
( ~ inductive(domain_of(restrict(identity_relation,X0,X1)))
| ~ inductive(diagonalise(cross_product(X0,X1))) ),
inference(superposition,[],[f408,f29]) ).
fof(f538,plain,
! [X2,X3,X0,X1] : restrict(cross_product(X0,X1),X2,X3) = restrict(cross_product(X2,X3),X0,X1),
inference(superposition,[],[f28,f29]) ).
fof(f535,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(singleton(X3),cross_product(X0,X1)) ),
inference(superposition,[],[f177,f29]) ).
fof(f534,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(singleton(X3),X2) ),
inference(superposition,[],[f176,f29]) ).
fof(f533,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,restrict(X2,X0,X1))
| member(omega,cross_product(X0,X1)) ),
inference(superposition,[],[f173,f29]) ).
fof(f530,plain,
! [X2,X0,X1] :
( ~ inductive(restrict(X2,X0,X1))
| member(null_class,cross_product(X0,X1)) ),
inference(superposition,[],[f126,f29]) ).
fof(f528,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X2,X0,X1))
| member(X3,cross_product(X0,X1)) ),
inference(superposition,[],[f21,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f281,plain,
! [X0] :
( ~ subclass(universal_class,complement(inverse(subset_relation)))
| ~ member(singleton(X0),identity_relation) ),
inference(resolution,[],[f175,f129]) ).
fof(f516,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(singleton(X3),X0) ),
inference(superposition,[],[f177,f28]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(singleton(X2),X0) ),
inference(resolution,[],[f162,f21]) ).
fof(f512,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(singleton(X3),cross_product(X1,X2)) ),
inference(superposition,[],[f176,f28]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(singleton(X2),X1) ),
inference(resolution,[],[f162,f22]) ).
fof(f506,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(omega,X0) ),
inference(resolution,[],[f495,f163]) ).
fof(f509,plain,
! [X2,X3,X0,X1,X4] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,restrict(X2,X3,X4)) ),
inference(resolution,[],[f495,f161]) ).
fof(f507,plain,
! [X2,X0,X1] :
( member(regular(restrict(X0,X1,X2)),X0)
| null_class = restrict(X0,X1,X2) ),
inference(resolution,[],[f495,f66]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(restrict(X0,X1,X2),X3) ),
inference(resolution,[],[f495,f2]) ).
fof(f495,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,X0) ),
inference(superposition,[],[f21,f28]) ).
fof(f497,plain,
! [X2,X0,X1] :
( ~ inductive(restrict(X0,X1,X2))
| member(null_class,X0) ),
inference(superposition,[],[f126,f28]) ).
fof(f500,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(omega,X0) ),
inference(superposition,[],[f173,f28]) ).
fof(f499,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,restrict(X0,X1,X2))
| member(omega,cross_product(X1,X2)) ),
inference(superposition,[],[f172,f28]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f389,plain,
( null_class = complement(subset_relation)
| ~ member(regular(complement(subset_relation)),identity_relation) ),
inference(resolution,[],[f120,f134]) ).
fof(f272,plain,
( omega = image(successor_relation,omega)
| ~ inductive(image(successor_relation,omega)) ),
inference(subsumption_resolution,[],[f269,f50]) ).
fof(f269,plain,
( omega = image(successor_relation,omega)
| ~ inductive(image(successor_relation,omega))
| ~ inductive(omega) ),
inference(resolution,[],[f214,f48]) ).
fof(f469,plain,
! [X2,X0,X1] : ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2)))),
inference(subsumption_resolution,[],[f462,f11]) ).
fof(f462,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2))))
| ~ member(unordered_pair(X1,X2),universal_class) ),
inference(resolution,[],[f263,f10]) ).
fof(f468,plain,
! [X2,X0,X1] : ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2))),
inference(subsumption_resolution,[],[f461,f11]) ).
fof(f461,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2)))
| ~ member(unordered_pair(X0,X1),universal_class) ),
inference(resolution,[],[f263,f9]) ).
fof(f470,plain,
! [X0,X1] : ~ subclass(universal_class,complement(singleton(unordered_pair(X0,X1)))),
inference(subsumption_resolution,[],[f463,f11]) ).
fof(f463,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(singleton(unordered_pair(X0,X1))))
| ~ member(unordered_pair(X0,X1),universal_class) ),
inference(resolution,[],[f263,f124]) ).
fof(f465,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(inverse(subset_relation)))
| ~ member(unordered_pair(X0,X1),identity_relation) ),
inference(resolution,[],[f263,f129]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(X0)) ),
inference(resolution,[],[f161,f24]) ).
fof(f457,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,X1)))
| ~ inductive(power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f402,f26]) ).
fof(f456,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| ~ subclass(universal_class,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f276,f26]) ).
fof(f454,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| ~ member(omega,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f171,f26]) ).
fof(f453,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(X0,X1)))
| ~ inductive(power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f151,f26]) ).
fof(f458,plain,
! [X0,X1] :
( union(X0,X1) = null_class
| ~ member(regular(union(X0,X1)),intersection(complement(X0),complement(X1))) ),
inference(forward_demodulation,[],[f452,f26]) ).
fof(f452,plain,
! [X0,X1] :
( ~ member(regular(union(X0,X1)),intersection(complement(X0),complement(X1)))
| complement(intersection(complement(X0),complement(X1))) = null_class ),
inference(superposition,[],[f120,f26]) ).
fof(f451,plain,
! [X0,X1] :
( ~ inductive(union(X0,X1))
| ~ member(null_class,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f119,f26]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f194,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(composition_function) ),
inference(resolution,[],[f158,f95]) ).
fof(f423,plain,
! [X0] :
( member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class)
| null_class = complement(complement(X0)) ),
inference(resolution,[],[f25,f120]) ).
fof(f25,axiom,
! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f174,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(omega,X1) ),
inference(resolution,[],[f163,f1]) ).
fof(f409,plain,
! [X0,X1] :
( member(not_subclass_element(identity_relation,X0),X1)
| ~ subclass(subset_relation,X1)
| subclass(identity_relation,X0) ),
inference(resolution,[],[f170,f2]) ).
fof(f170,plain,
! [X0,X1] :
( ~ member(X1,identity_relation)
| member(X1,X0)
| ~ subclass(subset_relation,X0) ),
inference(resolution,[],[f1,f134]) ).
fof(f408,plain,
! [X0] :
( ~ inductive(domain_of(intersection(X0,identity_relation)))
| ~ inductive(diagonalise(X0)) ),
inference(resolution,[],[f154,f47]) ).
fof(f154,plain,
! [X0] :
( ~ member(null_class,domain_of(intersection(X0,identity_relation)))
| ~ inductive(diagonalise(X0)) ),
inference(superposition,[],[f119,f76]) ).
fof(f406,plain,
! [X0] :
( ~ inductive(image(element_relation,diagonalise(X0)))
| ~ inductive(power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f402,f76]) ).
fof(f405,plain,
! [X0] :
( ~ inductive(image(element_relation,power_class(X0)))
| ~ inductive(power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f402,f55]) ).
fof(f402,plain,
! [X0] :
( ~ inductive(image(element_relation,complement(X0)))
| ~ inductive(power_class(X0)) ),
inference(resolution,[],[f151,f47]) ).
fof(f404,plain,
! [X0] :
( ~ member(null_class,image(element_relation,diagonalise(X0)))
| ~ inductive(power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f151,f76]) ).
fof(f403,plain,
! [X0] :
( ~ member(null_class,image(element_relation,power_class(X0)))
| ~ inductive(power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f151,f55]) ).
fof(f151,plain,
! [X0] :
( ~ member(null_class,image(element_relation,complement(X0)))
| ~ inductive(power_class(X0)) ),
inference(superposition,[],[f119,f55]) ).
fof(f394,plain,
! [X0,X1] :
( member(not_subclass_element(null_class,X0),X1)
| null_class = X1
| subclass(null_class,X0) ),
inference(resolution,[],[f291,f2]) ).
fof(f291,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| null_class = X0 ),
inference(superposition,[],[f21,f67]) ).
fof(f393,plain,
! [X0] :
( null_class = diagonalise(X0)
| ~ member(regular(diagonalise(X0)),domain_of(intersection(X0,identity_relation))) ),
inference(forward_demodulation,[],[f391,f76]) ).
fof(f391,plain,
! [X0] :
( ~ member(regular(diagonalise(X0)),domain_of(intersection(X0,identity_relation)))
| null_class = complement(domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f120,f76]) ).
fof(f392,plain,
! [X0] :
( null_class = power_class(X0)
| ~ member(regular(power_class(X0)),image(element_relation,complement(X0))) ),
inference(forward_demodulation,[],[f390,f55]) ).
fof(f390,plain,
! [X0] :
( ~ member(regular(power_class(X0)),image(element_relation,complement(X0)))
| null_class = complement(image(element_relation,complement(X0))) ),
inference(superposition,[],[f120,f55]) ).
fof(f388,plain,
( null_class = complement(inverse(subset_relation))
| ~ member(regular(complement(inverse(subset_relation))),identity_relation) ),
inference(resolution,[],[f120,f129]) ).
fof(f120,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f66,f24]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f345,plain,
( member(regular(singleton_relation),element_relation)
| null_class = singleton_relation ),
inference(resolution,[],[f323,f66]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f347,plain,
! [X0,X1] :
( member(unordered_pair(X0,X1),element_relation)
| ~ subclass(universal_class,singleton_relation) ),
inference(resolution,[],[f323,f161]) ).
fof(f346,plain,
! [X0] :
( member(singleton(X0),element_relation)
| ~ subclass(universal_class,singleton_relation) ),
inference(resolution,[],[f323,f162]) ).
fof(f344,plain,
( member(omega,element_relation)
| ~ subclass(universal_class,singleton_relation) ),
inference(resolution,[],[f323,f163]) ).
fof(f341,plain,
! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) ),
inference(resolution,[],[f323,f2]) ).
fof(f323,plain,
! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ),
inference(superposition,[],[f22,f104]) ).
fof(f325,plain,
( ~ inductive(singleton_relation)
| member(null_class,element_relation) ),
inference(superposition,[],[f131,f104]) ).
fof(f327,plain,
( ~ subclass(universal_class,singleton_relation)
| member(omega,complement(compose(element_relation,complement(identity_relation)))) ),
inference(superposition,[],[f173,f104]) ).
fof(f326,plain,
( ~ subclass(universal_class,singleton_relation)
| member(omega,element_relation) ),
inference(superposition,[],[f172,f104]) ).
fof(f324,plain,
( ~ inductive(singleton_relation)
| member(null_class,complement(compose(element_relation,complement(identity_relation)))) ),
inference(superposition,[],[f126,f104]) ).
fof(f322,plain,
! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) ),
inference(superposition,[],[f21,f104]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f100,axiom,
! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
fof(f99,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),domain_relation)
| domain_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
fof(f282,plain,
! [X0] :
( ~ subclass(universal_class,complement(subset_relation))
| ~ member(singleton(X0),identity_relation) ),
inference(resolution,[],[f175,f134]) ).
fof(f290,plain,
! [X0] :
( ~ inductive(null_class)
| member(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f126,f67]) ).
fof(f284,plain,
! [X0,X1] : ~ subclass(universal_class,complement(unordered_pair(X0,singleton(X1)))),
inference(subsumption_resolution,[],[f279,f118]) ).
fof(f279,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(X0,singleton(X1))))
| ~ member(singleton(X1),universal_class) ),
inference(resolution,[],[f175,f10]) ).
fof(f283,plain,
! [X0,X1] : ~ subclass(universal_class,complement(unordered_pair(singleton(X0),X1))),
inference(subsumption_resolution,[],[f278,f118]) ).
fof(f278,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(singleton(X0),X1)))
| ~ member(singleton(X0),universal_class) ),
inference(resolution,[],[f175,f9]) ).
fof(f292,plain,
! [X0] :
( ~ subclass(universal_class,power_class(X0))
| ~ subclass(universal_class,image(element_relation,complement(X0))) ),
inference(superposition,[],[f276,f55]) ).
fof(f276,plain,
! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f175,f162]) ).
fof(f288,plain,
! [X0] :
( ~ inductive(null_class)
| member(null_class,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f131,f67]) ).
fof(f287,plain,
! [X0] :
( ~ subclass(universal_class,null_class)
| member(omega,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f172,f67]) ).
fof(f286,plain,
! [X0] :
( ~ subclass(universal_class,null_class)
| member(omega,X0)
| null_class = X0 ),
inference(superposition,[],[f173,f67]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f285,plain,
! [X0] : ~ subclass(universal_class,complement(singleton(singleton(X0)))),
inference(subsumption_resolution,[],[f280,f118]) ).
fof(f280,plain,
! [X0] :
( ~ subclass(universal_class,complement(singleton(singleton(X0))))
| ~ member(singleton(X0),universal_class) ),
inference(resolution,[],[f175,f124]) ).
fof(f277,plain,
~ subclass(universal_class,complement(universal_class)),
inference(resolution,[],[f175,f118]) ).
fof(f175,plain,
! [X0,X1] :
( ~ member(singleton(X1),X0)
| ~ subclass(universal_class,complement(X0)) ),
inference(resolution,[],[f162,f24]) ).
fof(f173,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(omega,X0) ),
inference(resolution,[],[f163,f21]) ).
fof(f172,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(omega,X1) ),
inference(resolution,[],[f163,f22]) ).
fof(f214,plain,
! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) ),
inference(resolution,[],[f7,f51]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f161,f1]) ).
fof(f161,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f11]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),successor_relation)
| successor(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
fof(f184,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(element_relation) ),
inference(resolution,[],[f158,f18]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f217,plain,
( ~ subclass(subset_relation,identity_relation)
| identity_relation = subset_relation ),
inference(resolution,[],[f7,f157]) ).
fof(f231,plain,
( universal_class = cross_product(universal_class,universal_class)
| ~ function(universal_class) ),
inference(resolution,[],[f206,f62]) ).
fof(f181,plain,
! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) ),
inference(resolution,[],[f158,f4]) ).
fof(f196,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(application_function) ),
inference(resolution,[],[f158,f105]) ).
fof(f195,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(domain_relation) ),
inference(resolution,[],[f158,f98]) ).
fof(f193,plain,
! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose_class(X0)) ),
inference(resolution,[],[f158,f92]) ).
fof(f190,plain,
! [X0,X1] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) ),
inference(resolution,[],[f158,f57]) ).
fof(f188,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation) ),
inference(resolution,[],[f158,f44]) ).
fof(f186,plain,
! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) ),
inference(resolution,[],[f158,f35]) ).
fof(f183,plain,
! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) ),
inference(resolution,[],[f158,f62]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f47]) ).
fof(f171,plain,
! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ member(omega,X0) ),
inference(resolution,[],[f163,f24]) ).
fof(f162,plain,
! [X0,X1] :
( member(singleton(X1),X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f118]) ).
fof(f163,plain,
! [X0] :
( member(omega,X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f52]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f157,plain,
subclass(identity_relation,subset_relation),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f156,plain,
( subclass(identity_relation,subset_relation)
| subclass(identity_relation,subset_relation) ),
inference(resolution,[],[f135,f2]) ).
fof(f135,plain,
! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),identity_relation)
| subclass(X0,subset_relation) ),
inference(resolution,[],[f134,f3]) ).
fof(f76,axiom,
! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalisation) ).
fof(f63,axiom,
! [X8] :
( subclass(compose(X8,inverse(X8)),identity_relation)
| ~ function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
fof(f131,plain,
! [X0,X1] :
( ~ inductive(intersection(X1,X0))
| member(null_class,X0) ),
inference(resolution,[],[f22,f47]) ).
fof(f129,plain,
! [X0] :
( member(X0,inverse(subset_relation))
| ~ member(X0,identity_relation) ),
inference(superposition,[],[f21,f75]) ).
fof(f130,plain,
( ~ inductive(identity_relation)
| member(null_class,inverse(subset_relation)) ),
inference(superposition,[],[f126,f75]) ).
fof(f134,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) ),
inference(superposition,[],[f22,f75]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f126,plain,
! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(null_class,X0) ),
inference(resolution,[],[f21,f47]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f19,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f124,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f62,axiom,
! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f56,axiom,
! [X2] :
( member(power_class(X2),universal_class)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
fof(f54,axiom,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f48,axiom,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f119,plain,
! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) ),
inference(resolution,[],[f24,f47]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f118,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f11,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f51,axiom,
! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f47,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f114,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f115,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
fof(f27,axiom,
! [X0,X1] : intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET151-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 16:39:53 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (23917)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (23923)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)
% 0.12/0.37 % (23920)WARNING: value z3 for option sas not known
% 0.12/0.37 % (23921)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (23922)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)
% 0.12/0.37 % (23919)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37 % (23920)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)
% 0.12/0.37 % (23924)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)
% 0.19/0.37 % (23918)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.41 TRYING [1]
% 0.19/0.42 TRYING [2]
% 0.19/0.47 TRYING [3]
% 0.19/0.52 TRYING [1]
% 0.19/0.52 TRYING [2]
% 0.19/0.53 TRYING [3]
% 1.34/0.54 TRYING [1]
% 1.48/0.55 TRYING [2]
% 1.48/0.60 TRYING [4]
% 1.48/0.63 TRYING [4]
% 2.31/0.68 TRYING [3]
% 2.96/0.77 TRYING [5]
% 3.57/0.91 % (23920)First to succeed.
% 4.11/0.94 % (23920)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23917"
% 4.11/0.94 % (23920)Refutation found. Thanks to Tanya!
% 4.11/0.94 % SZS status Unsatisfiable for theBenchmark
% 4.11/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/0.96 % (23920)------------------------------
% 4.11/0.96 % (23920)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.11/0.96 % (23920)Termination reason: Refutation
% 4.11/0.96
% 4.11/0.96 % (23920)Memory used [KB]: 6958
% 4.11/0.96 % (23920)Time elapsed: 0.571 s
% 4.11/0.96 % (23920)Instructions burned: 1163 (million)
% 4.11/0.96 % (23917)Success in time 0.597 s
%------------------------------------------------------------------------------