TSTP Solution File: SEU200+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU200+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : 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 09:28:33 EDT 2024
% Result : Theorem 0.21s 0.59s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 645
% Syntax : Number of formulae : 2040 ( 424 unt; 0 def)
% Number of atoms : 6637 ( 955 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 7574 (2977 ~;3201 |; 661 &)
% ( 537 <=>; 197 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 437 ( 435 usr; 410 prp; 0-3 aty)
% Number of functors : 88 ( 88 usr; 7 con; 0-4 aty)
% Number of variables : 3991 (3758 !; 233 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6245,plain,
$false,
inference(avatar_sat_refutation,[],[f1102,f1107,f1112,f1117,f1122,f1127,f1132,f1137,f1142,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1180,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1214,f1218,f1222,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1259,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1292,f1296,f1300,f1304,f1308,f1312,f1316,f1320,f1348,f1355,f1361,f1366,f1371,f1381,f1392,f1396,f1400,f1405,f1409,f1413,f1417,f1421,f1425,f1429,f1433,f1437,f1441,f1445,f1449,f1453,f1459,f1483,f1487,f1491,f1495,f1501,f1511,f1516,f1526,f1532,f1536,f1540,f1544,f1548,f1553,f1557,f1561,f1565,f1571,f1575,f1579,f1583,f1587,f1591,f1595,f1599,f1620,f1630,f1690,f1694,f1698,f1702,f1707,f1711,f1715,f1719,f1723,f1727,f1732,f1737,f1741,f1745,f1749,f1763,f1767,f1771,f1845,f1858,f1862,f1907,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1963,f1967,f1971,f1975,f1979,f1983,f2042,f2046,f2050,f2056,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2113,f2117,f2190,f2194,f2198,f2202,f2207,f2211,f2215,f2219,f2223,f2278,f2284,f2290,f2294,f2298,f2302,f2306,f2310,f2319,f2323,f2327,f2331,f2335,f2339,f2343,f2347,f2351,f2355,f2360,f2366,f2370,f2488,f2537,f2541,f2585,f2589,f2593,f2597,f2601,f2605,f2609,f2613,f2618,f2622,f2626,f2630,f2634,f2684,f2707,f2711,f2716,f2720,f2724,f2728,f2732,f2736,f2740,f2744,f2906,f2910,f2914,f2918,f2929,f2933,f2937,f2941,f2945,f2949,f2953,f2957,f2971,f3059,f3063,f3067,f3071,f3075,f3079,f3083,f3130,f3180,f3184,f3188,f3192,f3196,f3200,f3204,f3208,f3212,f3250,f3255,f3261,f3265,f3269,f3274,f3278,f3282,f3286,f3306,f3360,f3364,f3369,f3373,f3377,f3381,f3385,f3389,f3393,f3397,f3401,f3405,f3409,f3416,f3420,f3424,f3428,f3476,f3555,f3559,f3563,f3567,f3723,f3727,f3732,f3736,f3795,f3799,f3803,f3807,f3811,f3815,f3823,f3827,f3831,f3835,f3920,f3971,f3975,f3979,f4006,f4010,f4014,f4018,f4022,f4026,f4088,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4253,f4475,f4479,f4483,f4487,f4522,f4546,f4551,f4557,f4561,f4565,f4582,f4586,f4616,f4701,f4705,f4710,f4763,f4768,f4774,f4796,f4802,f4828,f4833,f4858,f4862,f4866,f4917,f4934,f4938,f4942,f5070,f5084,f5089,f5093,f5098,f5102,f5106,f5110,f5165,f5186,f5190,f5249,f5253,f5258,f5294,f5298,f5331,f5356,f5361,f5366,f5370,f5374,f5378,f5448,f5452,f5457,f5478,f5565,f5569,f5574,f5578,f5621,f5627,f5675,f5679,f5746,f5752,f5758,f5762,f5824,f5828,f5834,f5840,f5846,f5850,f5854,f5858,f6050,f6056,f6060,f6086,f6091,f6110,f6116,f6176,f6180,f6196,f6199,f6209,f6214,f6219,f6223,f6227,f6231,f6235,f6239,f6243,f6244]) ).
fof(f6244,plain,
( ~ spl81_1
| ~ spl81_75
| spl81_396 ),
inference(avatar_split_clause,[],[f6112,f6107,f1481,f1099]) ).
fof(f1099,plain,
( spl81_1
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_1])]) ).
fof(f1481,plain,
( spl81_75
<=> ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_75])]) ).
fof(f6107,plain,
( spl81_396
<=> subset(relation_rng_restriction(sK18,sK19),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_396])]) ).
fof(f6112,plain,
( ~ relation(sK19)
| ~ spl81_75
| spl81_396 ),
inference(resolution,[],[f6109,f1482]) ).
fof(f1482,plain,
( ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) )
| ~ spl81_75 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f6109,plain,
( ~ subset(relation_rng_restriction(sK18,sK19),sK19)
| spl81_396 ),
inference(avatar_component_clause,[],[f6107]) ).
fof(f6243,plain,
( spl81_409
| ~ spl81_79
| ~ spl81_81
| ~ spl81_119 ),
inference(avatar_split_clause,[],[f1900,f1769,f1514,f1499,f6241]) ).
fof(f6241,plain,
( spl81_409
<=> ! [X0] : sP15(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_409])]) ).
fof(f1499,plain,
( spl81_79
<=> ! [X0] : sK78 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_79])]) ).
fof(f1514,plain,
( spl81_81
<=> ! [X0] : set_difference(X0,sK78) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_81])]) ).
fof(f1769,plain,
( spl81_119
<=> ! [X0,X1] : sP15(X1,X0,set_difference(X0,set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_119])]) ).
fof(f1900,plain,
( ! [X0] : sP15(X0,X0,X0)
| ~ spl81_79
| ~ spl81_81
| ~ spl81_119 ),
inference(forward_demodulation,[],[f1893,f1515]) ).
fof(f1515,plain,
( ! [X0] : set_difference(X0,sK78) = X0
| ~ spl81_81 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f1893,plain,
( ! [X0] : sP15(X0,X0,set_difference(X0,sK78))
| ~ spl81_79
| ~ spl81_119 ),
inference(superposition,[],[f1770,f1500]) ).
fof(f1500,plain,
( ! [X0] : sK78 = set_difference(X0,X0)
| ~ spl81_79 ),
inference(avatar_component_clause,[],[f1499]) ).
fof(f1770,plain,
( ! [X0,X1] : sP15(X1,X0,set_difference(X0,set_difference(X0,X1)))
| ~ spl81_119 ),
inference(avatar_component_clause,[],[f1769]) ).
fof(f6239,plain,
( spl81_408
| ~ spl81_39
| ~ spl81_52
| ~ spl81_79
| ~ spl81_119 ),
inference(avatar_split_clause,[],[f1899,f1769,f1499,f1345,f1270,f6237]) ).
fof(f6237,plain,
( spl81_408
<=> ! [X0] : sP15(sK78,X0,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_408])]) ).
fof(f1270,plain,
( spl81_39
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_39])]) ).
fof(f1345,plain,
( spl81_52
<=> empty_set = sK78 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_52])]) ).
fof(f1899,plain,
( ! [X0] : sP15(sK78,X0,sK78)
| ~ spl81_39
| ~ spl81_52
| ~ spl81_79
| ~ spl81_119 ),
inference(forward_demodulation,[],[f1898,f1347]) ).
fof(f1347,plain,
( empty_set = sK78
| ~ spl81_52 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f1898,plain,
( ! [X0] : sP15(empty_set,X0,sK78)
| ~ spl81_39
| ~ spl81_79
| ~ spl81_119 ),
inference(forward_demodulation,[],[f1892,f1500]) ).
fof(f1892,plain,
( ! [X0] : sP15(empty_set,X0,set_difference(X0,X0))
| ~ spl81_39
| ~ spl81_119 ),
inference(superposition,[],[f1770,f1271]) ).
fof(f1271,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl81_39 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f6235,plain,
( spl81_407
| ~ spl81_37
| ~ spl81_39
| ~ spl81_52
| ~ spl81_119 ),
inference(avatar_split_clause,[],[f1897,f1769,f1345,f1270,f1262,f6233]) ).
fof(f6233,plain,
( spl81_407
<=> ! [X0] : sP15(X0,sK78,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_407])]) ).
fof(f1262,plain,
( spl81_37
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_37])]) ).
fof(f1897,plain,
( ! [X0] : sP15(X0,sK78,sK78)
| ~ spl81_37
| ~ spl81_39
| ~ spl81_52
| ~ spl81_119 ),
inference(forward_demodulation,[],[f1896,f1347]) ).
fof(f1896,plain,
( ! [X0] : sP15(X0,empty_set,empty_set)
| ~ spl81_37
| ~ spl81_39
| ~ spl81_119 ),
inference(forward_demodulation,[],[f1891,f1271]) ).
fof(f1891,plain,
( ! [X0] : sP15(X0,empty_set,set_difference(empty_set,empty_set))
| ~ spl81_37
| ~ spl81_119 ),
inference(superposition,[],[f1770,f1263]) ).
fof(f1263,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl81_37 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f6231,plain,
( spl81_406
| ~ spl81_73
| ~ spl81_79 ),
inference(avatar_split_clause,[],[f1504,f1499,f1451,f6229]) ).
fof(f6229,plain,
( spl81_406
<=> ! [X0] : sP17(X0,X0,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_406])]) ).
fof(f1451,plain,
( spl81_73
<=> ! [X0,X1] : sP17(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_73])]) ).
fof(f1504,plain,
( ! [X0] : sP17(X0,X0,sK78)
| ~ spl81_73
| ~ spl81_79 ),
inference(superposition,[],[f1452,f1500]) ).
fof(f1452,plain,
( ! [X0,X1] : sP17(X1,X0,set_difference(X0,X1))
| ~ spl81_73 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f6227,plain,
( spl81_405
| ~ spl81_20
| ~ spl81_68 ),
inference(avatar_split_clause,[],[f1468,f1431,f1187,f6225]) ).
fof(f6225,plain,
( spl81_405
<=> ! [X0] : element(X0,sK22(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_405])]) ).
fof(f1187,plain,
( spl81_20
<=> ! [X0] : in(X0,sK22(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_20])]) ).
fof(f1431,plain,
( spl81_68
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_68])]) ).
fof(f1468,plain,
( ! [X0] : element(X0,sK22(X0))
| ~ spl81_20
| ~ spl81_68 ),
inference(resolution,[],[f1432,f1188]) ).
fof(f1188,plain,
( ! [X0] : in(X0,sK22(X0))
| ~ spl81_20 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1432,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl81_68 ),
inference(avatar_component_clause,[],[f1431]) ).
fof(f6223,plain,
( spl81_404
| ~ spl81_20
| ~ spl81_67 ),
inference(avatar_split_clause,[],[f1464,f1427,f1187,f6221]) ).
fof(f6221,plain,
( spl81_404
<=> ! [X0] : ~ in(sK22(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_404])]) ).
fof(f1427,plain,
( spl81_67
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_67])]) ).
fof(f1464,plain,
( ! [X0] : ~ in(sK22(X0),X0)
| ~ spl81_20
| ~ spl81_67 ),
inference(resolution,[],[f1428,f1188]) ).
fof(f1428,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl81_67 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f6219,plain,
( ~ spl81_403
| ~ spl81_35
| ~ spl81_52
| ~ spl81_57 ),
inference(avatar_split_clause,[],[f1388,f1378,f1345,f1253,f6216]) ).
fof(f6216,plain,
( spl81_403
<=> sK78 = powerset(sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_403])]) ).
fof(f1253,plain,
( spl81_35
<=> ! [X0] : empty_set != unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_35])]) ).
fof(f1378,plain,
( spl81_57
<=> powerset(sK78) = unordered_pair(sK78,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_57])]) ).
fof(f1388,plain,
( sK78 != powerset(sK78)
| ~ spl81_35
| ~ spl81_52
| ~ spl81_57 ),
inference(forward_demodulation,[],[f1387,f1347]) ).
fof(f1387,plain,
( empty_set != powerset(sK78)
| ~ spl81_35
| ~ spl81_57 ),
inference(superposition,[],[f1254,f1380]) ).
fof(f1380,plain,
( powerset(sK78) = unordered_pair(sK78,sK78)
| ~ spl81_57 ),
inference(avatar_component_clause,[],[f1378]) ).
fof(f1254,plain,
( ! [X0] : empty_set != unordered_pair(X0,X0)
| ~ spl81_35 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f6214,plain,
( spl81_402
| ~ spl81_36
| ~ spl81_57 ),
inference(avatar_split_clause,[],[f1386,f1378,f1257,f6211]) ).
fof(f6211,plain,
( spl81_402
<=> in(sK78,powerset(sK78)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_402])]) ).
fof(f1257,plain,
( spl81_36
<=> ! [X3] : in(X3,unordered_pair(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_36])]) ).
fof(f1386,plain,
( in(sK78,powerset(sK78))
| ~ spl81_36
| ~ spl81_57 ),
inference(superposition,[],[f1258,f1380]) ).
fof(f1258,plain,
( ! [X3] : in(X3,unordered_pair(X3,X3))
| ~ spl81_36 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f6209,plain,
( spl81_401
| ~ spl81_27
| ~ spl81_30 ),
inference(avatar_split_clause,[],[f1260,f1233,f1216,f6207]) ).
fof(f6207,plain,
( spl81_401
<=> ! [X0] : sP12(powerset(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_401])]) ).
fof(f1216,plain,
( spl81_27
<=> ! [X0] : sP12(X0,union(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_27])]) ).
fof(f1233,plain,
( spl81_30
<=> ! [X0] : union(powerset(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_30])]) ).
fof(f1260,plain,
( ! [X0] : sP12(powerset(X0),X0)
| ~ spl81_27
| ~ spl81_30 ),
inference(superposition,[],[f1217,f1234]) ).
fof(f1234,plain,
( ! [X0] : union(powerset(X0)) = X0
| ~ spl81_30 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f1217,plain,
( ! [X0] : sP12(X0,union(X0))
| ~ spl81_27 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f6199,plain,
( ~ spl81_1
| ~ spl81_63
| spl81_395 ),
inference(avatar_split_clause,[],[f6111,f6103,f1411,f1099]) ).
fof(f1411,plain,
( spl81_63
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_63])]) ).
fof(f6103,plain,
( spl81_395
<=> relation(relation_rng_restriction(sK18,sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_395])]) ).
fof(f6111,plain,
( ~ relation(sK19)
| ~ spl81_63
| spl81_395 ),
inference(resolution,[],[f6105,f1412]) ).
fof(f1412,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl81_63 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f6105,plain,
( ~ relation(relation_rng_restriction(sK18,sK19))
| spl81_395 ),
inference(avatar_component_clause,[],[f6103]) ).
fof(f6196,plain,
( spl81_400
| ~ spl81_24
| ~ spl81_51 ),
inference(avatar_split_clause,[],[f1350,f1318,f1203,f6194]) ).
fof(f6194,plain,
( spl81_400
<=> ! [X0] : ~ empty(sK50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_400])]) ).
fof(f1203,plain,
( spl81_24
<=> ! [X0] : in(X0,sK50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_24])]) ).
fof(f1318,plain,
( spl81_51
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_51])]) ).
fof(f1350,plain,
( ! [X0] : ~ empty(sK50(X0))
| ~ spl81_24
| ~ spl81_51 ),
inference(resolution,[],[f1319,f1204]) ).
fof(f1204,plain,
( ! [X0] : in(X0,sK50(X0))
| ~ spl81_24 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1319,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl81_51 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f6180,plain,
( spl81_399
| ~ spl81_17
| ~ spl81_52
| ~ spl81_105 ),
inference(avatar_split_clause,[],[f1825,f1700,f1345,f1173,f6178]) ).
fof(f6178,plain,
( spl81_399
<=> ! [X0] : disjoint(X0,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_399])]) ).
fof(f1173,plain,
( spl81_17
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_17])]) ).
fof(f1700,plain,
( spl81_105
<=> ! [X0,X1] :
( in(sK24(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_105])]) ).
fof(f1825,plain,
( ! [X0] : disjoint(X0,sK78)
| ~ spl81_17
| ~ spl81_52
| ~ spl81_105 ),
inference(forward_demodulation,[],[f1820,f1347]) ).
fof(f1820,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl81_17
| ~ spl81_105 ),
inference(resolution,[],[f1701,f1174]) ).
fof(f1174,plain,
( ! [X2] : ~ in(X2,empty_set)
| ~ spl81_17 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f1701,plain,
( ! [X0,X1] :
( in(sK24(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl81_105 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f6176,plain,
( spl81_398
| ~ spl81_17
| ~ spl81_52
| ~ spl81_104 ),
inference(avatar_split_clause,[],[f1819,f1696,f1345,f1173,f6174]) ).
fof(f6174,plain,
( spl81_398
<=> ! [X0] : disjoint(sK78,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_398])]) ).
fof(f1696,plain,
( spl81_104
<=> ! [X0,X1] :
( in(sK24(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_104])]) ).
fof(f1819,plain,
( ! [X0] : disjoint(sK78,X0)
| ~ spl81_17
| ~ spl81_52
| ~ spl81_104 ),
inference(forward_demodulation,[],[f1814,f1347]) ).
fof(f1814,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl81_17
| ~ spl81_104 ),
inference(resolution,[],[f1697,f1174]) ).
fof(f1697,plain,
( ! [X0,X1] :
( in(sK24(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl81_104 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f6116,plain,
( spl81_397
| ~ spl81_1
| ~ spl81_269 ),
inference(avatar_split_clause,[],[f3581,f3553,f1099,f6114]) ).
fof(f6114,plain,
( spl81_397
<=> ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_difference(relation_dom(sK19),set_difference(relation_dom(sK19),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_397])]) ).
fof(f3553,plain,
( spl81_269
<=> ! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_269])]) ).
fof(f3581,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_difference(relation_dom(sK19),set_difference(relation_dom(sK19),X0))
| ~ spl81_1
| ~ spl81_269 ),
inference(resolution,[],[f3554,f1101]) ).
fof(f1101,plain,
( relation(sK19)
| ~ spl81_1 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f3554,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) )
| ~ spl81_269 ),
inference(avatar_component_clause,[],[f3553]) ).
fof(f6110,plain,
( ~ spl81_395
| ~ spl81_1
| ~ spl81_396
| spl81_2
| ~ spl81_225 ),
inference(avatar_split_clause,[],[f3101,f3061,f1104,f6107,f1099,f6103]) ).
fof(f1104,plain,
( spl81_2
<=> subset(relation_rng(relation_rng_restriction(sK18,sK19)),relation_rng(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_2])]) ).
fof(f3061,plain,
( spl81_225
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_225])]) ).
fof(f3101,plain,
( ~ subset(relation_rng_restriction(sK18,sK19),sK19)
| ~ relation(sK19)
| ~ relation(relation_rng_restriction(sK18,sK19))
| spl81_2
| ~ spl81_225 ),
inference(resolution,[],[f3062,f1106]) ).
fof(f1106,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK18,sK19)),relation_rng(sK19))
| spl81_2 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f3062,plain,
( ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_225 ),
inference(avatar_component_clause,[],[f3061]) ).
fof(f6091,plain,
( spl81_394
| ~ spl81_88
| ~ spl81_393 ),
inference(avatar_split_clause,[],[f6087,f6084,f1551,f6089]) ).
fof(f6089,plain,
( spl81_394
<=> ! [X0,X5,X2,X1] :
( ~ in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK34(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),X5),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_394])]) ).
fof(f1551,plain,
( spl81_88
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_88])]) ).
fof(f6084,plain,
( spl81_393
<=> ! [X0,X5,X2,X1] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK34(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),X5),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_393])]) ).
fof(f6087,plain,
( ! [X2,X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK34(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),X5),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1) )
| ~ spl81_88
| ~ spl81_393 ),
inference(forward_demodulation,[],[f6085,f1552]) ).
fof(f1552,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl81_88 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f6085,plain,
( ! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK34(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),X5),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) )
| ~ spl81_393 ),
inference(avatar_component_clause,[],[f6084]) ).
fof(f6086,plain,
spl81_393,
inference(avatar_split_clause,[],[f990,f6084]) ).
fof(f990,plain,
! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK34(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),X5),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f732,f931,f931,f931]) ).
fof(f931,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f780,f583]) ).
fof(f583,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f175]) ).
fof(f175,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f780,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f732,plain,
! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(ordered_pair(X5,sK34(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK33(X0,X1,X2),X5),X1)
| ~ in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f442,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK34(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK33(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),X0)
& in(ordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),X1) )
| in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ( in(ordered_pair(sK36(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK36(X0,X1,X7,X8)),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f438,f441,f440,f439]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK34(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK33(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK34(X0,X1,X2)),X0)
& in(ordered_pair(sK33(X0,X1,X2),X6),X1) )
| in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK34(X0,X1,X2)),X0)
& in(ordered_pair(sK33(X0,X1,X2),X6),X1) )
=> ( in(ordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),X0)
& in(ordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f441,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
=> ( in(ordered_pair(sK36(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK36(X0,X1,X7,X8)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f437]) ).
fof(f437,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f6060,plain,
( spl81_392
| ~ spl81_88
| ~ spl81_390 ),
inference(avatar_split_clause,[],[f6052,f6048,f1551,f6058]) ).
fof(f6058,plain,
( spl81_392
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK43(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_392])]) ).
fof(f6048,plain,
( spl81_390
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_390])]) ).
fof(f6052,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK43(X0,X1,X2),X1) )
| ~ spl81_88
| ~ spl81_390 ),
inference(forward_demodulation,[],[f6051,f1552]) ).
fof(f6051,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) )
| ~ spl81_88
| ~ spl81_390 ),
inference(forward_demodulation,[],[f6049,f1552]) ).
fof(f6049,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) )
| ~ spl81_390 ),
inference(avatar_component_clause,[],[f6048]) ).
fof(f6056,plain,
spl81_391,
inference(avatar_split_clause,[],[f1089,f6054]) ).
fof(f6054,plain,
( spl81_391
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2)
| ~ in(sK59(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_391])]) ).
fof(f1089,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2)
| ~ in(sK59(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f1088,f777]) ).
fof(f777,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1088,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2)
| ~ in(sK59(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1021,f777]) ).
fof(f1021,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| ~ in(sK59(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f816,f931,f931]) ).
fof(f816,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
| ~ in(sK59(X0,X1,X2),X1)
| ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f502,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
| ~ in(sK59(X0,X1,X2),X1)
| ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
& in(sK59(X0,X1,X2),X1) )
| in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP8(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f500,f501]) ).
fof(f501,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
| ~ in(sK59(X0,X1,X2),X1)
| ~ in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
& in(sK59(X0,X1,X2),X1) )
| in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f500,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP8(X0,X1,X2) ) ),
inference(rectify,[],[f499]) ).
fof(f499,plain,
! [X1,X0,X2] :
( ( sP8(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP8(X1,X0,X2) ) ),
inference(flattening,[],[f498]) ).
fof(f498,plain,
! [X1,X0,X2] :
( ( sP8(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP8(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X1,X0,X2] :
( sP8(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f6050,plain,
spl81_390,
inference(avatar_split_clause,[],[f1004,f6048]) ).
fof(f1004,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f749,f931,f931]) ).
fof(f749,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f461,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
& in(sK43(X0,X1,X2),X1) )
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f459,f460]) ).
fof(f460,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
| ~ in(sK43(X0,X1,X2),X1)
| ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
& in(sK43(X0,X1,X2),X1) )
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f459,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f458]) ).
fof(f458,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(flattening,[],[f457]) ).
fof(f457,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f5858,plain,
( spl81_389
| ~ spl81_88
| ~ spl81_385 ),
inference(avatar_split_clause,[],[f5842,f5838,f1551,f5856]) ).
fof(f5856,plain,
( spl81_389
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_389])]) ).
fof(f5838,plain,
( spl81_385
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_385])]) ).
fof(f5842,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2) )
| ~ spl81_88
| ~ spl81_385 ),
inference(forward_demodulation,[],[f5841,f1552]) ).
fof(f5841,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) )
| ~ spl81_88
| ~ spl81_385 ),
inference(forward_demodulation,[],[f5839,f1552]) ).
fof(f5839,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) )
| ~ spl81_385 ),
inference(avatar_component_clause,[],[f5838]) ).
fof(f5854,plain,
( spl81_388
| ~ spl81_88
| ~ spl81_384 ),
inference(avatar_split_clause,[],[f5836,f5832,f1551,f5852]) ).
fof(f5852,plain,
( spl81_388
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_388])]) ).
fof(f5832,plain,
( spl81_384
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_384])]) ).
fof(f5836,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| sP0(X0,X1,X2) )
| ~ spl81_88
| ~ spl81_384 ),
inference(forward_demodulation,[],[f5835,f1552]) ).
fof(f5835,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) )
| ~ spl81_88
| ~ spl81_384 ),
inference(forward_demodulation,[],[f5833,f1552]) ).
fof(f5833,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) )
| ~ spl81_384 ),
inference(avatar_component_clause,[],[f5832]) ).
fof(f5850,plain,
( spl81_387
| ~ spl81_88
| ~ spl81_383 ),
inference(avatar_split_clause,[],[f5830,f5826,f1551,f5848]) ).
fof(f5848,plain,
( spl81_387
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_387])]) ).
fof(f5826,plain,
( spl81_383
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_383])]) ).
fof(f5830,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl81_88
| ~ spl81_383 ),
inference(forward_demodulation,[],[f5829,f1552]) ).
fof(f5829,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) )
| ~ spl81_88
| ~ spl81_383 ),
inference(forward_demodulation,[],[f5827,f1552]) ).
fof(f5827,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) )
| ~ spl81_383 ),
inference(avatar_component_clause,[],[f5826]) ).
fof(f5846,plain,
spl81_386,
inference(avatar_split_clause,[],[f1091,f5844]) ).
fof(f5844,plain,
( spl81_386
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_386])]) ).
fof(f1091,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2) ),
inference(forward_demodulation,[],[f1090,f777]) ).
fof(f1090,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| sP8(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1022,f777]) ).
fof(f1022,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f815,f931,f931]) ).
fof(f815,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X0)
| in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f5840,plain,
spl81_385,
inference(avatar_split_clause,[],[f1005,f5838]) ).
fof(f1005,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f748,f931,f931]) ).
fof(f748,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f5834,plain,
spl81_384,
inference(avatar_split_clause,[],[f992,f5832]) ).
fof(f992,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f730,f931,f931]) ).
fof(f730,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(sK33(X0,X1,X2),sK35(X0,X1,X2)),X1)
| in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f5828,plain,
spl81_383,
inference(avatar_split_clause,[],[f991,f5826]) ).
fof(f991,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK35(X0,X1,X2),sK35(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f731,f931,f931]) ).
fof(f731,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(sK35(X0,X1,X2),sK34(X0,X1,X2)),X0)
| in(ordered_pair(sK33(X0,X1,X2),sK34(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f5824,plain,
( spl81_382
| ~ spl81_38
| ~ spl81_52
| ~ spl81_89
| ~ spl81_144
| ~ spl81_268 ),
inference(avatar_split_clause,[],[f3543,f3473,f2064,f1555,f1345,f1266,f5821]) ).
fof(f5821,plain,
( spl81_382
<=> relation_field(sK19) = set_union2(relation_field(sK19),relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_382])]) ).
fof(f1266,plain,
( spl81_38
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_38])]) ).
fof(f1555,plain,
( spl81_89
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_89])]) ).
fof(f2064,plain,
( spl81_144
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_144])]) ).
fof(f3473,plain,
( spl81_268
<=> sK78 = set_difference(relation_dom(sK19),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_268])]) ).
fof(f3543,plain,
( relation_field(sK19) = set_union2(relation_field(sK19),relation_dom(sK19))
| ~ spl81_38
| ~ spl81_52
| ~ spl81_89
| ~ spl81_144
| ~ spl81_268 ),
inference(forward_demodulation,[],[f3542,f1647]) ).
fof(f1647,plain,
( ! [X0] : set_union2(sK78,X0) = X0
| ~ spl81_38
| ~ spl81_52
| ~ spl81_89 ),
inference(forward_demodulation,[],[f1635,f1347]) ).
fof(f1635,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl81_38
| ~ spl81_89 ),
inference(superposition,[],[f1556,f1267]) ).
fof(f1267,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl81_38 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1556,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl81_89 ),
inference(avatar_component_clause,[],[f1555]) ).
fof(f3542,plain,
( set_union2(relation_field(sK19),relation_dom(sK19)) = set_union2(sK78,relation_field(sK19))
| ~ spl81_89
| ~ spl81_144
| ~ spl81_268 ),
inference(forward_demodulation,[],[f3529,f1556]) ).
fof(f3529,plain,
( set_union2(relation_field(sK19),relation_dom(sK19)) = set_union2(relation_field(sK19),sK78)
| ~ spl81_144
| ~ spl81_268 ),
inference(superposition,[],[f2065,f3475]) ).
fof(f3475,plain,
( sK78 = set_difference(relation_dom(sK19),relation_field(sK19))
| ~ spl81_268 ),
inference(avatar_component_clause,[],[f3473]) ).
fof(f2065,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))
| ~ spl81_144 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f5762,plain,
( spl81_381
| ~ spl81_88
| ~ spl81_379 ),
inference(avatar_split_clause,[],[f5754,f5750,f1551,f5760]) ).
fof(f5760,plain,
( spl81_381
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK31(X0,X1),sK31(X0,X1)),unordered_pair(sK31(X0,X1),sK32(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_381])]) ).
fof(f5750,plain,
( spl81_379
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_379])]) ).
fof(f5754,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK31(X0,X1),sK31(X0,X1)),unordered_pair(sK31(X0,X1),sK32(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_379 ),
inference(forward_demodulation,[],[f5753,f1552]) ).
fof(f5753,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_379 ),
inference(forward_demodulation,[],[f5751,f1552]) ).
fof(f5751,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_379 ),
inference(avatar_component_clause,[],[f5750]) ).
fof(f5758,plain,
( spl81_380
| ~ spl81_88
| ~ spl81_378 ),
inference(avatar_split_clause,[],[f5748,f5744,f1551,f5756]) ).
fof(f5756,plain,
( spl81_380
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK31(X0,X1)),unordered_pair(sK31(X0,X1),sK32(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_380])]) ).
fof(f5744,plain,
( spl81_378
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_378])]) ).
fof(f5748,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK31(X0,X1)),unordered_pair(sK31(X0,X1),sK32(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_378 ),
inference(forward_demodulation,[],[f5747,f1552]) ).
fof(f5747,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_378 ),
inference(forward_demodulation,[],[f5745,f1552]) ).
fof(f5745,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_378 ),
inference(avatar_component_clause,[],[f5744]) ).
fof(f5752,plain,
spl81_379,
inference(avatar_split_clause,[],[f987,f5750]) ).
fof(f987,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f723,f931,f931]) ).
fof(f723,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f434]) ).
fof(f434,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| ~ in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& ( in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f432,f433]) ).
fof(f433,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( ~ in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| ~ in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& ( in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f432,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f431]) ).
fof(f431,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f5746,plain,
spl81_378,
inference(avatar_split_clause,[],[f986,f5744]) ).
fof(f986,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK32(X0,X1),sK31(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f724,f931,f931]) ).
fof(f724,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK32(X0,X1),sK31(X0,X1)),X0)
| ~ in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f434]) ).
fof(f5679,plain,
( spl81_377
| ~ spl81_88
| ~ spl81_375 ),
inference(avatar_split_clause,[],[f5629,f5625,f1551,f5677]) ).
fof(f5677,plain,
( spl81_377
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_377])]) ).
fof(f5625,plain,
( spl81_375
<=> ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_375])]) ).
fof(f5629,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_375 ),
inference(forward_demodulation,[],[f5628,f1552]) ).
fof(f5628,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_375 ),
inference(forward_demodulation,[],[f5626,f1552]) ).
fof(f5626,plain,
( ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_375 ),
inference(avatar_component_clause,[],[f5625]) ).
fof(f5675,plain,
( spl81_376
| ~ spl81_88
| ~ spl81_374 ),
inference(avatar_split_clause,[],[f5623,f5619,f1551,f5673]) ).
fof(f5673,plain,
( spl81_376
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_376])]) ).
fof(f5619,plain,
( spl81_374
<=> ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_374])]) ).
fof(f5623,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_374 ),
inference(forward_demodulation,[],[f5622,f1552]) ).
fof(f5622,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_374 ),
inference(forward_demodulation,[],[f5620,f1552]) ).
fof(f5620,plain,
( ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_374 ),
inference(avatar_component_clause,[],[f5619]) ).
fof(f5627,plain,
spl81_375,
inference(avatar_split_clause,[],[f980,f5625]) ).
fof(f980,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f716,f931,f931]) ).
fof(f716,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) )
& ( in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f424,f425]) ).
fof(f425,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
=> ( ( ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) )
& ( in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f424,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f423]) ).
fof(f423,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f5621,plain,
spl81_374,
inference(avatar_split_clause,[],[f979,f5619]) ).
fof(f979,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f717,f931,f931]) ).
fof(f717,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f426]) ).
fof(f5578,plain,
( spl81_373
| ~ spl81_88
| ~ spl81_371 ),
inference(avatar_split_clause,[],[f5570,f5567,f1551,f5576]) ).
fof(f5576,plain,
( spl81_373
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X8,sK36(X0,X1,X7,X8)),unordered_pair(sK36(X0,X1,X7,X8),sK36(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_373])]) ).
fof(f5567,plain,
( spl81_371
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X7,X8),X8),unordered_pair(sK36(X0,X1,X7,X8),sK36(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_371])]) ).
fof(f5570,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK36(X0,X1,X7,X8)),unordered_pair(sK36(X0,X1,X7,X8),sK36(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl81_88
| ~ spl81_371 ),
inference(forward_demodulation,[],[f5568,f1552]) ).
fof(f5568,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X7,X8),X8),unordered_pair(sK36(X0,X1,X7,X8),sK36(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl81_371 ),
inference(avatar_component_clause,[],[f5567]) ).
fof(f5574,plain,
spl81_372,
inference(avatar_split_clause,[],[f1094,f5572]) ).
fof(f5572,plain,
( spl81_372
<=> ! [X2,X0,X1] :
( sK68(X0,X1,X2) = unordered_pair(unordered_pair(sK70(X0,X1,X2),sK69(X0,X1,X2)),unordered_pair(sK69(X0,X1,X2),sK69(X0,X1,X2)))
| sP13(X0,X1,X2)
| in(sK68(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_372])]) ).
fof(f1094,plain,
! [X2,X0,X1] :
( sK68(X0,X1,X2) = unordered_pair(unordered_pair(sK70(X0,X1,X2),sK69(X0,X1,X2)),unordered_pair(sK69(X0,X1,X2),sK69(X0,X1,X2)))
| sP13(X0,X1,X2)
| in(sK68(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f1035,f777]) ).
fof(f1035,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| sK68(X0,X1,X2) = unordered_pair(unordered_pair(sK69(X0,X1,X2),sK70(X0,X1,X2)),unordered_pair(sK69(X0,X1,X2),sK69(X0,X1,X2)))
| in(sK68(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f888,f931]) ).
fof(f888,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| sK68(X0,X1,X2) = ordered_pair(sK69(X0,X1,X2),sK70(X0,X1,X2))
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK68(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK68(X0,X1,X2),X2) )
& ( ( sK68(X0,X1,X2) = ordered_pair(sK69(X0,X1,X2),sK70(X0,X1,X2))
& in(sK70(X0,X1,X2),X0)
& in(sK69(X0,X1,X2),X1) )
| in(sK68(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK71(X0,X1,X8),sK72(X0,X1,X8)) = X8
& in(sK72(X0,X1,X8),X0)
& in(sK71(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70,sK71,sK72])],[f537,f540,f539,f538]) ).
fof(f538,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK68(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK68(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK68(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK68(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK68(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK68(X0,X1,X2) = ordered_pair(sK69(X0,X1,X2),sK70(X0,X1,X2))
& in(sK70(X0,X1,X2),X0)
& in(sK69(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f540,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK71(X0,X1,X8),sK72(X0,X1,X8)) = X8
& in(sK72(X0,X1,X8),X0)
& in(sK71(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f536]) ).
fof(f536,plain,
! [X1,X0,X2] :
( ( sP13(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP13(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X1,X0,X2] :
( sP13(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f5569,plain,
spl81_371,
inference(avatar_split_clause,[],[f994,f5567]) ).
fof(f994,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X7,X8),X8),unordered_pair(sK36(X0,X1,X7,X8),sK36(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f728,f931,f931]) ).
fof(f728,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK36(X0,X1,X7,X8),X8),X0)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f5565,plain,
spl81_370,
inference(avatar_split_clause,[],[f1085,f5563]) ).
fof(f5563,plain,
( spl81_370
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK57(X0,X1),sK57(X0,X1)),unordered_pair(sK57(X0,X1),sK57(X0,X1))),X1)
| sP6(X0,X1)
| sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK57(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_370])]) ).
fof(f1085,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK57(X0,X1),sK57(X0,X1)),unordered_pair(sK57(X0,X1),sK57(X0,X1))),X1)
| sP6(X0,X1)
| sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK57(X0,X1),X0) ),
inference(inner_rewriting,[],[f1084]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK57(X0,X1),sK56(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1)
| sP6(X0,X1)
| sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK56(X0,X1),X0) ),
inference(forward_demodulation,[],[f1015,f777]) ).
fof(f1015,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK56(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK56(X0,X1),sK57(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1) ),
inference(definition_unfolding,[],[f807,f931]) ).
fof(f807,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK56(X0,X1),X0)
| ~ in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK56(X0,X1),X0)
| ~ in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) )
& ( ( sK56(X0,X1) = sK57(X0,X1)
& in(sK56(X0,X1),X0) )
| in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f493,f494]) ).
fof(f494,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK56(X0,X1) != sK57(X0,X1)
| ~ in(sK56(X0,X1),X0)
| ~ in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) )
& ( ( sK56(X0,X1) = sK57(X0,X1)
& in(sK56(X0,X1),X0) )
| in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f493,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(rectify,[],[f492]) ).
fof(f492,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(flattening,[],[f491]) ).
fof(f491,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(nnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f5478,plain,
( spl81_369
| ~ spl81_88
| ~ spl81_367 ),
inference(avatar_split_clause,[],[f5453,f5450,f1551,f5476]) ).
fof(f5476,plain,
( spl81_369
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_369])]) ).
fof(f5450,plain,
( spl81_367
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_367])]) ).
fof(f5453,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2)
| sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1) )
| ~ spl81_88
| ~ spl81_367 ),
inference(forward_demodulation,[],[f5451,f1552]) ).
fof(f5451,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) )
| ~ spl81_367 ),
inference(avatar_component_clause,[],[f5450]) ).
fof(f5457,plain,
spl81_368,
inference(avatar_split_clause,[],[f1092,f5455]) ).
fof(f5455,plain,
( spl81_368
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| sP8(X0,X1,X2)
| in(sK59(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_368])]) ).
fof(f1092,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK59(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2)
| sP8(X0,X1,X2)
| in(sK59(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f1023,f777]) ).
fof(f1023,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(sK59(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK58(X0,X1,X2),sK58(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f814,f931]) ).
fof(f814,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(sK59(X0,X1,X2),X1)
| in(ordered_pair(sK58(X0,X1,X2),sK59(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f5452,plain,
spl81_367,
inference(avatar_split_clause,[],[f1006,f5450]) ).
fof(f1006,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK43(X0,X1,X2),sK43(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f747,f931]) ).
fof(f747,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK43(X0,X1,X2),X1)
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f5448,plain,
spl81_366,
inference(avatar_split_clause,[],[f993,f5446]) ).
fof(f5446,plain,
( spl81_366
<=> ! [X1,X0,X8,X9,X2,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_366])]) ).
fof(f993,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f729,f931,f931,f931]) ).
fof(f729,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f5378,plain,
( spl81_365
| ~ spl81_88
| ~ spl81_361 ),
inference(avatar_split_clause,[],[f5362,f5359,f1551,f5376]) ).
fof(f5376,plain,
( spl81_365
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK41(X0,X1),sK41(X0,X1)),unordered_pair(sK41(X0,X1),sK40(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK40(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_365])]) ).
fof(f5359,plain,
( spl81_361
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK41(X0,X1),sK41(X0,X1))),X0)
| in(sK40(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_361])]) ).
fof(f5362,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK41(X0,X1),sK41(X0,X1)),unordered_pair(sK41(X0,X1),sK40(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK40(X0,X1),X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_361 ),
inference(forward_demodulation,[],[f5360,f1552]) ).
fof(f5360,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK41(X0,X1),sK41(X0,X1))),X0)
| in(sK40(X0,X1),X1)
| ~ relation(X0) )
| ~ spl81_361 ),
inference(avatar_component_clause,[],[f5359]) ).
fof(f5374,plain,
( spl81_364
| ~ spl81_88
| ~ spl81_360 ),
inference(avatar_split_clause,[],[f5357,f5354,f1551,f5372]) ).
fof(f5372,plain,
( spl81_364
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK38(X0,X1),sK37(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK37(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_364])]) ).
fof(f5354,plain,
( spl81_360
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK37(X0,X1),sK38(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| in(sK37(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_360])]) ).
fof(f5357,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK38(X0,X1),sK37(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK37(X0,X1),X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_360 ),
inference(forward_demodulation,[],[f5355,f1552]) ).
fof(f5355,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK37(X0,X1),sK38(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| in(sK37(X0,X1),X1)
| ~ relation(X0) )
| ~ spl81_360 ),
inference(avatar_component_clause,[],[f5354]) ).
fof(f5370,plain,
spl81_363,
inference(avatar_split_clause,[],[f1095,f5368]) ).
fof(f5368,plain,
( spl81_363
<=> ! [X0,X8,X2,X1] :
( unordered_pair(unordered_pair(sK72(X0,X1,X8),sK71(X0,X1,X8)),unordered_pair(sK71(X0,X1,X8),sK71(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_363])]) ).
fof(f1095,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK72(X0,X1,X8),sK71(X0,X1,X8)),unordered_pair(sK71(X0,X1,X8),sK71(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ),
inference(forward_demodulation,[],[f1037,f777]) ).
fof(f1037,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK71(X0,X1,X8),sK72(X0,X1,X8)),unordered_pair(sK71(X0,X1,X8),sK71(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ),
inference(definition_unfolding,[],[f884,f931]) ).
fof(f884,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK71(X0,X1,X8),sK72(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f5366,plain,
spl81_362,
inference(avatar_split_clause,[],[f1034,f5364]) ).
fof(f5364,plain,
( spl81_362
<=> ! [X4,X0,X5,X2,X1] :
( sP13(X0,X1,X2)
| sK68(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK68(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_362])]) ).
fof(f1034,plain,
! [X2,X0,X1,X4,X5] :
( sP13(X0,X1,X2)
| sK68(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK68(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f889,f931]) ).
fof(f889,plain,
! [X2,X0,X1,X4,X5] :
( sP13(X0,X1,X2)
| ordered_pair(X4,X5) != sK68(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f5361,plain,
spl81_361,
inference(avatar_split_clause,[],[f1001,f5359]) ).
fof(f1001,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK41(X0,X1),sK41(X0,X1))),X0)
| in(sK40(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f740,f931]) ).
fof(f740,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK41(X0,X1),sK40(X0,X1)),X0)
| in(sK40(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f454]) ).
fof(f454,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK40(X0,X1)),X0)
| ~ in(sK40(X0,X1),X1) )
& ( in(ordered_pair(sK41(X0,X1),sK40(X0,X1)),X0)
| in(sK40(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK42(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42])],[f450,f453,f452,f451]) ).
fof(f451,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK40(X0,X1)),X0)
| ~ in(sK40(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK40(X0,X1)),X0)
| in(sK40(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f452,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK40(X0,X1)),X0)
=> in(ordered_pair(sK41(X0,X1),sK40(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f453,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK42(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f450,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f449]) ).
fof(f449,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f5356,plain,
spl81_360,
inference(avatar_split_clause,[],[f997,f5354]) ).
fof(f997,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK37(X0,X1),sK38(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| in(sK37(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f736,f931]) ).
fof(f736,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK37(X0,X1),sK38(X0,X1)),X0)
| in(sK37(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f448]) ).
fof(f448,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK37(X0,X1),X3),X0)
| ~ in(sK37(X0,X1),X1) )
& ( in(ordered_pair(sK37(X0,X1),sK38(X0,X1)),X0)
| in(sK37(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK39(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39])],[f444,f447,f446,f445]) ).
fof(f445,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK37(X0,X1),X3),X0)
| ~ in(sK37(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK37(X0,X1),X4),X0)
| in(sK37(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f446,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK37(X0,X1),X4),X0)
=> in(ordered_pair(sK37(X0,X1),sK38(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f447,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK39(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f444,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f443]) ).
fof(f443,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5331,plain,
spl81_359,
inference(avatar_split_clause,[],[f1086,f5329]) ).
fof(f5329,plain,
( spl81_359
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1),sK56(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1)
| sP6(X0,X1)
| sK56(X0,X1) = sK57(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_359])]) ).
fof(f1086,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1),sK56(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1)
| sP6(X0,X1)
| sK56(X0,X1) = sK57(X0,X1) ),
inference(forward_demodulation,[],[f1016,f777]) ).
fof(f1016,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK56(X0,X1) = sK57(X0,X1)
| in(unordered_pair(unordered_pair(sK56(X0,X1),sK57(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1) ),
inference(definition_unfolding,[],[f806,f931]) ).
fof(f806,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK56(X0,X1) = sK57(X0,X1)
| in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f5298,plain,
( spl81_358
| ~ spl81_54
| ~ spl81_345 ),
inference(avatar_split_clause,[],[f5166,f5087,f1359,f5296]) ).
fof(f5296,plain,
( spl81_358
<=> ! [X0] : ~ proper_subset(relation_field(sK19),set_difference(relation_dom(sK19),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_358])]) ).
fof(f1359,plain,
( spl81_54
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_54])]) ).
fof(f5087,plain,
( spl81_345
<=> ! [X0] : subset(set_difference(relation_dom(sK19),X0),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_345])]) ).
fof(f5166,plain,
( ! [X0] : ~ proper_subset(relation_field(sK19),set_difference(relation_dom(sK19),X0))
| ~ spl81_54
| ~ spl81_345 ),
inference(resolution,[],[f5088,f1360]) ).
fof(f1360,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl81_54 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f5088,plain,
( ! [X0] : subset(set_difference(relation_dom(sK19),X0),relation_field(sK19))
| ~ spl81_345 ),
inference(avatar_component_clause,[],[f5087]) ).
fof(f5294,plain,
( spl81_357
| ~ spl81_88
| ~ spl81_355 ),
inference(avatar_split_clause,[],[f5254,f5251,f1551,f5292]) ).
fof(f5292,plain,
( spl81_357
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK36(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_357])]) ).
fof(f5251,plain,
( spl81_355
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,sK36(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_355])]) ).
fof(f5254,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK36(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl81_88
| ~ spl81_355 ),
inference(forward_demodulation,[],[f5252,f1552]) ).
fof(f5252,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK36(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl81_355 ),
inference(avatar_component_clause,[],[f5251]) ).
fof(f5258,plain,
spl81_356,
inference(avatar_split_clause,[],[f996,f5256]) ).
fof(f5256,plain,
( spl81_356
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK37(X0,X1),X3),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| ~ in(sK37(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_356])]) ).
fof(f996,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK37(X0,X1),X3),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| ~ in(sK37(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f737,f931]) ).
fof(f737,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK37(X0,X1),X3),X0)
| ~ in(sK37(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f448]) ).
fof(f5253,plain,
spl81_355,
inference(avatar_split_clause,[],[f995,f5251]) ).
fof(f995,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK36(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f727,f931,f931]) ).
fof(f727,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK36(X0,X1,X7,X8)),X1)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f442]) ).
fof(f5249,plain,
spl81_354,
inference(avatar_split_clause,[],[f966,f5247]) ).
fof(f5247,plain,
( spl81_354
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_354])]) ).
fof(f966,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f686,f931,f931]) ).
fof(f686,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(flattening,[],[f415]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(nnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
| ~ relation(X3) ),
inference(ennf_transformation,[],[f179]) ).
fof(f179,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f5190,plain,
spl81_353,
inference(avatar_split_clause,[],[f1087,f5188]) ).
fof(f5188,plain,
( spl81_353
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1),sK56(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1)
| sP6(X0,X1)
| in(sK56(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_353])]) ).
fof(f1087,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1),sK56(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1)
| sP6(X0,X1)
| in(sK56(X0,X1),X0) ),
inference(forward_demodulation,[],[f1017,f777]) ).
fof(f1017,plain,
! [X0,X1] :
( sP6(X0,X1)
| in(sK56(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK56(X0,X1),sK57(X0,X1)),unordered_pair(sK56(X0,X1),sK56(X0,X1))),X1) ),
inference(definition_unfolding,[],[f805,f931]) ).
fof(f805,plain,
! [X0,X1] :
( sP6(X0,X1)
| in(sK56(X0,X1),X0)
| in(ordered_pair(sK56(X0,X1),sK57(X0,X1)),X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f5186,plain,
spl81_352,
inference(avatar_split_clause,[],[f1024,f5184]) ).
fof(f5184,plain,
( spl81_352
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X6,X1)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_352])]) ).
fof(f1024,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X6,X1)
| ~ sP8(X0,X1,X2) ),
inference(definition_unfolding,[],[f813,f931,f931]) ).
fof(f813,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f5165,plain,
spl81_351,
inference(avatar_split_clause,[],[f1007,f5163]) ).
fof(f5163,plain,
( spl81_351
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_351])]) ).
fof(f1007,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f746,f931,f931]) ).
fof(f746,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f5110,plain,
( spl81_350
| ~ spl81_88
| ~ spl81_346 ),
inference(avatar_split_clause,[],[f5094,f5091,f1551,f5108]) ).
fof(f5108,plain,
( spl81_350
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_350])]) ).
fof(f5091,plain,
( spl81_346
<=> ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_346])]) ).
fof(f5094,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_346 ),
inference(forward_demodulation,[],[f5092,f1552]) ).
fof(f5092,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_346 ),
inference(avatar_component_clause,[],[f5091]) ).
fof(f5106,plain,
( spl81_349
| ~ spl81_88
| ~ spl81_344 ),
inference(avatar_split_clause,[],[f5085,f5082,f1551,f5104]) ).
fof(f5104,plain,
( spl81_349
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_349])]) ).
fof(f5082,plain,
( spl81_344
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_344])]) ).
fof(f5085,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_344 ),
inference(forward_demodulation,[],[f5083,f1552]) ).
fof(f5083,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl81_344 ),
inference(avatar_component_clause,[],[f5082]) ).
fof(f5102,plain,
spl81_348,
inference(avatar_split_clause,[],[f1047,f5100]) ).
fof(f5100,plain,
( spl81_348
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_348])]) ).
fof(f1047,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f989]) ).
fof(f989,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f721,f931,f931]) ).
fof(f721,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f434]) ).
fof(f5098,plain,
spl81_347,
inference(avatar_split_clause,[],[f1046,f5096]) ).
fof(f5096,plain,
( spl81_347
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_347])]) ).
fof(f1046,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f988]) ).
fof(f988,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f722,f931,f931]) ).
fof(f722,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f434]) ).
fof(f5093,plain,
spl81_346,
inference(avatar_split_clause,[],[f984,f5091]) ).
fof(f984,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f719,f931]) ).
fof(f719,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1)
& in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f428,f429]) ).
fof(f429,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1)
& in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f428,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f427]) ).
fof(f427,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f5089,plain,
( spl81_345
| ~ spl81_34
| ~ spl81_306 ),
inference(avatar_split_clause,[],[f4923,f4150,f1249,f5087]) ).
fof(f1249,plain,
( spl81_34
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_34])]) ).
fof(f4150,plain,
( spl81_306
<=> ! [X0] :
( subset(X0,relation_field(sK19))
| ~ subset(X0,relation_dom(sK19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_306])]) ).
fof(f4923,plain,
( ! [X0] : subset(set_difference(relation_dom(sK19),X0),relation_field(sK19))
| ~ spl81_34
| ~ spl81_306 ),
inference(resolution,[],[f4151,f1250]) ).
fof(f1250,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl81_34 ),
inference(avatar_component_clause,[],[f1249]) ).
fof(f4151,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK19))
| subset(X0,relation_field(sK19)) )
| ~ spl81_306 ),
inference(avatar_component_clause,[],[f4150]) ).
fof(f5084,plain,
spl81_344,
inference(avatar_split_clause,[],[f983,f5082]) ).
fof(f983,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f720,f931]) ).
fof(f720,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f430]) ).
fof(f5070,plain,
spl81_343,
inference(avatar_split_clause,[],[f967,f5068]) ).
fof(f5068,plain,
( spl81_343
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_343])]) ).
fof(f967,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f685,f931,f931]) ).
fof(f685,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f416]) ).
fof(f4942,plain,
spl81_342,
inference(avatar_split_clause,[],[f921,f4940]) ).
fof(f4940,plain,
( spl81_342
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(sK76(X0,X1,X2),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(sK76(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_342])]) ).
fof(f921,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(sK76(X0,X1,X2),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(sK76(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f565,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ( ( in(sK76(X0,X1,X2),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(sK76(X0,X1,X2),X2) )
& ( ( ~ in(sK76(X0,X1,X2),X0)
& in(sK76(X0,X1,X2),X1) )
| in(sK76(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f563,f564]) ).
fof(f564,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK76(X0,X1,X2),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(sK76(X0,X1,X2),X2) )
& ( ( ~ in(sK76(X0,X1,X2),X0)
& in(sK76(X0,X1,X2),X1) )
| in(sK76(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f563,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f562]) ).
fof(f562,plain,
! [X1,X0,X2] :
( ( sP17(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP17(X1,X0,X2) ) ),
inference(flattening,[],[f561]) ).
fof(f561,plain,
! [X1,X0,X2] :
( ( sP17(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP17(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X1,X0,X2] :
( sP17(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f4938,plain,
spl81_341,
inference(avatar_split_clause,[],[f911,f4936]) ).
fof(f4936,plain,
( spl81_341
<=> ! [X2,X0,X1] :
( sP16(X0,X1,X2)
| in(sK75(X0,X1,X2),X0)
| in(sK75(X0,X1,X2),X1)
| in(sK75(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_341])]) ).
fof(f911,plain,
! [X2,X0,X1] :
( sP16(X0,X1,X2)
| in(sK75(X0,X1,X2),X0)
| in(sK75(X0,X1,X2),X1)
| in(sK75(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ( sP16(X0,X1,X2)
| ( ( ( ~ in(sK75(X0,X1,X2),X0)
& ~ in(sK75(X0,X1,X2),X1) )
| ~ in(sK75(X0,X1,X2),X2) )
& ( in(sK75(X0,X1,X2),X0)
| in(sK75(X0,X1,X2),X1)
| in(sK75(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP16(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f557,f558]) ).
fof(f558,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK75(X0,X1,X2),X0)
& ~ in(sK75(X0,X1,X2),X1) )
| ~ in(sK75(X0,X1,X2),X2) )
& ( in(sK75(X0,X1,X2),X0)
| in(sK75(X0,X1,X2),X1)
| in(sK75(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f557,plain,
! [X0,X1,X2] :
( ( sP16(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP16(X0,X1,X2) ) ),
inference(rectify,[],[f556]) ).
fof(f556,plain,
! [X1,X0,X2] :
( ( sP16(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP16(X1,X0,X2) ) ),
inference(flattening,[],[f555]) ).
fof(f555,plain,
! [X1,X0,X2] :
( ( sP16(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP16(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X1,X0,X2] :
( sP16(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f4934,plain,
spl81_340,
inference(avatar_split_clause,[],[f905,f4932]) ).
fof(f4932,plain,
( spl81_340
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(sK74(X0,X1,X2),X0)
| ~ in(sK74(X0,X1,X2),X1)
| ~ in(sK74(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_340])]) ).
fof(f905,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(sK74(X0,X1,X2),X0)
| ~ in(sK74(X0,X1,X2),X1)
| ~ in(sK74(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f553,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ( ( ~ in(sK74(X0,X1,X2),X0)
| ~ in(sK74(X0,X1,X2),X1)
| ~ in(sK74(X0,X1,X2),X2) )
& ( ( in(sK74(X0,X1,X2),X0)
& in(sK74(X0,X1,X2),X1) )
| in(sK74(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f551,f552]) ).
fof(f552,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK74(X0,X1,X2),X0)
| ~ in(sK74(X0,X1,X2),X1)
| ~ in(sK74(X0,X1,X2),X2) )
& ( ( in(sK74(X0,X1,X2),X0)
& in(sK74(X0,X1,X2),X1) )
| in(sK74(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f551,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f550]) ).
fof(f550,plain,
! [X1,X0,X2] :
( ( sP15(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(flattening,[],[f549]) ).
fof(f549,plain,
! [X1,X0,X2] :
( ( sP15(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X1,X0,X2] :
( sP15(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f4917,plain,
spl81_339,
inference(avatar_split_clause,[],[f895,f4915]) ).
fof(f4915,plain,
( spl81_339
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) = X0
| sK73(X0,X1,X2) = X1
| in(sK73(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_339])]) ).
fof(f895,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) = X0
| sK73(X0,X1,X2) = X1
| in(sK73(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f547,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ( ( ( sK73(X0,X1,X2) != X0
& sK73(X0,X1,X2) != X1 )
| ~ in(sK73(X0,X1,X2),X2) )
& ( sK73(X0,X1,X2) = X0
| sK73(X0,X1,X2) = X1
| in(sK73(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f545,f546]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK73(X0,X1,X2) != X0
& sK73(X0,X1,X2) != X1 )
| ~ in(sK73(X0,X1,X2),X2) )
& ( sK73(X0,X1,X2) = X0
| sK73(X0,X1,X2) = X1
| in(sK73(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f545,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(rectify,[],[f544]) ).
fof(f544,plain,
! [X1,X0,X2] :
( ( sP14(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP14(X1,X0,X2) ) ),
inference(flattening,[],[f543]) ).
fof(f543,plain,
! [X1,X0,X2] :
( ( sP14(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP14(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X1,X0,X2] :
( sP14(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f4866,plain,
spl81_338,
inference(avatar_split_clause,[],[f1025,f4864]) ).
fof(f4864,plain,
( spl81_338
<=> ! [X6,X0,X5,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_338])]) ).
fof(f1025,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP8(X0,X1,X2) ),
inference(definition_unfolding,[],[f812,f931,f931]) ).
fof(f812,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f4862,plain,
spl81_337,
inference(avatar_split_clause,[],[f1008,f4860]) ).
fof(f4860,plain,
( spl81_337
<=> ! [X6,X0,X5,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_337])]) ).
fof(f1008,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f745,f931,f931]) ).
fof(f745,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f4858,plain,
spl81_336,
inference(avatar_split_clause,[],[f1000,f4856]) ).
fof(f4856,plain,
( spl81_336
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK40(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK40(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_336])]) ).
fof(f1000,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK40(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK40(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f741,f931]) ).
fof(f741,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK40(X0,X1)),X0)
| ~ in(sK40(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f454]) ).
fof(f4833,plain,
( spl81_335
| ~ spl81_88
| ~ spl81_334 ),
inference(avatar_split_clause,[],[f4829,f4826,f1551,f4831]) ).
fof(f4831,plain,
( spl81_335
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK42(X0,X5)),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_335])]) ).
fof(f4826,plain,
( spl81_334
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK42(X0,X5),X5),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_334])]) ).
fof(f4829,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK42(X0,X5)),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_334 ),
inference(forward_demodulation,[],[f4827,f1552]) ).
fof(f4827,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK42(X0,X5),X5),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl81_334 ),
inference(avatar_component_clause,[],[f4826]) ).
fof(f4828,plain,
spl81_334,
inference(avatar_split_clause,[],[f1052,f4826]) ).
fof(f1052,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK42(X0,X5),X5),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1003]) ).
fof(f1003,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK42(X0,X5),X5),unordered_pair(sK42(X0,X5),sK42(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f738,f931]) ).
fof(f738,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK42(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f454]) ).
fof(f4802,plain,
( spl81_333
| ~ spl81_21
| ~ spl81_52
| ~ spl81_332 ),
inference(avatar_split_clause,[],[f4798,f4794,f1345,f1191,f4800]) ).
fof(f4800,plain,
( spl81_333
<=> ! [X0,X1] :
( sK78 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_333])]) ).
fof(f1191,plain,
( spl81_21
<=> ! [X0] : cast_to_subset(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_21])]) ).
fof(f4794,plain,
( spl81_332
<=> ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_332])]) ).
fof(f4798,plain,
( ! [X0,X1] :
( sK78 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_21
| ~ spl81_52
| ~ spl81_332 ),
inference(forward_demodulation,[],[f4797,f1347]) ).
fof(f4797,plain,
( ! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_21
| ~ spl81_332 ),
inference(forward_demodulation,[],[f4795,f1192]) ).
fof(f1192,plain,
( ! [X0] : cast_to_subset(X0) = X0
| ~ spl81_21 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f4795,plain,
( ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_332 ),
inference(avatar_component_clause,[],[f4794]) ).
fof(f4796,plain,
spl81_332,
inference(avatar_split_clause,[],[f634,f4794]) ).
fof(f634,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f247]) ).
fof(f247,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f159]) ).
fof(f159,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f4774,plain,
( spl81_331
| ~ spl81_21
| ~ spl81_52
| ~ spl81_330 ),
inference(avatar_split_clause,[],[f4770,f4766,f1345,f1191,f4772]) ).
fof(f4772,plain,
( spl81_331
<=> ! [X0,X1] :
( sK78 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_331])]) ).
fof(f4766,plain,
( spl81_330
<=> ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_330])]) ).
fof(f4770,plain,
( ! [X0,X1] :
( sK78 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_21
| ~ spl81_52
| ~ spl81_330 ),
inference(forward_demodulation,[],[f4769,f1347]) ).
fof(f4769,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_21
| ~ spl81_330 ),
inference(forward_demodulation,[],[f4767,f1192]) ).
fof(f4767,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_330 ),
inference(avatar_component_clause,[],[f4766]) ).
fof(f4768,plain,
spl81_330,
inference(avatar_split_clause,[],[f633,f4766]) ).
fof(f633,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f245]) ).
fof(f245,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f160]) ).
fof(f160,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f4763,plain,
spl81_329,
inference(avatar_split_clause,[],[f1072,f4761]) ).
fof(f4761,plain,
( spl81_329
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_329])]) ).
fof(f1072,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP13(X0,X1,X2) ),
inference(equality_resolution,[],[f1036]) ).
fof(f1036,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP13(X0,X1,X2) ),
inference(definition_unfolding,[],[f885,f931]) ).
fof(f885,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f4710,plain,
( spl81_328
| ~ spl81_72
| ~ spl81_297 ),
inference(avatar_split_clause,[],[f4572,f4085,f1447,f4707]) ).
fof(f4707,plain,
( spl81_328
<=> sP16(relation_field(sK19),relation_dom(sK19),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_328])]) ).
fof(f1447,plain,
( spl81_72
<=> ! [X0,X1] : sP16(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_72])]) ).
fof(f4085,plain,
( spl81_297
<=> relation_field(sK19) = set_union2(relation_dom(sK19),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_297])]) ).
fof(f4572,plain,
( sP16(relation_field(sK19),relation_dom(sK19),relation_field(sK19))
| ~ spl81_72
| ~ spl81_297 ),
inference(superposition,[],[f1448,f4087]) ).
fof(f4087,plain,
( relation_field(sK19) = set_union2(relation_dom(sK19),relation_field(sK19))
| ~ spl81_297 ),
inference(avatar_component_clause,[],[f4085]) ).
fof(f1448,plain,
( ! [X0,X1] : sP16(X1,X0,set_union2(X0,X1))
| ~ spl81_72 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f4705,plain,
spl81_327,
inference(avatar_split_clause,[],[f838,f4703]) ).
fof(f4703,plain,
( spl81_327
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| ~ in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| ~ in(sK60(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_327])]) ).
fof(f838,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| ~ in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| ~ in(sK60(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f509]) ).
fof(f509,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ( ( ~ in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| ~ in(sK60(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| in(sK60(X0,X1,X2),X2) )
& element(sK60(X0,X1,X2),powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP10(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f507,f508]) ).
fof(f508,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) )
=> ( ( ~ in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| ~ in(sK60(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| in(sK60(X0,X1,X2),X2) )
& element(sK60(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f507,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP10(X0,X1,X2) ) ),
inference(rectify,[],[f506]) ).
fof(f506,plain,
! [X1,X0,X2] :
( ( sP10(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP10(X1,X0,X2) ) ),
inference(flattening,[],[f505]) ).
fof(f505,plain,
! [X1,X0,X2] :
( ( sP10(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP10(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X1,X0,X2] :
( sP10(X1,X0,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f4701,plain,
spl81_326,
inference(avatar_split_clause,[],[f837,f4699]) ).
fof(f4699,plain,
( spl81_326
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| in(sK60(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_326])]) ).
fof(f837,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(subset_complement(X1,sK60(X0,X1,X2)),X0)
| in(sK60(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f509]) ).
fof(f4616,plain,
( spl81_325
| ~ spl81_88
| ~ spl81_322 ),
inference(avatar_split_clause,[],[f4566,f4563,f1551,f4614]) ).
fof(f4614,plain,
( spl81_325
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK47(X4),sK46(X4)),unordered_pair(sK46(X4),sK46(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_325])]) ).
fof(f4563,plain,
( spl81_322
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK46(X4),sK47(X4)),unordered_pair(sK46(X4),sK46(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_322])]) ).
fof(f4566,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK47(X4),sK46(X4)),unordered_pair(sK46(X4),sK46(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_322 ),
inference(forward_demodulation,[],[f4564,f1552]) ).
fof(f4564,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK46(X4),sK47(X4)),unordered_pair(sK46(X4),sK46(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl81_322 ),
inference(avatar_component_clause,[],[f4563]) ).
fof(f4586,plain,
( spl81_324
| ~ spl81_52
| ~ spl81_88
| ~ spl81_319 ),
inference(avatar_split_clause,[],[f4553,f4549,f1551,f1345,f4584]) ).
fof(f4584,plain,
( spl81_324
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK21(X0),sK20(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| sK78 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_324])]) ).
fof(f4549,plain,
( spl81_319
<=> ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK20(X0),sK21(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_319])]) ).
fof(f4553,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK21(X0),sK20(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| sK78 = X0
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_88
| ~ spl81_319 ),
inference(forward_demodulation,[],[f4552,f1552]) ).
fof(f4552,plain,
( ! [X0] :
( sK78 = X0
| in(unordered_pair(unordered_pair(sK20(X0),sK21(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_319 ),
inference(forward_demodulation,[],[f4550,f1347]) ).
fof(f4550,plain,
( ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK20(X0),sK21(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| ~ relation(X0) )
| ~ spl81_319 ),
inference(avatar_component_clause,[],[f4549]) ).
fof(f4582,plain,
( spl81_323
| ~ spl81_52
| ~ spl81_318 ),
inference(avatar_split_clause,[],[f4547,f4544,f1345,f4580]) ).
fof(f4580,plain,
( spl81_323
<=> ! [X2,X0,X1] :
( sK78 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_323])]) ).
fof(f4544,plain,
( spl81_318
<=> ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_318])]) ).
fof(f4547,plain,
( ! [X2,X0,X1] :
( sK78 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) )
| ~ spl81_52
| ~ spl81_318 ),
inference(forward_demodulation,[],[f4545,f1347]) ).
fof(f4545,plain,
( ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 )
| ~ spl81_318 ),
inference(avatar_component_clause,[],[f4544]) ).
fof(f4565,plain,
spl81_322,
inference(avatar_split_clause,[],[f1011,f4563]) ).
fof(f1011,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK46(X4),sK47(X4)),unordered_pair(sK46(X4),sK46(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f759,f931]) ).
fof(f759,plain,
! [X0,X4] :
( ordered_pair(sK46(X4),sK47(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f466]) ).
fof(f466,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK45(X0)
& in(sK45(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK46(X4),sK47(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47])],[f463,f465,f464]) ).
fof(f464,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK45(X0)
& in(sK45(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f465,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK46(X4),sK47(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f463,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f462]) ).
fof(f462,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f4561,plain,
spl81_321,
inference(avatar_split_clause,[],[f970,f4559]) ).
fof(f4559,plain,
( spl81_321
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_321])]) ).
fof(f970,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f687,f931,f931]) ).
fof(f687,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) = ordered_pair(X0,X1)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f4557,plain,
spl81_320,
inference(avatar_split_clause,[],[f969,f4555]) ).
fof(f4555,plain,
( spl81_320
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_320])]) ).
fof(f969,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f688,f931,f931]) ).
fof(f688,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f4551,plain,
spl81_319,
inference(avatar_split_clause,[],[f934,f4549]) ).
fof(f934,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK20(X0),sK21(X0)),unordered_pair(sK20(X0),sK20(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f591,f931]) ).
fof(f591,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK20(X0),sK21(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f387]) ).
fof(f387,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK20(X0),sK21(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f212,f386]) ).
fof(f386,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK20(X0),sK21(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f212,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f211]) ).
fof(f211,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f167]) ).
fof(f167,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f4546,plain,
spl81_318,
inference(avatar_split_clause,[],[f600,f4544]) ).
fof(f600,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f165]) ).
fof(f165,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f4522,plain,
( spl81_317
| ~ spl81_88
| ~ spl81_316 ),
inference(avatar_split_clause,[],[f4488,f4485,f1551,f4520]) ).
fof(f4520,plain,
( spl81_317
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK39(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_317])]) ).
fof(f4485,plain,
( spl81_316
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK39(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_316])]) ).
fof(f4488,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK39(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl81_88
| ~ spl81_316 ),
inference(forward_demodulation,[],[f4486,f1552]) ).
fof(f4486,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK39(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl81_316 ),
inference(avatar_component_clause,[],[f4485]) ).
fof(f4487,plain,
spl81_316,
inference(avatar_split_clause,[],[f1050,f4485]) ).
fof(f1050,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK39(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f999]) ).
fof(f999,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK39(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f734,f931]) ).
fof(f734,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK39(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f448]) ).
fof(f4483,plain,
( spl81_315
| ~ spl81_197
| ~ spl81_253 ),
inference(avatar_split_clause,[],[f3410,f3366,f2624,f4481]) ).
fof(f4481,plain,
( spl81_315
<=> ! [X0] :
( ~ in(X0,relation_rng(sK19))
| in(X0,relation_field(sK19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_315])]) ).
fof(f2624,plain,
( spl81_197
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_197])]) ).
fof(f3366,plain,
( spl81_253
<=> sP16(relation_rng(sK19),relation_dom(sK19),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_253])]) ).
fof(f3410,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK19))
| in(X0,relation_field(sK19)) )
| ~ spl81_197
| ~ spl81_253 ),
inference(resolution,[],[f3368,f2625]) ).
fof(f2625,plain,
( ! [X2,X0,X1,X4] :
( ~ sP16(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl81_197 ),
inference(avatar_component_clause,[],[f2624]) ).
fof(f3368,plain,
( sP16(relation_rng(sK19),relation_dom(sK19),relation_field(sK19))
| ~ spl81_253 ),
inference(avatar_component_clause,[],[f3366]) ).
fof(f4479,plain,
spl81_314,
inference(avatar_split_clause,[],[f971,f4477]) ).
fof(f4477,plain,
( spl81_314
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_314])]) ).
fof(f971,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f692,f931]) ).
fof(f692,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f417]) ).
fof(f417,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f110,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f4475,plain,
spl81_313,
inference(avatar_split_clause,[],[f968,f4473]) ).
fof(f4473,plain,
( spl81_313
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_313])]) ).
fof(f968,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f684,f931]) ).
fof(f684,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f416]) ).
fof(f4253,plain,
( spl81_312
| ~ spl81_156
| ~ spl81_223 ),
inference(avatar_split_clause,[],[f3053,f2968,f2196,f4251]) ).
fof(f4251,plain,
( spl81_312
<=> ! [X0] :
( ~ in(X0,relation_dom(sK19))
| in(X0,relation_field(sK19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_312])]) ).
fof(f2196,plain,
( spl81_156
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_156])]) ).
fof(f2968,plain,
( spl81_223
<=> subset(relation_dom(sK19),relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_223])]) ).
fof(f3053,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK19))
| in(X0,relation_field(sK19)) )
| ~ spl81_156
| ~ spl81_223 ),
inference(resolution,[],[f2970,f2197]) ).
fof(f2197,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl81_156 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f2970,plain,
( subset(relation_dom(sK19),relation_field(sK19))
| ~ spl81_223 ),
inference(avatar_component_clause,[],[f2968]) ).
fof(f4172,plain,
spl81_311,
inference(avatar_split_clause,[],[f920,f4170]) ).
fof(f4170,plain,
( spl81_311
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ in(sK76(X0,X1,X2),X0)
| in(sK76(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_311])]) ).
fof(f920,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ in(sK76(X0,X1,X2),X0)
| in(sK76(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f4168,plain,
spl81_310,
inference(avatar_split_clause,[],[f919,f4166]) ).
fof(f4166,plain,
( spl81_310
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(sK76(X0,X1,X2),X1)
| in(sK76(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_310])]) ).
fof(f919,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(sK76(X0,X1,X2),X1)
| in(sK76(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f4164,plain,
spl81_309,
inference(avatar_split_clause,[],[f913,f4162]) ).
fof(f4162,plain,
( spl81_309
<=> ! [X2,X0,X1] :
( sP16(X0,X1,X2)
| ~ in(sK75(X0,X1,X2),X0)
| ~ in(sK75(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_309])]) ).
fof(f913,plain,
! [X2,X0,X1] :
( sP16(X0,X1,X2)
| ~ in(sK75(X0,X1,X2),X0)
| ~ in(sK75(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f4160,plain,
spl81_308,
inference(avatar_split_clause,[],[f912,f4158]) ).
fof(f4158,plain,
( spl81_308
<=> ! [X2,X0,X1] :
( sP16(X0,X1,X2)
| ~ in(sK75(X0,X1,X2),X1)
| ~ in(sK75(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_308])]) ).
fof(f912,plain,
! [X2,X0,X1] :
( sP16(X0,X1,X2)
| ~ in(sK75(X0,X1,X2),X1)
| ~ in(sK75(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f4156,plain,
spl81_307,
inference(avatar_split_clause,[],[f904,f4154]) ).
fof(f4154,plain,
( spl81_307
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK74(X0,X1,X2),X0)
| in(sK74(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_307])]) ).
fof(f904,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK74(X0,X1,X2),X0)
| in(sK74(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f4152,plain,
( spl81_306
| ~ spl81_151
| ~ spl81_223 ),
inference(avatar_split_clause,[],[f3050,f2968,f2092,f4150]) ).
fof(f2092,plain,
( spl81_151
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_151])]) ).
fof(f3050,plain,
( ! [X0] :
( subset(X0,relation_field(sK19))
| ~ subset(X0,relation_dom(sK19)) )
| ~ spl81_151
| ~ spl81_223 ),
inference(resolution,[],[f2970,f2093]) ).
fof(f2093,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl81_151 ),
inference(avatar_component_clause,[],[f2092]) ).
fof(f4148,plain,
spl81_305,
inference(avatar_split_clause,[],[f903,f4146]) ).
fof(f4146,plain,
( spl81_305
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK74(X0,X1,X2),X1)
| in(sK74(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_305])]) ).
fof(f903,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK74(X0,X1,X2),X1)
| in(sK74(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f4144,plain,
spl81_304,
inference(avatar_split_clause,[],[f887,f4142]) ).
fof(f4142,plain,
( spl81_304
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X0)
| in(sK68(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_304])]) ).
fof(f887,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X0)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f4140,plain,
spl81_303,
inference(avatar_split_clause,[],[f886,f4138]) ).
fof(f4138,plain,
( spl81_303
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK69(X0,X1,X2),X1)
| in(sK68(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_303])]) ).
fof(f886,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK69(X0,X1,X2),X1)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f4136,plain,
spl81_302,
inference(avatar_split_clause,[],[f881,f4134]) ).
fof(f4134,plain,
( spl81_302
<=> ! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_302])]) ).
fof(f881,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f351]) ).
fof(f351,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f4132,plain,
spl81_301,
inference(avatar_split_clause,[],[f864,f4130]) ).
fof(f4130,plain,
( spl81_301
<=> ! [X0,X1,X3] :
( sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(sK63(X0,X1),X3)
| ~ in(sK63(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_301])]) ).
fof(f864,plain,
! [X3,X0,X1] :
( sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(sK63(X0,X1),X3)
| ~ in(sK63(X0,X1),X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f525,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK63(X0,X1),X3) )
| ~ in(sK63(X0,X1),X1) )
& ( ( in(sK64(X0,X1),X0)
& in(sK63(X0,X1),sK64(X0,X1)) )
| in(sK63(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK65(X0,X5),X0)
& in(X5,sK65(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP12(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64,sK65])],[f521,f524,f523,f522]) ).
fof(f522,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK63(X0,X1),X3) )
| ~ in(sK63(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK63(X0,X1),X4) )
| in(sK63(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f523,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK63(X0,X1),X4) )
=> ( in(sK64(X0,X1),X0)
& in(sK63(X0,X1),sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f524,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK65(X0,X5),X0)
& in(X5,sK65(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f521,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| ~ sP12(X0,X1) ) ),
inference(rectify,[],[f520]) ).
fof(f520,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| ~ sP12(X0,X1) ) ),
inference(nnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0,X1] :
( sP12(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f4128,plain,
spl81_300,
inference(avatar_split_clause,[],[f835,f4126]) ).
fof(f4126,plain,
( spl81_300
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_300])]) ).
fof(f835,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f509]) ).
fof(f4124,plain,
spl81_299,
inference(avatar_split_clause,[],[f834,f4122]) ).
fof(f4122,plain,
( spl81_299
<=> ! [X2,X4,X0,X1] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_299])]) ).
fof(f834,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f509]) ).
fof(f4120,plain,
spl81_298,
inference(avatar_split_clause,[],[f790,f4118]) ).
fof(f4118,plain,
( spl81_298
<=> ! [X4,X0,X1] :
( sP4(X0,X1)
| in(sK53(X0,X1),X4)
| ~ in(X4,X0)
| in(sK53(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_298])]) ).
fof(f790,plain,
! [X0,X1,X4] :
( sP4(X0,X1)
| in(sK53(X0,X1),X4)
| ~ in(X4,X0)
| in(sK53(X0,X1),X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f487,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ( ~ in(sK53(X0,X1),sK54(X0,X1))
& in(sK54(X0,X1),X0) )
| ~ in(sK53(X0,X1),X1) )
& ( ! [X4] :
( in(sK53(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK53(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK55(X0,X5))
& in(sK55(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55])],[f483,f486,f485,f484]) ).
fof(f484,plain,
! [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) )
=> ( ( ? [X3] :
( ~ in(sK53(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK53(X0,X1),X1) )
& ( ! [X4] :
( in(sK53(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK53(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f485,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK53(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK53(X0,X1),sK54(X0,X1))
& in(sK54(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f486,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK55(X0,X5))
& in(sK55(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f483,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f482]) ).
fof(f482,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(nnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0,X1] :
( sP4(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f4088,plain,
( spl81_297
| ~ spl81_108
| ~ spl81_223 ),
inference(avatar_split_clause,[],[f3048,f2968,f1713,f4085]) ).
fof(f1713,plain,
( spl81_108
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_108])]) ).
fof(f3048,plain,
( relation_field(sK19) = set_union2(relation_dom(sK19),relation_field(sK19))
| ~ spl81_108
| ~ spl81_223 ),
inference(resolution,[],[f2970,f1714]) ).
fof(f1714,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl81_108 ),
inference(avatar_component_clause,[],[f1713]) ).
fof(f4026,plain,
spl81_296,
inference(avatar_split_clause,[],[f1026,f4024]) ).
fof(f4024,plain,
( spl81_296
<=> ! [X5,X0,X6,X2,X1] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_296])]) ).
fof(f1026,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP8(X0,X1,X2) ),
inference(definition_unfolding,[],[f811,f931]) ).
fof(f811,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f502]) ).
fof(f4022,plain,
spl81_295,
inference(avatar_split_clause,[],[f1009,f4020]) ).
fof(f4020,plain,
( spl81_295
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_295])]) ).
fof(f1009,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f744,f931]) ).
fof(f744,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f461]) ).
fof(f4018,plain,
spl81_294,
inference(avatar_split_clause,[],[f632,f4016]) ).
fof(f4016,plain,
( spl81_294
<=> ! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_294])]) ).
fof(f632,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f396,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f4014,plain,
spl81_293,
inference(avatar_split_clause,[],[f631,f4012]) ).
fof(f4012,plain,
( spl81_293
<=> ! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_293])]) ).
fof(f631,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f4010,plain,
spl81_292,
inference(avatar_split_clause,[],[f599,f4008]) ).
fof(f4008,plain,
( spl81_292
<=> ! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_292])]) ).
fof(f599,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f155]) ).
fof(f155,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f4006,plain,
spl81_291,
inference(avatar_split_clause,[],[f598,f4004]) ).
fof(f4004,plain,
( spl81_291
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_291])]) ).
fof(f598,plain,
! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f3979,plain,
spl81_290,
inference(avatar_split_clause,[],[f880,f3977]) ).
fof(f3977,plain,
( spl81_290
<=> ! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_290])]) ).
fof(f880,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f349]) ).
fof(f349,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f3975,plain,
spl81_289,
inference(avatar_split_clause,[],[f862,f3973]) ).
fof(f3973,plain,
( spl81_289
<=> ! [X0,X1] :
( sP12(X0,X1)
| in(sK63(X0,X1),sK64(X0,X1))
| in(sK63(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_289])]) ).
fof(f862,plain,
! [X0,X1] :
( sP12(X0,X1)
| in(sK63(X0,X1),sK64(X0,X1))
| in(sK63(X0,X1),X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f3971,plain,
spl81_288,
inference(avatar_split_clause,[],[f792,f3969]) ).
fof(f3969,plain,
( spl81_288
<=> ! [X0,X1] :
( sP4(X0,X1)
| ~ in(sK53(X0,X1),sK54(X0,X1))
| ~ in(sK53(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_288])]) ).
fof(f792,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ in(sK53(X0,X1),sK54(X0,X1))
| ~ in(sK53(X0,X1),X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f3920,plain,
( spl81_287
| ~ spl81_81
| ~ spl81_119
| ~ spl81_268 ),
inference(avatar_split_clause,[],[f3541,f3473,f1769,f1514,f3917]) ).
fof(f3917,plain,
( spl81_287
<=> sP15(relation_field(sK19),relation_dom(sK19),relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_287])]) ).
fof(f3541,plain,
( sP15(relation_field(sK19),relation_dom(sK19),relation_dom(sK19))
| ~ spl81_81
| ~ spl81_119
| ~ spl81_268 ),
inference(forward_demodulation,[],[f3527,f1515]) ).
fof(f3527,plain,
( sP15(relation_field(sK19),relation_dom(sK19),set_difference(relation_dom(sK19),sK78))
| ~ spl81_119
| ~ spl81_268 ),
inference(superposition,[],[f1770,f3475]) ).
fof(f3835,plain,
spl81_286,
inference(avatar_split_clause,[],[f1061,f3833]) ).
fof(f3833,plain,
( spl81_286
<=> ! [X5,X1,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_286])]) ).
fof(f1061,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP6(X0,X1) ),
inference(equality_resolution,[],[f1018]) ).
fof(f1018,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f804,f931]) ).
fof(f804,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f3831,plain,
spl81_285,
inference(avatar_split_clause,[],[f1031,f3829]) ).
fof(f3829,plain,
( spl81_285
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK66(X0,X1) = X0
| in(sK66(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_285])]) ).
fof(f1031,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK66(X0,X1) = X0
| in(sK66(X0,X1),X1) ),
inference(definition_unfolding,[],[f869,f583]) ).
fof(f869,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK66(X0,X1) = X0
| in(sK66(X0,X1),X1) ),
inference(cnf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK66(X0,X1) != X0
| ~ in(sK66(X0,X1),X1) )
& ( sK66(X0,X1) = X0
| in(sK66(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f528,f529]) ).
fof(f529,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK66(X0,X1) != X0
| ~ in(sK66(X0,X1),X1) )
& ( sK66(X0,X1) = X0
| in(sK66(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f528,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f527]) ).
fof(f527,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3827,plain,
spl81_284,
inference(avatar_split_clause,[],[f1020,f3825]) ).
fof(f3825,plain,
( spl81_284
<=> ! [X4,X0,X5,X1] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_284])]) ).
fof(f1020,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f802,f931]) ).
fof(f802,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f3823,plain,
spl81_283,
inference(avatar_split_clause,[],[f1019,f3821]) ).
fof(f3821,plain,
( spl81_283
<=> ! [X4,X5,X1,X0] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_283])]) ).
fof(f1019,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f803,f931]) ).
fof(f803,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f3815,plain,
spl81_282,
inference(avatar_split_clause,[],[f960,f3813]) ).
fof(f3813,plain,
( spl81_282
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_282])]) ).
fof(f960,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f661,f931]) ).
fof(f661,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f257]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f127]) ).
fof(f127,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f3811,plain,
spl81_281,
inference(avatar_split_clause,[],[f959,f3809]) ).
fof(f3809,plain,
( spl81_281
<=> ! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_281])]) ).
fof(f959,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f662,f931]) ).
fof(f662,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f258]) ).
fof(f3807,plain,
spl81_280,
inference(avatar_split_clause,[],[f958,f3805]) ).
fof(f3805,plain,
( spl81_280
<=> ! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_280])]) ).
fof(f958,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f659,f931]) ).
fof(f659,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f3803,plain,
spl81_279,
inference(avatar_split_clause,[],[f957,f3801]) ).
fof(f3801,plain,
( spl81_279
<=> ! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_279])]) ).
fof(f957,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f660,f931]) ).
fof(f660,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f3799,plain,
spl81_278,
inference(avatar_split_clause,[],[f668,f3797]) ).
fof(f3797,plain,
( spl81_278
<=> ! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_278])]) ).
fof(f668,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f411]) ).
fof(f411,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f3795,plain,
spl81_277,
inference(avatar_split_clause,[],[f665,f3793]) ).
fof(f3793,plain,
( spl81_277
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_277])]) ).
fof(f665,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f409]) ).
fof(f409,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f3736,plain,
spl81_276,
inference(avatar_split_clause,[],[f874,f3734]) ).
fof(f3734,plain,
( spl81_276
<=> ! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK67(X0,X1),X0)
| ~ in(sK67(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_276])]) ).
fof(f874,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK67(X0,X1),X0)
| ~ in(sK67(X0,X1),X1) ),
inference(cnf_transformation,[],[f534]) ).
fof(f534,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK67(X0,X1),X0)
| ~ in(sK67(X0,X1),X1) )
& ( subset(sK67(X0,X1),X0)
| in(sK67(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f532,f533]) ).
fof(f533,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK67(X0,X1),X0)
| ~ in(sK67(X0,X1),X1) )
& ( subset(sK67(X0,X1),X0)
| in(sK67(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f532,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f531]) ).
fof(f531,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3732,plain,
( spl81_275
| ~ spl81_73
| ~ spl81_268 ),
inference(avatar_split_clause,[],[f3525,f3473,f1451,f3729]) ).
fof(f3729,plain,
( spl81_275
<=> sP17(relation_field(sK19),relation_dom(sK19),sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_275])]) ).
fof(f3525,plain,
( sP17(relation_field(sK19),relation_dom(sK19),sK78)
| ~ spl81_73
| ~ spl81_268 ),
inference(superposition,[],[f1452,f3475]) ).
fof(f3727,plain,
spl81_274,
inference(avatar_split_clause,[],[f873,f3725]) ).
fof(f3725,plain,
( spl81_274
<=> ! [X0,X1] :
( powerset(X0) = X1
| subset(sK67(X0,X1),X0)
| in(sK67(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_274])]) ).
fof(f873,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK67(X0,X1),X0)
| in(sK67(X0,X1),X1) ),
inference(cnf_transformation,[],[f534]) ).
fof(f3723,plain,
spl81_273,
inference(avatar_split_clause,[],[f839,f3721]) ).
fof(f3721,plain,
( spl81_273
<=> ! [X2,X0,X1] :
( sP11(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_273])]) ).
fof(f839,plain,
! [X2,X0,X1] :
( sP11(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0,X1] :
( ! [X2] :
( sP11(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f328,f370,f369]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ( complements_of_subsets(X0,X1) = X2
<=> sP10(X1,X0,X2) )
| ~ sP11(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f328,plain,
! [X0,X1] :
( ! [X2] :
( ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f3567,plain,
spl81_272,
inference(avatar_split_clause,[],[f973,f3565]) ).
fof(f3565,plain,
( spl81_272
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_272])]) ).
fof(f973,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f690,f931]) ).
fof(f690,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f418]) ).
fof(f3563,plain,
spl81_271,
inference(avatar_split_clause,[],[f972,f3561]) ).
fof(f3561,plain,
( spl81_271
<=> ! [X0,X3,X2,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_271])]) ).
fof(f972,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f691,f931]) ).
fof(f691,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f418]) ).
fof(f3559,plain,
spl81_270,
inference(avatar_split_clause,[],[f961,f3557]) ).
fof(f3557,plain,
( spl81_270
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_270])]) ).
fof(f961,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f669,f608,f608]) ).
fof(f608,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f161]) ).
fof(f161,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f669,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f3555,plain,
spl81_269,
inference(avatar_split_clause,[],[f938,f3553]) ).
fof(f938,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f621,f608]) ).
fof(f621,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f3476,plain,
( spl81_268
| ~ spl81_122
| ~ spl81_223 ),
inference(avatar_split_clause,[],[f3049,f2968,f1860,f3473]) ).
fof(f1860,plain,
( spl81_122
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK78
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_122])]) ).
fof(f3049,plain,
( sK78 = set_difference(relation_dom(sK19),relation_field(sK19))
| ~ spl81_122
| ~ spl81_223 ),
inference(resolution,[],[f2970,f1861]) ).
fof(f1861,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK78 )
| ~ spl81_122 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f3428,plain,
spl81_267,
inference(avatar_split_clause,[],[f1097,f3426]) ).
fof(f3426,plain,
( spl81_267
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_267])]) ).
fof(f1097,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f896]) ).
fof(f896,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X1
| ~ in(sK73(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f3424,plain,
spl81_266,
inference(avatar_split_clause,[],[f1096,f3422]) ).
fof(f3422,plain,
( spl81_266
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_266])]) ).
fof(f1096,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f897]) ).
fof(f897,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| sK73(X0,X1,X2) != X0
| ~ in(sK73(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f3420,plain,
spl81_265,
inference(avatar_split_clause,[],[f918,f3418]) ).
fof(f3418,plain,
( spl81_265
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_265])]) ).
fof(f918,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f3416,plain,
spl81_264,
inference(avatar_split_clause,[],[f908,f3414]) ).
fof(f3414,plain,
( spl81_264
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_264])]) ).
fof(f908,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f3409,plain,
spl81_263,
inference(avatar_split_clause,[],[f902,f3407]) ).
fof(f3407,plain,
( spl81_263
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_263])]) ).
fof(f902,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f3405,plain,
spl81_262,
inference(avatar_split_clause,[],[f892,f3403]) ).
fof(f3403,plain,
( spl81_262
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_262])]) ).
fof(f892,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f3401,plain,
spl81_261,
inference(avatar_split_clause,[],[f883,f3399]) ).
fof(f3399,plain,
( spl81_261
<=> ! [X0,X8,X2,X1] :
( in(sK72(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_261])]) ).
fof(f883,plain,
! [X2,X0,X1,X8] :
( in(sK72(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f3397,plain,
spl81_260,
inference(avatar_split_clause,[],[f882,f3395]) ).
fof(f3395,plain,
( spl81_260
<=> ! [X0,X8,X2,X1] :
( in(sK71(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_260])]) ).
fof(f882,plain,
! [X2,X0,X1,X8] :
( in(sK71(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f3393,plain,
spl81_259,
inference(avatar_split_clause,[],[f863,f3391]) ).
fof(f3391,plain,
( spl81_259
<=> ! [X0,X1] :
( sP12(X0,X1)
| in(sK64(X0,X1),X0)
| in(sK63(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_259])]) ).
fof(f863,plain,
! [X0,X1] :
( sP12(X0,X1)
| in(sK64(X0,X1),X0)
| in(sK63(X0,X1),X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f3389,plain,
spl81_258,
inference(avatar_split_clause,[],[f849,f3387]) ).
fof(f3387,plain,
( spl81_258
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK61(X0,X1),X1)
| ~ in(sK61(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_258])]) ).
fof(f849,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK61(X0,X1),X1)
| ~ in(sK61(X0,X1),X0) ),
inference(cnf_transformation,[],[f512]) ).
fof(f512,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK61(X0,X1),X1)
| ~ in(sK61(X0,X1),X0) )
& ( in(sK61(X0,X1),X1)
| in(sK61(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f510,f511]) ).
fof(f511,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK61(X0,X1),X1)
| ~ in(sK61(X0,X1),X0) )
& ( in(sK61(X0,X1),X1)
| in(sK61(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f510,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f3385,plain,
spl81_257,
inference(avatar_split_clause,[],[f848,f3383]) ).
fof(f3383,plain,
( spl81_257
<=> ! [X0,X1] :
( X0 = X1
| in(sK61(X0,X1),X1)
| in(sK61(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_257])]) ).
fof(f848,plain,
! [X0,X1] :
( X0 = X1
| in(sK61(X0,X1),X1)
| in(sK61(X0,X1),X0) ),
inference(cnf_transformation,[],[f512]) ).
fof(f3381,plain,
spl81_256,
inference(avatar_split_clause,[],[f833,f3379]) ).
fof(f3379,plain,
( spl81_256
<=> ! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP10(X2,X1,X0)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_256])]) ).
fof(f833,plain,
! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP10(X2,X1,X0)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f504]) ).
fof(f504,plain,
! [X0,X1,X2] :
( ( ( complements_of_subsets(X1,X2) = X0
| ~ sP10(X2,X1,X0) )
& ( sP10(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0 ) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f503]) ).
fof(f503,plain,
! [X2,X0,X1] :
( ( ( complements_of_subsets(X0,X1) = X2
| ~ sP10(X1,X0,X2) )
& ( sP10(X1,X0,X2)
| complements_of_subsets(X0,X1) != X2 ) )
| ~ sP11(X2,X0,X1) ),
inference(nnf_transformation,[],[f370]) ).
fof(f3377,plain,
spl81_255,
inference(avatar_split_clause,[],[f810,f3375]) ).
fof(f3375,plain,
( spl81_255
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP8(X2,X1,X0)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_255])]) ).
fof(f810,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP8(X2,X1,X0)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f497]) ).
fof(f497,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP8(X2,X1,X0) )
& ( sP8(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP9(X0,X1,X2) ),
inference(rectify,[],[f496]) ).
fof(f496,plain,
! [X2,X0,X1] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP8(X1,X0,X2) )
& ( sP8(X1,X0,X2)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP9(X2,X0,X1) ),
inference(nnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ( relation_rng_restriction(X0,X1) = X2
<=> sP8(X1,X0,X2) )
| ~ sP9(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f3373,plain,
spl81_254,
inference(avatar_split_clause,[],[f791,f3371]) ).
fof(f3371,plain,
( spl81_254
<=> ! [X0,X1] :
( sP4(X0,X1)
| in(sK54(X0,X1),X0)
| ~ in(sK53(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_254])]) ).
fof(f791,plain,
! [X0,X1] :
( sP4(X0,X1)
| in(sK54(X0,X1),X0)
| ~ in(sK53(X0,X1),X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f3369,plain,
( spl81_253
| ~ spl81_72
| ~ spl81_203 ),
inference(avatar_split_clause,[],[f2922,f2713,f1447,f3366]) ).
fof(f2713,plain,
( spl81_203
<=> relation_field(sK19) = set_union2(relation_dom(sK19),relation_rng(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_203])]) ).
fof(f2922,plain,
( sP16(relation_rng(sK19),relation_dom(sK19),relation_field(sK19))
| ~ spl81_72
| ~ spl81_203 ),
inference(superposition,[],[f1448,f2715]) ).
fof(f2715,plain,
( relation_field(sK19) = set_union2(relation_dom(sK19),relation_rng(sK19))
| ~ spl81_203 ),
inference(avatar_component_clause,[],[f2713]) ).
fof(f3364,plain,
spl81_252,
inference(avatar_split_clause,[],[f743,f3362]) ).
fof(f3362,plain,
( spl81_252
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_252])]) ).
fof(f743,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1,X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f455]) ).
fof(f455,plain,
! [X2,X1,X0] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ sP3(X2,X1,X0) ),
inference(nnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X2,X1,X0] :
( ( relation_dom_restriction(X0,X1) = X2
<=> sP2(X0,X1,X2) )
| ~ sP3(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f3360,plain,
spl81_251,
inference(avatar_split_clause,[],[f726,f3358]) ).
fof(f3358,plain,
( spl81_251
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_251])]) ).
fof(f726,plain,
! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f436]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ( ( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_composition(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f435]) ).
fof(f435,plain,
! [X2,X0,X1] :
( ( ( relation_composition(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| relation_composition(X0,X1) != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ( relation_composition(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f3306,plain,
( spl81_250
| ~ spl81_52
| ~ spl81_245 ),
inference(avatar_split_clause,[],[f3270,f3267,f1345,f3304]) ).
fof(f3304,plain,
( spl81_250
<=> ! [X0,X1] :
( sK78 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_250])]) ).
fof(f3267,plain,
( spl81_245
<=> ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_245])]) ).
fof(f3270,plain,
( ! [X0,X1] :
( sK78 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl81_52
| ~ spl81_245 ),
inference(forward_demodulation,[],[f3268,f1347]) ).
fof(f3268,plain,
( ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl81_245 ),
inference(avatar_component_clause,[],[f3267]) ).
fof(f3286,plain,
( spl81_249
| ~ spl81_52
| ~ spl81_242 ),
inference(avatar_split_clause,[],[f3257,f3253,f1345,f3284]) ).
fof(f3284,plain,
( spl81_249
<=> ! [X0,X1] :
( sK78 = X1
| complements_of_subsets(X0,X1) != sK78
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_249])]) ).
fof(f3253,plain,
( spl81_242
<=> ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_242])]) ).
fof(f3257,plain,
( ! [X0,X1] :
( sK78 = X1
| complements_of_subsets(X0,X1) != sK78
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_52
| ~ spl81_242 ),
inference(forward_demodulation,[],[f3256,f1347]) ).
fof(f3256,plain,
( ! [X0,X1] :
( complements_of_subsets(X0,X1) != sK78
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_52
| ~ spl81_242 ),
inference(forward_demodulation,[],[f3254,f1347]) ).
fof(f3254,plain,
( ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl81_242 ),
inference(avatar_component_clause,[],[f3253]) ).
fof(f3282,plain,
spl81_248,
inference(avatar_split_clause,[],[f1093,f3280]) ).
fof(f3280,plain,
( spl81_248
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK66(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_248])]) ).
fof(f1093,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK66(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK66(X0,X1) != X0
| ~ in(sK66(X0,X1),X1) ),
inference(definition_unfolding,[],[f870,f583]) ).
fof(f870,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK66(X0,X1) != X0
| ~ in(sK66(X0,X1),X1) ),
inference(cnf_transformation,[],[f530]) ).
fof(f3278,plain,
spl81_247,
inference(avatar_split_clause,[],[f965,f3276]) ).
fof(f3276,plain,
( spl81_247
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_247])]) ).
fof(f965,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f679,f608]) ).
fof(f679,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f274]) ).
fof(f274,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f3274,plain,
spl81_246,
inference(avatar_split_clause,[],[f962,f3272]) ).
fof(f3272,plain,
( spl81_246
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_246])]) ).
fof(f962,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f673,f583]) ).
fof(f673,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f264]) ).
fof(f264,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f3269,plain,
spl81_245,
inference(avatar_split_clause,[],[f946,f3267]) ).
fof(f946,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f641,f583,f583]) ).
fof(f641,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f400]) ).
fof(f400,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f145]) ).
fof(f145,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f3265,plain,
spl81_244,
inference(avatar_split_clause,[],[f696,f3263]) ).
fof(f3263,plain,
( spl81_244
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_244])]) ).
fof(f696,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f3261,plain,
spl81_243,
inference(avatar_split_clause,[],[f689,f3259]) ).
fof(f3259,plain,
( spl81_243
<=> ! [X0,X3,X2,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_243])]) ).
fof(f689,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f280]) ).
fof(f280,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f3255,plain,
spl81_242,
inference(avatar_split_clause,[],[f635,f3253]) ).
fof(f635,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f249]) ).
fof(f249,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f156]) ).
fof(f156,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( empty_set = complements_of_subsets(X0,X1)
& empty_set != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f3250,plain,
( spl81_172
| ~ spl81_241
| ~ spl81_61
| ~ spl81_203 ),
inference(avatar_split_clause,[],[f2920,f2713,f1403,f3247,f2316]) ).
fof(f2316,plain,
( spl81_172
<=> empty(relation_rng(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_172])]) ).
fof(f3247,plain,
( spl81_241
<=> empty(relation_field(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_241])]) ).
fof(f1403,plain,
( spl81_61
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_61])]) ).
fof(f2920,plain,
( ~ empty(relation_field(sK19))
| empty(relation_rng(sK19))
| ~ spl81_61
| ~ spl81_203 ),
inference(superposition,[],[f1404,f2715]) ).
fof(f1404,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) )
| ~ spl81_61 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f3212,plain,
spl81_240,
inference(avatar_split_clause,[],[f1063,f3210]) ).
fof(f3210,plain,
( spl81_240
<=> ! [X2,X1] :
( sP10(X2,X1,complements_of_subsets(X1,X2))
| ~ sP11(complements_of_subsets(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_240])]) ).
fof(f1063,plain,
! [X2,X1] :
( sP10(X2,X1,complements_of_subsets(X1,X2))
| ~ sP11(complements_of_subsets(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f832]) ).
fof(f832,plain,
! [X2,X0,X1] :
( sP10(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f504]) ).
fof(f3208,plain,
spl81_239,
inference(avatar_split_clause,[],[f1062,f3206]) ).
fof(f3206,plain,
( spl81_239
<=> ! [X2,X1] :
( sP8(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP9(relation_rng_restriction(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_239])]) ).
fof(f1062,plain,
! [X2,X1] :
( sP8(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP9(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f809]) ).
fof(f809,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f497]) ).
fof(f3204,plain,
spl81_238,
inference(avatar_split_clause,[],[f1053,f3202]) ).
fof(f3202,plain,
( spl81_238
<=> ! [X2,X1] :
( sP2(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP3(relation_dom_restriction(X2,X1),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_238])]) ).
fof(f1053,plain,
! [X2,X1] :
( sP2(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP3(relation_dom_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f742]) ).
fof(f742,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f456]) ).
fof(f3200,plain,
spl81_237,
inference(avatar_split_clause,[],[f1048,f3198]) ).
fof(f3198,plain,
( spl81_237
<=> ! [X2,X1] :
( sP0(X2,X1,relation_composition(X1,X2))
| ~ sP1(relation_composition(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_237])]) ).
fof(f1048,plain,
! [X2,X1] :
( sP0(X2,X1,relation_composition(X1,X2))
| ~ sP1(relation_composition(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f725]) ).
fof(f725,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_composition(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f436]) ).
fof(f3196,plain,
spl81_236,
inference(avatar_split_clause,[],[f861,f3194]) ).
fof(f3194,plain,
( spl81_236
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_236])]) ).
fof(f861,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f3192,plain,
spl81_235,
inference(avatar_split_clause,[],[f831,f3190]) ).
fof(f3190,plain,
( spl81_235
<=> ! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_235])]) ).
fof(f831,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f3188,plain,
spl81_234,
inference(avatar_split_clause,[],[f830,f3186]) ).
fof(f3186,plain,
( spl81_234
<=> ! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_234])]) ).
fof(f830,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f3184,plain,
spl81_233,
inference(avatar_split_clause,[],[f787,f3182]) ).
fof(f3182,plain,
( spl81_233
<=> ! [X0,X5,X1,X7] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_233])]) ).
fof(f787,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f3180,plain,
spl81_232,
inference(avatar_split_clause,[],[f768,f3178]) ).
fof(f3178,plain,
( spl81_232
<=> ! [X2,X0,X4] :
( in(X4,sK51(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_232])]) ).
fof(f768,plain,
! [X2,X0,X4] :
( in(X4,sK51(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK50(X0)) ),
inference(cnf_transformation,[],[f476]) ).
fof(f476,plain,
! [X0] :
( ! [X2] :
( ( ! [X4] :
( in(X4,sK51(X0,X2))
| ~ subset(X4,X2) )
& in(sK51(X0,X2),sK50(X0)) )
| ~ in(X2,sK50(X0)) )
& ! [X5,X6] :
( in(X6,sK50(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK50(X0)) )
& in(X0,sK50(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f473,f475,f474]) ).
fof(f474,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK50(X0)) )
| ~ in(X2,sK50(X0)) )
& ! [X6,X5] :
( in(X6,sK50(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK50(X0)) )
& in(X0,sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f475,plain,
! [X0,X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK50(X0)) )
=> ( ! [X4] :
( in(X4,sK51(X0,X2))
| ~ subset(X4,X2) )
& in(sK51(X0,X2),sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f473,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f304]) ).
fof(f304,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(flattening,[],[f303]) ).
fof(f303,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0] :
? [X1] :
( ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f198]) ).
fof(f198,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(rectify,[],[f193]) ).
fof(f193,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(f3130,plain,
( ~ spl81_231
| ~ spl81_54
| ~ spl81_223 ),
inference(avatar_split_clause,[],[f3047,f2968,f1359,f3127]) ).
fof(f3127,plain,
( spl81_231
<=> proper_subset(relation_field(sK19),relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_231])]) ).
fof(f3047,plain,
( ~ proper_subset(relation_field(sK19),relation_dom(sK19))
| ~ spl81_54
| ~ spl81_223 ),
inference(resolution,[],[f2970,f1360]) ).
fof(f3083,plain,
spl81_230,
inference(avatar_split_clause,[],[f1010,f3081]) ).
fof(f3081,plain,
( spl81_230
<=> ! [X2,X0,X3] :
( relation(X0)
| sK45(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_230])]) ).
fof(f1010,plain,
! [X2,X3,X0] :
( relation(X0)
| sK45(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f761,f931]) ).
fof(f761,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK45(X0) ),
inference(cnf_transformation,[],[f466]) ).
fof(f3079,plain,
spl81_229,
inference(avatar_split_clause,[],[f937,f3077]) ).
fof(f3077,plain,
( spl81_229
<=> ! [X0,X1] :
( in(sK23(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_229])]) ).
fof(f937,plain,
! [X0,X1] :
( in(sK23(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f611,f608]) ).
fof(f611,plain,
! [X0,X1] :
( in(sK23(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK23(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f227,f392]) ).
fof(f392,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK23(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f3075,plain,
spl81_228,
inference(avatar_split_clause,[],[f674,f3073]) ).
fof(f3073,plain,
( spl81_228
<=> ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_228])]) ).
fof(f674,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f166]) ).
fof(f166,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f3071,plain,
spl81_227,
inference(avatar_split_clause,[],[f667,f3069]) ).
fof(f3069,plain,
( spl81_227
<=> ! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_227])]) ).
fof(f667,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f3067,plain,
spl81_226,
inference(avatar_split_clause,[],[f664,f3065]) ).
fof(f3065,plain,
( spl81_226
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_226])]) ).
fof(f664,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f3063,plain,
spl81_225,
inference(avatar_split_clause,[],[f597,f3061]) ).
fof(f597,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f3059,plain,
spl81_224,
inference(avatar_split_clause,[],[f596,f3057]) ).
fof(f3057,plain,
( spl81_224
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_224])]) ).
fof(f596,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f2971,plain,
( spl81_223
| ~ spl81_33
| ~ spl81_203 ),
inference(avatar_split_clause,[],[f2919,f2713,f1245,f2968]) ).
fof(f1245,plain,
( spl81_33
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_33])]) ).
fof(f2919,plain,
( subset(relation_dom(sK19),relation_field(sK19))
| ~ spl81_33
| ~ spl81_203 ),
inference(superposition,[],[f1246,f2715]) ).
fof(f1246,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl81_33 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f2957,plain,
spl81_222,
inference(avatar_split_clause,[],[f860,f2955]) ).
fof(f2955,plain,
( spl81_222
<=> ! [X5,X0,X1] :
( in(sK65(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_222])]) ).
fof(f860,plain,
! [X0,X1,X5] :
( in(sK65(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f2953,plain,
spl81_221,
inference(avatar_split_clause,[],[f859,f2951]) ).
fof(f2951,plain,
( spl81_221
<=> ! [X5,X0,X1] :
( in(X5,sK65(X0,X5))
| ~ in(X5,X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_221])]) ).
fof(f859,plain,
! [X0,X1,X5] :
( in(X5,sK65(X0,X5))
| ~ in(X5,X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f2949,plain,
spl81_220,
inference(avatar_split_clause,[],[f836,f2947]) ).
fof(f2947,plain,
( spl81_220
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| element(sK60(X0,X1,X2),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_220])]) ).
fof(f836,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| element(sK60(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f509]) ).
fof(f2945,plain,
spl81_219,
inference(avatar_split_clause,[],[f829,f2943]) ).
fof(f2943,plain,
( spl81_219
<=> ! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_219])]) ).
fof(f829,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f2941,plain,
spl81_218,
inference(avatar_split_clause,[],[f828,f2939]) ).
fof(f2939,plain,
( spl81_218
<=> ! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_218])]) ).
fof(f828,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f2937,plain,
spl81_217,
inference(avatar_split_clause,[],[f827,f2935]) ).
fof(f2935,plain,
( spl81_217
<=> ! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_217])]) ).
fof(f827,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f2933,plain,
spl81_216,
inference(avatar_split_clause,[],[f826,f2931]) ).
fof(f2931,plain,
( spl81_216
<=> ! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_216])]) ).
fof(f826,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f2929,plain,
spl81_215,
inference(avatar_split_clause,[],[f825,f2927]) ).
fof(f2927,plain,
( spl81_215
<=> ! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_215])]) ).
fof(f825,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f2918,plain,
spl81_214,
inference(avatar_split_clause,[],[f824,f2916]) ).
fof(f2916,plain,
( spl81_214
<=> ! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_214])]) ).
fof(f824,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f2914,plain,
spl81_213,
inference(avatar_split_clause,[],[f789,f2912]) ).
fof(f2912,plain,
( spl81_213
<=> ! [X5,X1,X0] :
( in(X5,X1)
| ~ in(X5,sK55(X0,X5))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_213])]) ).
fof(f789,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK55(X0,X5))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f2910,plain,
spl81_212,
inference(avatar_split_clause,[],[f788,f2908]) ).
fof(f2908,plain,
( spl81_212
<=> ! [X5,X1,X0] :
( in(X5,X1)
| in(sK55(X0,X5),X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_212])]) ).
fof(f788,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK55(X0,X5),X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f487]) ).
fof(f2906,plain,
spl81_211,
inference(avatar_split_clause,[],[f766,f2904]) ).
fof(f2904,plain,
( spl81_211
<=> ! [X6,X0,X5] :
( in(X6,sK50(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_211])]) ).
fof(f766,plain,
! [X0,X6,X5] :
( in(X6,sK50(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK50(X0)) ),
inference(cnf_transformation,[],[f476]) ).
fof(f2744,plain,
spl81_210,
inference(avatar_split_clause,[],[f1038,f2742]) ).
fof(f2742,plain,
( spl81_210
<=> ! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP15(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_210])]) ).
fof(f1038,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP15(X1,X0,X2) ),
inference(definition_unfolding,[],[f907,f608]) ).
fof(f907,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP15(X1,X0,X2) ),
inference(cnf_transformation,[],[f554]) ).
fof(f554,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP15(X1,X0,X2) )
& ( sP15(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP15(X1,X0,X2) ),
inference(definition_folding,[],[f23,f378]) ).
fof(f23,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f2740,plain,
spl81_209,
inference(avatar_split_clause,[],[f1014,f2738]) ).
fof(f2738,plain,
( spl81_209
<=> ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_209])]) ).
fof(f1014,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f778,f608,f608]) ).
fof(f778,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2736,plain,
spl81_208,
inference(avatar_split_clause,[],[f683,f2734]) ).
fof(f2734,plain,
( spl81_208
<=> ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_208])]) ).
fof(f683,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f414]) ).
fof(f414,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f413]) ).
fof(f413,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f143]) ).
fof(f143,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f2732,plain,
spl81_207,
inference(avatar_split_clause,[],[f680,f2730]) ).
fof(f2730,plain,
( spl81_207
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_207])]) ).
fof(f680,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f276]) ).
fof(f276,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f2728,plain,
spl81_206,
inference(avatar_split_clause,[],[f666,f2726]) ).
fof(f2726,plain,
( spl81_206
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_206])]) ).
fof(f666,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f2724,plain,
spl81_205,
inference(avatar_split_clause,[],[f663,f2722]) ).
fof(f2722,plain,
( spl81_205
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_205])]) ).
fof(f663,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f2720,plain,
spl81_204,
inference(avatar_split_clause,[],[f603,f2718]) ).
fof(f2718,plain,
( spl81_204
<=> ! [X4,X0,X3] :
( in(X4,sK22(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK22(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_204])]) ).
fof(f603,plain,
! [X3,X0,X4] :
( in(X4,sK22(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK22(X0)) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0] :
( ! [X2] :
( in(powerset(X2),sK22(X0))
| ~ in(X2,sK22(X0)) )
& ! [X3,X4] :
( in(X4,sK22(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK22(X0)) )
& in(X0,sK22(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f389,f390]) ).
fof(f390,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(powerset(X2),sK22(X0))
| ~ in(X2,sK22(X0)) )
& ! [X4,X3] :
( in(X4,sK22(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK22(X0)) )
& in(X0,sK22(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f389,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f226]) ).
fof(f226,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(flattening,[],[f225]) ).
fof(f225,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f195]) ).
fof(f195,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f2716,plain,
( spl81_203
| ~ spl81_1
| ~ spl81_187 ),
inference(avatar_split_clause,[],[f2648,f2583,f1099,f2713]) ).
fof(f2583,plain,
( spl81_187
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_187])]) ).
fof(f2648,plain,
( relation_field(sK19) = set_union2(relation_dom(sK19),relation_rng(sK19))
| ~ spl81_1
| ~ spl81_187 ),
inference(resolution,[],[f2584,f1101]) ).
fof(f2584,plain,
( ! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) )
| ~ spl81_187 ),
inference(avatar_component_clause,[],[f2583]) ).
fof(f2711,plain,
spl81_202,
inference(avatar_split_clause,[],[f595,f2709]) ).
fof(f2709,plain,
( spl81_202
<=> ! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_202])]) ).
fof(f595,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f2707,plain,
spl81_201,
inference(avatar_split_clause,[],[f594,f2705]) ).
fof(f2705,plain,
( spl81_201
<=> ! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_201])]) ).
fof(f594,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f152,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f2684,plain,
( spl81_200
| ~ spl81_1
| ~ spl81_165 ),
inference(avatar_split_clause,[],[f2382,f2288,f1099,f2682]) ).
fof(f2682,plain,
( spl81_200
<=> ! [X0] : relation_dom_restriction(sK19,X0) = relation_composition(identity_relation(X0),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_200])]) ).
fof(f2288,plain,
( spl81_165
<=> ! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_165])]) ).
fof(f2382,plain,
( ! [X0] : relation_dom_restriction(sK19,X0) = relation_composition(identity_relation(X0),sK19)
| ~ spl81_1
| ~ spl81_165 ),
inference(resolution,[],[f2289,f1101]) ).
fof(f2289,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) )
| ~ spl81_165 ),
inference(avatar_component_clause,[],[f2288]) ).
fof(f2634,plain,
spl81_199,
inference(avatar_split_clause,[],[f917,f2632]) ).
fof(f2632,plain,
( spl81_199
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_199])]) ).
fof(f917,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f2630,plain,
spl81_198,
inference(avatar_split_clause,[],[f916,f2628]) ).
fof(f2628,plain,
( spl81_198
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_198])]) ).
fof(f916,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f565]) ).
fof(f2626,plain,
spl81_197,
inference(avatar_split_clause,[],[f910,f2624]) ).
fof(f910,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f2622,plain,
spl81_196,
inference(avatar_split_clause,[],[f909,f2620]) ).
fof(f2620,plain,
( spl81_196
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_196])]) ).
fof(f909,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f2618,plain,
spl81_195,
inference(avatar_split_clause,[],[f901,f2616]) ).
fof(f2616,plain,
( spl81_195
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_195])]) ).
fof(f901,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f2613,plain,
spl81_194,
inference(avatar_split_clause,[],[f900,f2611]) ).
fof(f2611,plain,
( spl81_194
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_194])]) ).
fof(f900,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f2609,plain,
spl81_193,
inference(avatar_split_clause,[],[f879,f2607]) ).
fof(f2607,plain,
( spl81_193
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_193])]) ).
fof(f879,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f2605,plain,
spl81_192,
inference(avatar_split_clause,[],[f823,f2603]) ).
fof(f2603,plain,
( spl81_192
<=> ! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_192])]) ).
fof(f823,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f2601,plain,
spl81_191,
inference(avatar_split_clause,[],[f801,f2599]) ).
fof(f2599,plain,
( spl81_191
<=> ! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP6(X1,X0)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_191])]) ).
fof(f801,plain,
! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP6(X1,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0,X1] :
( ( ( identity_relation(X1) = X0
| ~ sP6(X1,X0) )
& ( sP6(X1,X0)
| identity_relation(X1) != X0 ) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f489]) ).
fof(f489,plain,
! [X1,X0] :
( ( ( identity_relation(X0) = X1
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| identity_relation(X0) != X1 ) )
| ~ sP7(X1,X0) ),
inference(nnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X1,X0] :
( ( identity_relation(X0) = X1
<=> sP6(X0,X1) )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f2597,plain,
spl81_190,
inference(avatar_split_clause,[],[f786,f2595]) ).
fof(f2595,plain,
( spl81_190
<=> ! [X0,X1] :
( set_meet(X1) = X0
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_190])]) ).
fof(f786,plain,
! [X0,X1] :
( set_meet(X1) = X0
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f481]) ).
fof(f481,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f480]) ).
fof(f480,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP4(X0,X1) )
& ( sP4(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP5(X1,X0) ),
inference(nnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP4(X0,X1) )
| ~ sP5(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f2593,plain,
spl81_189,
inference(avatar_split_clause,[],[f767,f2591]) ).
fof(f2591,plain,
( spl81_189
<=> ! [X2,X0] :
( in(sK51(X0,X2),sK50(X0))
| ~ in(X2,sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_189])]) ).
fof(f767,plain,
! [X2,X0] :
( in(sK51(X0,X2),sK50(X0))
| ~ in(X2,sK50(X0)) ),
inference(cnf_transformation,[],[f476]) ).
fof(f2589,plain,
spl81_188,
inference(avatar_split_clause,[],[f733,f2587]) ).
fof(f2587,plain,
( spl81_188
<=> ! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_188])]) ).
fof(f733,plain,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f290,f355,f354]) ).
fof(f290,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f2585,plain,
spl81_187,
inference(avatar_split_clause,[],[f713,f2583]) ).
fof(f713,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f2541,plain,
( spl81_186
| ~ spl81_52
| ~ spl81_182 ),
inference(avatar_split_clause,[],[f2361,f2358,f1345,f2539]) ).
fof(f2539,plain,
( spl81_186
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK78
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_186])]) ).
fof(f2358,plain,
( spl81_182
<=> ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_182])]) ).
fof(f2361,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK78
| ~ disjoint(X0,X1) )
| ~ spl81_52
| ~ spl81_182 ),
inference(forward_demodulation,[],[f2359,f1347]) ).
fof(f2359,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl81_182 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f2537,plain,
( spl81_185
| ~ spl81_52
| ~ spl81_181 ),
inference(avatar_split_clause,[],[f2356,f2353,f1345,f2535]) ).
fof(f2535,plain,
( spl81_185
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK78
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_185])]) ).
fof(f2353,plain,
( spl81_181
<=> ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_181])]) ).
fof(f2356,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK78
| disjoint(X0,X1) )
| ~ spl81_52
| ~ spl81_181 ),
inference(forward_demodulation,[],[f2354,f1347]) ).
fof(f2354,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) )
| ~ spl81_181 ),
inference(avatar_component_clause,[],[f2353]) ).
fof(f2488,plain,
( ~ spl81_1
| ~ spl81_41
| spl81_171 ),
inference(avatar_split_clause,[],[f2362,f2312,f1278,f1099]) ).
fof(f1278,plain,
( spl81_41
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_41])]) ).
fof(f2312,plain,
( spl81_171
<=> relation(relation_inverse(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_171])]) ).
fof(f2362,plain,
( ~ relation(sK19)
| ~ spl81_41
| spl81_171 ),
inference(resolution,[],[f2314,f1279]) ).
fof(f1279,plain,
( ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) )
| ~ spl81_41 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f2314,plain,
( ~ relation(relation_inverse(sK19))
| spl81_171 ),
inference(avatar_component_clause,[],[f2312]) ).
fof(f2370,plain,
( spl81_184
| ~ spl81_52
| ~ spl81_164 ),
inference(avatar_split_clause,[],[f2286,f2282,f1345,f2368]) ).
fof(f2368,plain,
( spl81_184
<=> ! [X0] :
( relation_rng(X0) != sK78
| relation_dom(X0) = sK78
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_184])]) ).
fof(f2282,plain,
( spl81_164
<=> ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_164])]) ).
fof(f2286,plain,
( ! [X0] :
( relation_rng(X0) != sK78
| relation_dom(X0) = sK78
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_164 ),
inference(forward_demodulation,[],[f2285,f1347]) ).
fof(f2285,plain,
( ! [X0] :
( relation_dom(X0) = sK78
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_164 ),
inference(forward_demodulation,[],[f2283,f1347]) ).
fof(f2283,plain,
( ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl81_164 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f2366,plain,
( spl81_183
| ~ spl81_52
| ~ spl81_163 ),
inference(avatar_split_clause,[],[f2280,f2276,f1345,f2364]) ).
fof(f2364,plain,
( spl81_183
<=> ! [X0] :
( relation_dom(X0) != sK78
| relation_rng(X0) = sK78
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_183])]) ).
fof(f2276,plain,
( spl81_163
<=> ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_163])]) ).
fof(f2280,plain,
( ! [X0] :
( relation_dom(X0) != sK78
| relation_rng(X0) = sK78
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_163 ),
inference(forward_demodulation,[],[f2279,f1347]) ).
fof(f2279,plain,
( ! [X0] :
( relation_rng(X0) = sK78
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_163 ),
inference(forward_demodulation,[],[f2277,f1347]) ).
fof(f2277,plain,
( ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl81_163 ),
inference(avatar_component_clause,[],[f2276]) ).
fof(f2360,plain,
spl81_182,
inference(avatar_split_clause,[],[f1029,f2358]) ).
fof(f1029,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f854,f608]) ).
fof(f854,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f515]) ).
fof(f515,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f2355,plain,
spl81_181,
inference(avatar_split_clause,[],[f1028,f2353]) ).
fof(f1028,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f855,f608]) ).
fof(f855,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f515]) ).
fof(f2351,plain,
spl81_180,
inference(avatar_split_clause,[],[f1027,f2349]) ).
fof(f2349,plain,
( spl81_180
<=> ! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_180])]) ).
fof(f1027,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f842,f608]) ).
fof(f842,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f333]) ).
fof(f333,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f2347,plain,
spl81_179,
inference(avatar_split_clause,[],[f964,f2345]) ).
fof(f2345,plain,
( spl81_179
<=> ! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_179])]) ).
fof(f964,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f676,f583]) ).
fof(f676,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f2343,plain,
spl81_178,
inference(avatar_split_clause,[],[f963,f2341]) ).
fof(f2341,plain,
( spl81_178
<=> ! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_178])]) ).
fof(f963,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f675,f583]) ).
fof(f675,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f194]) ).
fof(f194,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f2339,plain,
spl81_177,
inference(avatar_split_clause,[],[f955,f2337]) ).
fof(f2337,plain,
( spl81_177
<=> ! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_177])]) ).
fof(f955,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f655,f583]) ).
fof(f655,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f174]) ).
fof(f174,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f2335,plain,
spl81_176,
inference(avatar_split_clause,[],[f954,f2333]) ).
fof(f2333,plain,
( spl81_176
<=> ! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_176])]) ).
fof(f954,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f656,f583]) ).
fof(f656,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f408]) ).
fof(f2331,plain,
spl81_175,
inference(avatar_split_clause,[],[f943,f2329]) ).
fof(f2329,plain,
( spl81_175
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_175])]) ).
fof(f943,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f636,f583,f583]) ).
fof(f636,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f2327,plain,
spl81_174,
inference(avatar_split_clause,[],[f942,f2325]) ).
fof(f2325,plain,
( spl81_174
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_174])]) ).
fof(f942,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f627,f608]) ).
fof(f627,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f131]) ).
fof(f131,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f2323,plain,
spl81_173,
inference(avatar_split_clause,[],[f940,f2321]) ).
fof(f2321,plain,
( spl81_173
<=> ! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_173])]) ).
fof(f940,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f625,f583]) ).
fof(f625,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f2319,plain,
( spl81_138
| ~ spl81_171
| ~ spl81_172
| ~ spl81_85
| ~ spl81_120 ),
inference(avatar_split_clause,[],[f1957,f1842,f1538,f2316,f2312,f2035]) ).
fof(f2035,plain,
( spl81_138
<=> empty(relation_inverse(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_138])]) ).
fof(f1538,plain,
( spl81_85
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_85])]) ).
fof(f1842,plain,
( spl81_120
<=> relation_rng(sK19) = relation_dom(relation_inverse(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_120])]) ).
fof(f1957,plain,
( ~ empty(relation_rng(sK19))
| ~ relation(relation_inverse(sK19))
| empty(relation_inverse(sK19))
| ~ spl81_85
| ~ spl81_120 ),
inference(superposition,[],[f1539,f1844]) ).
fof(f1844,plain,
( relation_rng(sK19) = relation_dom(relation_inverse(sK19))
| ~ spl81_120 ),
inference(avatar_component_clause,[],[f1842]) ).
fof(f1539,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl81_85 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f2310,plain,
spl81_170,
inference(avatar_split_clause,[],[f936,f2308]) ).
fof(f2308,plain,
( spl81_170
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_170])]) ).
fof(f936,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f612,f608]) ).
fof(f612,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f393]) ).
fof(f2306,plain,
spl81_169,
inference(avatar_split_clause,[],[f672,f2304]) ).
fof(f2304,plain,
( spl81_169
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_169])]) ).
fof(f672,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f2302,plain,
spl81_168,
inference(avatar_split_clause,[],[f671,f2300]) ).
fof(f2300,plain,
( spl81_168
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_168])]) ).
fof(f671,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f2298,plain,
spl81_167,
inference(avatar_split_clause,[],[f670,f2296]) ).
fof(f2296,plain,
( spl81_167
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_167])]) ).
fof(f670,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f2294,plain,
spl81_166,
inference(avatar_split_clause,[],[f630,f2292]) ).
fof(f2292,plain,
( spl81_166
<=> ! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_166])]) ).
fof(f630,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f2290,plain,
spl81_165,
inference(avatar_split_clause,[],[f620,f2288]) ).
fof(f620,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f190]) ).
fof(f190,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f2284,plain,
spl81_164,
inference(avatar_split_clause,[],[f593,f2282]) ).
fof(f593,plain,
! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f388]) ).
fof(f388,plain,
! [X0] :
( ( ( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0) )
& ( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ( empty_set = relation_dom(X0)
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f173]) ).
fof(f173,axiom,
! [X0] :
( relation(X0)
=> ( empty_set = relation_dom(X0)
<=> empty_set = relation_rng(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f2278,plain,
spl81_163,
inference(avatar_split_clause,[],[f592,f2276]) ).
fof(f592,plain,
! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f388]) ).
fof(f2223,plain,
spl81_162,
inference(avatar_split_clause,[],[f924,f2221]) ).
fof(f2221,plain,
( spl81_162
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_162])]) ).
fof(f924,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f168]) ).
fof(f168,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f2219,plain,
spl81_161,
inference(avatar_split_clause,[],[f923,f2217]) ).
fof(f2217,plain,
( spl81_161
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP17(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_161])]) ).
fof(f923,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP17(X1,X0,X2) ),
inference(cnf_transformation,[],[f566]) ).
fof(f566,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP17(X1,X0,X2) )
& ( sP17(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP17(X1,X0,X2) ),
inference(definition_folding,[],[f27,f382]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2215,plain,
spl81_160,
inference(avatar_split_clause,[],[f915,f2213]) ).
fof(f2213,plain,
( spl81_160
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP16(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_160])]) ).
fof(f915,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP16(X1,X0,X2) ),
inference(cnf_transformation,[],[f560]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP16(X1,X0,X2) )
& ( sP16(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP16(X1,X0,X2) ),
inference(definition_folding,[],[f19,f380]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f2211,plain,
spl81_159,
inference(avatar_split_clause,[],[f899,f2209]) ).
fof(f2209,plain,
( spl81_159
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP14(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_159])]) ).
fof(f899,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP14(X1,X0,X2) ),
inference(cnf_transformation,[],[f548]) ).
fof(f548,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP14(X1,X0,X2) )
& ( sP14(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP14(X1,X0,X2) ),
inference(definition_folding,[],[f18,f376]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f2207,plain,
( ~ spl81_158
| ~ spl81_47
| spl81_139 ),
inference(avatar_split_clause,[],[f2156,f2039,f1302,f2204]) ).
fof(f2204,plain,
( spl81_158
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_158])]) ).
fof(f1302,plain,
( spl81_47
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_47])]) ).
fof(f2039,plain,
( spl81_139
<=> relation(relation_rng(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_139])]) ).
fof(f2156,plain,
( ~ empty(sK19)
| ~ spl81_47
| spl81_139 ),
inference(resolution,[],[f2040,f1303]) ).
fof(f1303,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl81_47 ),
inference(avatar_component_clause,[],[f1302]) ).
fof(f2040,plain,
( ~ relation(relation_rng(sK19))
| spl81_139 ),
inference(avatar_component_clause,[],[f2039]) ).
fof(f2202,plain,
spl81_157,
inference(avatar_split_clause,[],[f891,f2200]) ).
fof(f2200,plain,
( spl81_157
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP13(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_157])]) ).
fof(f891,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP13(X1,X0,X2) ),
inference(cnf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP13(X1,X0,X2) )
& ( sP13(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP13(X1,X0,X2) ),
inference(definition_folding,[],[f20,f374]) ).
fof(f20,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f2198,plain,
spl81_156,
inference(avatar_split_clause,[],[f856,f2196]) ).
fof(f856,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f519]) ).
fof(f519,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK62(X0,X1),X1)
& in(sK62(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f517,f518]) ).
fof(f518,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK62(X0,X1),X1)
& in(sK62(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f517,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f516]) ).
fof(f516,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f344]) ).
fof(f344,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2194,plain,
spl81_155,
inference(avatar_split_clause,[],[f853,f2192]) ).
fof(f2192,plain,
( spl81_155
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_155])]) ).
fof(f853,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f342]) ).
fof(f342,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f2190,plain,
spl81_154,
inference(avatar_split_clause,[],[f852,f2188]) ).
fof(f2188,plain,
( spl81_154
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_154])]) ).
fof(f852,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f514]) ).
fof(f514,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f513]) ).
fof(f513,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2117,plain,
( spl81_153
| ~ spl81_52
| ~ spl81_142 ),
inference(avatar_split_clause,[],[f2058,f2054,f1345,f2115]) ).
fof(f2115,plain,
( spl81_153
<=> ! [X0] :
( relation_rng(X0) != sK78
| sK78 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_153])]) ).
fof(f2054,plain,
( spl81_142
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_142])]) ).
fof(f2058,plain,
( ! [X0] :
( relation_rng(X0) != sK78
| sK78 = X0
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_142 ),
inference(forward_demodulation,[],[f2057,f1347]) ).
fof(f2057,plain,
( ! [X0] :
( sK78 = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_142 ),
inference(forward_demodulation,[],[f2055,f1347]) ).
fof(f2055,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl81_142 ),
inference(avatar_component_clause,[],[f2054]) ).
fof(f2113,plain,
( spl81_152
| ~ spl81_52
| ~ spl81_141 ),
inference(avatar_split_clause,[],[f2052,f2048,f1345,f2111]) ).
fof(f2111,plain,
( spl81_152
<=> ! [X0] :
( relation_dom(X0) != sK78
| sK78 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_152])]) ).
fof(f2048,plain,
( spl81_141
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_141])]) ).
fof(f2052,plain,
( ! [X0] :
( relation_dom(X0) != sK78
| sK78 = X0
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_141 ),
inference(forward_demodulation,[],[f2051,f1347]) ).
fof(f2051,plain,
( ! [X0] :
( sK78 = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl81_52
| ~ spl81_141 ),
inference(forward_demodulation,[],[f2049,f1347]) ).
fof(f2049,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl81_141 ),
inference(avatar_component_clause,[],[f2048]) ).
fof(f2094,plain,
spl81_151,
inference(avatar_split_clause,[],[f678,f2092]) ).
fof(f678,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f2090,plain,
spl81_150,
inference(avatar_split_clause,[],[f677,f2088]) ).
fof(f2088,plain,
( spl81_150
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_150])]) ).
fof(f677,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f171]) ).
fof(f171,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f2086,plain,
spl81_149,
inference(avatar_split_clause,[],[f638,f2084]) ).
fof(f2084,plain,
( spl81_149
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK25(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_149])]) ).
fof(f638,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK25(X0,X1),X1) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK25(X0,X1),X1)
& in(sK25(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f252,f397]) ).
fof(f397,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK25(X0,X1),X1)
& in(sK25(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f2082,plain,
spl81_148,
inference(avatar_split_clause,[],[f637,f2080]) ).
fof(f2080,plain,
( spl81_148
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| in(sK25(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_148])]) ).
fof(f637,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK25(X0,X1),X0) ),
inference(cnf_transformation,[],[f398]) ).
fof(f2078,plain,
spl81_147,
inference(avatar_split_clause,[],[f619,f2076]) ).
fof(f2076,plain,
( spl81_147
<=> ! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_147])]) ).
fof(f619,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f2074,plain,
spl81_146,
inference(avatar_split_clause,[],[f615,f2072]) ).
fof(f2072,plain,
( spl81_146
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_146])]) ).
fof(f615,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f395]) ).
fof(f395,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK24(X0,X1),X1)
& in(sK24(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f228,f394]) ).
fof(f394,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK24(X0,X1),X1)
& in(sK24(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f2070,plain,
spl81_145,
inference(avatar_split_clause,[],[f610,f2068]) ).
fof(f2068,plain,
( spl81_145
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_145])]) ).
fof(f610,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f150]) ).
fof(f150,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f2066,plain,
spl81_144,
inference(avatar_split_clause,[],[f609,f2064]) ).
fof(f609,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f144]) ).
fof(f144,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f2062,plain,
spl81_143,
inference(avatar_split_clause,[],[f604,f2060]) ).
fof(f2060,plain,
( spl81_143
<=> ! [X2,X0] :
( in(powerset(X2),sK22(X0))
| ~ in(X2,sK22(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_143])]) ).
fof(f604,plain,
! [X2,X0] :
( in(powerset(X2),sK22(X0))
| ~ in(X2,sK22(X0)) ),
inference(cnf_transformation,[],[f391]) ).
fof(f2056,plain,
spl81_142,
inference(avatar_split_clause,[],[f590,f2054]) ).
fof(f590,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(flattening,[],[f209]) ).
fof(f209,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,axiom,
! [X0] :
( relation(X0)
=> ( ( empty_set = relation_rng(X0)
| empty_set = relation_dom(X0) )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f2050,plain,
spl81_141,
inference(avatar_split_clause,[],[f589,f2048]) ).
fof(f589,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f2046,plain,
spl81_140,
inference(avatar_split_clause,[],[f586,f2044]) ).
fof(f2044,plain,
( spl81_140
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_140])]) ).
fof(f586,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f2042,plain,
( ~ spl81_138
| spl81_139
| ~ spl81_45
| ~ spl81_120 ),
inference(avatar_split_clause,[],[f1958,f1842,f1294,f2039,f2035]) ).
fof(f1294,plain,
( spl81_45
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_45])]) ).
fof(f1958,plain,
( relation(relation_rng(sK19))
| ~ empty(relation_inverse(sK19))
| ~ spl81_45
| ~ spl81_120 ),
inference(superposition,[],[f1295,f1844]) ).
fof(f1295,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl81_45 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f1983,plain,
spl81_137,
inference(avatar_split_clause,[],[f1060,f1981]) ).
fof(f1981,plain,
( spl81_137
<=> ! [X1] :
( sP6(X1,identity_relation(X1))
| ~ sP7(identity_relation(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_137])]) ).
fof(f1060,plain,
! [X1] :
( sP6(X1,identity_relation(X1))
| ~ sP7(identity_relation(X1),X1) ),
inference(equality_resolution,[],[f800]) ).
fof(f800,plain,
! [X0,X1] :
( sP6(X1,X0)
| identity_relation(X1) != X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f1979,plain,
spl81_136,
inference(avatar_split_clause,[],[f1055,f1977]) ).
fof(f1977,plain,
( spl81_136
<=> ! [X1] :
( sP4(X1,set_meet(X1))
| ~ sP5(set_meet(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_136])]) ).
fof(f1055,plain,
! [X1] :
( sP4(X1,set_meet(X1))
| ~ sP5(set_meet(X1),X1) ),
inference(equality_resolution,[],[f785]) ).
fof(f785,plain,
! [X0,X1] :
( sP4(X1,X0)
| set_meet(X1) != X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f481]) ).
fof(f1975,plain,
spl81_135,
inference(avatar_split_clause,[],[f858,f1973]) ).
fof(f1973,plain,
( spl81_135
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK62(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_135])]) ).
fof(f858,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK62(X0,X1),X1) ),
inference(cnf_transformation,[],[f519]) ).
fof(f1971,plain,
spl81_134,
inference(avatar_split_clause,[],[f857,f1969]) ).
fof(f1969,plain,
( spl81_134
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK62(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_134])]) ).
fof(f857,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK62(X0,X1),X0) ),
inference(cnf_transformation,[],[f519]) ).
fof(f1967,plain,
spl81_133,
inference(avatar_split_clause,[],[f847,f1965]) ).
fof(f1965,plain,
( spl81_133
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_133])]) ).
fof(f847,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f339]) ).
fof(f339,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f1963,plain,
spl81_132,
inference(avatar_split_clause,[],[f846,f1961]) ).
fof(f1961,plain,
( spl81_132
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_132])]) ).
fof(f846,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1956,plain,
spl81_131,
inference(avatar_split_clause,[],[f845,f1954]) ).
fof(f1954,plain,
( spl81_131
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_131])]) ).
fof(f845,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f337]) ).
fof(f337,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f1952,plain,
spl81_130,
inference(avatar_split_clause,[],[f844,f1950]) ).
fof(f1950,plain,
( spl81_130
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_130])]) ).
fof(f844,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f1948,plain,
spl81_129,
inference(avatar_split_clause,[],[f843,f1946]) ).
fof(f1946,plain,
( spl81_129
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_129])]) ).
fof(f843,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f335]) ).
fof(f335,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f1944,plain,
spl81_128,
inference(avatar_split_clause,[],[f841,f1942]) ).
fof(f1942,plain,
( spl81_128
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_128])]) ).
fof(f841,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f331]) ).
fof(f331,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f1940,plain,
spl81_127,
inference(avatar_split_clause,[],[f840,f1938]) ).
fof(f1938,plain,
( spl81_127
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_127])]) ).
fof(f840,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f329]) ).
fof(f329,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f1936,plain,
spl81_126,
inference(avatar_split_clause,[],[f817,f1934]) ).
fof(f1934,plain,
( spl81_126
<=> ! [X2,X0,X1] :
( sP9(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_126])]) ).
fof(f817,plain,
! [X2,X0,X1] :
( sP9(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0,X1] :
( ! [X2] :
( sP9(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f312,f367,f366]) ).
fof(f312,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f1932,plain,
spl81_125,
inference(avatar_split_clause,[],[f781,f1930]) ).
fof(f1930,plain,
( spl81_125
<=> ! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_125])]) ).
fof(f781,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f479,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f1928,plain,
spl81_124,
inference(avatar_split_clause,[],[f750,f1926]) ).
fof(f1926,plain,
( spl81_124
<=> ! [X2,X0,X1] :
( sP3(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_124])]) ).
fof(f750,plain,
! [X2,X0,X1] :
( sP3(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1,X2] :
( sP3(X2,X1,X0)
| ~ relation(X2) )
| ~ relation(X0) ),
inference(definition_folding,[],[f293,f358,f357]) ).
fof(f293,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f1907,plain,
( spl81_123
| ~ spl81_1
| ~ spl81_103 ),
inference(avatar_split_clause,[],[f1800,f1692,f1099,f1904]) ).
fof(f1904,plain,
( spl81_123
<=> relation_dom(sK19) = relation_rng(relation_inverse(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_123])]) ).
fof(f1692,plain,
( spl81_103
<=> ! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_103])]) ).
fof(f1800,plain,
( relation_dom(sK19) = relation_rng(relation_inverse(sK19))
| ~ spl81_1
| ~ spl81_103 ),
inference(resolution,[],[f1693,f1101]) ).
fof(f1693,plain,
( ! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ spl81_103 ),
inference(avatar_component_clause,[],[f1692]) ).
fof(f1862,plain,
( spl81_122
| ~ spl81_52
| ~ spl81_112 ),
inference(avatar_split_clause,[],[f1733,f1730,f1345,f1860]) ).
fof(f1730,plain,
( spl81_112
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_112])]) ).
fof(f1733,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK78
| ~ subset(X0,X1) )
| ~ spl81_52
| ~ spl81_112 ),
inference(forward_demodulation,[],[f1731,f1347]) ).
fof(f1731,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl81_112 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f1858,plain,
( spl81_121
| ~ spl81_52
| ~ spl81_111 ),
inference(avatar_split_clause,[],[f1728,f1725,f1345,f1856]) ).
fof(f1856,plain,
( spl81_121
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK78
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_121])]) ).
fof(f1725,plain,
( spl81_111
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_111])]) ).
fof(f1728,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK78
| subset(X0,X1) )
| ~ spl81_52
| ~ spl81_111 ),
inference(forward_demodulation,[],[f1726,f1347]) ).
fof(f1726,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl81_111 ),
inference(avatar_component_clause,[],[f1725]) ).
fof(f1845,plain,
( spl81_120
| ~ spl81_1
| ~ spl81_102 ),
inference(avatar_split_clause,[],[f1779,f1688,f1099,f1842]) ).
fof(f1688,plain,
( spl81_102
<=> ! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_102])]) ).
fof(f1779,plain,
( relation_rng(sK19) = relation_dom(relation_inverse(sK19))
| ~ spl81_1
| ~ spl81_102 ),
inference(resolution,[],[f1689,f1101]) ).
fof(f1689,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ spl81_102 ),
inference(avatar_component_clause,[],[f1688]) ).
fof(f1771,plain,
spl81_119,
inference(avatar_split_clause,[],[f1077,f1769]) ).
fof(f1077,plain,
! [X0,X1] : sP15(X1,X0,set_difference(X0,set_difference(X0,X1))),
inference(equality_resolution,[],[f1039]) ).
fof(f1039,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f906,f608]) ).
fof(f906,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f554]) ).
fof(f1767,plain,
spl81_118,
inference(avatar_split_clause,[],[f1069,f1765]) ).
fof(f1765,plain,
( spl81_118
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_118])]) ).
fof(f1069,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f1033]) ).
fof(f1033,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f867,f583]) ).
fof(f867,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f530]) ).
fof(f1763,plain,
spl81_117,
inference(avatar_split_clause,[],[f956,f1761]) ).
fof(f1761,plain,
( spl81_117
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_117])]) ).
fof(f956,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f658,f583]) ).
fof(f658,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f254]) ).
fof(f254,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f1749,plain,
spl81_116,
inference(avatar_split_clause,[],[f950,f1747]) ).
fof(f1747,plain,
( spl81_116
<=> ! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_116])]) ).
fof(f950,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f648,f583]) ).
fof(f648,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f404]) ).
fof(f404,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f1745,plain,
spl81_115,
inference(avatar_split_clause,[],[f939,f1743]) ).
fof(f1743,plain,
( spl81_115
<=> ! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_115])]) ).
fof(f939,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f622,f583]) ).
fof(f622,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f1741,plain,
spl81_114,
inference(avatar_split_clause,[],[f682,f1739]) ).
fof(f1739,plain,
( spl81_114
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_114])]) ).
fof(f682,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f414]) ).
fof(f1737,plain,
spl81_113,
inference(avatar_split_clause,[],[f681,f1735]) ).
fof(f1735,plain,
( spl81_113
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_113])]) ).
fof(f681,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f414]) ).
fof(f1732,plain,
spl81_112,
inference(avatar_split_clause,[],[f652,f1730]) ).
fof(f652,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f406]) ).
fof(f406,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f1727,plain,
spl81_111,
inference(avatar_split_clause,[],[f651,f1725]) ).
fof(f651,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f406]) ).
fof(f1723,plain,
spl81_110,
inference(avatar_split_clause,[],[f640,f1721]) ).
fof(f1721,plain,
( spl81_110
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_110])]) ).
fof(f640,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f399]) ).
fof(f399,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f182]) ).
fof(f182,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f1719,plain,
spl81_109,
inference(avatar_split_clause,[],[f639,f1717]) ).
fof(f1717,plain,
( spl81_109
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_109])]) ).
fof(f639,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f399]) ).
fof(f1715,plain,
spl81_108,
inference(avatar_split_clause,[],[f628,f1713]) ).
fof(f628,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f1711,plain,
spl81_107,
inference(avatar_split_clause,[],[f618,f1709]) ).
fof(f1709,plain,
( spl81_107
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_107])]) ).
fof(f618,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f1707,plain,
( spl81_106
| ~ spl81_6
| ~ spl81_9
| ~ spl81_42 ),
inference(avatar_split_clause,[],[f1328,f1282,f1139,f1124,f1704]) ).
fof(f1704,plain,
( spl81_106
<=> sK78 = sK80 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_106])]) ).
fof(f1124,plain,
( spl81_6
<=> empty(sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_6])]) ).
fof(f1139,plain,
( spl81_9
<=> empty(sK80) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_9])]) ).
fof(f1282,plain,
( spl81_42
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_42])]) ).
fof(f1328,plain,
( sK78 = sK80
| ~ spl81_6
| ~ spl81_9
| ~ spl81_42 ),
inference(forward_demodulation,[],[f1327,f1326]) ).
fof(f1326,plain,
( empty_set = sK78
| ~ spl81_6
| ~ spl81_42 ),
inference(resolution,[],[f1283,f1126]) ).
fof(f1126,plain,
( empty(sK78)
| ~ spl81_6 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f1283,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl81_42 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f1327,plain,
( empty_set = sK80
| ~ spl81_9
| ~ spl81_42 ),
inference(resolution,[],[f1283,f1141]) ).
fof(f1141,plain,
( empty(sK80)
| ~ spl81_9 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1702,plain,
spl81_105,
inference(avatar_split_clause,[],[f614,f1700]) ).
fof(f614,plain,
! [X0,X1] :
( in(sK24(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
fof(f1698,plain,
spl81_104,
inference(avatar_split_clause,[],[f613,f1696]) ).
fof(f613,plain,
! [X0,X1] :
( in(sK24(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
fof(f1694,plain,
spl81_103,
inference(avatar_split_clause,[],[f588,f1692]) ).
fof(f588,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f140]) ).
fof(f140,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f1690,plain,
spl81_102,
inference(avatar_split_clause,[],[f587,f1688]) ).
fof(f587,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1630,plain,
( spl81_101
| ~ spl81_52
| ~ spl81_87 ),
inference(avatar_split_clause,[],[f1549,f1546,f1345,f1628]) ).
fof(f1628,plain,
( spl81_101
<=> ! [X0] :
( sK78 = X0
| in(sK48(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_101])]) ).
fof(f1546,plain,
( spl81_87
<=> ! [X0] :
( empty_set = X0
| in(sK48(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_87])]) ).
fof(f1549,plain,
( ! [X0] :
( sK78 = X0
| in(sK48(X0),X0) )
| ~ spl81_52
| ~ spl81_87 ),
inference(forward_demodulation,[],[f1547,f1347]) ).
fof(f1547,plain,
( ! [X0] :
( empty_set = X0
| in(sK48(X0),X0) )
| ~ spl81_87 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f1620,plain,
( spl81_100
| ~ spl81_1
| ~ spl81_84 ),
inference(avatar_split_clause,[],[f1607,f1534,f1099,f1617]) ).
fof(f1617,plain,
( spl81_100
<=> sK19 = relation_inverse(relation_inverse(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_100])]) ).
fof(f1534,plain,
( spl81_84
<=> ! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_84])]) ).
fof(f1607,plain,
( sK19 = relation_inverse(relation_inverse(sK19))
| ~ spl81_1
| ~ spl81_84 ),
inference(resolution,[],[f1535,f1101]) ).
fof(f1535,plain,
( ! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 )
| ~ spl81_84 ),
inference(avatar_component_clause,[],[f1534]) ).
fof(f1599,plain,
spl81_99,
inference(avatar_split_clause,[],[f1075,f1597]) ).
fof(f1597,plain,
( spl81_99
<=> ! [X2,X0,X4] :
( in(X4,X2)
| ~ sP14(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_99])]) ).
fof(f1075,plain,
! [X2,X0,X4] :
( in(X4,X2)
| ~ sP14(X0,X4,X2) ),
inference(equality_resolution,[],[f893]) ).
fof(f893,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f1595,plain,
spl81_98,
inference(avatar_split_clause,[],[f1074,f1593]) ).
fof(f1593,plain,
( spl81_98
<=> ! [X2,X1,X4] :
( in(X4,X2)
| ~ sP14(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_98])]) ).
fof(f1074,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ sP14(X4,X1,X2) ),
inference(equality_resolution,[],[f894]) ).
fof(f894,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f1591,plain,
spl81_97,
inference(avatar_split_clause,[],[f1071,f1589]) ).
fof(f1589,plain,
( spl81_97
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_97])]) ).
fof(f1071,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f871]) ).
fof(f871,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f534]) ).
fof(f1587,plain,
spl81_96,
inference(avatar_split_clause,[],[f1070,f1585]) ).
fof(f1585,plain,
( spl81_96
<=> ! [X0,X3] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_96])]) ).
fof(f1070,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f872]) ).
fof(f872,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f534]) ).
fof(f1583,plain,
spl81_95,
inference(avatar_split_clause,[],[f877,f1581]) ).
fof(f1581,plain,
( spl81_95
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_95])]) ).
fof(f877,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f1579,plain,
spl81_94,
inference(avatar_split_clause,[],[f876,f1577]) ).
fof(f1577,plain,
( spl81_94
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_94])]) ).
fof(f876,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f535]) ).
fof(f535,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f147,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f1575,plain,
spl81_93,
inference(avatar_split_clause,[],[f875,f1573]) ).
fof(f1573,plain,
( spl81_93
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_93])]) ).
fof(f875,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f535]) ).
fof(f1571,plain,
spl81_92,
inference(avatar_split_clause,[],[f866,f1569]) ).
fof(f1569,plain,
( spl81_92
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_92])]) ).
fof(f866,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f526]) ).
fof(f526,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP12(X0,X1) )
& ( sP12(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP12(X0,X1) ),
inference(definition_folding,[],[f26,f372]) ).
fof(f26,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f1565,plain,
spl81_91,
inference(avatar_split_clause,[],[f784,f1563]) ).
fof(f1563,plain,
( spl81_91
<=> ! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_91])]) ).
fof(f784,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f1561,plain,
spl81_90,
inference(avatar_split_clause,[],[f783,f1559]) ).
fof(f1559,plain,
( spl81_90
<=> ! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_90])]) ).
fof(f783,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f1557,plain,
spl81_89,
inference(avatar_split_clause,[],[f779,f1555]) ).
fof(f779,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1553,plain,
spl81_88,
inference(avatar_split_clause,[],[f777,f1551]) ).
fof(f1548,plain,
spl81_87,
inference(avatar_split_clause,[],[f763,f1546]) ).
fof(f763,plain,
! [X0] :
( empty_set = X0
| in(sK48(X0),X0) ),
inference(cnf_transformation,[],[f470]) ).
fof(f470,plain,
! [X0] :
( ( empty_set = X0
| in(sK48(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f468,f469]) ).
fof(f469,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK48(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f468,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f467]) ).
fof(f467,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f1544,plain,
spl81_86,
inference(avatar_split_clause,[],[f758,f1542]) ).
fof(f1542,plain,
( spl81_86
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_86])]) ).
fof(f758,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f1540,plain,
spl81_85,
inference(avatar_split_clause,[],[f757,f1538]) ).
fof(f757,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f1536,plain,
spl81_84,
inference(avatar_split_clause,[],[f712,f1534]) ).
fof(f712,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f1532,plain,
spl81_83,
inference(avatar_split_clause,[],[f709,f1530]) ).
fof(f1530,plain,
( spl81_83
<=> ! [X0] :
( element(sK26(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_83])]) ).
fof(f709,plain,
! [X0] :
( element(sK26(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f422]) ).
fof(f422,plain,
! [X0] :
( ( ~ empty(sK26(X0))
& element(sK26(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f283,f421]) ).
fof(f421,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK26(X0))
& element(sK26(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f283,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f1526,plain,
( spl81_82
| ~ spl81_34
| ~ spl81_79 ),
inference(avatar_split_clause,[],[f1505,f1499,f1249,f1524]) ).
fof(f1524,plain,
( spl81_82
<=> ! [X0] : subset(sK78,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_82])]) ).
fof(f1505,plain,
( ! [X0] : subset(sK78,X0)
| ~ spl81_34
| ~ spl81_79 ),
inference(superposition,[],[f1250,f1500]) ).
fof(f1516,plain,
( spl81_81
| ~ spl81_79
| ~ spl81_80 ),
inference(avatar_split_clause,[],[f1512,f1509,f1499,f1514]) ).
fof(f1509,plain,
( spl81_80
<=> ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_80])]) ).
fof(f1512,plain,
( ! [X0] : set_difference(X0,sK78) = X0
| ~ spl81_79
| ~ spl81_80 ),
inference(forward_demodulation,[],[f1510,f1500]) ).
fof(f1510,plain,
( ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0
| ~ spl81_80 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f1511,plain,
spl81_80,
inference(avatar_split_clause,[],[f1013,f1509]) ).
fof(f1013,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f775,f608]) ).
fof(f775,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f1501,plain,
( spl81_79
| ~ spl81_39
| ~ spl81_52
| ~ spl81_78 ),
inference(avatar_split_clause,[],[f1497,f1493,f1345,f1270,f1499]) ).
fof(f1493,plain,
( spl81_78
<=> ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_78])]) ).
fof(f1497,plain,
( ! [X0] : sK78 = set_difference(X0,X0)
| ~ spl81_39
| ~ spl81_52
| ~ spl81_78 ),
inference(forward_demodulation,[],[f1496,f1347]) ).
fof(f1496,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl81_39
| ~ spl81_78 ),
inference(forward_demodulation,[],[f1494,f1271]) ).
fof(f1494,plain,
( ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set))
| ~ spl81_78 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f1495,plain,
spl81_78,
inference(avatar_split_clause,[],[f978,f1493]) ).
fof(f978,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f704,f608]) ).
fof(f704,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f132]) ).
fof(f132,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f1491,plain,
spl81_77,
inference(avatar_split_clause,[],[f623,f1489]) ).
fof(f1489,plain,
( spl81_77
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_77])]) ).
fof(f623,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f1487,plain,
spl81_76,
inference(avatar_split_clause,[],[f617,f1485]) ).
fof(f1485,plain,
( spl81_76
<=> ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_76])]) ).
fof(f617,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f184]) ).
fof(f184,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f1483,plain,
spl81_75,
inference(avatar_split_clause,[],[f616,f1481]) ).
fof(f616,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f1459,plain,
( spl81_74
| ~ spl81_52
| ~ spl81_60 ),
inference(avatar_split_clause,[],[f1401,f1398,f1345,f1457]) ).
fof(f1457,plain,
( spl81_74
<=> ! [X0,X1] :
( sK78 = X0
| sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_74])]) ).
fof(f1398,plain,
( spl81_60
<=> ! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_60])]) ).
fof(f1401,plain,
( ! [X0,X1] :
( sK78 = X0
| sP5(X1,X0) )
| ~ spl81_52
| ~ spl81_60 ),
inference(forward_demodulation,[],[f1399,f1347]) ).
fof(f1399,plain,
( ! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 )
| ~ spl81_60 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1453,plain,
spl81_73,
inference(avatar_split_clause,[],[f1079,f1451]) ).
fof(f1079,plain,
! [X0,X1] : sP17(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f922]) ).
fof(f922,plain,
! [X2,X0,X1] :
( sP17(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f566]) ).
fof(f1449,plain,
spl81_72,
inference(avatar_split_clause,[],[f1078,f1447]) ).
fof(f1078,plain,
! [X0,X1] : sP16(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f914]) ).
fof(f914,plain,
! [X2,X0,X1] :
( sP16(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f560]) ).
fof(f1445,plain,
spl81_71,
inference(avatar_split_clause,[],[f1076,f1443]) ).
fof(f1443,plain,
( spl81_71
<=> ! [X0,X1] : sP14(X1,X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_71])]) ).
fof(f1076,plain,
! [X0,X1] : sP14(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f898]) ).
fof(f898,plain,
! [X2,X0,X1] :
( sP14(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f548]) ).
fof(f1441,plain,
spl81_70,
inference(avatar_split_clause,[],[f1073,f1439]) ).
fof(f1439,plain,
( spl81_70
<=> ! [X0,X1] : sP13(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_70])]) ).
fof(f1073,plain,
! [X0,X1] : sP13(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f890]) ).
fof(f890,plain,
! [X2,X0,X1] :
( sP13(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f542]) ).
fof(f1437,plain,
( spl81_69
| ~ spl81_11
| ~ spl81_52
| ~ spl81_54 ),
inference(avatar_split_clause,[],[f1376,f1359,f1345,f1149,f1435]) ).
fof(f1435,plain,
( spl81_69
<=> ! [X0] : ~ proper_subset(X0,sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_69])]) ).
fof(f1149,plain,
( spl81_11
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_11])]) ).
fof(f1376,plain,
( ! [X0] : ~ proper_subset(X0,sK78)
| ~ spl81_11
| ~ spl81_52
| ~ spl81_54 ),
inference(forward_demodulation,[],[f1372,f1347]) ).
fof(f1372,plain,
( ! [X0] : ~ proper_subset(X0,empty_set)
| ~ spl81_11
| ~ spl81_54 ),
inference(resolution,[],[f1360,f1150]) ).
fof(f1150,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl81_11 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1433,plain,
spl81_68,
inference(avatar_split_clause,[],[f822,f1431]) ).
fof(f822,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f1429,plain,
spl81_67,
inference(avatar_split_clause,[],[f821,f1427]) ).
fof(f821,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f317]) ).
fof(f317,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1425,plain,
spl81_66,
inference(avatar_split_clause,[],[f819,f1423]) ).
fof(f1423,plain,
( spl81_66
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_66])]) ).
fof(f819,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f1421,plain,
spl81_65,
inference(avatar_split_clause,[],[f818,f1419]) ).
fof(f1419,plain,
( spl81_65
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_65])]) ).
fof(f818,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f1417,plain,
spl81_64,
inference(avatar_split_clause,[],[f799,f1415]) ).
fof(f1415,plain,
( spl81_64
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_64])]) ).
fof(f799,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f1413,plain,
spl81_63,
inference(avatar_split_clause,[],[f798,f1411]) ).
fof(f798,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f1409,plain,
spl81_62,
inference(avatar_split_clause,[],[f797,f1407]) ).
fof(f1407,plain,
( spl81_62
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_62])]) ).
fof(f797,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f308]) ).
fof(f308,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f1405,plain,
spl81_61,
inference(avatar_split_clause,[],[f796,f1403]) ).
fof(f796,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f1400,plain,
spl81_60,
inference(avatar_split_clause,[],[f793,f1398]) ).
fof(f793,plain,
! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f488]) ).
fof(f488,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP5(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP5(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f306,f361,f360]) ).
fof(f306,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f1396,plain,
spl81_59,
inference(avatar_split_clause,[],[f760,f1394]) ).
fof(f1394,plain,
( spl81_59
<=> ! [X0] :
( relation(X0)
| in(sK45(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_59])]) ).
fof(f760,plain,
! [X0] :
( relation(X0)
| in(sK45(X0),X0) ),
inference(cnf_transformation,[],[f466]) ).
fof(f1392,plain,
( spl81_58
| ~ spl81_20
| ~ spl81_51 ),
inference(avatar_split_clause,[],[f1349,f1318,f1187,f1390]) ).
fof(f1390,plain,
( spl81_58
<=> ! [X0] : ~ empty(sK22(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_58])]) ).
fof(f1349,plain,
( ! [X0] : ~ empty(sK22(X0))
| ~ spl81_20
| ~ spl81_51 ),
inference(resolution,[],[f1319,f1188]) ).
fof(f1381,plain,
( spl81_57
| ~ spl81_52
| ~ spl81_55 ),
inference(avatar_split_clause,[],[f1367,f1363,f1345,f1378]) ).
fof(f1363,plain,
( spl81_55
<=> powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_55])]) ).
fof(f1367,plain,
( powerset(sK78) = unordered_pair(sK78,sK78)
| ~ spl81_52
| ~ spl81_55 ),
inference(forward_demodulation,[],[f1365,f1347]) ).
fof(f1365,plain,
( powerset(empty_set) = unordered_pair(empty_set,empty_set)
| ~ spl81_55 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f1371,plain,
( spl81_56
| ~ spl81_52
| ~ spl81_53 ),
inference(avatar_split_clause,[],[f1357,f1353,f1345,f1369]) ).
fof(f1369,plain,
( spl81_56
<=> ! [X0] :
( ~ subset(X0,sK78)
| sK78 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_56])]) ).
fof(f1353,plain,
( spl81_53
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_53])]) ).
fof(f1357,plain,
( ! [X0] :
( ~ subset(X0,sK78)
| sK78 = X0 )
| ~ spl81_52
| ~ spl81_53 ),
inference(forward_demodulation,[],[f1356,f1347]) ).
fof(f1356,plain,
( ! [X0] :
( sK78 = X0
| ~ subset(X0,empty_set) )
| ~ spl81_52
| ~ spl81_53 ),
inference(forward_demodulation,[],[f1354,f1347]) ).
fof(f1354,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl81_53 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f1366,plain,
spl81_55,
inference(avatar_split_clause,[],[f932,f1363]) ).
fof(f932,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f577,f583]) ).
fof(f577,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f126]) ).
fof(f126,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f1361,plain,
spl81_54,
inference(avatar_split_clause,[],[f657,f1359]) ).
fof(f657,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f1355,plain,
spl81_53,
inference(avatar_split_clause,[],[f601,f1353]) ).
fof(f601,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f149]) ).
fof(f149,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f1348,plain,
( spl81_52
| ~ spl81_6
| ~ spl81_42 ),
inference(avatar_split_clause,[],[f1326,f1282,f1124,f1345]) ).
fof(f1320,plain,
spl81_51,
inference(avatar_split_clause,[],[f878,f1318]) ).
fof(f878,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f1316,plain,
spl81_50,
inference(avatar_split_clause,[],[f808,f1314]) ).
fof(f1314,plain,
( spl81_50
<=> ! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_50])]) ).
fof(f808,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f311,f364,f363]) ).
fof(f311,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f1312,plain,
spl81_49,
inference(avatar_split_clause,[],[f776,f1310]) ).
fof(f1310,plain,
( spl81_49
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_49])]) ).
fof(f776,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f1308,plain,
spl81_48,
inference(avatar_split_clause,[],[f769,f1306]) ).
fof(f1306,plain,
( spl81_48
<=> ! [X0] : element(sK52(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_48])]) ).
fof(f769,plain,
! [X0] : element(sK52(X0),powerset(X0)),
inference(cnf_transformation,[],[f478]) ).
fof(f478,plain,
! [X0] :
( empty(sK52(X0))
& element(sK52(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f103,f477]) ).
fof(f477,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK52(X0))
& element(sK52(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f1304,plain,
spl81_47,
inference(avatar_split_clause,[],[f756,f1302]) ).
fof(f756,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f1300,plain,
spl81_46,
inference(avatar_split_clause,[],[f755,f1298]) ).
fof(f1298,plain,
( spl81_46
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_46])]) ).
fof(f755,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f1296,plain,
spl81_45,
inference(avatar_split_clause,[],[f754,f1294]) ).
fof(f754,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f1292,plain,
spl81_44,
inference(avatar_split_clause,[],[f753,f1290]) ).
fof(f1290,plain,
( spl81_44
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_44])]) ).
fof(f753,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f1288,plain,
( spl81_43
| ~ spl81_14
| ~ spl81_22 ),
inference(avatar_split_clause,[],[f1224,f1195,f1161,f1286]) ).
fof(f1286,plain,
( spl81_43
<=> ! [X0] : relation(sK52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_43])]) ).
fof(f1161,plain,
( spl81_14
<=> ! [X0] : empty(sK52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_14])]) ).
fof(f1195,plain,
( spl81_22
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_22])]) ).
fof(f1224,plain,
( ! [X0] : relation(sK52(X0))
| ~ spl81_14
| ~ spl81_22 ),
inference(resolution,[],[f1196,f1162]) ).
fof(f1162,plain,
( ! [X0] : empty(sK52(X0))
| ~ spl81_14 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f1196,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl81_22 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1284,plain,
spl81_42,
inference(avatar_split_clause,[],[f752,f1282]) ).
fof(f752,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f1280,plain,
spl81_41,
inference(avatar_split_clause,[],[f711,f1278]) ).
fof(f711,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f1276,plain,
spl81_40,
inference(avatar_split_clause,[],[f710,f1274]) ).
fof(f1274,plain,
( spl81_40
<=> ! [X0] :
( ~ empty(sK26(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_40])]) ).
fof(f710,plain,
! [X0] :
( ~ empty(sK26(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f422]) ).
fof(f1272,plain,
spl81_39,
inference(avatar_split_clause,[],[f707,f1270]) ).
fof(f707,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f146]) ).
fof(f146,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f1268,plain,
spl81_38,
inference(avatar_split_clause,[],[f706,f1266]) ).
fof(f706,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f1264,plain,
spl81_37,
inference(avatar_split_clause,[],[f705,f1262]) ).
fof(f705,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f162]) ).
fof(f162,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f1259,plain,
spl81_36,
inference(avatar_split_clause,[],[f1068,f1257]) ).
fof(f1068,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f1067]) ).
fof(f1067,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f1032]) ).
fof(f1032,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f868,f583]) ).
fof(f868,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f530]) ).
fof(f1255,plain,
spl81_35,
inference(avatar_split_clause,[],[f933,f1253]) ).
fof(f933,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f581,f583]) ).
fof(f581,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f1251,plain,
spl81_34,
inference(avatar_split_clause,[],[f607,f1249]) ).
fof(f607,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f139]) ).
fof(f139,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f1247,plain,
spl81_33,
inference(avatar_split_clause,[],[f605,f1245]) ).
fof(f605,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f181]) ).
fof(f181,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f1243,plain,
spl81_32,
inference(avatar_split_clause,[],[f585,f1241]) ).
fof(f1241,plain,
( spl81_32
<=> ! [X0] : relation_rng(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_32])]) ).
fof(f585,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f178]) ).
fof(f178,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f1239,plain,
spl81_31,
inference(avatar_split_clause,[],[f584,f1237]) ).
fof(f1237,plain,
( spl81_31
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl81_31])]) ).
fof(f584,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f178]) ).
fof(f1235,plain,
spl81_30,
inference(avatar_split_clause,[],[f582,f1233]) ).
fof(f582,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f192]) ).
fof(f192,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f1231,plain,
( spl81_29
| ~ spl81_6
| ~ spl81_22 ),
inference(avatar_split_clause,[],[f1225,f1195,f1124,f1228]) ).
fof(f1228,plain,
( spl81_29
<=> relation(sK78) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_29])]) ).
fof(f1225,plain,
( relation(sK78)
| ~ spl81_6
| ~ spl81_22 ),
inference(resolution,[],[f1196,f1126]) ).
fof(f1222,plain,
spl81_28,
inference(avatar_split_clause,[],[f1083,f1220]) ).
fof(f1220,plain,
( spl81_28
<=> ! [X0] : element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_28])]) ).
fof(f1083,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f708,f703]) ).
fof(f703,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f708,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f1218,plain,
spl81_27,
inference(avatar_split_clause,[],[f1066,f1216]) ).
fof(f1066,plain,
! [X0] : sP12(X0,union(X0)),
inference(equality_resolution,[],[f865]) ).
fof(f865,plain,
! [X0,X1] :
( sP12(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f526]) ).
fof(f1214,plain,
spl81_26,
inference(avatar_split_clause,[],[f1057,f1211]) ).
fof(f1211,plain,
( spl81_26
<=> empty_set = set_meet(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_26])]) ).
fof(f1057,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f1056]) ).
fof(f1056,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f795]) ).
fof(f795,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f488]) ).
fof(f1209,plain,
spl81_25,
inference(avatar_split_clause,[],[f773,f1207]) ).
fof(f1207,plain,
( spl81_25
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_25])]) ).
fof(f773,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f1205,plain,
spl81_24,
inference(avatar_split_clause,[],[f765,f1203]) ).
fof(f765,plain,
! [X0] : in(X0,sK50(X0)),
inference(cnf_transformation,[],[f476]) ).
fof(f1201,plain,
spl81_23,
inference(avatar_split_clause,[],[f764,f1199]) ).
fof(f1199,plain,
( spl81_23
<=> ! [X0] : element(sK49(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_23])]) ).
fof(f764,plain,
! [X0] : element(sK49(X0),X0),
inference(cnf_transformation,[],[f472]) ).
fof(f472,plain,
! [X0] : element(sK49(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f63,f471]) ).
fof(f471,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK49(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f63,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f1197,plain,
spl81_22,
inference(avatar_split_clause,[],[f751,f1195]) ).
fof(f751,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f1193,plain,
spl81_21,
inference(avatar_split_clause,[],[f703,f1191]) ).
fof(f1189,plain,
spl81_20,
inference(avatar_split_clause,[],[f602,f1187]) ).
fof(f602,plain,
! [X0] : in(X0,sK22(X0)),
inference(cnf_transformation,[],[f391]) ).
fof(f1185,plain,
spl81_19,
inference(avatar_split_clause,[],[f579,f1182]) ).
fof(f1182,plain,
( spl81_19
<=> empty_set = relation_rng(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_19])]) ).
fof(f579,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f169]) ).
fof(f169,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f1180,plain,
spl81_18,
inference(avatar_split_clause,[],[f578,f1177]) ).
fof(f1177,plain,
( spl81_18
<=> empty_set = relation_dom(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_18])]) ).
fof(f578,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f169]) ).
fof(f1175,plain,
spl81_17,
inference(avatar_split_clause,[],[f1054,f1173]) ).
fof(f1054,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f762]) ).
fof(f762,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f470]) ).
fof(f1171,plain,
spl81_16,
inference(avatar_split_clause,[],[f772,f1169]) ).
fof(f1169,plain,
( spl81_16
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_16])]) ).
fof(f772,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f1167,plain,
spl81_15,
inference(avatar_split_clause,[],[f771,f1165]) ).
fof(f1165,plain,
( spl81_15
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_15])]) ).
fof(f771,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f1163,plain,
spl81_14,
inference(avatar_split_clause,[],[f770,f1161]) ).
fof(f770,plain,
! [X0] : empty(sK52(X0)),
inference(cnf_transformation,[],[f478]) ).
fof(f1159,plain,
spl81_13,
inference(avatar_split_clause,[],[f702,f1157]) ).
fof(f1157,plain,
( spl81_13
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_13])]) ).
fof(f702,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f1155,plain,
spl81_12,
inference(avatar_split_clause,[],[f701,f1153]) ).
fof(f1153,plain,
( spl81_12
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_12])]) ).
fof(f701,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f1151,plain,
spl81_11,
inference(avatar_split_clause,[],[f580,f1149]) ).
fof(f580,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f135]) ).
fof(f135,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f1147,plain,
spl81_10,
inference(avatar_split_clause,[],[f930,f1144]) ).
fof(f1144,plain,
( spl81_10
<=> relation(sK80) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_10])]) ).
fof(f930,plain,
relation(sK80),
inference(cnf_transformation,[],[f574]) ).
fof(f574,plain,
( relation(sK80)
& empty(sK80) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f99,f573]) ).
fof(f573,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK80)
& empty(sK80) ) ),
introduced(choice_axiom,[]) ).
fof(f99,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f1142,plain,
spl81_9,
inference(avatar_split_clause,[],[f929,f1139]) ).
fof(f929,plain,
empty(sK80),
inference(cnf_transformation,[],[f574]) ).
fof(f1137,plain,
spl81_8,
inference(avatar_split_clause,[],[f928,f1134]) ).
fof(f1134,plain,
( spl81_8
<=> relation(sK79) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_8])]) ).
fof(f928,plain,
relation(sK79),
inference(cnf_transformation,[],[f572]) ).
fof(f572,plain,
( relation(sK79)
& ~ empty(sK79) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f102,f571]) ).
fof(f571,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK79)
& ~ empty(sK79) ) ),
introduced(choice_axiom,[]) ).
fof(f102,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f1132,plain,
~ spl81_7,
inference(avatar_split_clause,[],[f927,f1129]) ).
fof(f1129,plain,
( spl81_7
<=> empty(sK79) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_7])]) ).
fof(f927,plain,
~ empty(sK79),
inference(cnf_transformation,[],[f572]) ).
fof(f1127,plain,
spl81_6,
inference(avatar_split_clause,[],[f926,f1124]) ).
fof(f926,plain,
empty(sK78),
inference(cnf_transformation,[],[f570]) ).
fof(f570,plain,
empty(sK78),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f101,f569]) ).
fof(f569,plain,
( ? [X0] : empty(X0)
=> empty(sK78) ),
introduced(choice_axiom,[]) ).
fof(f101,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f1122,plain,
~ spl81_5,
inference(avatar_split_clause,[],[f925,f1119]) ).
fof(f1119,plain,
( spl81_5
<=> empty(sK77) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_5])]) ).
fof(f925,plain,
~ empty(sK77),
inference(cnf_transformation,[],[f568]) ).
fof(f568,plain,
~ empty(sK77),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f104,f567]) ).
fof(f567,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK77) ),
introduced(choice_axiom,[]) ).
fof(f104,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f1117,plain,
spl81_4,
inference(avatar_split_clause,[],[f699,f1114]) ).
fof(f1114,plain,
( spl81_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_4])]) ).
fof(f699,plain,
relation(empty_set),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f1112,plain,
spl81_3,
inference(avatar_split_clause,[],[f697,f1109]) ).
fof(f1109,plain,
( spl81_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_3])]) ).
fof(f697,plain,
empty(empty_set),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f1107,plain,
~ spl81_2,
inference(avatar_split_clause,[],[f576,f1104]) ).
fof(f576,plain,
~ subset(relation_rng(relation_rng_restriction(sK18,sK19)),relation_rng(sK19)),
inference(cnf_transformation,[],[f385]) ).
fof(f385,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK18,sK19)),relation_rng(sK19))
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f206,f384]) ).
fof(f384,plain,
( ? [X0,X1] :
( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_rng(relation_rng_restriction(sK18,sK19)),relation_rng(sK19))
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f206,plain,
? [X0,X1] :
( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(negated_conjecture,[],[f115]) ).
fof(f115,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f1102,plain,
spl81_1,
inference(avatar_split_clause,[],[f575,f1099]) ).
fof(f575,plain,
relation(sK19),
inference(cnf_transformation,[],[f385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU200+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 12:25:45 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (2190)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (2193)WARNING: value z3 for option sas not known
% 0.15/0.38 % (2192)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (2191)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (2194)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (2193)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)
% 0.15/0.38 % (2195)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)
% 0.15/0.38 % (2196)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)
% 0.15/0.38 % (2197)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)
% 0.21/0.42 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.47 TRYING [3]
% 0.21/0.50 TRYING [1]
% 0.21/0.51 TRYING [2]
% 0.21/0.57 % (2195)First to succeed.
% 0.21/0.59 % (2195)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2190"
% 0.21/0.59 % (2195)Refutation found. Thanks to Tanya!
% 0.21/0.59 % SZS status Theorem for theBenchmark
% 0.21/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.60 % (2195)------------------------------
% 0.21/0.60 % (2195)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.60 % (2195)Termination reason: Refutation
% 0.21/0.60
% 0.21/0.60 % (2195)Memory used [KB]: 4688
% 0.21/0.60 % (2195)Time elapsed: 0.210 s
% 0.21/0.60 % (2195)Instructions burned: 441 (million)
% 0.21/0.60 % (2190)Success in time 0.241 s
%------------------------------------------------------------------------------