TSTP Solution File: SEU219+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU219+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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:24:32 EDT 2024
% Result : Theorem 1.98s 0.64s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 879
% Syntax : Number of formulae : 2808 ( 518 unt; 0 def)
% Number of atoms : 9405 (1300 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 11005 (4408 ~;4663 |; 921 &)
% ( 755 <=>; 257 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 626 ( 624 usr; 589 prp; 0-4 aty)
% Number of functors : 106 ( 106 usr; 10 con; 0-4 aty)
% Number of variables : 5114 (4823 !; 291 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9064,plain,
$false,
inference(avatar_sat_refutation,[],[f1376,f1381,f1386,f1391,f1396,f1401,f1406,f1411,f1416,f1421,f1426,f1431,f1436,f1441,f1446,f1451,f1456,f1461,f1466,f1471,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1508,f1512,f1517,f1522,f1526,f1530,f1534,f1538,f1542,f1546,f1550,f1554,f1558,f1563,f1567,f1571,f1581,f1608,f1613,f1617,f1621,f1625,f1629,f1633,f1637,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1748,f1758,f1764,f1769,f1774,f1784,f1790,f1801,f1805,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1860,f1867,f1890,f1899,f1903,f1907,f1911,f1917,f1927,f1932,f1937,f1949,f1953,f1957,f1961,f1965,f1969,f1974,f1979,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2021,f2025,f2029,f2033,f2064,f2069,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2167,f2171,f2175,f2179,f2183,f2188,f2193,f2197,f2201,f2205,f2209,f2213,f2217,f2311,f2315,f2348,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2459,f2463,f2467,f2557,f2566,f2570,f2574,f2580,f2586,f2590,f2594,f2599,f2603,f2607,f2611,f2615,f2619,f2623,f2627,f2631,f2677,f2681,f2685,f2780,f2784,f2788,f2792,f2796,f2801,f2806,f2810,f2814,f2818,f2822,f2874,f2890,f2896,f2902,f2906,f2910,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2943,f2947,f2951,f2955,f2960,f2965,f2969,f2974,f2979,f2983,f3054,f3167,f3176,f3214,f3218,f3222,f3227,f3231,f3236,f3240,f3244,f3248,f3252,f3256,f3260,f3264,f3268,f3272,f3276,f3281,f3285,f3312,f3349,f3353,f3357,f3361,f3366,f3370,f3374,f3378,f3382,f3386,f3550,f3554,f3558,f3562,f3566,f3570,f3575,f3579,f3583,f3587,f3591,f3595,f3599,f3603,f3607,f3611,f3615,f3686,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3822,f3859,f3863,f3867,f3871,f3875,f3879,f3883,f3887,f3892,f3896,f3936,f3940,f3944,f3950,f3954,f3958,f3962,f3966,f3971,f3975,f3980,f3984,f3988,f4018,f4101,f4154,f4158,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4235,f4239,f4243,f4247,f4251,f4255,f4260,f4264,f4271,f4391,f4414,f4421,f4425,f4429,f4433,f4437,f4441,f4445,f4449,f4453,f4685,f4689,f4693,f4697,f4701,f4781,f4785,f4789,f4794,f4825,f4829,f4833,f4837,f4841,f4845,f4849,f4853,f4857,f5016,f5020,f5024,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5256,f5260,f5719,f5723,f5727,f5733,f5768,f5796,f5803,f5808,f5814,f5818,f5823,f5827,f5832,f5836,f5883,f5934,f5991,f5995,f5999,f6065,f6070,f6074,f6080,f6084,f6088,f6093,f6097,f6119,f6141,f6202,f6206,f6258,f6264,f6286,f6293,f6315,f6320,f6350,f6354,f6358,f6397,f6421,f6425,f6429,f6433,f6585,f6589,f6593,f6597,f6699,f6714,f6734,f6739,f6744,f6748,f6759,f6763,f6803,f6833,f6837,f6842,f6846,f6850,f6855,f6859,f6910,f6948,f7029,f7033,f7038,f7081,f7118,f7131,f7163,f7168,f7173,f7177,f7181,f7185,f7261,f7265,f7270,f7274,f7279,f7284,f7307,f7325,f7329,f7362,f7450,f7454,f7458,f7463,f7467,f7518,f7524,f7530,f7534,f7613,f7619,f7625,f7629,f7702,f7708,f7714,f7720,f7724,f7728,f7732,f7958,f7964,f7968,f7998,f8003,f8020,f8033,f8037,f8074,f8089,f8093,f8097,f8203,f8207,f8211,f8215,f8219,f8246,f8251,f8256,f8261,f8265,f8270,f8275,f8280,f8284,f8305,f8309,f8314,f8319,f8323,f8327,f8331,f8335,f8339,f8343,f8376,f8421,f8443,f8448,f8452,f8456,f8460,f8464,f8468,f8472,f8484,f8509,f8513,f8517,f8521,f8525,f8529,f8533,f8538,f8542,f8546,f8550,f8554,f8558,f8562,f8566,f8713,f8717,f8721,f8725,f8730,f8734,f8738,f8742,f8746,f8750,f8754,f8758,f8763,f8768,f8773,f8787,f8792,f8796,f8800,f8804,f8808,f8812,f8816,f8820,f8828,f8994,f9024,f9029,f9042,f9062,f9063]) ).
fof(f9063,plain,
( spl102_21
| ~ spl102_149
| ~ spl102_502 ),
inference(avatar_split_clause,[],[f8022,f8017,f2345,f1473]) ).
fof(f1473,plain,
( spl102_21
<=> relation_rng(sK25) = relation_dom(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_21])]) ).
fof(f2345,plain,
( spl102_149
<=> relation_rng(sK25) = relation_dom(relation_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_149])]) ).
fof(f8017,plain,
( spl102_502
<=> function_inverse(sK25) = relation_inverse(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_502])]) ).
fof(f8022,plain,
( relation_rng(sK25) = relation_dom(function_inverse(sK25))
| ~ spl102_149
| ~ spl102_502 ),
inference(superposition,[],[f2347,f8019]) ).
fof(f8019,plain,
( function_inverse(sK25) = relation_inverse(sK25)
| ~ spl102_502 ),
inference(avatar_component_clause,[],[f8017]) ).
fof(f2347,plain,
( relation_rng(sK25) = relation_dom(relation_inverse(sK25))
| ~ spl102_149 ),
inference(avatar_component_clause,[],[f2345]) ).
fof(f9062,plain,
( ~ spl102_523
| spl102_587
| ~ spl102_588
| ~ spl102_22
| ~ spl102_190 ),
inference(avatar_split_clause,[],[f9002,f2683,f1477,f9059,f9055,f8302]) ).
fof(f8302,plain,
( spl102_523
<=> relation(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_523])]) ).
fof(f9055,plain,
( spl102_587
<=> function_inverse(sK25) = sK95 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_587])]) ).
fof(f9059,plain,
( spl102_588
<=> relation_dom(sK25) = sK95 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_588])]) ).
fof(f1477,plain,
( spl102_22
<=> relation_dom(sK25) = relation_rng(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_22])]) ).
fof(f2683,plain,
( spl102_190
<=> ! [X0] :
( relation_rng(X0) != sK95
| sK95 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_190])]) ).
fof(f9002,plain,
( relation_dom(sK25) != sK95
| function_inverse(sK25) = sK95
| ~ relation(function_inverse(sK25))
| ~ spl102_22
| ~ spl102_190 ),
inference(superposition,[],[f2684,f1478]) ).
fof(f1478,plain,
( relation_dom(sK25) = relation_rng(function_inverse(sK25))
| ~ spl102_22 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f2684,plain,
( ! [X0] :
( relation_rng(X0) != sK95
| sK95 = X0
| ~ relation(X0) )
| ~ spl102_190 ),
inference(avatar_component_clause,[],[f2683]) ).
fof(f9042,plain,
( ~ spl102_523
| spl102_586
| ~ spl102_22
| ~ spl102_182 ),
inference(avatar_split_clause,[],[f9001,f2609,f1477,f9040,f8302]) ).
fof(f9040,plain,
( spl102_586
<=> ! [X0] : subset(relation_rng(relation_dom_restriction(function_inverse(sK25),X0)),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_586])]) ).
fof(f2609,plain,
( spl102_182
<=> ! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_182])]) ).
fof(f9001,plain,
( ! [X0] :
( subset(relation_rng(relation_dom_restriction(function_inverse(sK25),X0)),relation_dom(sK25))
| ~ relation(function_inverse(sK25)) )
| ~ spl102_22
| ~ spl102_182 ),
inference(superposition,[],[f2610,f1478]) ).
fof(f2610,plain,
( ! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) )
| ~ spl102_182 ),
inference(avatar_component_clause,[],[f2609]) ).
fof(f9029,plain,
( ~ spl102_523
| spl102_585
| ~ spl102_22
| ~ spl102_131 ),
inference(avatar_split_clause,[],[f8998,f2152,f1477,f9027,f8302]) ).
fof(f9027,plain,
( spl102_585
<=> ! [X0] : subset(relation_image(function_inverse(sK25),X0),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_585])]) ).
fof(f2152,plain,
( spl102_131
<=> ! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_131])]) ).
fof(f8998,plain,
( ! [X0] :
( subset(relation_image(function_inverse(sK25),X0),relation_dom(sK25))
| ~ relation(function_inverse(sK25)) )
| ~ spl102_22
| ~ spl102_131 ),
inference(superposition,[],[f2153,f1478]) ).
fof(f2153,plain,
( ! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) )
| ~ spl102_131 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f9024,plain,
( spl102_505
| ~ spl102_523
| ~ spl102_584
| ~ spl102_22
| ~ spl102_105 ),
inference(avatar_split_clause,[],[f8997,f1955,f1477,f9021,f8302,f8071]) ).
fof(f8071,plain,
( spl102_505
<=> empty(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_505])]) ).
fof(f9021,plain,
( spl102_584
<=> empty(relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_584])]) ).
fof(f1955,plain,
( spl102_105
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_105])]) ).
fof(f8997,plain,
( ~ empty(relation_dom(sK25))
| ~ relation(function_inverse(sK25))
| empty(function_inverse(sK25))
| ~ spl102_22
| ~ spl102_105 ),
inference(superposition,[],[f1956,f1478]) ).
fof(f1956,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl102_105 ),
inference(avatar_component_clause,[],[f1955]) ).
fof(f8994,plain,
( spl102_22
| ~ spl102_157
| ~ spl102_502 ),
inference(avatar_split_clause,[],[f8021,f8017,f2408,f1477]) ).
fof(f2408,plain,
( spl102_157
<=> relation_dom(sK25) = relation_rng(relation_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_157])]) ).
fof(f8021,plain,
( relation_dom(sK25) = relation_rng(function_inverse(sK25))
| ~ spl102_157
| ~ spl102_502 ),
inference(superposition,[],[f2410,f8019]) ).
fof(f2410,plain,
( relation_dom(sK25) = relation_rng(relation_inverse(sK25))
| ~ spl102_157 ),
inference(avatar_component_clause,[],[f2408]) ).
fof(f8828,plain,
( ~ spl102_583
| ~ spl102_73
| ~ spl102_563 ),
inference(avatar_split_clause,[],[f8774,f8727,f1762,f8825]) ).
fof(f8825,plain,
( spl102_583
<=> proper_subset(relation_field(sK25),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_583])]) ).
fof(f1762,plain,
( spl102_73
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_73])]) ).
fof(f8727,plain,
( spl102_563
<=> subset(relation_dom(sK25),relation_field(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_563])]) ).
fof(f8774,plain,
( ~ proper_subset(relation_field(sK25),relation_dom(sK25))
| ~ spl102_73
| ~ spl102_563 ),
inference(resolution,[],[f8729,f1763]) ).
fof(f1763,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl102_73 ),
inference(avatar_component_clause,[],[f1762]) ).
fof(f8729,plain,
( subset(relation_dom(sK25),relation_field(sK25))
| ~ spl102_563 ),
inference(avatar_component_clause,[],[f8727]) ).
fof(f8820,plain,
( spl102_582
| ~ spl102_70
| ~ spl102_164 ),
inference(avatar_split_clause,[],[f2546,f2437,f1705,f8818]) ).
fof(f8818,plain,
( spl102_582
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_582])]) ).
fof(f1705,plain,
( spl102_70
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_70])]) ).
fof(f2437,plain,
( spl102_164
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK79(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_164])]) ).
fof(f2546,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl102_70
| ~ spl102_164 ),
inference(resolution,[],[f2438,f1706]) ).
fof(f1706,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl102_70 ),
inference(avatar_component_clause,[],[f1705]) ).
fof(f2438,plain,
( ! [X0,X1] :
( in(sK79(X0,X1),X0)
| subset(X0,X1) )
| ~ spl102_164 ),
inference(avatar_component_clause,[],[f2437]) ).
fof(f8816,plain,
( spl102_581
| ~ spl102_89
| ~ spl102_123 ),
inference(avatar_split_clause,[],[f2125,f2031,f1844,f8814]) ).
fof(f8814,plain,
( spl102_581
<=> ! [X0,X1] : in(X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_581])]) ).
fof(f1844,plain,
( spl102_89
<=> ! [X0,X1] : sP21(X1,X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_89])]) ).
fof(f2031,plain,
( spl102_123
<=> ! [X2,X0,X4] :
( in(X4,X2)
| ~ sP21(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_123])]) ).
fof(f2125,plain,
( ! [X0,X1] : in(X0,unordered_pair(X0,X1))
| ~ spl102_89
| ~ spl102_123 ),
inference(resolution,[],[f2032,f1845]) ).
fof(f1845,plain,
( ! [X0,X1] : sP21(X1,X0,unordered_pair(X0,X1))
| ~ spl102_89 ),
inference(avatar_component_clause,[],[f1844]) ).
fof(f2032,plain,
( ! [X2,X0,X4] :
( ~ sP21(X0,X4,X2)
| in(X4,X2) )
| ~ spl102_123 ),
inference(avatar_component_clause,[],[f2031]) ).
fof(f8812,plain,
( spl102_580
| ~ spl102_89
| ~ spl102_122 ),
inference(avatar_split_clause,[],[f2124,f2027,f1844,f8810]) ).
fof(f8810,plain,
( spl102_580
<=> ! [X0,X1] : in(X0,unordered_pair(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_580])]) ).
fof(f2027,plain,
( spl102_122
<=> ! [X2,X1,X4] :
( in(X4,X2)
| ~ sP21(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_122])]) ).
fof(f2124,plain,
( ! [X0,X1] : in(X0,unordered_pair(X1,X0))
| ~ spl102_89
| ~ spl102_122 ),
inference(resolution,[],[f2028,f1845]) ).
fof(f2028,plain,
( ! [X2,X1,X4] :
( ~ sP21(X4,X1,X2)
| in(X4,X2) )
| ~ spl102_122 ),
inference(avatar_component_clause,[],[f2027]) ).
fof(f8808,plain,
( spl102_579
| ~ spl102_7
| ~ spl102_118 ),
inference(avatar_split_clause,[],[f2110,f2010,f1403,f8806]) ).
fof(f8806,plain,
( spl102_579
<=> ! [X0] :
( sK95 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_579])]) ).
fof(f1403,plain,
( spl102_7
<=> empty(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_7])]) ).
fof(f2010,plain,
( spl102_118
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_118])]) ).
fof(f2110,plain,
( ! [X0] :
( sK95 = X0
| ~ empty(X0) )
| ~ spl102_7
| ~ spl102_118 ),
inference(resolution,[],[f2011,f1405]) ).
fof(f1405,plain,
( empty(sK95)
| ~ spl102_7 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f2011,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl102_118 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f8804,plain,
( spl102_578
| ~ spl102_39
| ~ spl102_116 ),
inference(avatar_split_clause,[],[f2100,f2002,f1548,f8802]) ).
fof(f8802,plain,
( spl102_578
<=> ! [X0] : subset(sK66(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_578])]) ).
fof(f1548,plain,
( spl102_39
<=> ! [X0] : element(sK66(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_39])]) ).
fof(f2002,plain,
( spl102_116
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_116])]) ).
fof(f2100,plain,
( ! [X0] : subset(sK66(powerset(X0)),X0)
| ~ spl102_39
| ~ spl102_116 ),
inference(resolution,[],[f2003,f1549]) ).
fof(f1549,plain,
( ! [X0] : element(sK66(X0),X0)
| ~ spl102_39 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f2003,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl102_116 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f8800,plain,
( spl102_577
| ~ spl102_39
| ~ spl102_113 ),
inference(avatar_split_clause,[],[f2092,f1990,f1548,f8798]) ).
fof(f8798,plain,
( spl102_577
<=> ! [X0] :
( empty(sK66(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_577])]) ).
fof(f1990,plain,
( spl102_113
<=> ! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_113])]) ).
fof(f2092,plain,
( ! [X0] :
( empty(sK66(X0))
| ~ empty(X0) )
| ~ spl102_39
| ~ spl102_113 ),
inference(resolution,[],[f1991,f1549]) ).
fof(f1991,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| empty(X1)
| ~ empty(X0) )
| ~ spl102_113 ),
inference(avatar_component_clause,[],[f1990]) ).
fof(f8796,plain,
( spl102_576
| ~ spl102_7
| ~ spl102_56
| ~ spl102_59
| ~ spl102_112 ),
inference(avatar_split_clause,[],[f2086,f1986,f1661,f1649,f1403,f8794]) ).
fof(f8794,plain,
( spl102_576
<=> ! [X0] : set_union2(sK95,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_576])]) ).
fof(f1649,plain,
( spl102_56
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_56])]) ).
fof(f1661,plain,
( spl102_59
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_59])]) ).
fof(f1986,plain,
( spl102_112
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_112])]) ).
fof(f2086,plain,
( ! [X0] : set_union2(sK95,X0) = X0
| ~ spl102_7
| ~ spl102_56
| ~ spl102_59
| ~ spl102_112 ),
inference(forward_demodulation,[],[f2074,f1713]) ).
fof(f1713,plain,
( empty_set = sK95
| ~ spl102_7
| ~ spl102_59 ),
inference(resolution,[],[f1662,f1405]) ).
fof(f1662,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl102_59 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f2074,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl102_56
| ~ spl102_112 ),
inference(superposition,[],[f1987,f1650]) ).
fof(f1650,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl102_56 ),
inference(avatar_component_clause,[],[f1649]) ).
fof(f1987,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl102_112 ),
inference(avatar_component_clause,[],[f1986]) ).
fof(f8792,plain,
( spl102_575
| ~ spl102_5
| ~ spl102_7
| ~ spl102_59
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2049,f1951,f1661,f1403,f1393,f8789]) ).
fof(f8789,plain,
( spl102_575
<=> sK95 = relation_inverse(relation_inverse(sK95)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_575])]) ).
fof(f1393,plain,
( spl102_5
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_5])]) ).
fof(f1951,plain,
( spl102_104
<=> ! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_104])]) ).
fof(f2049,plain,
( sK95 = relation_inverse(relation_inverse(sK95))
| ~ spl102_5
| ~ spl102_7
| ~ spl102_59
| ~ spl102_104 ),
inference(forward_demodulation,[],[f2037,f1713]) ).
fof(f2037,plain,
( empty_set = relation_inverse(relation_inverse(empty_set))
| ~ spl102_5
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1395]) ).
fof(f1395,plain,
( relation(empty_set)
| ~ spl102_5 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f1952,plain,
( ! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 )
| ~ spl102_104 ),
inference(avatar_component_clause,[],[f1951]) ).
fof(f8787,plain,
( spl102_574
| ~ spl102_15
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2047,f1951,f1443,f8784]) ).
fof(f8784,plain,
( spl102_574
<=> sK100 = relation_inverse(relation_inverse(sK100)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_574])]) ).
fof(f1443,plain,
( spl102_15
<=> relation(sK100) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_15])]) ).
fof(f2047,plain,
( sK100 = relation_inverse(relation_inverse(sK100))
| ~ spl102_15
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1445]) ).
fof(f1445,plain,
( relation(sK100)
| ~ spl102_15 ),
inference(avatar_component_clause,[],[f1443]) ).
fof(f8773,plain,
( spl102_573
| ~ spl102_13
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2046,f1951,f1433,f8770]) ).
fof(f8770,plain,
( spl102_573
<=> sK99 = relation_inverse(relation_inverse(sK99)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_573])]) ).
fof(f1433,plain,
( spl102_13
<=> relation(sK99) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_13])]) ).
fof(f2046,plain,
( sK99 = relation_inverse(relation_inverse(sK99))
| ~ spl102_13
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1435]) ).
fof(f1435,plain,
( relation(sK99)
| ~ spl102_13 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f8768,plain,
( spl102_572
| ~ spl102_12
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2045,f1951,f1428,f8765]) ).
fof(f8765,plain,
( spl102_572
<=> sK98 = relation_inverse(relation_inverse(sK98)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_572])]) ).
fof(f1428,plain,
( spl102_12
<=> relation(sK98) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_12])]) ).
fof(f2045,plain,
( sK98 = relation_inverse(relation_inverse(sK98))
| ~ spl102_12
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1430]) ).
fof(f1430,plain,
( relation(sK98)
| ~ spl102_12 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f8763,plain,
( spl102_571
| ~ spl102_9
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2043,f1951,f1413,f8760]) ).
fof(f8760,plain,
( spl102_571
<=> sK96 = relation_inverse(relation_inverse(sK96)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_571])]) ).
fof(f1413,plain,
( spl102_9
<=> relation(sK96) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_9])]) ).
fof(f2043,plain,
( sK96 = relation_inverse(relation_inverse(sK96))
| ~ spl102_9
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1415]) ).
fof(f1415,plain,
( relation(sK96)
| ~ spl102_9 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f8758,plain,
( spl102_570
| ~ spl102_37
| ~ spl102_66 ),
inference(avatar_split_clause,[],[f1750,f1689,f1540,f8756]) ).
fof(f8756,plain,
( spl102_570
<=> ! [X0] :
( ~ relation(X0)
| sP8(relation_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_570])]) ).
fof(f1540,plain,
( spl102_37
<=> ! [X0] :
( sP8(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_37])]) ).
fof(f1689,plain,
( spl102_66
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_66])]) ).
fof(f1750,plain,
( ! [X0] :
( ~ relation(X0)
| sP8(relation_inverse(X0)) )
| ~ spl102_37
| ~ spl102_66 ),
inference(resolution,[],[f1690,f1541]) ).
fof(f1541,plain,
( ! [X0] :
( ~ relation(X0)
| sP8(X0) )
| ~ spl102_37 ),
inference(avatar_component_clause,[],[f1540]) ).
fof(f1690,plain,
( ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) )
| ~ spl102_66 ),
inference(avatar_component_clause,[],[f1689]) ).
fof(f8754,plain,
( spl102_569
| ~ spl102_38
| ~ spl102_66 ),
inference(avatar_split_clause,[],[f1749,f1689,f1544,f8752]) ).
fof(f8752,plain,
( spl102_569
<=> ! [X0] :
( ~ relation(X0)
| sP10(relation_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_569])]) ).
fof(f1544,plain,
( spl102_38
<=> ! [X0] :
( sP10(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_38])]) ).
fof(f1749,plain,
( ! [X0] :
( ~ relation(X0)
| sP10(relation_inverse(X0)) )
| ~ spl102_38
| ~ spl102_66 ),
inference(resolution,[],[f1690,f1545]) ).
fof(f1545,plain,
( ! [X0] :
( ~ relation(X0)
| sP10(X0) )
| ~ spl102_38 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f8750,plain,
( spl102_568
| ~ spl102_37
| ~ spl102_65 ),
inference(avatar_split_clause,[],[f1741,f1685,f1540,f8748]) ).
fof(f8748,plain,
( spl102_568
<=> ! [X0] :
( ~ empty(X0)
| sP8(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_568])]) ).
fof(f1685,plain,
( spl102_65
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_65])]) ).
fof(f1741,plain,
( ! [X0] :
( ~ empty(X0)
| sP8(relation_dom(X0)) )
| ~ spl102_37
| ~ spl102_65 ),
inference(resolution,[],[f1686,f1541]) ).
fof(f1686,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl102_65 ),
inference(avatar_component_clause,[],[f1685]) ).
fof(f8746,plain,
( spl102_567
| ~ spl102_38
| ~ spl102_65 ),
inference(avatar_split_clause,[],[f1740,f1685,f1544,f8744]) ).
fof(f8744,plain,
( spl102_567
<=> ! [X0] :
( ~ empty(X0)
| sP10(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_567])]) ).
fof(f1740,plain,
( ! [X0] :
( ~ empty(X0)
| sP10(relation_dom(X0)) )
| ~ spl102_38
| ~ spl102_65 ),
inference(resolution,[],[f1686,f1545]) ).
fof(f8742,plain,
( spl102_566
| ~ spl102_35
| ~ spl102_64 ),
inference(avatar_split_clause,[],[f1736,f1681,f1532,f8740]) ).
fof(f8740,plain,
( spl102_566
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_566])]) ).
fof(f1532,plain,
( spl102_35
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_35])]) ).
fof(f1681,plain,
( spl102_64
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_64])]) ).
fof(f1736,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl102_35
| ~ spl102_64 ),
inference(resolution,[],[f1682,f1533]) ).
fof(f1533,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl102_35 ),
inference(avatar_component_clause,[],[f1532]) ).
fof(f1682,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl102_64 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f8738,plain,
( spl102_565
| ~ spl102_37
| ~ spl102_63 ),
inference(avatar_split_clause,[],[f1731,f1677,f1540,f8736]) ).
fof(f8736,plain,
( spl102_565
<=> ! [X0] :
( ~ empty(X0)
| sP8(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_565])]) ).
fof(f1677,plain,
( spl102_63
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_63])]) ).
fof(f1731,plain,
( ! [X0] :
( ~ empty(X0)
| sP8(relation_rng(X0)) )
| ~ spl102_37
| ~ spl102_63 ),
inference(resolution,[],[f1678,f1541]) ).
fof(f1678,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl102_63 ),
inference(avatar_component_clause,[],[f1677]) ).
fof(f8734,plain,
( spl102_564
| ~ spl102_38
| ~ spl102_63 ),
inference(avatar_split_clause,[],[f1730,f1677,f1544,f8732]) ).
fof(f8732,plain,
( spl102_564
<=> ! [X0] :
( ~ empty(X0)
| sP10(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_564])]) ).
fof(f1730,plain,
( ! [X0] :
( ~ empty(X0)
| sP10(relation_rng(X0)) )
| ~ spl102_38
| ~ spl102_63 ),
inference(resolution,[],[f1678,f1545]) ).
fof(f8730,plain,
( spl102_563
| ~ spl102_251
| ~ spl102_552 ),
inference(avatar_split_clause,[],[f8665,f8540,f3363,f8727]) ).
fof(f3363,plain,
( spl102_251
<=> relation_field(sK25) = set_union2(relation_rng(sK25),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_251])]) ).
fof(f8540,plain,
( spl102_552
<=> ! [X0,X1] : subset(X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_552])]) ).
fof(f8665,plain,
( subset(relation_dom(sK25),relation_field(sK25))
| ~ spl102_251
| ~ spl102_552 ),
inference(superposition,[],[f8541,f3365]) ).
fof(f3365,plain,
( relation_field(sK25) = set_union2(relation_rng(sK25),relation_dom(sK25))
| ~ spl102_251 ),
inference(avatar_component_clause,[],[f3363]) ).
fof(f8541,plain,
( ! [X0,X1] : subset(X0,set_union2(X1,X0))
| ~ spl102_552 ),
inference(avatar_component_clause,[],[f8540]) ).
fof(f8725,plain,
( spl102_562
| ~ spl102_35
| ~ spl102_62 ),
inference(avatar_split_clause,[],[f1726,f1673,f1532,f8723]) ).
fof(f8723,plain,
( spl102_562
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_562])]) ).
fof(f1673,plain,
( spl102_62
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_62])]) ).
fof(f1726,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl102_35
| ~ spl102_62 ),
inference(resolution,[],[f1674,f1533]) ).
fof(f1674,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl102_62 ),
inference(avatar_component_clause,[],[f1673]) ).
fof(f8721,plain,
( spl102_561
| ~ spl102_37
| ~ spl102_61 ),
inference(avatar_split_clause,[],[f1723,f1669,f1540,f8719]) ).
fof(f8719,plain,
( spl102_561
<=> ! [X0] :
( ~ empty(X0)
| sP8(relation_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_561])]) ).
fof(f1669,plain,
( spl102_61
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_61])]) ).
fof(f1723,plain,
( ! [X0] :
( ~ empty(X0)
| sP8(relation_inverse(X0)) )
| ~ spl102_37
| ~ spl102_61 ),
inference(resolution,[],[f1670,f1541]) ).
fof(f1670,plain,
( ! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) )
| ~ spl102_61 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f8717,plain,
( spl102_560
| ~ spl102_38
| ~ spl102_61 ),
inference(avatar_split_clause,[],[f1722,f1669,f1544,f8715]) ).
fof(f8715,plain,
( spl102_560
<=> ! [X0] :
( ~ empty(X0)
| sP10(relation_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_560])]) ).
fof(f1722,plain,
( ! [X0] :
( ~ empty(X0)
| sP10(relation_inverse(X0)) )
| ~ spl102_38
| ~ spl102_61 ),
inference(resolution,[],[f1670,f1545]) ).
fof(f8713,plain,
( spl102_559
| ~ spl102_35
| ~ spl102_60 ),
inference(avatar_split_clause,[],[f1720,f1665,f1532,f8711]) ).
fof(f8711,plain,
( spl102_559
<=> ! [X0] :
( ~ empty(X0)
| function(relation_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_559])]) ).
fof(f1665,plain,
( spl102_60
<=> ! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_60])]) ).
fof(f1720,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_inverse(X0)) )
| ~ spl102_35
| ~ spl102_60 ),
inference(resolution,[],[f1666,f1533]) ).
fof(f1666,plain,
( ! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) )
| ~ spl102_60 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f8566,plain,
( spl102_558
| ~ spl102_7
| ~ spl102_27
| ~ spl102_59
| ~ spl102_67
| ~ spl102_101
| ~ spl102_264 ),
inference(avatar_split_clause,[],[f3651,f3577,f1930,f1693,f1661,f1498,f1403,f8564]) ).
fof(f8564,plain,
( spl102_558
<=> ! [X0] : subset_complement(X0,sK95) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_558])]) ).
fof(f1498,plain,
( spl102_27
<=> ! [X0] : empty(sK69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_27])]) ).
fof(f1693,plain,
( spl102_67
<=> ! [X0] : element(sK69(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_67])]) ).
fof(f1930,plain,
( spl102_101
<=> ! [X0] : set_difference(X0,sK95) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_101])]) ).
fof(f3577,plain,
( spl102_264
<=> ! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_264])]) ).
fof(f3651,plain,
( ! [X0] : subset_complement(X0,sK95) = X0
| ~ spl102_7
| ~ spl102_27
| ~ spl102_59
| ~ spl102_67
| ~ spl102_101
| ~ spl102_264 ),
inference(forward_demodulation,[],[f3650,f1931]) ).
fof(f1931,plain,
( ! [X0] : set_difference(X0,sK95) = X0
| ~ spl102_101 ),
inference(avatar_component_clause,[],[f1930]) ).
fof(f3650,plain,
( ! [X0] : set_difference(X0,sK95) = subset_complement(X0,sK95)
| ~ spl102_7
| ~ spl102_27
| ~ spl102_59
| ~ spl102_67
| ~ spl102_264 ),
inference(forward_demodulation,[],[f3649,f1713]) ).
fof(f3649,plain,
( ! [X0] : set_difference(X0,empty_set) = subset_complement(X0,empty_set)
| ~ spl102_27
| ~ spl102_59
| ~ spl102_67
| ~ spl102_264 ),
inference(forward_demodulation,[],[f3647,f1712]) ).
fof(f1712,plain,
( ! [X0] : empty_set = sK69(X0)
| ~ spl102_27
| ~ spl102_59 ),
inference(resolution,[],[f1662,f1499]) ).
fof(f1499,plain,
( ! [X0] : empty(sK69(X0))
| ~ spl102_27 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f3647,plain,
( ! [X0] : set_difference(X0,sK69(X0)) = subset_complement(X0,sK69(X0))
| ~ spl102_67
| ~ spl102_264 ),
inference(resolution,[],[f3578,f1694]) ).
fof(f1694,plain,
( ! [X0] : element(sK69(X0),powerset(X0))
| ~ spl102_67 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f3578,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) )
| ~ spl102_264 ),
inference(avatar_component_clause,[],[f3577]) ).
fof(f8562,plain,
( spl102_557
| ~ spl102_44
| ~ spl102_99
| ~ spl102_264 ),
inference(avatar_split_clause,[],[f3648,f3577,f1915,f1569,f8560]) ).
fof(f8560,plain,
( spl102_557
<=> ! [X0] : sK95 = subset_complement(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_557])]) ).
fof(f1569,plain,
( spl102_44
<=> ! [X0] : element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_44])]) ).
fof(f1915,plain,
( spl102_99
<=> ! [X0] : sK95 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_99])]) ).
fof(f3648,plain,
( ! [X0] : sK95 = subset_complement(X0,X0)
| ~ spl102_44
| ~ spl102_99
| ~ spl102_264 ),
inference(forward_demodulation,[],[f3641,f1916]) ).
fof(f1916,plain,
( ! [X0] : sK95 = set_difference(X0,X0)
| ~ spl102_99 ),
inference(avatar_component_clause,[],[f1915]) ).
fof(f3641,plain,
( ! [X0] : set_difference(X0,X0) = subset_complement(X0,X0)
| ~ spl102_44
| ~ spl102_264 ),
inference(resolution,[],[f3578,f1570]) ).
fof(f1570,plain,
( ! [X0] : element(X0,powerset(X0))
| ~ spl102_44 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f8558,plain,
( spl102_556
| ~ spl102_25
| ~ spl102_48
| ~ spl102_49
| ~ spl102_68
| ~ spl102_245 ),
inference(avatar_split_clause,[],[f3341,f3283,f1697,f1619,f1615,f1490,f8556]) ).
fof(f8556,plain,
( spl102_556
<=> ! [X0] : relation_field(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_556])]) ).
fof(f1490,plain,
( spl102_25
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_25])]) ).
fof(f1615,plain,
( spl102_48
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_48])]) ).
fof(f1619,plain,
( spl102_49
<=> ! [X0] : relation_rng(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_49])]) ).
fof(f1697,plain,
( spl102_68
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_68])]) ).
fof(f3283,plain,
( spl102_245
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_245])]) ).
fof(f3341,plain,
( ! [X0] : relation_field(identity_relation(X0)) = X0
| ~ spl102_25
| ~ spl102_48
| ~ spl102_49
| ~ spl102_68
| ~ spl102_245 ),
inference(forward_demodulation,[],[f3340,f1698]) ).
fof(f1698,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl102_68 ),
inference(avatar_component_clause,[],[f1697]) ).
fof(f3340,plain,
( ! [X0] : set_union2(X0,X0) = relation_field(identity_relation(X0))
| ~ spl102_25
| ~ spl102_48
| ~ spl102_49
| ~ spl102_245 ),
inference(forward_demodulation,[],[f3339,f1620]) ).
fof(f1620,plain,
( ! [X0] : relation_rng(identity_relation(X0)) = X0
| ~ spl102_49 ),
inference(avatar_component_clause,[],[f1619]) ).
fof(f3339,plain,
( ! [X0] : relation_field(identity_relation(X0)) = set_union2(relation_rng(identity_relation(X0)),X0)
| ~ spl102_25
| ~ spl102_48
| ~ spl102_245 ),
inference(forward_demodulation,[],[f3319,f1616]) ).
fof(f1616,plain,
( ! [X0] : relation_dom(identity_relation(X0)) = X0
| ~ spl102_48 ),
inference(avatar_component_clause,[],[f1615]) ).
fof(f3319,plain,
( ! [X0] : relation_field(identity_relation(X0)) = set_union2(relation_rng(identity_relation(X0)),relation_dom(identity_relation(X0)))
| ~ spl102_25
| ~ spl102_245 ),
inference(resolution,[],[f3284,f1491]) ).
fof(f1491,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl102_25 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f3284,plain,
( ! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0)) )
| ~ spl102_245 ),
inference(avatar_component_clause,[],[f3283]) ).
fof(f8554,plain,
( spl102_555
| ~ spl102_68
| ~ spl102_99
| ~ spl102_177 ),
inference(avatar_split_clause,[],[f2695,f2588,f1915,f1697,f8552]) ).
fof(f8552,plain,
( spl102_555
<=> ! [X0] : set_union2(X0,sK95) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_555])]) ).
fof(f2588,plain,
( spl102_177
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_177])]) ).
fof(f2695,plain,
( ! [X0] : set_union2(X0,sK95) = X0
| ~ spl102_68
| ~ spl102_99
| ~ spl102_177 ),
inference(forward_demodulation,[],[f2689,f1698]) ).
fof(f2689,plain,
( ! [X0] : set_union2(X0,X0) = set_union2(X0,sK95)
| ~ spl102_99
| ~ spl102_177 ),
inference(superposition,[],[f2589,f1916]) ).
fof(f2589,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))
| ~ spl102_177 ),
inference(avatar_component_clause,[],[f2588]) ).
fof(f8550,plain,
( spl102_554
| ~ spl102_70
| ~ spl102_129 ),
inference(avatar_split_clause,[],[f2267,f2144,f1705,f8548]) ).
fof(f8548,plain,
( spl102_554
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_554])]) ).
fof(f2144,plain,
( spl102_129
<=> ! [X0,X1] :
( in(sK32(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_129])]) ).
fof(f2267,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) )
| ~ spl102_70
| ~ spl102_129 ),
inference(resolution,[],[f2145,f1706]) ).
fof(f2145,plain,
( ! [X0,X1] :
( in(sK32(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl102_129 ),
inference(avatar_component_clause,[],[f2144]) ).
fof(f8546,plain,
( spl102_553
| ~ spl102_70
| ~ spl102_128 ),
inference(avatar_split_clause,[],[f2261,f2140,f1705,f8544]) ).
fof(f8544,plain,
( spl102_553
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_553])]) ).
fof(f2140,plain,
( spl102_128
<=> ! [X0,X1] :
( in(sK32(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_128])]) ).
fof(f2261,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) )
| ~ spl102_70
| ~ spl102_128 ),
inference(resolution,[],[f2141,f1706]) ).
fof(f2141,plain,
( ! [X0,X1] :
( in(sK32(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl102_128 ),
inference(avatar_component_clause,[],[f2140]) ).
fof(f8542,plain,
( spl102_552
| ~ spl102_50
| ~ spl102_112 ),
inference(avatar_split_clause,[],[f2079,f1986,f1623,f8540]) ).
fof(f1623,plain,
( spl102_50
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_50])]) ).
fof(f2079,plain,
( ! [X0,X1] : subset(X0,set_union2(X1,X0))
| ~ spl102_50
| ~ spl102_112 ),
inference(superposition,[],[f1624,f1987]) ).
fof(f1624,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl102_50 ),
inference(avatar_component_clause,[],[f1623]) ).
fof(f8538,plain,
( spl102_551
| ~ spl102_77
| ~ spl102_89 ),
inference(avatar_split_clause,[],[f1882,f1844,f1787,f8535]) ).
fof(f8535,plain,
( spl102_551
<=> sP21(sK95,sK95,powerset(sK95)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_551])]) ).
fof(f1787,plain,
( spl102_77
<=> powerset(sK95) = unordered_pair(sK95,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_77])]) ).
fof(f1882,plain,
( sP21(sK95,sK95,powerset(sK95))
| ~ spl102_77
| ~ spl102_89 ),
inference(superposition,[],[f1845,f1789]) ).
fof(f1789,plain,
( powerset(sK95) = unordered_pair(sK95,sK95)
| ~ spl102_77 ),
inference(avatar_component_clause,[],[f1787]) ).
fof(f8533,plain,
( spl102_550
| ~ spl102_53
| ~ spl102_87 ),
inference(avatar_split_clause,[],[f1880,f1836,f1635,f8531]) ).
fof(f8531,plain,
( spl102_550
<=> ! [X0] : element(X0,unordered_pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_550])]) ).
fof(f1635,plain,
( spl102_53
<=> ! [X3] : in(X3,unordered_pair(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_53])]) ).
fof(f1836,plain,
( spl102_87
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_87])]) ).
fof(f1880,plain,
( ! [X0] : element(X0,unordered_pair(X0,X0))
| ~ spl102_53
| ~ spl102_87 ),
inference(resolution,[],[f1837,f1636]) ).
fof(f1636,plain,
( ! [X3] : in(X3,unordered_pair(X3,X3))
| ~ spl102_53 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f1837,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl102_87 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f8529,plain,
( spl102_549
| ~ spl102_53
| ~ spl102_86 ),
inference(avatar_split_clause,[],[f1876,f1832,f1635,f8527]) ).
fof(f8527,plain,
( spl102_549
<=> ! [X0] : ~ in(unordered_pair(X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_549])]) ).
fof(f1832,plain,
( spl102_86
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_86])]) ).
fof(f1876,plain,
( ! [X0] : ~ in(unordered_pair(X0,X0),X0)
| ~ spl102_53
| ~ spl102_86 ),
inference(resolution,[],[f1833,f1636]) ).
fof(f1833,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl102_86 ),
inference(avatar_component_clause,[],[f1832]) ).
fof(f8525,plain,
( spl102_548
| ~ spl102_51
| ~ spl102_75 ),
inference(avatar_split_clause,[],[f1793,f1772,f1627,f8523]) ).
fof(f8523,plain,
( spl102_548
<=> ! [X0] : sK95 = set_difference(sK95,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_548])]) ).
fof(f1627,plain,
( spl102_51
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_51])]) ).
fof(f1772,plain,
( spl102_75
<=> ! [X0] :
( ~ subset(X0,sK95)
| sK95 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_75])]) ).
fof(f1793,plain,
( ! [X0] : sK95 = set_difference(sK95,X0)
| ~ spl102_51
| ~ spl102_75 ),
inference(resolution,[],[f1773,f1628]) ).
fof(f1628,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl102_51 ),
inference(avatar_component_clause,[],[f1627]) ).
fof(f1773,plain,
( ! [X0] :
( ~ subset(X0,sK95)
| sK95 = X0 )
| ~ spl102_75 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f8521,plain,
( spl102_547
| ~ spl102_50
| ~ spl102_73 ),
inference(avatar_split_clause,[],[f1778,f1762,f1623,f8519]) ).
fof(f8519,plain,
( spl102_547
<=> ! [X0,X1] : ~ proper_subset(set_union2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_547])]) ).
fof(f1778,plain,
( ! [X0,X1] : ~ proper_subset(set_union2(X0,X1),X0)
| ~ spl102_50
| ~ spl102_73 ),
inference(resolution,[],[f1763,f1624]) ).
fof(f8517,plain,
( spl102_546
| ~ spl102_51
| ~ spl102_73 ),
inference(avatar_split_clause,[],[f1777,f1762,f1627,f8515]) ).
fof(f8515,plain,
( spl102_546
<=> ! [X0,X1] : ~ proper_subset(X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_546])]) ).
fof(f1777,plain,
( ! [X0,X1] : ~ proper_subset(X0,set_difference(X0,X1))
| ~ spl102_51
| ~ spl102_73 ),
inference(resolution,[],[f1763,f1628]) ).
fof(f8513,plain,
( spl102_545
| ~ spl102_49
| ~ spl102_63 ),
inference(avatar_split_clause,[],[f1733,f1677,f1619,f8511]) ).
fof(f8511,plain,
( spl102_545
<=> ! [X0] :
( relation(X0)
| ~ empty(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_545])]) ).
fof(f1733,plain,
( ! [X0] :
( relation(X0)
| ~ empty(identity_relation(X0)) )
| ~ spl102_49
| ~ spl102_63 ),
inference(superposition,[],[f1678,f1620]) ).
fof(f8509,plain,
( spl102_544
| ~ spl102_49
| ~ spl102_62 ),
inference(avatar_split_clause,[],[f1728,f1673,f1619,f8507]) ).
fof(f8507,plain,
( spl102_544
<=> ! [X0] :
( empty(X0)
| ~ empty(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_544])]) ).
fof(f1728,plain,
( ! [X0] :
( empty(X0)
| ~ empty(identity_relation(X0)) )
| ~ spl102_49
| ~ spl102_62 ),
inference(superposition,[],[f1674,f1620]) ).
fof(f8484,plain,
( spl102_543
| ~ spl102_38
| ~ spl102_523 ),
inference(avatar_split_clause,[],[f8345,f8302,f1544,f8481]) ).
fof(f8481,plain,
( spl102_543
<=> sP10(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_543])]) ).
fof(f8345,plain,
( sP10(function_inverse(sK25))
| ~ spl102_38
| ~ spl102_523 ),
inference(resolution,[],[f8304,f1545]) ).
fof(f8304,plain,
( relation(function_inverse(sK25))
| ~ spl102_523 ),
inference(avatar_component_clause,[],[f8302]) ).
fof(f8472,plain,
( spl102_542
| ~ spl102_519
| ~ spl102_535 ),
inference(avatar_split_clause,[],[f8444,f8441,f8267,f8470]) ).
fof(f8470,plain,
( spl102_542
<=> ! [X0] : sK69(X0) = sK95 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_542])]) ).
fof(f8267,plain,
( spl102_519
<=> empty_set = sK95 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_519])]) ).
fof(f8441,plain,
( spl102_535
<=> ! [X0] : empty_set = sK69(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_535])]) ).
fof(f8444,plain,
( ! [X0] : sK69(X0) = sK95
| ~ spl102_519
| ~ spl102_535 ),
inference(forward_demodulation,[],[f8442,f8269]) ).
fof(f8269,plain,
( empty_set = sK95
| ~ spl102_519 ),
inference(avatar_component_clause,[],[f8267]) ).
fof(f8442,plain,
( ! [X0] : empty_set = sK69(X0)
| ~ spl102_535 ),
inference(avatar_component_clause,[],[f8441]) ).
fof(f8468,plain,
( spl102_541
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_91 ),
inference(avatar_split_clause,[],[f1895,f1852,f1661,f1653,f1403,f8466]) ).
fof(f8466,plain,
( spl102_541
<=> ! [X0] : sP24(sK95,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_541])]) ).
fof(f1653,plain,
( spl102_57
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_57])]) ).
fof(f1852,plain,
( spl102_91
<=> ! [X0,X1] : sP24(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_91])]) ).
fof(f1895,plain,
( ! [X0] : sP24(sK95,X0,X0)
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_91 ),
inference(forward_demodulation,[],[f1893,f1713]) ).
fof(f1893,plain,
( ! [X0] : sP24(empty_set,X0,X0)
| ~ spl102_57
| ~ spl102_91 ),
inference(superposition,[],[f1853,f1654]) ).
fof(f1654,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl102_57 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f1853,plain,
( ! [X0,X1] : sP24(X1,X0,set_difference(X0,X1))
| ~ spl102_91 ),
inference(avatar_component_clause,[],[f1852]) ).
fof(f8464,plain,
( spl102_540
| ~ spl102_7
| ~ spl102_55
| ~ spl102_59
| ~ spl102_91 ),
inference(avatar_split_clause,[],[f1894,f1852,f1661,f1645,f1403,f8462]) ).
fof(f8462,plain,
( spl102_540
<=> ! [X0] : sP24(X0,sK95,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_540])]) ).
fof(f1645,plain,
( spl102_55
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_55])]) ).
fof(f1894,plain,
( ! [X0] : sP24(X0,sK95,sK95)
| ~ spl102_7
| ~ spl102_55
| ~ spl102_59
| ~ spl102_91 ),
inference(forward_demodulation,[],[f1892,f1713]) ).
fof(f1892,plain,
( ! [X0] : sP24(X0,empty_set,empty_set)
| ~ spl102_55
| ~ spl102_91 ),
inference(superposition,[],[f1853,f1646]) ).
fof(f1646,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl102_55 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f8460,plain,
( spl102_539
| ~ spl102_7
| ~ spl102_56
| ~ spl102_59
| ~ spl102_90 ),
inference(avatar_split_clause,[],[f1885,f1848,f1661,f1649,f1403,f8458]) ).
fof(f8458,plain,
( spl102_539
<=> ! [X0] : sP23(sK95,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_539])]) ).
fof(f1848,plain,
( spl102_90
<=> ! [X0,X1] : sP23(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_90])]) ).
fof(f1885,plain,
( ! [X0] : sP23(sK95,X0,X0)
| ~ spl102_7
| ~ spl102_56
| ~ spl102_59
| ~ spl102_90 ),
inference(forward_demodulation,[],[f1883,f1713]) ).
fof(f1883,plain,
( ! [X0] : sP23(empty_set,X0,X0)
| ~ spl102_56
| ~ spl102_90 ),
inference(superposition,[],[f1849,f1650]) ).
fof(f1849,plain,
( ! [X0,X1] : sP23(X1,X0,set_union2(X0,X1))
| ~ spl102_90 ),
inference(avatar_component_clause,[],[f1848]) ).
fof(f8456,plain,
( spl102_538
| ~ spl102_68
| ~ spl102_90 ),
inference(avatar_split_clause,[],[f1884,f1848,f1697,f8454]) ).
fof(f8454,plain,
( spl102_538
<=> ! [X0] : sP23(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_538])]) ).
fof(f1884,plain,
( ! [X0] : sP23(X0,X0,X0)
| ~ spl102_68
| ~ spl102_90 ),
inference(superposition,[],[f1849,f1698]) ).
fof(f8452,plain,
( spl102_537
| ~ spl102_40
| ~ spl102_87 ),
inference(avatar_split_clause,[],[f1879,f1836,f1552,f8450]) ).
fof(f8450,plain,
( spl102_537
<=> ! [X0] : element(X0,sK67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_537])]) ).
fof(f1552,plain,
( spl102_40
<=> ! [X0] : in(X0,sK67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_40])]) ).
fof(f1879,plain,
( ! [X0] : element(X0,sK67(X0))
| ~ spl102_40
| ~ spl102_87 ),
inference(resolution,[],[f1837,f1553]) ).
fof(f1553,plain,
( ! [X0] : in(X0,sK67(X0))
| ~ spl102_40 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f8448,plain,
( spl102_536
| ~ spl102_40
| ~ spl102_86 ),
inference(avatar_split_clause,[],[f1875,f1832,f1552,f8446]) ).
fof(f8446,plain,
( spl102_536
<=> ! [X0] : ~ in(sK67(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_536])]) ).
fof(f1875,plain,
( ! [X0] : ~ in(sK67(X0),X0)
| ~ spl102_40
| ~ spl102_86 ),
inference(resolution,[],[f1833,f1553]) ).
fof(f8443,plain,
( spl102_535
| ~ spl102_27
| ~ spl102_59 ),
inference(avatar_split_clause,[],[f1712,f1661,f1498,f8441]) ).
fof(f8421,plain,
( spl102_534
| ~ spl102_37
| ~ spl102_523 ),
inference(avatar_split_clause,[],[f8344,f8302,f1540,f8418]) ).
fof(f8418,plain,
( spl102_534
<=> sP8(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_534])]) ).
fof(f8344,plain,
( sP8(function_inverse(sK25))
| ~ spl102_37
| ~ spl102_523 ),
inference(resolution,[],[f8304,f1541]) ).
fof(f8376,plain,
( spl102_533
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_184 ),
inference(avatar_split_clause,[],[f2749,f2617,f1661,f1510,f1403,f8374]) ).
fof(f8374,plain,
( spl102_533
<=> ! [X0] : element(sK95,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_533])]) ).
fof(f1510,plain,
( spl102_30
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_30])]) ).
fof(f2617,plain,
( spl102_184
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| in(sK34(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_184])]) ).
fof(f2749,plain,
( ! [X0] : element(sK95,powerset(X0))
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_184 ),
inference(forward_demodulation,[],[f2747,f1713]) ).
fof(f2747,plain,
( ! [X0] : element(empty_set,powerset(X0))
| ~ spl102_30
| ~ spl102_184 ),
inference(resolution,[],[f2618,f1511]) ).
fof(f1511,plain,
( ! [X2] : ~ in(X2,empty_set)
| ~ spl102_30 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f2618,plain,
( ! [X0,X1] :
( in(sK34(X0,X1),X0)
| element(X0,powerset(X1)) )
| ~ spl102_184 ),
inference(avatar_component_clause,[],[f2617]) ).
fof(f8343,plain,
( spl102_532
| ~ spl102_99
| ~ spl102_101
| ~ spl102_146 ),
inference(avatar_split_clause,[],[f2358,f2215,f1930,f1915,f8341]) ).
fof(f8341,plain,
( spl102_532
<=> ! [X0] : sP22(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_532])]) ).
fof(f2215,plain,
( spl102_146
<=> ! [X0,X1] : sP22(X1,X0,set_difference(X0,set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_146])]) ).
fof(f2358,plain,
( ! [X0] : sP22(X0,X0,X0)
| ~ spl102_99
| ~ spl102_101
| ~ spl102_146 ),
inference(forward_demodulation,[],[f2351,f1931]) ).
fof(f2351,plain,
( ! [X0] : sP22(X0,X0,set_difference(X0,sK95))
| ~ spl102_99
| ~ spl102_146 ),
inference(superposition,[],[f2216,f1916]) ).
fof(f2216,plain,
( ! [X0,X1] : sP22(X1,X0,set_difference(X0,set_difference(X0,X1)))
| ~ spl102_146 ),
inference(avatar_component_clause,[],[f2215]) ).
fof(f8339,plain,
( spl102_531
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_99
| ~ spl102_146 ),
inference(avatar_split_clause,[],[f2357,f2215,f1915,f1661,f1653,f1403,f8337]) ).
fof(f8337,plain,
( spl102_531
<=> ! [X0] : sP22(sK95,X0,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_531])]) ).
fof(f2357,plain,
( ! [X0] : sP22(sK95,X0,sK95)
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_99
| ~ spl102_146 ),
inference(forward_demodulation,[],[f2356,f1713]) ).
fof(f2356,plain,
( ! [X0] : sP22(empty_set,X0,sK95)
| ~ spl102_57
| ~ spl102_99
| ~ spl102_146 ),
inference(forward_demodulation,[],[f2350,f1916]) ).
fof(f2350,plain,
( ! [X0] : sP22(empty_set,X0,set_difference(X0,X0))
| ~ spl102_57
| ~ spl102_146 ),
inference(superposition,[],[f2216,f1654]) ).
fof(f8335,plain,
( spl102_530
| ~ spl102_7
| ~ spl102_55
| ~ spl102_57
| ~ spl102_59
| ~ spl102_146 ),
inference(avatar_split_clause,[],[f2355,f2215,f1661,f1653,f1645,f1403,f8333]) ).
fof(f8333,plain,
( spl102_530
<=> ! [X0] : sP22(X0,sK95,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_530])]) ).
fof(f2355,plain,
( ! [X0] : sP22(X0,sK95,sK95)
| ~ spl102_7
| ~ spl102_55
| ~ spl102_57
| ~ spl102_59
| ~ spl102_146 ),
inference(forward_demodulation,[],[f2354,f1713]) ).
fof(f2354,plain,
( ! [X0] : sP22(X0,empty_set,empty_set)
| ~ spl102_55
| ~ spl102_57
| ~ spl102_146 ),
inference(forward_demodulation,[],[f2349,f1654]) ).
fof(f2349,plain,
( ! [X0] : sP22(X0,empty_set,set_difference(empty_set,empty_set))
| ~ spl102_55
| ~ spl102_146 ),
inference(superposition,[],[f2216,f1646]) ).
fof(f8331,plain,
( spl102_529
| ~ spl102_91
| ~ spl102_99 ),
inference(avatar_split_clause,[],[f1920,f1915,f1852,f8329]) ).
fof(f8329,plain,
( spl102_529
<=> ! [X0] : sP24(X0,X0,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_529])]) ).
fof(f1920,plain,
( ! [X0] : sP24(X0,X0,sK95)
| ~ spl102_91
| ~ spl102_99 ),
inference(superposition,[],[f1853,f1916]) ).
fof(f8327,plain,
( spl102_528
| ~ spl102_33
| ~ spl102_87 ),
inference(avatar_split_clause,[],[f1878,f1836,f1524,f8325]) ).
fof(f8325,plain,
( spl102_528
<=> ! [X0] : element(X0,sK30(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_528])]) ).
fof(f1524,plain,
( spl102_33
<=> ! [X0] : in(X0,sK30(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_33])]) ).
fof(f1878,plain,
( ! [X0] : element(X0,sK30(X0))
| ~ spl102_33
| ~ spl102_87 ),
inference(resolution,[],[f1837,f1525]) ).
fof(f1525,plain,
( ! [X0] : in(X0,sK30(X0))
| ~ spl102_33 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f8323,plain,
( spl102_527
| ~ spl102_33
| ~ spl102_86 ),
inference(avatar_split_clause,[],[f1874,f1832,f1524,f8321]) ).
fof(f8321,plain,
( spl102_527
<=> ! [X0] : ~ in(sK30(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_527])]) ).
fof(f1874,plain,
( ! [X0] : ~ in(sK30(X0),X0)
| ~ spl102_33
| ~ spl102_86 ),
inference(resolution,[],[f1833,f1525]) ).
fof(f8319,plain,
( ~ spl102_526
| ~ spl102_7
| ~ spl102_52
| ~ spl102_59
| ~ spl102_77 ),
inference(avatar_split_clause,[],[f1797,f1787,f1661,f1631,f1403,f8316]) ).
fof(f8316,plain,
( spl102_526
<=> sK95 = powerset(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_526])]) ).
fof(f1631,plain,
( spl102_52
<=> ! [X0] : empty_set != unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_52])]) ).
fof(f1797,plain,
( sK95 != powerset(sK95)
| ~ spl102_7
| ~ spl102_52
| ~ spl102_59
| ~ spl102_77 ),
inference(forward_demodulation,[],[f1796,f1713]) ).
fof(f1796,plain,
( empty_set != powerset(sK95)
| ~ spl102_52
| ~ spl102_77 ),
inference(superposition,[],[f1632,f1789]) ).
fof(f1632,plain,
( ! [X0] : empty_set != unordered_pair(X0,X0)
| ~ spl102_52 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f8314,plain,
( spl102_525
| ~ spl102_53
| ~ spl102_77 ),
inference(avatar_split_clause,[],[f1795,f1787,f1635,f8311]) ).
fof(f8311,plain,
( spl102_525
<=> in(sK95,powerset(sK95)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_525])]) ).
fof(f1795,plain,
( in(sK95,powerset(sK95))
| ~ spl102_53
| ~ spl102_77 ),
inference(superposition,[],[f1636,f1789]) ).
fof(f8309,plain,
( spl102_524
| ~ spl102_43
| ~ spl102_46 ),
inference(avatar_split_clause,[],[f1638,f1606,f1565,f8307]) ).
fof(f8307,plain,
( spl102_524
<=> ! [X0] : sP19(powerset(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_524])]) ).
fof(f1565,plain,
( spl102_43
<=> ! [X0] : sP19(X0,union(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_43])]) ).
fof(f1606,plain,
( spl102_46
<=> ! [X0] : union(powerset(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_46])]) ).
fof(f1638,plain,
( ! [X0] : sP19(powerset(X0),X0)
| ~ spl102_43
| ~ spl102_46 ),
inference(superposition,[],[f1566,f1607]) ).
fof(f1607,plain,
( ! [X0] : union(powerset(X0)) = X0
| ~ spl102_46 ),
inference(avatar_component_clause,[],[f1606]) ).
fof(f1566,plain,
( ! [X0] : sP19(X0,union(X0))
| ~ spl102_43 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f8305,plain,
( ~ spl102_1
| spl102_523
| ~ spl102_66
| ~ spl102_502 ),
inference(avatar_split_clause,[],[f8027,f8017,f1689,f8302,f1373]) ).
fof(f1373,plain,
( spl102_1
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_1])]) ).
fof(f8027,plain,
( relation(function_inverse(sK25))
| ~ relation(sK25)
| ~ spl102_66
| ~ spl102_502 ),
inference(superposition,[],[f1690,f8019]) ).
fof(f8284,plain,
( spl102_522
| ~ spl102_40
| ~ spl102_70 ),
inference(avatar_split_clause,[],[f1753,f1705,f1552,f8282]) ).
fof(f8282,plain,
( spl102_522
<=> ! [X0] : ~ empty(sK67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_522])]) ).
fof(f1753,plain,
( ! [X0] : ~ empty(sK67(X0))
| ~ spl102_40
| ~ spl102_70 ),
inference(resolution,[],[f1706,f1553]) ).
fof(f8280,plain,
( spl102_521
| ~ spl102_7
| ~ spl102_19
| ~ spl102_59 ),
inference(avatar_split_clause,[],[f1717,f1661,f1463,f1403,f8277]) ).
fof(f8277,plain,
( spl102_521
<=> sK95 = sK101 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_521])]) ).
fof(f1463,plain,
( spl102_19
<=> empty(sK101) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_19])]) ).
fof(f1717,plain,
( sK95 = sK101
| ~ spl102_7
| ~ spl102_19
| ~ spl102_59 ),
inference(forward_demodulation,[],[f1715,f1713]) ).
fof(f1715,plain,
( empty_set = sK101
| ~ spl102_19
| ~ spl102_59 ),
inference(resolution,[],[f1662,f1465]) ).
fof(f1465,plain,
( empty(sK101)
| ~ spl102_19 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f8275,plain,
( spl102_520
| ~ spl102_7
| ~ spl102_10
| ~ spl102_59 ),
inference(avatar_split_clause,[],[f1716,f1661,f1418,f1403,f8272]) ).
fof(f8272,plain,
( spl102_520
<=> sK95 = sK97 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_520])]) ).
fof(f1418,plain,
( spl102_10
<=> empty(sK97) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_10])]) ).
fof(f1716,plain,
( sK95 = sK97
| ~ spl102_7
| ~ spl102_10
| ~ spl102_59 ),
inference(forward_demodulation,[],[f1714,f1713]) ).
fof(f1714,plain,
( empty_set = sK97
| ~ spl102_10
| ~ spl102_59 ),
inference(resolution,[],[f1662,f1420]) ).
fof(f1420,plain,
( empty(sK97)
| ~ spl102_10 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f8270,plain,
( spl102_519
| ~ spl102_7
| ~ spl102_59 ),
inference(avatar_split_clause,[],[f1713,f1661,f1403,f8267]) ).
fof(f8265,plain,
( spl102_518
| ~ spl102_25
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1596,f1544,f1490,f8263]) ).
fof(f8263,plain,
( spl102_518
<=> ! [X0] : sP10(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_518])]) ).
fof(f1596,plain,
( ! [X0] : sP10(identity_relation(X0))
| ~ spl102_25
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1491]) ).
fof(f8261,plain,
( spl102_517
| ~ spl102_125
| ~ spl102_502 ),
inference(avatar_split_clause,[],[f8024,f8017,f2066,f8258]) ).
fof(f8258,plain,
( spl102_517
<=> sK25 = relation_inverse(function_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_517])]) ).
fof(f2066,plain,
( spl102_125
<=> sK25 = relation_inverse(relation_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_125])]) ).
fof(f8024,plain,
( sK25 = relation_inverse(function_inverse(sK25))
| ~ spl102_125
| ~ spl102_502 ),
inference(superposition,[],[f2068,f8019]) ).
fof(f2068,plain,
( sK25 = relation_inverse(relation_inverse(sK25))
| ~ spl102_125 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f8256,plain,
( spl102_516
| ~ spl102_25
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1587,f1540,f1490,f8254]) ).
fof(f8254,plain,
( spl102_516
<=> ! [X0] : sP8(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_516])]) ).
fof(f1587,plain,
( ! [X0] : sP8(identity_relation(X0))
| ~ spl102_25
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1491]) ).
fof(f8251,plain,
( spl102_515
| ~ spl102_27
| ~ spl102_36 ),
inference(avatar_split_clause,[],[f1583,f1536,f1498,f8249]) ).
fof(f8249,plain,
( spl102_515
<=> ! [X0] : relation(sK69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_515])]) ).
fof(f1536,plain,
( spl102_36
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_36])]) ).
fof(f1583,plain,
( ! [X0] : relation(sK69(X0))
| ~ spl102_27
| ~ spl102_36 ),
inference(resolution,[],[f1537,f1499]) ).
fof(f1537,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl102_36 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f8246,plain,
( spl102_514
| ~ spl102_27
| ~ spl102_35 ),
inference(avatar_split_clause,[],[f1573,f1532,f1498,f8244]) ).
fof(f8244,plain,
( spl102_514
<=> ! [X0] : function(sK69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_514])]) ).
fof(f1573,plain,
( ! [X0] : function(sK69(X0))
| ~ spl102_27
| ~ spl102_35 ),
inference(resolution,[],[f1533,f1499]) ).
fof(f8219,plain,
( spl102_513
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_129 ),
inference(avatar_split_clause,[],[f2269,f2144,f1661,f1510,f1403,f8217]) ).
fof(f8217,plain,
( spl102_513
<=> ! [X0] : disjoint(X0,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_513])]) ).
fof(f2269,plain,
( ! [X0] : disjoint(X0,sK95)
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_129 ),
inference(forward_demodulation,[],[f2264,f1713]) ).
fof(f2264,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl102_30
| ~ spl102_129 ),
inference(resolution,[],[f2145,f1511]) ).
fof(f8215,plain,
( spl102_512
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_128 ),
inference(avatar_split_clause,[],[f2263,f2140,f1661,f1510,f1403,f8213]) ).
fof(f8213,plain,
( spl102_512
<=> ! [X0] : disjoint(sK95,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_512])]) ).
fof(f2263,plain,
( ! [X0] : disjoint(sK95,X0)
| ~ spl102_7
| ~ spl102_30
| ~ spl102_59
| ~ spl102_128 ),
inference(forward_demodulation,[],[f2258,f1713]) ).
fof(f2258,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl102_30
| ~ spl102_128 ),
inference(resolution,[],[f2141,f1511]) ).
fof(f8211,plain,
( spl102_511
| ~ spl102_51
| ~ spl102_99 ),
inference(avatar_split_clause,[],[f1921,f1915,f1627,f8209]) ).
fof(f8209,plain,
( spl102_511
<=> ! [X0] : subset(sK95,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_511])]) ).
fof(f1921,plain,
( ! [X0] : subset(sK95,X0)
| ~ spl102_51
| ~ spl102_99 ),
inference(superposition,[],[f1628,f1916]) ).
fof(f8207,plain,
( spl102_510
| ~ spl102_7
| ~ spl102_23
| ~ spl102_59
| ~ spl102_73 ),
inference(avatar_split_clause,[],[f1779,f1762,f1661,f1482,f1403,f8205]) ).
fof(f8205,plain,
( spl102_510
<=> ! [X0] : ~ proper_subset(X0,sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_510])]) ).
fof(f1482,plain,
( spl102_23
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_23])]) ).
fof(f1779,plain,
( ! [X0] : ~ proper_subset(X0,sK95)
| ~ spl102_7
| ~ spl102_23
| ~ spl102_59
| ~ spl102_73 ),
inference(forward_demodulation,[],[f1775,f1713]) ).
fof(f1775,plain,
( ! [X0] : ~ proper_subset(X0,empty_set)
| ~ spl102_23
| ~ spl102_73 ),
inference(resolution,[],[f1763,f1483]) ).
fof(f1483,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl102_23 ),
inference(avatar_component_clause,[],[f1482]) ).
fof(f8203,plain,
( spl102_509
| ~ spl102_33
| ~ spl102_70 ),
inference(avatar_split_clause,[],[f1752,f1705,f1524,f8201]) ).
fof(f8201,plain,
( spl102_509
<=> ! [X0] : ~ empty(sK30(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_509])]) ).
fof(f1752,plain,
( ! [X0] : ~ empty(sK30(X0))
| ~ spl102_33
| ~ spl102_70 ),
inference(resolution,[],[f1706,f1525]) ).
fof(f8097,plain,
( spl102_508
| ~ spl102_1
| ~ spl102_351 ),
inference(avatar_split_clause,[],[f4809,f4792,f1373,f8095]) ).
fof(f8095,plain,
( spl102_508
<=> ! [X0] : relation_image(sK25,X0) = relation_image(sK25,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(sK25))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_508])]) ).
fof(f4792,plain,
( spl102_351
<=> ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1)))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_351])]) ).
fof(f4809,plain,
( ! [X0] : relation_image(sK25,X0) = relation_image(sK25,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(sK25)))))
| ~ spl102_1
| ~ spl102_351 ),
inference(resolution,[],[f4793,f1375]) ).
fof(f1375,plain,
( relation(sK25)
| ~ spl102_1 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f4793,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1))))) )
| ~ spl102_351 ),
inference(avatar_component_clause,[],[f4792]) ).
fof(f8093,plain,
( spl102_507
| ~ spl102_1
| ~ spl102_338 ),
inference(avatar_split_clause,[],[f4543,f4435,f1373,f8091]) ).
fof(f8091,plain,
( spl102_507
<=> ! [X0] : relation_dom(relation_dom_restriction(sK25,X0)) = set_difference(relation_dom(sK25),set_difference(relation_dom(sK25),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_507])]) ).
fof(f4435,plain,
( spl102_338
<=> ! [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,[spl102_338])]) ).
fof(f4543,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK25,X0)) = set_difference(relation_dom(sK25),set_difference(relation_dom(sK25),X0))
| ~ spl102_1
| ~ spl102_338 ),
inference(resolution,[],[f4436,f1375]) ).
fof(f4436,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) )
| ~ spl102_338 ),
inference(avatar_component_clause,[],[f4435]) ).
fof(f8089,plain,
( spl102_506
| ~ spl102_1
| ~ spl102_337 ),
inference(avatar_split_clause,[],[f4502,f4431,f1373,f8087]) ).
fof(f8087,plain,
( spl102_506
<=> ! [X0] : relation_rng(relation_rng_restriction(X0,sK25)) = set_difference(relation_rng(sK25),set_difference(relation_rng(sK25),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_506])]) ).
fof(f4431,plain,
( spl102_337
<=> ! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_337])]) ).
fof(f4502,plain,
( ! [X0] : relation_rng(relation_rng_restriction(X0,sK25)) = set_difference(relation_rng(sK25),set_difference(relation_rng(sK25),X0))
| ~ spl102_1
| ~ spl102_337 ),
inference(resolution,[],[f4432,f1375]) ).
fof(f4432,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0)) )
| ~ spl102_337 ),
inference(avatar_component_clause,[],[f4431]) ).
fof(f8074,plain,
( ~ spl102_505
| spl102_133
| ~ spl102_502 ),
inference(avatar_split_clause,[],[f8023,f8017,f2160,f8071]) ).
fof(f2160,plain,
( spl102_133
<=> empty(relation_inverse(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_133])]) ).
fof(f8023,plain,
( ~ empty(function_inverse(sK25))
| spl102_133
| ~ spl102_502 ),
inference(superposition,[],[f2162,f8019]) ).
fof(f2162,plain,
( ~ empty(relation_inverse(sK25))
| spl102_133 ),
inference(avatar_component_clause,[],[f2160]) ).
fof(f8037,plain,
( spl102_504
| ~ spl102_1
| ~ spl102_298 ),
inference(avatar_split_clause,[],[f4033,f3948,f1373,f8035]) ).
fof(f8035,plain,
( spl102_504
<=> ! [X0,X1] : relation_dom_restriction(relation_rng_restriction(X0,sK25),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK25,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_504])]) ).
fof(f3948,plain,
( spl102_298
<=> ! [X2,X0,X1] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_298])]) ).
fof(f4033,plain,
( ! [X0,X1] : relation_dom_restriction(relation_rng_restriction(X0,sK25),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK25,X1))
| ~ spl102_1
| ~ spl102_298 ),
inference(resolution,[],[f3949,f1375]) ).
fof(f3949,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) )
| ~ spl102_298 ),
inference(avatar_component_clause,[],[f3948]) ).
fof(f8033,plain,
( spl102_503
| ~ spl102_1
| ~ spl102_295 ),
inference(avatar_split_clause,[],[f4003,f3934,f1373,f8031]) ).
fof(f8031,plain,
( spl102_503
<=> ! [X0] :
( relation_rng(relation_composition(X0,sK25)) = relation_image(sK25,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_503])]) ).
fof(f3934,plain,
( spl102_295
<=> ! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_295])]) ).
fof(f4003,plain,
( ! [X0] :
( relation_rng(relation_composition(X0,sK25)) = relation_image(sK25,relation_rng(X0))
| ~ relation(X0) )
| ~ spl102_1
| ~ spl102_295 ),
inference(resolution,[],[f3935,f1375]) ).
fof(f3935,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl102_295 ),
inference(avatar_component_clause,[],[f3934]) ).
fof(f8020,plain,
( ~ spl102_1
| ~ spl102_2
| spl102_502
| ~ spl102_3
| ~ spl102_259 ),
inference(avatar_split_clause,[],[f3629,f3556,f1383,f8017,f1378,f1373]) ).
fof(f1378,plain,
( spl102_2
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_2])]) ).
fof(f1383,plain,
( spl102_3
<=> one_to_one(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_3])]) ).
fof(f3556,plain,
( spl102_259
<=> ! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_259])]) ).
fof(f3629,plain,
( function_inverse(sK25) = relation_inverse(sK25)
| ~ function(sK25)
| ~ relation(sK25)
| ~ spl102_3
| ~ spl102_259 ),
inference(resolution,[],[f3557,f1385]) ).
fof(f1385,plain,
( one_to_one(sK25)
| ~ spl102_3 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f3557,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl102_259 ),
inference(avatar_component_clause,[],[f3556]) ).
fof(f8003,plain,
( spl102_501
| ~ spl102_111
| ~ spl102_500 ),
inference(avatar_split_clause,[],[f7999,f7996,f1982,f8001]) ).
fof(f8001,plain,
( spl102_501
<=> ! [X0,X5,X2,X1] :
( ~ in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| sP3(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK45(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),X5),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_501])]) ).
fof(f1982,plain,
( spl102_111
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_111])]) ).
fof(f7996,plain,
( spl102_500
<=> ! [X0,X5,X2,X1] :
( sP3(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK45(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),X5),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_500])]) ).
fof(f7999,plain,
( ! [X2,X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| sP3(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK45(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),X5),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1) )
| ~ spl102_111
| ~ spl102_500 ),
inference(forward_demodulation,[],[f7997,f1983]) ).
fof(f1983,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl102_111 ),
inference(avatar_component_clause,[],[f1982]) ).
fof(f7997,plain,
( ! [X2,X0,X1,X5] :
( sP3(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK45(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),X5),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) )
| ~ spl102_500 ),
inference(avatar_component_clause,[],[f7996]) ).
fof(f7998,plain,
spl102_500,
inference(avatar_split_clause,[],[f1238,f7996]) ).
fof(f1238,plain,
! [X2,X0,X1,X5] :
( sP3(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK45(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),X5),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f936,f1170,f1170,f1170]) ).
fof(f1170,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1008,f728]) ).
fof(f728,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f212]) ).
fof(f212,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f1008,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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(f936,plain,
! [X2,X0,X1,X5] :
( sP3(X0,X1,X2)
| ~ in(ordered_pair(X5,sK45(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK44(X0,X1,X2),X5),X1)
| ~ in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f562,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK45(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK44(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),X0)
& in(ordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),X1) )
| in(ordered_pair(sK44(X0,X1,X2),sK45(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(sK47(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK47(X0,X1,X7,X8)),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47])],[f558,f561,f560,f559]) ).
fof(f559,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,sK45(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK44(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK45(X0,X1,X2)),X0)
& in(ordered_pair(sK44(X0,X1,X2),X6),X1) )
| in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK45(X0,X1,X2)),X0)
& in(ordered_pair(sK44(X0,X1,X2),X6),X1) )
=> ( in(ordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),X0)
& in(ordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f561,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
=> ( in(ordered_pair(sK47(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK47(X0,X1,X7,X8)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f558,plain,
! [X0,X1,X2] :
( ( sP3(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) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f557]) ).
fof(f557,plain,
! [X1,X0,X2] :
( ( sP3(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) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f442]) ).
fof(f442,plain,
! [X1,X0,X2] :
( sP3(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,[sP3])]) ).
fof(f7968,plain,
( spl102_499
| ~ spl102_111
| ~ spl102_497 ),
inference(avatar_split_clause,[],[f7960,f7956,f1982,f7966]) ).
fof(f7966,plain,
( spl102_499
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2)
| ~ in(sK54(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_499])]) ).
fof(f7956,plain,
( spl102_497
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_497])]) ).
fof(f7960,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2)
| ~ in(sK54(X0,X1,X2),X1) )
| ~ spl102_111
| ~ spl102_497 ),
inference(forward_demodulation,[],[f7959,f1983]) ).
fof(f7959,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) )
| ~ spl102_111
| ~ spl102_497 ),
inference(forward_demodulation,[],[f7957,f1983]) ).
fof(f7957,plain,
( ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) )
| ~ spl102_497 ),
inference(avatar_component_clause,[],[f7956]) ).
fof(f7964,plain,
spl102_498,
inference(avatar_split_clause,[],[f1363,f7962]) ).
fof(f7962,plain,
( spl102_498
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2)
| ~ in(sK76(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_498])]) ).
fof(f1363,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2)
| ~ in(sK76(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f1362,f1005]) ).
fof(f1005,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1362,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1279,f1005]) ).
fof(f1279,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1044,f1170,f1170]) ).
fof(f1044,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f637,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
& in(sK76(X0,X1,X2),X1) )
| in(ordered_pair(sK75(X0,X1,X2),sK76(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) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76])],[f635,f636]) ).
fof(f636,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(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
| ~ in(sK76(X0,X1,X2),X1)
| ~ in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
& in(sK76(X0,X1,X2),X1) )
| in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f635,plain,
! [X0,X1,X2] :
( ( sP15(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) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f634]) ).
fof(f634,plain,
! [X1,X0,X2] :
( ( sP15(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) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(flattening,[],[f633]) ).
fof(f633,plain,
! [X1,X0,X2] :
( ( sP15(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) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f460]) ).
fof(f460,plain,
! [X1,X0,X2] :
( sP15(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,[sP15])]) ).
fof(f7958,plain,
spl102_497,
inference(avatar_split_clause,[],[f1252,f7956]) ).
fof(f1252,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f953,f1170,f1170]) ).
fof(f953,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f581,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
& in(sK54(X0,X1,X2),X1) )
| in(ordered_pair(sK54(X0,X1,X2),sK55(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) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f579,f580]) ).
fof(f580,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(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
| ~ in(sK54(X0,X1,X2),X1)
| ~ in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
& in(sK54(X0,X1,X2),X1) )
| in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f579,plain,
! [X0,X1,X2] :
( ( sP5(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) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f578]) ).
fof(f578,plain,
! [X0,X1,X2] :
( ( sP5(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) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(flattening,[],[f577]) ).
fof(f577,plain,
! [X0,X1,X2] :
( ( sP5(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) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f445]) ).
fof(f445,plain,
! [X0,X1,X2] :
( sP5(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,[sP5])]) ).
fof(f7732,plain,
( spl102_496
| ~ spl102_111
| ~ spl102_492 ),
inference(avatar_split_clause,[],[f7716,f7712,f1982,f7730]) ).
fof(f7730,plain,
( spl102_496
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_496])]) ).
fof(f7712,plain,
( spl102_492
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_492])]) ).
fof(f7716,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_492 ),
inference(forward_demodulation,[],[f7715,f1983]) ).
fof(f7715,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| sP5(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) )
| ~ spl102_111
| ~ spl102_492 ),
inference(forward_demodulation,[],[f7713,f1983]) ).
fof(f7713,plain,
( ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) )
| ~ spl102_492 ),
inference(avatar_component_clause,[],[f7712]) ).
fof(f7728,plain,
( spl102_495
| ~ spl102_111
| ~ spl102_491 ),
inference(avatar_split_clause,[],[f7710,f7706,f1982,f7726]) ).
fof(f7726,plain,
( spl102_495
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_495])]) ).
fof(f7706,plain,
( spl102_491
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_491])]) ).
fof(f7710,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| sP3(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_491 ),
inference(forward_demodulation,[],[f7709,f1983]) ).
fof(f7709,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) )
| ~ spl102_111
| ~ spl102_491 ),
inference(forward_demodulation,[],[f7707,f1983]) ).
fof(f7707,plain,
( ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) )
| ~ spl102_491 ),
inference(avatar_component_clause,[],[f7706]) ).
fof(f7724,plain,
( spl102_494
| ~ spl102_111
| ~ spl102_490 ),
inference(avatar_split_clause,[],[f7704,f7700,f1982,f7722]) ).
fof(f7722,plain,
( spl102_494
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2))),X0)
| sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_494])]) ).
fof(f7700,plain,
( spl102_490
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_490])]) ).
fof(f7704,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2))),X0)
| sP3(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_490 ),
inference(forward_demodulation,[],[f7703,f1983]) ).
fof(f7703,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2))),X0)
| sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) )
| ~ spl102_111
| ~ spl102_490 ),
inference(forward_demodulation,[],[f7701,f1983]) ).
fof(f7701,plain,
( ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) )
| ~ spl102_490 ),
inference(avatar_component_clause,[],[f7700]) ).
fof(f7720,plain,
spl102_493,
inference(avatar_split_clause,[],[f1365,f7718]) ).
fof(f7718,plain,
( spl102_493
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_493])]) ).
fof(f1365,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2) ),
inference(forward_demodulation,[],[f1364,f1005]) ).
fof(f1364,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| sP15(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1280,f1005]) ).
fof(f1280,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1043,f1170,f1170]) ).
fof(f1043,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X0)
| in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f7714,plain,
spl102_492,
inference(avatar_split_clause,[],[f1253,f7712]) ).
fof(f1253,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f952,f1170,f1170]) ).
fof(f952,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X0)
| in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f7708,plain,
spl102_491,
inference(avatar_split_clause,[],[f1240,f7706]) ).
fof(f1240,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f934,f1170,f1170]) ).
fof(f934,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(ordered_pair(sK44(X0,X1,X2),sK46(X0,X1,X2)),X1)
| in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f7702,plain,
spl102_490,
inference(avatar_split_clause,[],[f1239,f7700]) ).
fof(f1239,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK46(X0,X1,X2),sK46(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),unordered_pair(sK44(X0,X1,X2),sK44(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f935,f1170,f1170]) ).
fof(f935,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| in(ordered_pair(sK46(X0,X1,X2),sK45(X0,X1,X2)),X0)
| in(ordered_pair(sK44(X0,X1,X2),sK45(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f7629,plain,
( spl102_489
| ~ spl102_111
| ~ spl102_487 ),
inference(avatar_split_clause,[],[f7621,f7617,f1982,f7627]) ).
fof(f7627,plain,
( spl102_489
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1),sK42(X0,X1)),unordered_pair(sK42(X0,X1),sK43(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_489])]) ).
fof(f7617,plain,
( spl102_487
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_487])]) ).
fof(f7621,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1),sK42(X0,X1)),unordered_pair(sK42(X0,X1),sK43(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_487 ),
inference(forward_demodulation,[],[f7620,f1983]) ).
fof(f7620,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_487 ),
inference(forward_demodulation,[],[f7618,f1983]) ).
fof(f7618,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_487 ),
inference(avatar_component_clause,[],[f7617]) ).
fof(f7625,plain,
( spl102_488
| ~ spl102_111
| ~ spl102_486 ),
inference(avatar_split_clause,[],[f7615,f7611,f1982,f7623]) ).
fof(f7623,plain,
( spl102_488
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK42(X0,X1)),unordered_pair(sK42(X0,X1),sK43(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_488])]) ).
fof(f7611,plain,
( spl102_486
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_486])]) ).
fof(f7615,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK42(X0,X1)),unordered_pair(sK42(X0,X1),sK43(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_486 ),
inference(forward_demodulation,[],[f7614,f1983]) ).
fof(f7614,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_486 ),
inference(forward_demodulation,[],[f7612,f1983]) ).
fof(f7612,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_486 ),
inference(avatar_component_clause,[],[f7611]) ).
fof(f7619,plain,
spl102_487,
inference(avatar_split_clause,[],[f1235,f7617]) ).
fof(f1235,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f927,f1170,f1170]) ).
fof(f927,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK43(X0,X1),sK42(X0,X1)),X0)
| in(ordered_pair(sK42(X0,X1),sK43(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f554]) ).
fof(f554,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK43(X0,X1),sK42(X0,X1)),X0)
| ~ in(ordered_pair(sK42(X0,X1),sK43(X0,X1)),X1) )
& ( in(ordered_pair(sK43(X0,X1),sK42(X0,X1)),X0)
| in(ordered_pair(sK42(X0,X1),sK43(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,[sK42,sK43])],[f552,f553]) ).
fof(f553,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(sK43(X0,X1),sK42(X0,X1)),X0)
| ~ in(ordered_pair(sK42(X0,X1),sK43(X0,X1)),X1) )
& ( in(ordered_pair(sK43(X0,X1),sK42(X0,X1)),X0)
| in(ordered_pair(sK42(X0,X1),sK43(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f552,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,[],[f551]) ).
fof(f551,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,[],[f363]) ).
fof(f363,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,[],[f37]) ).
fof(f37,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(f7613,plain,
spl102_486,
inference(avatar_split_clause,[],[f1234,f7611]) ).
fof(f1234,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1),sK42(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1),sK43(X0,X1)),unordered_pair(sK42(X0,X1),sK42(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f928,f1170,f1170]) ).
fof(f928,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK43(X0,X1),sK42(X0,X1)),X0)
| ~ in(ordered_pair(sK42(X0,X1),sK43(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f554]) ).
fof(f7534,plain,
( spl102_485
| ~ spl102_111
| ~ spl102_483 ),
inference(avatar_split_clause,[],[f7526,f7522,f1982,f7532]) ).
fof(f7532,plain,
( spl102_485
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_485])]) ).
fof(f7522,plain,
( spl102_483
<=> ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_483])]) ).
fof(f7526,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_483 ),
inference(forward_demodulation,[],[f7525,f1983]) ).
fof(f7525,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_483 ),
inference(forward_demodulation,[],[f7523,f1983]) ).
fof(f7523,plain,
( ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_483 ),
inference(avatar_component_clause,[],[f7522]) ).
fof(f7530,plain,
( spl102_484
| ~ spl102_111
| ~ spl102_482 ),
inference(avatar_split_clause,[],[f7520,f7516,f1982,f7528]) ).
fof(f7528,plain,
( spl102_484
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_484])]) ).
fof(f7516,plain,
( spl102_482
<=> ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_482])]) ).
fof(f7520,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_482 ),
inference(forward_demodulation,[],[f7519,f1983]) ).
fof(f7519,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_482 ),
inference(forward_demodulation,[],[f7517,f1983]) ).
fof(f7517,plain,
( ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_482 ),
inference(avatar_component_clause,[],[f7516]) ).
fof(f7524,plain,
spl102_483,
inference(avatar_split_clause,[],[f1228,f7522]) ).
fof(f1228,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f920,f1170,f1170]) ).
fof(f920,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X1)
| in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f546]) ).
fof(f546,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X1)
| ~ in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0) )
& ( in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X1)
| in(ordered_pair(sK38(X0,X1),sK39(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,[sK38,sK39])],[f544,f545]) ).
fof(f545,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(sK38(X0,X1),sK39(X0,X1)),X1)
| ~ in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0) )
& ( in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X1)
| in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f544,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,[],[f543]) ).
fof(f543,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,[],[f361]) ).
fof(f361,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,[],[f20]) ).
fof(f20,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(f7518,plain,
spl102_482,
inference(avatar_split_clause,[],[f1227,f7516]) ).
fof(f1227,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f921,f1170,f1170]) ).
fof(f921,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X1)
| ~ in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f546]) ).
fof(f7467,plain,
( spl102_481
| ~ spl102_111
| ~ spl102_479 ),
inference(avatar_split_clause,[],[f7459,f7456,f1982,f7465]) ).
fof(f7465,plain,
( spl102_481
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X8,sK47(X0,X1,X7,X8)),unordered_pair(sK47(X0,X1,X7,X8),sK47(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_481])]) ).
fof(f7456,plain,
( spl102_479
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(sK47(X0,X1,X7,X8),X8),unordered_pair(sK47(X0,X1,X7,X8),sK47(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_479])]) ).
fof(f7459,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK47(X0,X1,X7,X8)),unordered_pair(sK47(X0,X1,X7,X8),sK47(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_479 ),
inference(forward_demodulation,[],[f7457,f1983]) ).
fof(f7457,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK47(X0,X1,X7,X8),X8),unordered_pair(sK47(X0,X1,X7,X8),sK47(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) )
| ~ spl102_479 ),
inference(avatar_component_clause,[],[f7456]) ).
fof(f7463,plain,
spl102_480,
inference(avatar_split_clause,[],[f1368,f7461]) ).
fof(f7461,plain,
( spl102_480
<=> ! [X2,X0,X1] :
( sK85(X0,X1,X2) = unordered_pair(unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK86(X0,X1,X2),sK86(X0,X1,X2)))
| sP20(X0,X1,X2)
| in(sK85(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_480])]) ).
fof(f1368,plain,
! [X2,X0,X1] :
( sK85(X0,X1,X2) = unordered_pair(unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK86(X0,X1,X2),sK86(X0,X1,X2)))
| sP20(X0,X1,X2)
| in(sK85(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f1293,f1005]) ).
fof(f1293,plain,
! [X2,X0,X1] :
( sP20(X0,X1,X2)
| sK85(X0,X1,X2) = unordered_pair(unordered_pair(sK86(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK86(X0,X1,X2),sK86(X0,X1,X2)))
| in(sK85(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1118,f1170]) ).
fof(f1118,plain,
! [X2,X0,X1] :
( sP20(X0,X1,X2)
| sK85(X0,X1,X2) = ordered_pair(sK86(X0,X1,X2),sK87(X0,X1,X2))
| in(sK85(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f676,plain,
! [X0,X1,X2] :
( ( sP20(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK85(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK85(X0,X1,X2),X2) )
& ( ( sK85(X0,X1,X2) = ordered_pair(sK86(X0,X1,X2),sK87(X0,X1,X2))
& in(sK87(X0,X1,X2),X0)
& in(sK86(X0,X1,X2),X1) )
| in(sK85(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK88(X0,X1,X8),sK89(X0,X1,X8)) = X8
& in(sK89(X0,X1,X8),X0)
& in(sK88(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP20(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87,sK88,sK89])],[f672,f675,f674,f673]) ).
fof(f673,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) != sK85(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK85(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK85(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK85(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f674,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK85(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK85(X0,X1,X2) = ordered_pair(sK86(X0,X1,X2),sK87(X0,X1,X2))
& in(sK87(X0,X1,X2),X0)
& in(sK86(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f675,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK88(X0,X1,X8),sK89(X0,X1,X8)) = X8
& in(sK89(X0,X1,X8),X0)
& in(sK88(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f672,plain,
! [X0,X1,X2] :
( ( sP20(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) ) )
| ~ sP20(X0,X1,X2) ) ),
inference(rectify,[],[f671]) ).
fof(f671,plain,
! [X1,X0,X2] :
( ( sP20(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) ) )
| ~ sP20(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f468]) ).
fof(f468,plain,
! [X1,X0,X2] :
( sP20(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,[sP20])]) ).
fof(f7458,plain,
spl102_479,
inference(avatar_split_clause,[],[f1242,f7456]) ).
fof(f1242,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK47(X0,X1,X7,X8),X8),unordered_pair(sK47(X0,X1,X7,X8),sK47(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ),
inference(definition_unfolding,[],[f932,f1170,f1170]) ).
fof(f932,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK47(X0,X1,X7,X8),X8),X0)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f7454,plain,
spl102_478,
inference(avatar_split_clause,[],[f757,f7452]) ).
fof(f7452,plain,
( spl102_478
<=> ! [X0,X1] :
( sP1(X0,X1)
| sK29(X0,X1) != apply(X0,sK28(X0,X1))
| ~ in(sK28(X0,X1),relation_rng(X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_478])]) ).
fof(f757,plain,
! [X0,X1] :
( sP1(X0,X1)
| sK29(X0,X1) != apply(X0,sK28(X0,X1))
| ~ in(sK28(X0,X1),relation_rng(X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f488,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( sK29(X0,X1) != apply(X0,sK28(X0,X1))
| ~ in(sK28(X0,X1),relation_rng(X1)) )
& sK28(X0,X1) = apply(X1,sK29(X0,X1))
& in(sK29(X0,X1),relation_dom(X1)) )
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP0(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f486,f487]) ).
fof(f487,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP0(X2,X3,X1,X0) )
=> ( ( ( sK29(X0,X1) != apply(X0,sK28(X0,X1))
| ~ in(sK28(X0,X1),relation_rng(X1)) )
& sK28(X0,X1) = apply(X1,sK29(X0,X1))
& in(sK29(X0,X1),relation_dom(X1)) )
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f486,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP0(X2,X3,X1,X0) )
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP0(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f485]) ).
fof(f485,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f484]) ).
fof(f484,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f439]) ).
fof(f439,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f7450,plain,
spl102_477,
inference(avatar_split_clause,[],[f1359,f7448]) ).
fof(f7448,plain,
( spl102_477
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK74(X0,X1),sK74(X0,X1)),unordered_pair(sK74(X0,X1),sK74(X0,X1))),X1)
| sP13(X0,X1)
| sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK74(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_477])]) ).
fof(f1359,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK74(X0,X1),sK74(X0,X1)),unordered_pair(sK74(X0,X1),sK74(X0,X1))),X1)
| sP13(X0,X1)
| sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK74(X0,X1),X0) ),
inference(inner_rewriting,[],[f1358]) ).
fof(f1358,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK74(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1)
| sP13(X0,X1)
| sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK73(X0,X1),X0) ),
inference(forward_demodulation,[],[f1273,f1005]) ).
fof(f1273,plain,
! [X0,X1] :
( sP13(X0,X1)
| sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK73(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK73(X0,X1),sK74(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1035,f1170]) ).
fof(f1035,plain,
! [X0,X1] :
( sP13(X0,X1)
| sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK73(X0,X1),X0)
| ~ in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f630,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ( sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK73(X0,X1),X0)
| ~ in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) )
& ( ( sK73(X0,X1) = sK74(X0,X1)
& in(sK73(X0,X1),X0) )
| in(ordered_pair(sK73(X0,X1),sK74(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) ) )
| ~ sP13(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f628,f629]) ).
fof(f629,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) ) )
=> ( ( sK73(X0,X1) != sK74(X0,X1)
| ~ in(sK73(X0,X1),X0)
| ~ in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) )
& ( ( sK73(X0,X1) = sK74(X0,X1)
& in(sK73(X0,X1),X0) )
| in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f628,plain,
! [X0,X1] :
( ( sP13(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) ) )
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f627]) ).
fof(f627,plain,
! [X0,X1] :
( ( sP13(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) ) )
| ~ sP13(X0,X1) ) ),
inference(flattening,[],[f626]) ).
fof(f626,plain,
! [X0,X1] :
( ( sP13(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) ) )
| ~ sP13(X0,X1) ) ),
inference(nnf_transformation,[],[f457]) ).
fof(f457,plain,
! [X0,X1] :
( sP13(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f7362,plain,
( spl102_476
| ~ spl102_7
| ~ spl102_59
| ~ spl102_202 ),
inference(avatar_split_clause,[],[f2875,f2871,f1661,f1403,f7359]) ).
fof(f7359,plain,
( spl102_476
<=> sP10(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_476])]) ).
fof(f2871,plain,
( spl102_202
<=> sP10(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_202])]) ).
fof(f2875,plain,
( sP10(sK95)
| ~ spl102_7
| ~ spl102_59
| ~ spl102_202 ),
inference(forward_demodulation,[],[f2873,f1713]) ).
fof(f2873,plain,
( sP10(empty_set)
| ~ spl102_202 ),
inference(avatar_component_clause,[],[f2871]) ).
fof(f7329,plain,
( spl102_475
| ~ spl102_111
| ~ spl102_471 ),
inference(avatar_split_clause,[],[f7280,f7277,f1982,f7327]) ).
fof(f7327,plain,
( spl102_475
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK60(X0,X1,X2),sK60(X0,X1,X2)),unordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2))),X1)
| sP9(X0,X1,X2)
| in(sK59(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_475])]) ).
fof(f7277,plain,
( spl102_471
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK60(X0,X1,X2),sK60(X0,X1,X2))),X1)
| in(sK59(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_471])]) ).
fof(f7280,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK60(X0,X1,X2),sK60(X0,X1,X2)),unordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2))),X1)
| sP9(X0,X1,X2)
| in(sK59(X0,X1,X2),X2) )
| ~ spl102_111
| ~ spl102_471 ),
inference(forward_demodulation,[],[f7278,f1983]) ).
fof(f7278,plain,
( ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK60(X0,X1,X2),sK60(X0,X1,X2))),X1)
| in(sK59(X0,X1,X2),X2) )
| ~ spl102_471 ),
inference(avatar_component_clause,[],[f7277]) ).
fof(f7325,plain,
( spl102_474
| ~ spl102_111
| ~ spl102_470 ),
inference(avatar_split_clause,[],[f7275,f7272,f1982,f7323]) ).
fof(f7323,plain,
( spl102_474
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| sP7(X0,X1,X2)
| in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_474])]) ).
fof(f7272,plain,
( spl102_470
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_470])]) ).
fof(f7275,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| sP7(X0,X1,X2)
| in(sK56(X0,X1,X2),X2) )
| ~ spl102_111
| ~ spl102_470 ),
inference(forward_demodulation,[],[f7273,f1983]) ).
fof(f7273,plain,
( ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| in(sK56(X0,X1,X2),X2) )
| ~ spl102_470 ),
inference(avatar_component_clause,[],[f7272]) ).
fof(f7307,plain,
( spl102_473
| ~ spl102_111
| ~ spl102_468 ),
inference(avatar_split_clause,[],[f7266,f7263,f1982,f7305]) ).
fof(f7305,plain,
( spl102_473
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_473])]) ).
fof(f7263,plain,
( spl102_468
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_468])]) ).
fof(f7266,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1,X2),sK54(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2)
| sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1) )
| ~ spl102_111
| ~ spl102_468 ),
inference(forward_demodulation,[],[f7264,f1983]) ).
fof(f7264,plain,
( ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) )
| ~ spl102_468 ),
inference(avatar_component_clause,[],[f7263]) ).
fof(f7284,plain,
spl102_472,
inference(avatar_split_clause,[],[f1366,f7282]) ).
fof(f7282,plain,
( spl102_472
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| sP15(X0,X1,X2)
| in(sK76(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_472])]) ).
fof(f1366,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK76(X0,X1,X2),sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| sP15(X0,X1,X2)
| in(sK76(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f1281,f1005]) ).
fof(f1281,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK76(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1042,f1170]) ).
fof(f1042,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK76(X0,X1,X2),X1)
| in(ordered_pair(sK75(X0,X1,X2),sK76(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f7279,plain,
spl102_471,
inference(avatar_split_clause,[],[f1263,f7277]) ).
fof(f1263,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),unordered_pair(sK60(X0,X1,X2),sK60(X0,X1,X2))),X1)
| in(sK59(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f969,f1170]) ).
fof(f969,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(ordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),X1)
| in(sK59(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f595,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK59(X0,X1,X2)),X1) )
| ~ in(sK59(X0,X1,X2),X2) )
& ( ( in(sK60(X0,X1,X2),X0)
& in(ordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),X1) )
| in(sK59(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ( in(sK61(X0,X1,X6),X0)
& in(ordered_pair(sK61(X0,X1,X6),X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61])],[f591,f594,f593,f592]) ).
fof(f592,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK59(X0,X1,X2)),X1) )
| ~ in(sK59(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK59(X0,X1,X2)),X1) )
| in(sK59(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f593,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK59(X0,X1,X2)),X1) )
=> ( in(sK60(X0,X1,X2),X0)
& in(ordered_pair(sK60(X0,X1,X2),sK59(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f594,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
=> ( in(sK61(X0,X1,X6),X0)
& in(ordered_pair(sK61(X0,X1,X6),X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f591,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f590]) ).
fof(f590,plain,
! [X1,X0,X2] :
( ( sP9(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| ~ sP9(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f451]) ).
fof(f451,plain,
! [X1,X0,X2] :
( sP9(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f7274,plain,
spl102_470,
inference(avatar_split_clause,[],[f1259,f7272]) ).
fof(f1259,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| in(sK56(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f960,f1170]) ).
fof(f960,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(ordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),X1)
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f588,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(sK56(X0,X1,X2),X4),X1) )
| ~ in(sK56(X0,X1,X2),X2) )
& ( ( in(sK57(X0,X1,X2),X0)
& in(ordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),X1) )
| in(sK56(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1) ) )
& ( ( in(sK58(X0,X1,X6),X0)
& in(ordered_pair(X6,sK58(X0,X1,X6)),X1) )
| ~ in(X6,X2) ) )
| ~ sP7(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58])],[f584,f587,f586,f585]) ).
fof(f585,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X3,X5),X1) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(sK56(X0,X1,X2),X4),X1) )
| ~ in(sK56(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK56(X0,X1,X2),X5),X1) )
| in(sK56(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f586,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK56(X0,X1,X2),X5),X1) )
=> ( in(sK57(X0,X1,X2),X0)
& in(ordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f587,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X6,X8),X1) )
=> ( in(sK58(X0,X1,X6),X0)
& in(ordered_pair(X6,sK58(X0,X1,X6)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f584,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X3,X5),X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1) ) )
& ( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X6,X8),X1) )
| ~ in(X6,X2) ) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f583]) ).
fof(f583,plain,
! [X1,X0,X2] :
( ( sP7(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) ) )
| ~ sP7(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f448]) ).
fof(f448,plain,
! [X1,X0,X2] :
( sP7(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f7270,plain,
spl102_469,
inference(avatar_split_clause,[],[f1258,f7268]) ).
fof(f7268,plain,
( spl102_469
<=> ! [X4,X0,X2,X1] :
( sP7(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK56(X0,X1,X2),X4),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| ~ in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_469])]) ).
fof(f1258,plain,
! [X2,X0,X1,X4] :
( sP7(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK56(X0,X1,X2),X4),unordered_pair(sK56(X0,X1,X2),sK56(X0,X1,X2))),X1)
| ~ in(sK56(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f962,f1170]) ).
fof(f962,plain,
! [X2,X0,X1,X4] :
( sP7(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(sK56(X0,X1,X2),X4),X1)
| ~ in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f7265,plain,
spl102_468,
inference(avatar_split_clause,[],[f1254,f7263]) ).
fof(f1254,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),unordered_pair(sK54(X0,X1,X2),sK54(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f951,f1170]) ).
fof(f951,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| in(sK54(X0,X1,X2),X1)
| in(ordered_pair(sK54(X0,X1,X2),sK55(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f7261,plain,
spl102_467,
inference(avatar_split_clause,[],[f1241,f7259]) ).
fof(f7259,plain,
( spl102_467
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_467])]) ).
fof(f1241,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)
| ~ sP3(X0,X1,X2) ),
inference(definition_unfolding,[],[f933,f1170,f1170,f1170]) ).
fof(f933,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f7185,plain,
( spl102_466
| ~ spl102_111
| ~ spl102_462 ),
inference(avatar_split_clause,[],[f7169,f7166,f1982,f7183]) ).
fof(f7183,plain,
( spl102_466
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK52(X0,X1),sK51(X0,X1)),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK51(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_466])]) ).
fof(f7166,plain,
( spl102_462
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK51(X0,X1),sK52(X0,X1)),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| in(sK51(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_462])]) ).
fof(f7169,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK52(X0,X1),sK51(X0,X1)),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK51(X0,X1),X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_462 ),
inference(forward_demodulation,[],[f7167,f1983]) ).
fof(f7167,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK51(X0,X1),sK52(X0,X1)),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| in(sK51(X0,X1),X1)
| ~ relation(X0) )
| ~ spl102_462 ),
inference(avatar_component_clause,[],[f7166]) ).
fof(f7181,plain,
( spl102_465
| ~ spl102_111
| ~ spl102_461 ),
inference(avatar_split_clause,[],[f7164,f7161,f1982,f7179]) ).
fof(f7179,plain,
( spl102_465
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK49(X0,X1),sK49(X0,X1)),unordered_pair(sK49(X0,X1),sK48(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK48(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_465])]) ).
fof(f7161,plain,
( spl102_461
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK49(X0,X1),sK48(X0,X1)),unordered_pair(sK49(X0,X1),sK49(X0,X1))),X0)
| in(sK48(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_461])]) ).
fof(f7164,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK49(X0,X1),sK49(X0,X1)),unordered_pair(sK49(X0,X1),sK48(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK48(X0,X1),X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_461 ),
inference(forward_demodulation,[],[f7162,f1983]) ).
fof(f7162,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK49(X0,X1),sK48(X0,X1)),unordered_pair(sK49(X0,X1),sK49(X0,X1))),X0)
| in(sK48(X0,X1),X1)
| ~ relation(X0) )
| ~ spl102_461 ),
inference(avatar_component_clause,[],[f7161]) ).
fof(f7177,plain,
spl102_464,
inference(avatar_split_clause,[],[f1369,f7175]) ).
fof(f7175,plain,
( spl102_464
<=> ! [X0,X8,X2,X1] :
( unordered_pair(unordered_pair(sK89(X0,X1,X8),sK88(X0,X1,X8)),unordered_pair(sK88(X0,X1,X8),sK88(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_464])]) ).
fof(f1369,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK89(X0,X1,X8),sK88(X0,X1,X8)),unordered_pair(sK88(X0,X1,X8),sK88(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ),
inference(forward_demodulation,[],[f1295,f1005]) ).
fof(f1295,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK88(X0,X1,X8),sK89(X0,X1,X8)),unordered_pair(sK88(X0,X1,X8),sK88(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ),
inference(definition_unfolding,[],[f1114,f1170]) ).
fof(f1114,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK88(X0,X1,X8),sK89(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f7173,plain,
spl102_463,
inference(avatar_split_clause,[],[f1292,f7171]) ).
fof(f7171,plain,
( spl102_463
<=> ! [X4,X0,X5,X2,X1] :
( sP20(X0,X1,X2)
| sK85(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK85(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_463])]) ).
fof(f1292,plain,
! [X2,X0,X1,X4,X5] :
( sP20(X0,X1,X2)
| sK85(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK85(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1119,f1170]) ).
fof(f1119,plain,
! [X2,X0,X1,X4,X5] :
( sP20(X0,X1,X2)
| ordered_pair(X4,X5) != sK85(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK85(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f7168,plain,
spl102_462,
inference(avatar_split_clause,[],[f1249,f7166]) ).
fof(f1249,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK51(X0,X1),sK52(X0,X1)),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| in(sK51(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f944,f1170]) ).
fof(f944,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK51(X0,X1),sK52(X0,X1)),X0)
| in(sK51(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f574,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK51(X0,X1),X3),X0)
| ~ in(sK51(X0,X1),X1) )
& ( in(ordered_pair(sK51(X0,X1),sK52(X0,X1)),X0)
| in(sK51(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK53(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53])],[f570,f573,f572,f571]) ).
fof(f571,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(sK51(X0,X1),X3),X0)
| ~ in(sK51(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK51(X0,X1),X4),X0)
| in(sK51(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f572,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK51(X0,X1),X4),X0)
=> in(ordered_pair(sK51(X0,X1),sK52(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f573,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK53(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f570,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,[],[f569]) ).
fof(f569,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,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,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(f7163,plain,
spl102_461,
inference(avatar_split_clause,[],[f1245,f7161]) ).
fof(f1245,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK49(X0,X1),sK48(X0,X1)),unordered_pair(sK49(X0,X1),sK49(X0,X1))),X0)
| in(sK48(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f940,f1170]) ).
fof(f940,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK49(X0,X1),sK48(X0,X1)),X0)
| in(sK48(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f568]) ).
fof(f568,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK48(X0,X1)),X0)
| ~ in(sK48(X0,X1),X1) )
& ( in(ordered_pair(sK49(X0,X1),sK48(X0,X1)),X0)
| in(sK48(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK50(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50])],[f564,f567,f566,f565]) ).
fof(f565,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,sK48(X0,X1)),X0)
| ~ in(sK48(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK48(X0,X1)),X0)
| in(sK48(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f566,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK48(X0,X1)),X0)
=> in(ordered_pair(sK49(X0,X1),sK48(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f567,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK50(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f564,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,[],[f563]) ).
fof(f563,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,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,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(f7131,plain,
spl102_460,
inference(avatar_split_clause,[],[f1360,f7129]) ).
fof(f7129,plain,
( spl102_460
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK74(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1)
| sP13(X0,X1)
| sK73(X0,X1) = sK74(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_460])]) ).
fof(f1360,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK74(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1)
| sP13(X0,X1)
| sK73(X0,X1) = sK74(X0,X1) ),
inference(forward_demodulation,[],[f1274,f1005]) ).
fof(f1274,plain,
! [X0,X1] :
( sP13(X0,X1)
| sK73(X0,X1) = sK74(X0,X1)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK74(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1034,f1170]) ).
fof(f1034,plain,
! [X0,X1] :
( sP13(X0,X1)
| sK73(X0,X1) = sK74(X0,X1)
| in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f7118,plain,
spl102_459,
inference(avatar_split_clause,[],[f756,f7116]) ).
fof(f7116,plain,
( spl102_459
<=> ! [X0,X1] :
( sP1(X0,X1)
| sK28(X0,X1) = apply(X1,sK29(X0,X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_459])]) ).
fof(f756,plain,
! [X0,X1] :
( sP1(X0,X1)
| sK28(X0,X1) = apply(X1,sK29(X0,X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f7081,plain,
( spl102_458
| ~ spl102_111
| ~ spl102_456 ),
inference(avatar_split_clause,[],[f7034,f7031,f1982,f7079]) ).
fof(f7079,plain,
( spl102_458
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK47(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_458])]) ).
fof(f7031,plain,
( spl102_456
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,sK47(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_456])]) ).
fof(f7034,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK47(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_456 ),
inference(forward_demodulation,[],[f7032,f1983]) ).
fof(f7032,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK47(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) )
| ~ spl102_456 ),
inference(avatar_component_clause,[],[f7031]) ).
fof(f7038,plain,
spl102_457,
inference(avatar_split_clause,[],[f1248,f7036]) ).
fof(f7036,plain,
( spl102_457
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1),X3),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| ~ in(sK51(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_457])]) ).
fof(f1248,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1),X3),unordered_pair(sK51(X0,X1),sK51(X0,X1))),X0)
| ~ in(sK51(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f945,f1170]) ).
fof(f945,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK51(X0,X1),X3),X0)
| ~ in(sK51(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f7033,plain,
spl102_456,
inference(avatar_split_clause,[],[f1243,f7031]) ).
fof(f1243,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK47(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP3(X0,X1,X2) ),
inference(definition_unfolding,[],[f931,f1170,f1170]) ).
fof(f931,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK47(X0,X1,X7,X8)),X1)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f562]) ).
fof(f7029,plain,
spl102_455,
inference(avatar_split_clause,[],[f1214,f7027]) ).
fof(f7027,plain,
( spl102_455
<=> ! [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,[spl102_455])]) ).
fof(f1214,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,[],[f877,f1170,f1170]) ).
fof(f877,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,[],[f536]) ).
fof(f536,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,[],[f535]) ).
fof(f535,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,[],[f346]) ).
fof(f346,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,[],[f216]) ).
fof(f216,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(f6948,plain,
( spl102_454
| ~ spl102_111
| ~ spl102_450 ),
inference(avatar_split_clause,[],[f6851,f6848,f1982,f6946]) ).
fof(f6946,plain,
( spl102_454
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK61(X0,X1,X6)),unordered_pair(sK61(X0,X1,X6),sK61(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_454])]) ).
fof(f6848,plain,
( spl102_450
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(sK61(X0,X1,X6),X6),unordered_pair(sK61(X0,X1,X6),sK61(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_450])]) ).
fof(f6851,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK61(X0,X1,X6)),unordered_pair(sK61(X0,X1,X6),sK61(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_450 ),
inference(forward_demodulation,[],[f6849,f1983]) ).
fof(f6849,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK61(X0,X1,X6),X6),unordered_pair(sK61(X0,X1,X6),sK61(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) )
| ~ spl102_450 ),
inference(avatar_component_clause,[],[f6848]) ).
fof(f6910,plain,
( spl102_453
| ~ spl102_111
| ~ spl102_447 ),
inference(avatar_split_clause,[],[f6838,f6835,f1982,f6908]) ).
fof(f6908,plain,
( spl102_453
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK36(X0,X1,X2)),unordered_pair(sK36(X0,X1,X2),sK36(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_453])]) ).
fof(f6835,plain,
( spl102_447
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X2),X0),unordered_pair(sK36(X0,X1,X2),sK36(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_447])]) ).
fof(f6838,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK36(X0,X1,X2)),unordered_pair(sK36(X0,X1,X2),sK36(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl102_111
| ~ spl102_447 ),
inference(forward_demodulation,[],[f6836,f1983]) ).
fof(f6836,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X2),X0),unordered_pair(sK36(X0,X1,X2),sK36(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl102_447 ),
inference(avatar_component_clause,[],[f6835]) ).
fof(f6859,plain,
spl102_452,
inference(avatar_split_clause,[],[f1361,f6857]) ).
fof(f6857,plain,
( spl102_452
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK74(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1)
| sP13(X0,X1)
| in(sK73(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_452])]) ).
fof(f1361,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK74(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1)
| sP13(X0,X1)
| in(sK73(X0,X1),X0) ),
inference(forward_demodulation,[],[f1275,f1005]) ).
fof(f1275,plain,
! [X0,X1] :
( sP13(X0,X1)
| in(sK73(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK74(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1033,f1170]) ).
fof(f1033,plain,
! [X0,X1] :
( sP13(X0,X1)
| in(sK73(X0,X1),X0)
| in(ordered_pair(sK73(X0,X1),sK74(X0,X1)),X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f6855,plain,
spl102_451,
inference(avatar_split_clause,[],[f1282,f6853]) ).
fof(f6853,plain,
( spl102_451
<=> ! [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)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_451])]) ).
fof(f1282,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)
| ~ sP15(X0,X1,X2) ),
inference(definition_unfolding,[],[f1041,f1170,f1170]) ).
fof(f1041,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f6850,plain,
spl102_450,
inference(avatar_split_clause,[],[f1265,f6848]) ).
fof(f1265,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK61(X0,X1,X6),X6),unordered_pair(sK61(X0,X1,X6),sK61(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ),
inference(definition_unfolding,[],[f966,f1170]) ).
fof(f966,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK61(X0,X1,X6),X6),X1)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f6846,plain,
spl102_449,
inference(avatar_split_clause,[],[f1262,f6844]) ).
fof(f6844,plain,
( spl102_449
<=> ! [X4,X0,X2,X1] :
( sP9(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK59(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK59(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_449])]) ).
fof(f1262,plain,
! [X2,X0,X1,X4] :
( sP9(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK59(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK59(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f971,f1170]) ).
fof(f971,plain,
! [X2,X0,X1,X4] :
( sP9(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK59(X0,X1,X2)),X1)
| ~ in(sK59(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f6842,plain,
spl102_448,
inference(avatar_split_clause,[],[f1255,f6840]) ).
fof(f6840,plain,
( spl102_448
<=> ! [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)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_448])]) ).
fof(f1255,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)
| ~ sP5(X0,X1,X2) ),
inference(definition_unfolding,[],[f950,f1170,f1170]) ).
fof(f950,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f6837,plain,
spl102_447,
inference(avatar_split_clause,[],[f1205,f6835]) ).
fof(f1205,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK36(X0,X1,X2),X0),unordered_pair(sK36(X0,X1,X2),sK36(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f848,f1170]) ).
fof(f848,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK36(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f526]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ( in(sK36(X0,X1,X2),X1)
& in(ordered_pair(sK36(X0,X1,X2),X0),X2)
& in(sK36(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f524,f525]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK36(X0,X1,X2),X1)
& in(ordered_pair(sK36(X0,X1,X2),X0),X2)
& in(sK36(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f524,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f523]) ).
fof(f523,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f6833,plain,
spl102_446,
inference(avatar_split_clause,[],[f811,f6831]) ).
fof(f6831,plain,
( spl102_446
<=> ! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_446])]) ).
fof(f811,plain,
! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f309]) ).
fof(f309,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f159]) ).
fof(f159,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f6803,plain,
( spl102_445
| ~ spl102_7
| ~ spl102_59
| ~ spl102_94 ),
inference(avatar_split_clause,[],[f1891,f1887,f1661,f1403,f6800]) ).
fof(f6800,plain,
( spl102_445
<=> sP8(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_445])]) ).
fof(f1887,plain,
( spl102_94
<=> sP8(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_94])]) ).
fof(f1891,plain,
( sP8(sK95)
| ~ spl102_7
| ~ spl102_59
| ~ spl102_94 ),
inference(forward_demodulation,[],[f1889,f1713]) ).
fof(f1889,plain,
( sP8(empty_set)
| ~ spl102_94 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f6763,plain,
( spl102_444
| ~ spl102_111
| ~ spl102_440 ),
inference(avatar_split_clause,[],[f6740,f6737,f1982,f6761]) ).
fof(f6761,plain,
( spl102_444
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_444])]) ).
fof(f6737,plain,
( spl102_440
<=> ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_440])]) ).
fof(f6740,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_440 ),
inference(forward_demodulation,[],[f6738,f1983]) ).
fof(f6738,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_440 ),
inference(avatar_component_clause,[],[f6737]) ).
fof(f6759,plain,
( spl102_443
| ~ spl102_111
| ~ spl102_439 ),
inference(avatar_split_clause,[],[f6735,f6732,f1982,f6757]) ).
fof(f6757,plain,
( spl102_443
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_443])]) ).
fof(f6732,plain,
( spl102_439
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_439])]) ).
fof(f6735,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK41(X0,X1),sK40(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_439 ),
inference(forward_demodulation,[],[f6733,f1983]) ).
fof(f6733,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl102_439 ),
inference(avatar_component_clause,[],[f6732]) ).
fof(f6748,plain,
spl102_442,
inference(avatar_split_clause,[],[f1316,f6746]) ).
fof(f6746,plain,
( spl102_442
<=> ! [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,[spl102_442])]) ).
fof(f1316,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,[],[f1237]) ).
fof(f1237,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,[],[f925,f1170,f1170]) ).
fof(f925,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,[],[f554]) ).
fof(f6744,plain,
spl102_441,
inference(avatar_split_clause,[],[f1315,f6742]) ).
fof(f6742,plain,
( spl102_441
<=> ! [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,[spl102_441])]) ).
fof(f1315,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,[],[f1236]) ).
fof(f1236,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,[],[f926,f1170,f1170]) ).
fof(f926,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,[],[f554]) ).
fof(f6739,plain,
spl102_440,
inference(avatar_split_clause,[],[f1232,f6737]) ).
fof(f1232,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f923,f1170]) ).
fof(f923,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK40(X0,X1),sK41(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f550]) ).
fof(f550,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK40(X0,X1),sK41(X0,X1)),X1)
& in(ordered_pair(sK40(X0,X1),sK41(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,[sK40,sK41])],[f548,f549]) ).
fof(f549,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK40(X0,X1),sK41(X0,X1)),X1)
& in(ordered_pair(sK40(X0,X1),sK41(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f548,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,[],[f547]) ).
fof(f547,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,[],[f362]) ).
fof(f362,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,[],[f25]) ).
fof(f25,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(f6734,plain,
spl102_439,
inference(avatar_split_clause,[],[f1231,f6732]) ).
fof(f1231,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK40(X0,X1),sK41(X0,X1)),unordered_pair(sK40(X0,X1),sK40(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f924,f1170]) ).
fof(f924,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK40(X0,X1),sK41(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f550]) ).
fof(f6714,plain,
spl102_438,
inference(avatar_split_clause,[],[f814,f6712]) ).
fof(f6712,plain,
( spl102_438
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_438])]) ).
fof(f814,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f506]) ).
fof(f506,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f505]) ).
fof(f505,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f311]) ).
fof(f311,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f157]) ).
fof(f157,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f6699,plain,
spl102_437,
inference(avatar_split_clause,[],[f755,f6697]) ).
fof(f6697,plain,
( spl102_437
<=> ! [X0,X1] :
( sP1(X0,X1)
| in(sK29(X0,X1),relation_dom(X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_437])]) ).
fof(f755,plain,
! [X0,X1] :
( sP1(X0,X1)
| in(sK29(X0,X1),relation_dom(X1))
| ~ sP0(sK28(X0,X1),sK29(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f6597,plain,
spl102_436,
inference(avatar_split_clause,[],[f1215,f6595]) ).
fof(f6595,plain,
( spl102_436
<=> ! [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,[spl102_436])]) ).
fof(f1215,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,[],[f876,f1170,f1170]) ).
fof(f876,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,[],[f536]) ).
fof(f6593,plain,
spl102_435,
inference(avatar_split_clause,[],[f1204,f6591]) ).
fof(f6591,plain,
( spl102_435
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_435])]) ).
fof(f1204,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f850,f1170]) ).
fof(f850,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f526]) ).
fof(f6589,plain,
spl102_434,
inference(avatar_split_clause,[],[f1202,f6587]) ).
fof(f6587,plain,
( spl102_434
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_434])]) ).
fof(f1202,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f846,f1170]) ).
fof(f846,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f522]) ).
fof(f522,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ( in(sK35(X0,X1,X2),X1)
& in(ordered_pair(X0,sK35(X0,X1,X2)),X2)
& in(sK35(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f520,f521]) ).
fof(f521,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK35(X0,X1,X2),X1)
& in(ordered_pair(X0,sK35(X0,X1,X2)),X2)
& in(sK35(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f520,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f519]) ).
fof(f519,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f6585,plain,
spl102_433,
inference(avatar_split_clause,[],[f810,f6583]) ).
fof(f6583,plain,
( spl102_433
<=> ! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_433])]) ).
fof(f810,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f308]) ).
fof(f308,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f307]) ).
fof(f307,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f160]) ).
fof(f160,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f6433,plain,
spl102_432,
inference(avatar_split_clause,[],[f1151,f6431]) ).
fof(f6431,plain,
( spl102_432
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| in(sK93(X0,X1,X2),X0)
| ~ in(sK93(X0,X1,X2),X1)
| ~ in(sK93(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_432])]) ).
fof(f1151,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| in(sK93(X0,X1,X2),X0)
| ~ in(sK93(X0,X1,X2),X1)
| ~ in(sK93(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f700,plain,
! [X0,X1,X2] :
( ( sP24(X0,X1,X2)
| ( ( in(sK93(X0,X1,X2),X0)
| ~ in(sK93(X0,X1,X2),X1)
| ~ in(sK93(X0,X1,X2),X2) )
& ( ( ~ in(sK93(X0,X1,X2),X0)
& in(sK93(X0,X1,X2),X1) )
| in(sK93(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP24(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f698,f699]) ).
fof(f699,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK93(X0,X1,X2),X0)
| ~ in(sK93(X0,X1,X2),X1)
| ~ in(sK93(X0,X1,X2),X2) )
& ( ( ~ in(sK93(X0,X1,X2),X0)
& in(sK93(X0,X1,X2),X1) )
| in(sK93(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f698,plain,
! [X0,X1,X2] :
( ( sP24(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) ) )
| ~ sP24(X0,X1,X2) ) ),
inference(rectify,[],[f697]) ).
fof(f697,plain,
! [X1,X0,X2] :
( ( sP24(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) ) )
| ~ sP24(X1,X0,X2) ) ),
inference(flattening,[],[f696]) ).
fof(f696,plain,
! [X1,X0,X2] :
( ( sP24(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) ) )
| ~ sP24(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f476]) ).
fof(f476,plain,
! [X1,X0,X2] :
( sP24(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f6429,plain,
spl102_431,
inference(avatar_split_clause,[],[f1141,f6427]) ).
fof(f6427,plain,
( spl102_431
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(sK92(X0,X1,X2),X0)
| in(sK92(X0,X1,X2),X1)
| in(sK92(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_431])]) ).
fof(f1141,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(sK92(X0,X1,X2),X0)
| in(sK92(X0,X1,X2),X1)
| in(sK92(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f694,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ( ( ( ~ in(sK92(X0,X1,X2),X0)
& ~ in(sK92(X0,X1,X2),X1) )
| ~ in(sK92(X0,X1,X2),X2) )
& ( in(sK92(X0,X1,X2),X0)
| in(sK92(X0,X1,X2),X1)
| in(sK92(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92])],[f692,f693]) ).
fof(f693,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK92(X0,X1,X2),X0)
& ~ in(sK92(X0,X1,X2),X1) )
| ~ in(sK92(X0,X1,X2),X2) )
& ( in(sK92(X0,X1,X2),X0)
| in(sK92(X0,X1,X2),X1)
| in(sK92(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f692,plain,
! [X0,X1,X2] :
( ( sP23(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) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(rectify,[],[f691]) ).
fof(f691,plain,
! [X1,X0,X2] :
( ( sP23(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) ) )
| ~ sP23(X1,X0,X2) ) ),
inference(flattening,[],[f690]) ).
fof(f690,plain,
! [X1,X0,X2] :
( ( sP23(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) ) )
| ~ sP23(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f474]) ).
fof(f474,plain,
! [X1,X0,X2] :
( sP23(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f6425,plain,
spl102_430,
inference(avatar_split_clause,[],[f1135,f6423]) ).
fof(f6423,plain,
( spl102_430
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ in(sK91(X0,X1,X2),X0)
| ~ in(sK91(X0,X1,X2),X1)
| ~ in(sK91(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_430])]) ).
fof(f1135,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ in(sK91(X0,X1,X2),X0)
| ~ in(sK91(X0,X1,X2),X1)
| ~ in(sK91(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f688,plain,
! [X0,X1,X2] :
( ( sP22(X0,X1,X2)
| ( ( ~ in(sK91(X0,X1,X2),X0)
| ~ in(sK91(X0,X1,X2),X1)
| ~ in(sK91(X0,X1,X2),X2) )
& ( ( in(sK91(X0,X1,X2),X0)
& in(sK91(X0,X1,X2),X1) )
| in(sK91(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP22(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91])],[f686,f687]) ).
fof(f687,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK91(X0,X1,X2),X0)
| ~ in(sK91(X0,X1,X2),X1)
| ~ in(sK91(X0,X1,X2),X2) )
& ( ( in(sK91(X0,X1,X2),X0)
& in(sK91(X0,X1,X2),X1) )
| in(sK91(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f686,plain,
! [X0,X1,X2] :
( ( sP22(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) ) )
| ~ sP22(X0,X1,X2) ) ),
inference(rectify,[],[f685]) ).
fof(f685,plain,
! [X1,X0,X2] :
( ( sP22(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) ) )
| ~ sP22(X1,X0,X2) ) ),
inference(flattening,[],[f684]) ).
fof(f684,plain,
! [X1,X0,X2] :
( ( sP22(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) ) )
| ~ sP22(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f472]) ).
fof(f472,plain,
! [X1,X0,X2] :
( sP22(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f6421,plain,
spl102_429,
inference(avatar_split_clause,[],[f1125,f6419]) ).
fof(f6419,plain,
( spl102_429
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) = X0
| sK90(X0,X1,X2) = X1
| in(sK90(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_429])]) ).
fof(f1125,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) = X0
| sK90(X0,X1,X2) = X1
| in(sK90(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f682,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ( ( ( sK90(X0,X1,X2) != X0
& sK90(X0,X1,X2) != X1 )
| ~ in(sK90(X0,X1,X2),X2) )
& ( sK90(X0,X1,X2) = X0
| sK90(X0,X1,X2) = X1
| in(sK90(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f680,f681]) ).
fof(f681,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK90(X0,X1,X2) != X0
& sK90(X0,X1,X2) != X1 )
| ~ in(sK90(X0,X1,X2),X2) )
& ( sK90(X0,X1,X2) = X0
| sK90(X0,X1,X2) = X1
| in(sK90(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f680,plain,
! [X0,X1,X2] :
( ( sP21(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) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(rectify,[],[f679]) ).
fof(f679,plain,
! [X1,X0,X2] :
( ( sP21(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) ) )
| ~ sP21(X1,X0,X2) ) ),
inference(flattening,[],[f678]) ).
fof(f678,plain,
! [X1,X0,X2] :
( ( sP21(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) ) )
| ~ sP21(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f470]) ).
fof(f470,plain,
! [X1,X0,X2] :
( sP21(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f6397,plain,
( spl102_428
| ~ spl102_18
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1604,f1544,f1458,f6394]) ).
fof(f6394,plain,
( spl102_428
<=> sP10(sK101) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_428])]) ).
fof(f1458,plain,
( spl102_18
<=> relation(sK101) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_18])]) ).
fof(f1604,plain,
( sP10(sK101)
| ~ spl102_18
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1460]) ).
fof(f1460,plain,
( relation(sK101)
| ~ spl102_18 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f6358,plain,
spl102_427,
inference(avatar_split_clause,[],[f1283,f6356]) ).
fof(f6356,plain,
( spl102_427
<=> ! [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)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_427])]) ).
fof(f1283,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)
| ~ sP15(X0,X1,X2) ),
inference(definition_unfolding,[],[f1040,f1170,f1170]) ).
fof(f1040,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f6354,plain,
spl102_426,
inference(avatar_split_clause,[],[f1256,f6352]) ).
fof(f6352,plain,
( spl102_426
<=> ! [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)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_426])]) ).
fof(f1256,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)
| ~ sP5(X0,X1,X2) ),
inference(definition_unfolding,[],[f949,f1170,f1170]) ).
fof(f949,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f6350,plain,
spl102_425,
inference(avatar_split_clause,[],[f1244,f6348]) ).
fof(f6348,plain,
( spl102_425
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK48(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK48(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_425])]) ).
fof(f1244,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK48(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK48(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f941,f1170]) ).
fof(f941,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK48(X0,X1)),X0)
| ~ in(sK48(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f568]) ).
fof(f6320,plain,
( spl102_424
| ~ spl102_111
| ~ spl102_423 ),
inference(avatar_split_clause,[],[f6316,f6313,f1982,f6318]) ).
fof(f6318,plain,
( spl102_424
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK50(X0,X5)),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_424])]) ).
fof(f6313,plain,
( spl102_423
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK50(X0,X5),X5),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_423])]) ).
fof(f6316,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK50(X0,X5)),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_423 ),
inference(forward_demodulation,[],[f6314,f1983]) ).
fof(f6314,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK50(X0,X5),X5),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl102_423 ),
inference(avatar_component_clause,[],[f6313]) ).
fof(f6315,plain,
spl102_423,
inference(avatar_split_clause,[],[f1319,f6313]) ).
fof(f1319,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK50(X0,X5),X5),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1247]) ).
fof(f1247,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK50(X0,X5),X5),unordered_pair(sK50(X0,X5),sK50(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f938,f1170]) ).
fof(f938,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK50(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f568]) ).
fof(f6293,plain,
( spl102_422
| ~ spl102_7
| ~ spl102_34
| ~ spl102_59
| ~ spl102_421 ),
inference(avatar_split_clause,[],[f6288,f6284,f1661,f1528,f1403,f6291]) ).
fof(f6291,plain,
( spl102_422
<=> ! [X0,X1] :
( sK95 = 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,[spl102_422])]) ).
fof(f1528,plain,
( spl102_34
<=> ! [X0] : cast_to_subset(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_34])]) ).
fof(f6284,plain,
( spl102_421
<=> ! [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,[spl102_421])]) ).
fof(f6288,plain,
( ! [X0,X1] :
( sK95 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl102_7
| ~ spl102_34
| ~ spl102_59
| ~ spl102_421 ),
inference(forward_demodulation,[],[f6287,f1713]) ).
fof(f6287,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))) )
| ~ spl102_34
| ~ spl102_421 ),
inference(forward_demodulation,[],[f6285,f1529]) ).
fof(f1529,plain,
( ! [X0] : cast_to_subset(X0) = X0
| ~ spl102_34 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f6285,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))) )
| ~ spl102_421 ),
inference(avatar_component_clause,[],[f6284]) ).
fof(f6286,plain,
spl102_421,
inference(avatar_split_clause,[],[f803,f6284]) ).
fof(f803,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,[],[f301]) ).
fof(f301,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,[],[f300]) ).
fof(f300,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,[],[f193]) ).
fof(f193,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(f6264,plain,
( spl102_420
| ~ spl102_7
| ~ spl102_34
| ~ spl102_59
| ~ spl102_419 ),
inference(avatar_split_clause,[],[f6260,f6256,f1661,f1528,f1403,f6262]) ).
fof(f6262,plain,
( spl102_420
<=> ! [X0,X1] :
( sK95 = 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,[spl102_420])]) ).
fof(f6256,plain,
( spl102_419
<=> ! [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,[spl102_419])]) ).
fof(f6260,plain,
( ! [X0,X1] :
( sK95 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl102_7
| ~ spl102_34
| ~ spl102_59
| ~ spl102_419 ),
inference(forward_demodulation,[],[f6259,f1713]) ).
fof(f6259,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))) )
| ~ spl102_34
| ~ spl102_419 ),
inference(forward_demodulation,[],[f6257,f1529]) ).
fof(f6257,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))) )
| ~ spl102_419 ),
inference(avatar_component_clause,[],[f6256]) ).
fof(f6258,plain,
spl102_419,
inference(avatar_split_clause,[],[f802,f6256]) ).
fof(f802,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,[],[f299]) ).
fof(f299,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,[],[f298]) ).
fof(f298,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,[],[f194]) ).
fof(f194,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(f6206,plain,
spl102_418,
inference(avatar_split_clause,[],[f1304,f6204]) ).
fof(f6204,plain,
( spl102_418
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK33(relation_dom(X1),X1) != apply(X1,sK33(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_418])]) ).
fof(f1304,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK33(relation_dom(X1),X1) != apply(X1,sK33(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f809]) ).
fof(f809,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK33(X0,X1) != apply(X1,sK33(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f504]) ).
fof(f504,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK33(X0,X1) != apply(X1,sK33(X0,X1))
& in(sK33(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f502,f503]) ).
fof(f503,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK33(X0,X1) != apply(X1,sK33(X0,X1))
& in(sK33(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f502,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f501]) ).
fof(f501,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f500]) ).
fof(f500,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f305]) ).
fof(f305,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f171]) ).
fof(f171,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f6202,plain,
spl102_417,
inference(avatar_split_clause,[],[f813,f6200]) ).
fof(f6200,plain,
( spl102_417
<=> ! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_417])]) ).
fof(f813,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f506]) ).
fof(f6141,plain,
( spl102_416
| ~ spl102_111
| ~ spl102_412 ),
inference(avatar_split_clause,[],[f6089,f6086,f1982,f6139]) ).
fof(f6139,plain,
( spl102_416
<=> ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X2,X0))),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_416])]) ).
fof(f6086,plain,
( spl102_412
<=> ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_412])]) ).
fof(f6089,plain,
( ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X2,X0))),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl102_111
| ~ spl102_412 ),
inference(forward_demodulation,[],[f6087,f1983]) ).
fof(f6087,plain,
( ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl102_412 ),
inference(avatar_component_clause,[],[f6086]) ).
fof(f6119,plain,
( spl102_415
| ~ spl102_111
| ~ spl102_409 ),
inference(avatar_split_clause,[],[f6075,f6072,f1982,f6117]) ).
fof(f6117,plain,
( spl102_415
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK58(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_415])]) ).
fof(f6072,plain,
( spl102_409
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK58(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_409])]) ).
fof(f6075,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK58(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) )
| ~ spl102_111
| ~ spl102_409 ),
inference(forward_demodulation,[],[f6073,f1983]) ).
fof(f6073,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK58(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) )
| ~ spl102_409 ),
inference(avatar_component_clause,[],[f6072]) ).
fof(f6097,plain,
( spl102_414
| ~ spl102_111
| ~ spl102_407 ),
inference(avatar_split_clause,[],[f6066,f6063,f1982,f6095]) ).
fof(f6095,plain,
( spl102_414
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK35(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_414])]) ).
fof(f6063,plain,
( spl102_407
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK35(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_407])]) ).
fof(f6066,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK35(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl102_111
| ~ spl102_407 ),
inference(forward_demodulation,[],[f6064,f1983]) ).
fof(f6064,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK35(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl102_407 ),
inference(avatar_component_clause,[],[f6063]) ).
fof(f6093,plain,
spl102_413,
inference(avatar_split_clause,[],[f1346,f6091]) ).
fof(f6091,plain,
( spl102_413
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_413])]) ).
fof(f1346,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP20(X0,X1,X2) ),
inference(equality_resolution,[],[f1294]) ).
fof(f1294,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)
| ~ sP20(X0,X1,X2) ),
inference(definition_unfolding,[],[f1115,f1170]) ).
fof(f1115,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f6088,plain,
spl102_412,
inference(avatar_split_clause,[],[f1312,f6086]) ).
fof(f1312,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(equality_resolution,[],[f1210]) ).
fof(f1210,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f867,f1170]) ).
fof(f867,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f532]) ).
fof(f532,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f531]) ).
fof(f531,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(nnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f336]) ).
fof(f336,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f223]) ).
fof(f223,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f6084,plain,
spl102_411,
inference(avatar_split_clause,[],[f1264,f6082]) ).
fof(f6082,plain,
( spl102_411
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_411])]) ).
fof(f1264,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP9(X0,X1,X2) ),
inference(definition_unfolding,[],[f968,f1170]) ).
fof(f968,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f6080,plain,
( ~ spl102_410
| ~ spl102_40
| ~ spl102_375 ),
inference(avatar_split_clause,[],[f5495,f5208,f1552,f6077]) ).
fof(f6077,plain,
( spl102_410
<=> in(sK67(relation_rng(sK25)),sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_410])]) ).
fof(f5208,plain,
( spl102_375
<=> ! [X0] :
( ~ in(X0,sK95)
| ~ in(relation_rng(sK25),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_375])]) ).
fof(f5495,plain,
( ~ in(sK67(relation_rng(sK25)),sK95)
| ~ spl102_40
| ~ spl102_375 ),
inference(resolution,[],[f5209,f1553]) ).
fof(f5209,plain,
( ! [X0] :
( ~ in(relation_rng(sK25),X0)
| ~ in(X0,sK95) )
| ~ spl102_375 ),
inference(avatar_component_clause,[],[f5208]) ).
fof(f6074,plain,
spl102_409,
inference(avatar_split_clause,[],[f1261,f6072]) ).
fof(f1261,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK58(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ),
inference(definition_unfolding,[],[f957,f1170]) ).
fof(f957,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK58(X0,X1,X6)),X1)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f6070,plain,
spl102_408,
inference(avatar_split_clause,[],[f1260,f6068]) ).
fof(f6068,plain,
( spl102_408
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_408])]) ).
fof(f1260,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP7(X0,X1,X2) ),
inference(definition_unfolding,[],[f959,f1170]) ).
fof(f959,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f6065,plain,
spl102_407,
inference(avatar_split_clause,[],[f1203,f6063]) ).
fof(f1203,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK35(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f844,f1170]) ).
fof(f844,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK35(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f522]) ).
fof(f5999,plain,
spl102_406,
inference(avatar_split_clause,[],[f1302,f5997]) ).
fof(f5997,plain,
( spl102_406
<=> ! [X2,X0,X3] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_406])]) ).
fof(f1302,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f759]) ).
fof(f759,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f491]) ).
fof(f491,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& apply(X3,X0) = X1
& in(X0,relation_rng(X2)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f490]) ).
fof(f490,plain,
! [X2,X3,X0,X1] :
( ( sP0(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(flattening,[],[f489]) ).
fof(f489,plain,
! [X2,X3,X0,X1] :
( ( sP0(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f438]) ).
fof(f438,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5995,plain,
spl102_405,
inference(avatar_split_clause,[],[f1066,f5993]) ).
fof(f5993,plain,
( spl102_405
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| ~ in(sK77(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_405])]) ).
fof(f1066,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| ~ in(sK77(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f644]) ).
fof(f644,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ( ( ~ in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| ~ in(sK77(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| in(sK77(X0,X1,X2),X2) )
& element(sK77(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)) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f642,f643]) ).
fof(f643,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,sK77(X0,X1,X2)),X0)
| ~ in(sK77(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| in(sK77(X0,X1,X2),X2) )
& element(sK77(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f642,plain,
! [X0,X1,X2] :
( ( sP17(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)) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f641]) ).
fof(f641,plain,
! [X1,X0,X2] :
( ( sP17(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)) )
| ~ sP17(X1,X0,X2) ) ),
inference(flattening,[],[f640]) ).
fof(f640,plain,
! [X1,X0,X2] :
( ( sP17(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)) )
| ~ sP17(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f463]) ).
fof(f463,plain,
! [X1,X0,X2] :
( sP17(X1,X0,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f5991,plain,
spl102_404,
inference(avatar_split_clause,[],[f1065,f5989]) ).
fof(f5989,plain,
( spl102_404
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| in(sK77(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_404])]) ).
fof(f1065,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| in(subset_complement(X1,sK77(X0,X1,X2)),X0)
| in(sK77(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f644]) ).
fof(f5934,plain,
( ~ spl102_403
| ~ spl102_33
| ~ spl102_375 ),
inference(avatar_split_clause,[],[f5494,f5208,f1524,f5931]) ).
fof(f5931,plain,
( spl102_403
<=> in(sK30(relation_rng(sK25)),sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_403])]) ).
fof(f5494,plain,
( ~ in(sK30(relation_rng(sK25)),sK95)
| ~ spl102_33
| ~ spl102_375 ),
inference(resolution,[],[f5209,f1525]) ).
fof(f5883,plain,
( spl102_402
| ~ spl102_111
| ~ spl102_399 ),
inference(avatar_split_clause,[],[f5828,f5825,f1982,f5881]) ).
fof(f5881,plain,
( spl102_402
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK64(X4),sK63(X4)),unordered_pair(sK63(X4),sK63(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_402])]) ).
fof(f5825,plain,
( spl102_399
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK63(X4),sK64(X4)),unordered_pair(sK63(X4),sK63(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_399])]) ).
fof(f5828,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK64(X4),sK63(X4)),unordered_pair(sK63(X4),sK63(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_399 ),
inference(forward_demodulation,[],[f5826,f1983]) ).
fof(f5826,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK63(X4),sK64(X4)),unordered_pair(sK63(X4),sK63(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl102_399 ),
inference(avatar_component_clause,[],[f5825]) ).
fof(f5836,plain,
( spl102_401
| ~ spl102_7
| ~ spl102_59
| ~ spl102_111
| ~ spl102_395 ),
inference(avatar_split_clause,[],[f5810,f5806,f1982,f1661,f1403,f5834]) ).
fof(f5834,plain,
( spl102_401
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK27(X0),sK26(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| sK95 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_401])]) ).
fof(f5806,plain,
( spl102_395
<=> ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK26(X0),sK27(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_395])]) ).
fof(f5810,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK27(X0),sK26(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| sK95 = X0
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_111
| ~ spl102_395 ),
inference(forward_demodulation,[],[f5809,f1983]) ).
fof(f5809,plain,
( ! [X0] :
( sK95 = X0
| in(unordered_pair(unordered_pair(sK26(X0),sK27(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_395 ),
inference(forward_demodulation,[],[f5807,f1713]) ).
fof(f5807,plain,
( ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK26(X0),sK27(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| ~ relation(X0) )
| ~ spl102_395 ),
inference(avatar_component_clause,[],[f5806]) ).
fof(f5832,plain,
( spl102_400
| ~ spl102_7
| ~ spl102_59
| ~ spl102_394 ),
inference(avatar_split_clause,[],[f5804,f5801,f1661,f1403,f5830]) ).
fof(f5830,plain,
( spl102_400
<=> ! [X2,X0,X1] :
( sK95 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_400])]) ).
fof(f5801,plain,
( spl102_394
<=> ! [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,[spl102_394])]) ).
fof(f5804,plain,
( ! [X2,X0,X1] :
( sK95 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_394 ),
inference(forward_demodulation,[],[f5802,f1713]) ).
fof(f5802,plain,
( ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 )
| ~ spl102_394 ),
inference(avatar_component_clause,[],[f5801]) ).
fof(f5827,plain,
spl102_399,
inference(avatar_split_clause,[],[f1269,f5825]) ).
fof(f1269,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK63(X4),sK64(X4)),unordered_pair(sK63(X4),sK63(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f987,f1170]) ).
fof(f987,plain,
! [X0,X4] :
( ordered_pair(sK63(X4),sK64(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f601]) ).
fof(f601,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK62(X0)
& in(sK62(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK63(X4),sK64(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63,sK64])],[f598,f600,f599]) ).
fof(f599,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK62(X0)
& in(sK62(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f600,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK63(X4),sK64(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f598,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,[],[f597]) ).
fof(f597,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,[],[f384]) ).
fof(f384,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,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(f5823,plain,
spl102_398,
inference(avatar_split_clause,[],[f1218,f5821]) ).
fof(f5821,plain,
( spl102_398
<=> ! [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,[spl102_398])]) ).
fof(f1218,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,[],[f878,f1170,f1170]) ).
fof(f878,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,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(f5818,plain,
spl102_397,
inference(avatar_split_clause,[],[f1217,f5816]) ).
fof(f5816,plain,
( spl102_397
<=> ! [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,[spl102_397])]) ).
fof(f1217,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,[],[f879,f1170,f1170]) ).
fof(f879,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f347]) ).
fof(f5814,plain,
spl102_396,
inference(avatar_split_clause,[],[f1211,f5812]) ).
fof(f5812,plain,
( spl102_396
<=> ! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_396])]) ).
fof(f1211,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f866,f1170]) ).
fof(f866,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f532]) ).
fof(f5808,plain,
spl102_395,
inference(avatar_split_clause,[],[f1173,f5806]) ).
fof(f1173,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK26(X0),sK27(X0)),unordered_pair(sK26(X0),sK26(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f737,f1170]) ).
fof(f737,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK26(X0),sK27(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f481]) ).
fof(f481,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK26(X0),sK27(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f254,f480]) ).
fof(f480,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK26(X0),sK27(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f253]) ).
fof(f253,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,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(f5803,plain,
spl102_394,
inference(avatar_split_clause,[],[f747,f5801]) ).
fof(f747,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,[],[f266]) ).
fof(f266,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,[],[f265]) ).
fof(f265,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,[],[f199]) ).
fof(f199,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(f5796,plain,
spl102_393,
inference(avatar_split_clause,[],[f1303,f5794]) ).
fof(f5794,plain,
( spl102_393
<=> ! [X2,X0,X3] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_393])]) ).
fof(f1303,plain,
! [X2,X3,X0] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f758]) ).
fof(f758,plain,
! [X2,X3,X0,X1] :
( in(X1,relation_dom(X2))
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f491]) ).
fof(f5768,plain,
( spl102_392
| ~ spl102_111
| ~ spl102_390 ),
inference(avatar_split_clause,[],[f5728,f5725,f1982,f5766]) ).
fof(f5766,plain,
( spl102_392
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK53(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_392])]) ).
fof(f5725,plain,
( spl102_390
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_390])]) ).
fof(f5728,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK53(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl102_111
| ~ spl102_390 ),
inference(forward_demodulation,[],[f5726,f1983]) ).
fof(f5726,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl102_390 ),
inference(avatar_component_clause,[],[f5725]) ).
fof(f5733,plain,
( ~ spl102_391
| ~ spl102_353
| ~ spl102_375 ),
inference(avatar_split_clause,[],[f5497,f5208,f4827,f5730]) ).
fof(f5730,plain,
( spl102_391
<=> in(relation_rng(sK25),sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_391])]) ).
fof(f4827,plain,
( spl102_353
<=> ! [X0] :
( ~ in(X0,sK95)
| in(X0,relation_rng(sK25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_353])]) ).
fof(f5497,plain,
( ~ in(relation_rng(sK25),sK95)
| ~ spl102_353
| ~ spl102_375 ),
inference(duplicate_literal_removal,[],[f5493]) ).
fof(f5493,plain,
( ~ in(relation_rng(sK25),sK95)
| ~ in(relation_rng(sK25),sK95)
| ~ spl102_353
| ~ spl102_375 ),
inference(resolution,[],[f5209,f4828]) ).
fof(f4828,plain,
( ! [X0] :
( in(X0,relation_rng(sK25))
| ~ in(X0,sK95) )
| ~ spl102_353 ),
inference(avatar_component_clause,[],[f4827]) ).
fof(f5727,plain,
spl102_390,
inference(avatar_split_clause,[],[f1321,f5725]) ).
fof(f1321,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1251]) ).
fof(f1251,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f942,f1170]) ).
fof(f942,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK53(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f5723,plain,
spl102_389,
inference(avatar_split_clause,[],[f1219,f5721]) ).
fof(f5721,plain,
( spl102_389
<=> ! [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,[spl102_389])]) ).
fof(f1219,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,[],[f883,f1170]) ).
fof(f883,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f538]) ).
fof(f538,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,[],[f537]) ).
fof(f537,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,[],[f129]) ).
fof(f129,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(f5719,plain,
spl102_388,
inference(avatar_split_clause,[],[f1216,f5717]) ).
fof(f5717,plain,
( spl102_388
<=> ! [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,[spl102_388])]) ).
fof(f1216,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,[],[f875,f1170]) ).
fof(f875,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f536]) ).
fof(f5260,plain,
spl102_387,
inference(avatar_split_clause,[],[f1150,f5258]) ).
fof(f5258,plain,
( spl102_387
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ in(sK93(X0,X1,X2),X0)
| in(sK93(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_387])]) ).
fof(f1150,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ in(sK93(X0,X1,X2),X0)
| in(sK93(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f5256,plain,
spl102_386,
inference(avatar_split_clause,[],[f1149,f5254]) ).
fof(f5254,plain,
( spl102_386
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| in(sK93(X0,X1,X2),X1)
| in(sK93(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_386])]) ).
fof(f1149,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| in(sK93(X0,X1,X2),X1)
| in(sK93(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f5250,plain,
spl102_385,
inference(avatar_split_clause,[],[f1143,f5248]) ).
fof(f5248,plain,
( spl102_385
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ in(sK92(X0,X1,X2),X0)
| ~ in(sK92(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_385])]) ).
fof(f1143,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ in(sK92(X0,X1,X2),X0)
| ~ in(sK92(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f5246,plain,
spl102_384,
inference(avatar_split_clause,[],[f1142,f5244]) ).
fof(f5244,plain,
( spl102_384
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ in(sK92(X0,X1,X2),X1)
| ~ in(sK92(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_384])]) ).
fof(f1142,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ in(sK92(X0,X1,X2),X1)
| ~ in(sK92(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f5242,plain,
spl102_383,
inference(avatar_split_clause,[],[f1134,f5240]) ).
fof(f5240,plain,
( spl102_383
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| in(sK91(X0,X1,X2),X0)
| in(sK91(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_383])]) ).
fof(f1134,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| in(sK91(X0,X1,X2),X0)
| in(sK91(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f5238,plain,
spl102_382,
inference(avatar_split_clause,[],[f1133,f5236]) ).
fof(f5236,plain,
( spl102_382
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| in(sK91(X0,X1,X2),X1)
| in(sK91(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_382])]) ).
fof(f1133,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| in(sK91(X0,X1,X2),X1)
| in(sK91(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f5234,plain,
spl102_381,
inference(avatar_split_clause,[],[f1117,f5232]) ).
fof(f5232,plain,
( spl102_381
<=> ! [X2,X0,X1] :
( sP20(X0,X1,X2)
| in(sK87(X0,X1,X2),X0)
| in(sK85(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_381])]) ).
fof(f1117,plain,
! [X2,X0,X1] :
( sP20(X0,X1,X2)
| in(sK87(X0,X1,X2),X0)
| in(sK85(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f5230,plain,
spl102_380,
inference(avatar_split_clause,[],[f1116,f5228]) ).
fof(f5228,plain,
( spl102_380
<=> ! [X2,X0,X1] :
( sP20(X0,X1,X2)
| in(sK86(X0,X1,X2),X1)
| in(sK85(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_380])]) ).
fof(f1116,plain,
! [X2,X0,X1] :
( sP20(X0,X1,X2)
| in(sK86(X0,X1,X2),X1)
| in(sK85(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f5226,plain,
spl102_379,
inference(avatar_split_clause,[],[f1111,f5224]) ).
fof(f5224,plain,
( spl102_379
<=> ! [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,[spl102_379])]) ).
fof(f1111,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f436]) ).
fof(f436,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f435]) ).
fof(f435,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,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(f5222,plain,
spl102_378,
inference(avatar_split_clause,[],[f1094,f5220]) ).
fof(f5220,plain,
( spl102_378
<=> ! [X0,X1,X3] :
( sP19(X0,X1)
| ~ in(X3,X0)
| ~ in(sK80(X0,X1),X3)
| ~ in(sK80(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_378])]) ).
fof(f1094,plain,
! [X3,X0,X1] :
( sP19(X0,X1)
| ~ in(X3,X0)
| ~ in(sK80(X0,X1),X3)
| ~ in(sK80(X0,X1),X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f660,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK80(X0,X1),X3) )
| ~ in(sK80(X0,X1),X1) )
& ( ( in(sK81(X0,X1),X0)
& in(sK80(X0,X1),sK81(X0,X1)) )
| in(sK80(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK82(X0,X5),X0)
& in(X5,sK82(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP19(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82])],[f656,f659,f658,f657]) ).
fof(f657,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(sK80(X0,X1),X3) )
| ~ in(sK80(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK80(X0,X1),X4) )
| in(sK80(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f658,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK80(X0,X1),X4) )
=> ( in(sK81(X0,X1),X0)
& in(sK80(X0,X1),sK81(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f659,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK82(X0,X5),X0)
& in(X5,sK82(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f656,plain,
! [X0,X1] :
( ( sP19(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) ) )
| ~ sP19(X0,X1) ) ),
inference(rectify,[],[f655]) ).
fof(f655,plain,
! [X0,X1] :
( ( sP19(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) ) )
| ~ sP19(X0,X1) ) ),
inference(nnf_transformation,[],[f466]) ).
fof(f466,plain,
! [X0,X1] :
( sP19(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f5218,plain,
spl102_377,
inference(avatar_split_clause,[],[f1063,f5216]) ).
fof(f5216,plain,
( spl102_377
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_377])]) ).
fof(f1063,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f644]) ).
fof(f5214,plain,
spl102_376,
inference(avatar_split_clause,[],[f1062,f5212]) ).
fof(f5212,plain,
( spl102_376
<=> ! [X2,X4,X0,X1] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_376])]) ).
fof(f1062,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f644]) ).
fof(f5210,plain,
( spl102_375
| ~ spl102_86
| ~ spl102_353 ),
inference(avatar_split_clause,[],[f5028,f4827,f1832,f5208]) ).
fof(f5028,plain,
( ! [X0] :
( ~ in(X0,sK95)
| ~ in(relation_rng(sK25),X0) )
| ~ spl102_86
| ~ spl102_353 ),
inference(resolution,[],[f4828,f1833]) ).
fof(f5206,plain,
spl102_374,
inference(avatar_split_clause,[],[f1018,f5204]) ).
fof(f5204,plain,
( spl102_374
<=> ! [X4,X0,X1] :
( sP11(X0,X1)
| in(sK70(X0,X1),X4)
| ~ in(X4,X0)
| in(sK70(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_374])]) ).
fof(f1018,plain,
! [X0,X1,X4] :
( sP11(X0,X1)
| in(sK70(X0,X1),X4)
| ~ in(X4,X0)
| in(sK70(X0,X1),X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f622,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ( ( ~ in(sK70(X0,X1),sK71(X0,X1))
& in(sK71(X0,X1),X0) )
| ~ in(sK70(X0,X1),X1) )
& ( ! [X4] :
( in(sK70(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK70(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK72(X0,X5))
& in(sK72(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP11(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71,sK72])],[f618,f621,f620,f619]) ).
fof(f619,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(sK70(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK70(X0,X1),X1) )
& ( ! [X4] :
( in(sK70(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK70(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f620,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK70(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK70(X0,X1),sK71(X0,X1))
& in(sK71(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f621,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK72(X0,X5))
& in(sK72(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f618,plain,
! [X0,X1] :
( ( sP11(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) ) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f617]) ).
fof(f617,plain,
! [X0,X1] :
( ( sP11(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) ) )
| ~ sP11(X0,X1) ) ),
inference(nnf_transformation,[],[f454]) ).
fof(f454,plain,
! [X0,X1] :
( sP11(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f5202,plain,
spl102_373,
inference(avatar_split_clause,[],[f970,f5200]) ).
fof(f5200,plain,
( spl102_373
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(sK60(X0,X1,X2),X0)
| in(sK59(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_373])]) ).
fof(f970,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(sK60(X0,X1,X2),X0)
| in(sK59(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f5198,plain,
spl102_372,
inference(avatar_split_clause,[],[f961,f5196]) ).
fof(f5196,plain,
( spl102_372
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(sK57(X0,X1,X2),X0)
| in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_372])]) ).
fof(f961,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| in(sK57(X0,X1,X2),X0)
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f5091,plain,
( spl102_371
| ~ spl102_87
| ~ spl102_353 ),
inference(avatar_split_clause,[],[f5027,f4827,f1836,f5089]) ).
fof(f5089,plain,
( spl102_371
<=> ! [X0] :
( ~ in(X0,sK95)
| element(X0,relation_rng(sK25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_371])]) ).
fof(f5027,plain,
( ! [X0] :
( ~ in(X0,sK95)
| element(X0,relation_rng(sK25)) )
| ~ spl102_87
| ~ spl102_353 ),
inference(resolution,[],[f4828,f1837]) ).
fof(f5087,plain,
spl102_370,
inference(avatar_split_clause,[],[f1305,f5085]) ).
fof(f5085,plain,
( spl102_370
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK33(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_370])]) ).
fof(f1305,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK33(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f808]) ).
fof(f808,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK33(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f504]) ).
fof(f5083,plain,
spl102_369,
inference(avatar_split_clause,[],[f1284,f5081]) ).
fof(f5081,plain,
( spl102_369
<=> ! [X5,X0,X6,X2,X1] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_369])]) ).
fof(f1284,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP15(X0,X1,X2) ),
inference(definition_unfolding,[],[f1039,f1170]) ).
fof(f1039,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f637]) ).
fof(f5079,plain,
spl102_368,
inference(avatar_split_clause,[],[f1257,f5077]) ).
fof(f5077,plain,
( spl102_368
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_368])]) ).
fof(f1257,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP5(X0,X1,X2) ),
inference(definition_unfolding,[],[f948,f1170]) ).
fof(f948,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f581]) ).
fof(f5075,plain,
spl102_367,
inference(avatar_split_clause,[],[f801,f5073]) ).
fof(f5073,plain,
( spl102_367
<=> ! [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,[spl102_367])]) ).
fof(f801,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f499]) ).
fof(f499,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,[],[f297]) ).
fof(f297,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,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(f5071,plain,
spl102_366,
inference(avatar_split_clause,[],[f800,f5069]) ).
fof(f5069,plain,
( spl102_366
<=> ! [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,[spl102_366])]) ).
fof(f800,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f499]) ).
fof(f5067,plain,
spl102_365,
inference(avatar_split_clause,[],[f746,f5065]) ).
fof(f5065,plain,
( spl102_365
<=> ! [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,[spl102_365])]) ).
fof(f746,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,[],[f264]) ).
fof(f264,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,[],[f263]) ).
fof(f263,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,[],[f192]) ).
fof(f192,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(f5063,plain,
spl102_364,
inference(avatar_split_clause,[],[f745,f5061]) ).
fof(f5061,plain,
( spl102_364
<=> ! [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,[spl102_364])]) ).
fof(f745,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,[],[f262]) ).
fof(f262,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,[],[f261]) ).
fof(f261,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,[],[f189]) ).
fof(f189,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(f5024,plain,
spl102_363,
inference(avatar_split_clause,[],[f1110,f5022]) ).
fof(f5022,plain,
( spl102_363
<=> ! [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,[spl102_363])]) ).
fof(f1110,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f434]) ).
fof(f434,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f433]) ).
fof(f433,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,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(f5020,plain,
spl102_362,
inference(avatar_split_clause,[],[f1092,f5018]) ).
fof(f5018,plain,
( spl102_362
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK80(X0,X1),sK81(X0,X1))
| in(sK80(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_362])]) ).
fof(f1092,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK80(X0,X1),sK81(X0,X1))
| in(sK80(X0,X1),X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f5016,plain,
spl102_361,
inference(avatar_split_clause,[],[f1020,f5014]) ).
fof(f5014,plain,
( spl102_361
<=> ! [X0,X1] :
( sP11(X0,X1)
| ~ in(sK70(X0,X1),sK71(X0,X1))
| ~ in(sK70(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_361])]) ).
fof(f1020,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ in(sK70(X0,X1),sK71(X0,X1))
| ~ in(sK70(X0,X1),X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f4857,plain,
spl102_360,
inference(avatar_split_clause,[],[f1335,f4855]) ).
fof(f4855,plain,
( spl102_360
<=> ! [X5,X1,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_360])]) ).
fof(f1335,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP13(X0,X1) ),
inference(equality_resolution,[],[f1276]) ).
fof(f1276,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP13(X0,X1) ),
inference(definition_unfolding,[],[f1032,f1170]) ).
fof(f1032,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f4853,plain,
spl102_359,
inference(avatar_split_clause,[],[f1289,f4851]) ).
fof(f4851,plain,
( spl102_359
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK83(X0,X1) = X0
| in(sK83(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_359])]) ).
fof(f1289,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK83(X0,X1) = X0
| in(sK83(X0,X1),X1) ),
inference(definition_unfolding,[],[f1099,f728]) ).
fof(f1099,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK83(X0,X1) = X0
| in(sK83(X0,X1),X1) ),
inference(cnf_transformation,[],[f665]) ).
fof(f665,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK83(X0,X1) != X0
| ~ in(sK83(X0,X1),X1) )
& ( sK83(X0,X1) = X0
| in(sK83(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f663,f664]) ).
fof(f664,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK83(X0,X1) != X0
| ~ in(sK83(X0,X1),X1) )
& ( sK83(X0,X1) = X0
| in(sK83(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f663,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,[],[f662]) ).
fof(f662,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,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4849,plain,
spl102_358,
inference(avatar_split_clause,[],[f1278,f4847]) ).
fof(f4847,plain,
( spl102_358
<=> ! [X4,X0,X5,X1] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_358])]) ).
fof(f1278,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP13(X0,X1) ),
inference(definition_unfolding,[],[f1030,f1170]) ).
fof(f1030,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f4845,plain,
spl102_357,
inference(avatar_split_clause,[],[f1277,f4843]) ).
fof(f4843,plain,
( spl102_357
<=> ! [X4,X5,X1,X0] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_357])]) ).
fof(f1277,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP13(X0,X1) ),
inference(definition_unfolding,[],[f1031,f1170]) ).
fof(f1031,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f4841,plain,
spl102_356,
inference(avatar_split_clause,[],[f1201,f4839]) ).
fof(f4839,plain,
( spl102_356
<=> ! [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,[spl102_356])]) ).
fof(f1201,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,[],[f841,f1170]) ).
fof(f841,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f321]) ).
fof(f321,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,[],[f156]) ).
fof(f156,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(f4837,plain,
spl102_355,
inference(avatar_split_clause,[],[f1200,f4835]) ).
fof(f4835,plain,
( spl102_355
<=> ! [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,[spl102_355])]) ).
fof(f1200,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,[],[f842,f1170]) ).
fof(f842,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f322]) ).
fof(f4833,plain,
spl102_354,
inference(avatar_split_clause,[],[f1199,f4831]) ).
fof(f4831,plain,
( spl102_354
<=> ! [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,[spl102_354])]) ).
fof(f1199,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,[],[f839,f1170]) ).
fof(f839,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f319]) ).
fof(f319,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,[],[f168]) ).
fof(f168,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(f4829,plain,
( spl102_353
| ~ spl102_242
| ~ spl102_331 ),
inference(avatar_split_clause,[],[f4362,f4268,f3270,f4827]) ).
fof(f3270,plain,
( spl102_242
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_242])]) ).
fof(f4268,plain,
( spl102_331
<=> sP24(relation_field(sK25),relation_rng(sK25),sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_331])]) ).
fof(f4362,plain,
( ! [X0] :
( ~ in(X0,sK95)
| in(X0,relation_rng(sK25)) )
| ~ spl102_242
| ~ spl102_331 ),
inference(resolution,[],[f4270,f3271]) ).
fof(f3271,plain,
( ! [X2,X0,X1,X4] :
( ~ sP24(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl102_242 ),
inference(avatar_component_clause,[],[f3270]) ).
fof(f4270,plain,
( sP24(relation_field(sK25),relation_rng(sK25),sK95)
| ~ spl102_331 ),
inference(avatar_component_clause,[],[f4268]) ).
fof(f4825,plain,
spl102_352,
inference(avatar_split_clause,[],[f1198,f4823]) ).
fof(f4823,plain,
( spl102_352
<=> ! [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,[spl102_352])]) ).
fof(f1198,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,[],[f840,f1170]) ).
fof(f840,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f320]) ).
fof(f4794,plain,
( spl102_351
| ~ spl102_25
| ~ spl102_49
| ~ spl102_337
| ~ spl102_350 ),
inference(avatar_split_clause,[],[f4790,f4787,f4431,f1619,f1490,f4792]) ).
fof(f4787,plain,
( spl102_350
<=> ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_350])]) ).
fof(f4790,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1)))))
| ~ relation(X1) )
| ~ spl102_25
| ~ spl102_49
| ~ spl102_337
| ~ spl102_350 ),
inference(forward_demodulation,[],[f4788,f4509]) ).
fof(f4509,plain,
( ! [X0,X1] : set_difference(X1,set_difference(X1,X0)) = relation_rng(relation_rng_restriction(X0,identity_relation(X1)))
| ~ spl102_25
| ~ spl102_49
| ~ spl102_337 ),
inference(forward_demodulation,[],[f4489,f1620]) ).
fof(f4489,plain,
( ! [X0,X1] : relation_rng(relation_rng_restriction(X0,identity_relation(X1))) = set_difference(relation_rng(identity_relation(X1)),set_difference(relation_rng(identity_relation(X1)),X0))
| ~ spl102_25
| ~ spl102_337 ),
inference(resolution,[],[f4432,f1491]) ).
fof(f4788,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) )
| ~ spl102_350 ),
inference(avatar_component_clause,[],[f4787]) ).
fof(f4789,plain,
spl102_350,
inference(avatar_split_clause,[],[f1179,f4787]) ).
fof(f1179,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f788,f771]) ).
fof(f771,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f195]) ).
fof(f195,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(f788,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f143]) ).
fof(f143,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f4785,plain,
spl102_349,
inference(avatar_split_clause,[],[f856,f4783]) ).
fof(f4783,plain,
( spl102_349
<=> ! [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,[spl102_349])]) ).
fof(f856,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,[],[f530]) ).
fof(f530,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,[],[f529]) ).
fof(f529,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,[],[f326]) ).
fof(f326,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,[],[f220]) ).
fof(f220,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(f4781,plain,
spl102_348,
inference(avatar_split_clause,[],[f853,f4779]) ).
fof(f4779,plain,
( spl102_348
<=> ! [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,[spl102_348])]) ).
fof(f853,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,[],[f528]) ).
fof(f528,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,[],[f527]) ).
fof(f527,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,[],[f325]) ).
fof(f325,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,[],[f131]) ).
fof(f131,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(f4701,plain,
( spl102_347
| ~ spl102_243
| ~ spl102_331 ),
inference(avatar_split_clause,[],[f4361,f4268,f3274,f4699]) ).
fof(f4699,plain,
( spl102_347
<=> ! [X0] :
( ~ in(X0,sK95)
| ~ in(X0,relation_field(sK25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_347])]) ).
fof(f3274,plain,
( spl102_243
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_243])]) ).
fof(f4361,plain,
( ! [X0] :
( ~ in(X0,sK95)
| ~ in(X0,relation_field(sK25)) )
| ~ spl102_243
| ~ spl102_331 ),
inference(resolution,[],[f4270,f3275]) ).
fof(f3275,plain,
( ! [X2,X0,X1,X4] :
( ~ sP24(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl102_243 ),
inference(avatar_component_clause,[],[f3274]) ).
fof(f4697,plain,
spl102_346,
inference(avatar_split_clause,[],[f1299,f4695]) ).
fof(f4695,plain,
( spl102_346
<=> ! [X5,X1,X0] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_346])]) ).
fof(f1299,plain,
! [X0,X1,X5] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f754]) ).
fof(f754,plain,
! [X0,X1,X4,X5] :
( apply(X0,X4) = X5
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f4693,plain,
spl102_345,
inference(avatar_split_clause,[],[f1104,f4691]) ).
fof(f4691,plain,
( spl102_345
<=> ! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK84(X0,X1),X0)
| ~ in(sK84(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_345])]) ).
fof(f1104,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK84(X0,X1),X0)
| ~ in(sK84(X0,X1),X1) ),
inference(cnf_transformation,[],[f669]) ).
fof(f669,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK84(X0,X1),X0)
| ~ in(sK84(X0,X1),X1) )
& ( subset(sK84(X0,X1),X0)
| in(sK84(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,[sK84])],[f667,f668]) ).
fof(f668,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK84(X0,X1),X0)
| ~ in(sK84(X0,X1),X1) )
& ( subset(sK84(X0,X1),X0)
| in(sK84(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f667,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,[],[f666]) ).
fof(f666,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,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4689,plain,
spl102_344,
inference(avatar_split_clause,[],[f1103,f4687]) ).
fof(f4687,plain,
( spl102_344
<=> ! [X0,X1] :
( powerset(X0) = X1
| subset(sK84(X0,X1),X0)
| in(sK84(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_344])]) ).
fof(f1103,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK84(X0,X1),X0)
| in(sK84(X0,X1),X1) ),
inference(cnf_transformation,[],[f669]) ).
fof(f4685,plain,
spl102_343,
inference(avatar_split_clause,[],[f1067,f4683]) ).
fof(f4683,plain,
( spl102_343
<=> ! [X2,X0,X1] :
( sP18(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_343])]) ).
fof(f1067,plain,
! [X2,X0,X1] :
( sP18(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f465]) ).
fof(f465,plain,
! [X0,X1] :
( ! [X2] :
( sP18(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f410,f464,f463]) ).
fof(f464,plain,
! [X2,X0,X1] :
( ( complements_of_subsets(X0,X1) = X2
<=> sP17(X1,X0,X2) )
| ~ sP18(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f410,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,[],[f40]) ).
fof(f40,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(f4453,plain,
( spl102_342
| ~ spl102_7
| ~ spl102_59
| ~ spl102_333 ),
inference(avatar_split_clause,[],[f4416,f4412,f1661,f1403,f4451]) ).
fof(f4451,plain,
( spl102_342
<=> ! [X0,X1] :
( sK95 = X0
| relation_inverse_image(X1,X0) != sK95
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_342])]) ).
fof(f4412,plain,
( spl102_333
<=> ! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_333])]) ).
fof(f4416,plain,
( ! [X0,X1] :
( sK95 = X0
| relation_inverse_image(X1,X0) != sK95
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_333 ),
inference(forward_demodulation,[],[f4415,f1713]) ).
fof(f4415,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,X0) != sK95
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_333 ),
inference(forward_demodulation,[],[f4413,f1713]) ).
fof(f4413,plain,
( ! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl102_333 ),
inference(avatar_component_clause,[],[f4412]) ).
fof(f4449,plain,
spl102_341,
inference(avatar_split_clause,[],[f1221,f4447]) ).
fof(f4447,plain,
( spl102_341
<=> ! [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,[spl102_341])]) ).
fof(f1221,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,[],[f881,f1170]) ).
fof(f881,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f538]) ).
fof(f4445,plain,
spl102_340,
inference(avatar_split_clause,[],[f1220,f4443]) ).
fof(f4443,plain,
( spl102_340
<=> ! [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,[spl102_340])]) ).
fof(f1220,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,[],[f882,f1170]) ).
fof(f882,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f538]) ).
fof(f4441,plain,
spl102_339,
inference(avatar_split_clause,[],[f1206,f4439]) ).
fof(f4439,plain,
( spl102_339
<=> ! [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,[spl102_339])]) ).
fof(f1206,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,[],[f857,f771,f771]) ).
fof(f857,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f162]) ).
fof(f162,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(f4437,plain,
spl102_338,
inference(avatar_split_clause,[],[f1178,f4435]) ).
fof(f1178,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,[],[f787,f771]) ).
fof(f787,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f226]) ).
fof(f226,axiom,
! [X0,X1] :
( relation(X1)
=> set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f4433,plain,
spl102_337,
inference(avatar_split_clause,[],[f1177,f4431]) ).
fof(f1177,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f786,f771]) ).
fof(f786,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f4429,plain,
spl102_336,
inference(avatar_split_clause,[],[f847,f4427]) ).
fof(f4427,plain,
( spl102_336
<=> ! [X2,X0,X1] :
( in(sK36(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_336])]) ).
fof(f847,plain,
! [X2,X0,X1] :
( in(sK36(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f526]) ).
fof(f4425,plain,
spl102_335,
inference(avatar_split_clause,[],[f843,f4423]) ).
fof(f4423,plain,
( spl102_335
<=> ! [X2,X0,X1] :
( in(sK35(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_335])]) ).
fof(f843,plain,
! [X2,X0,X1] :
( in(sK35(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f522]) ).
fof(f4421,plain,
( spl102_334
| ~ spl102_101
| ~ spl102_146
| ~ spl102_312 ),
inference(avatar_split_clause,[],[f4221,f4160,f2215,f1930,f4418]) ).
fof(f4418,plain,
( spl102_334
<=> sP22(relation_field(sK25),relation_rng(sK25),relation_rng(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_334])]) ).
fof(f4160,plain,
( spl102_312
<=> sK95 = set_difference(relation_rng(sK25),relation_field(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_312])]) ).
fof(f4221,plain,
( sP22(relation_field(sK25),relation_rng(sK25),relation_rng(sK25))
| ~ spl102_101
| ~ spl102_146
| ~ spl102_312 ),
inference(forward_demodulation,[],[f4207,f1931]) ).
fof(f4207,plain,
( sP22(relation_field(sK25),relation_rng(sK25),set_difference(relation_rng(sK25),sK95))
| ~ spl102_146
| ~ spl102_312 ),
inference(superposition,[],[f2216,f4162]) ).
fof(f4162,plain,
( sK95 = set_difference(relation_rng(sK25),relation_field(sK25))
| ~ spl102_312 ),
inference(avatar_component_clause,[],[f4160]) ).
fof(f4414,plain,
spl102_333,
inference(avatar_split_clause,[],[f789,f4412]) ).
fof(f789,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(flattening,[],[f285]) ).
fof(f285,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(ennf_transformation,[],[f148]) ).
fof(f148,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f4391,plain,
( spl102_332
| ~ spl102_7
| ~ spl102_59
| ~ spl102_328 ),
inference(avatar_split_clause,[],[f4256,f4253,f1661,f1403,f4389]) ).
fof(f4389,plain,
( spl102_332
<=> ! [X0,X1] :
( apply(X0,X1) = sK95
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_332])]) ).
fof(f4253,plain,
( spl102_328
<=> ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_328])]) ).
fof(f4256,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK95
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_328 ),
inference(forward_demodulation,[],[f4254,f1713]) ).
fof(f4254,plain,
( ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl102_328 ),
inference(avatar_component_clause,[],[f4253]) ).
fof(f4271,plain,
( spl102_331
| ~ spl102_91
| ~ spl102_312 ),
inference(avatar_split_clause,[],[f4205,f4160,f1852,f4268]) ).
fof(f4205,plain,
( sP24(relation_field(sK25),relation_rng(sK25),sK95)
| ~ spl102_91
| ~ spl102_312 ),
inference(superposition,[],[f1853,f4162]) ).
fof(f4264,plain,
spl102_330,
inference(avatar_split_clause,[],[f1371,f4262]) ).
fof(f4262,plain,
( spl102_330
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_330])]) ).
fof(f1371,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f1126]) ).
fof(f1126,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X1
| ~ in(sK90(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f4260,plain,
spl102_329,
inference(avatar_split_clause,[],[f1370,f4258]) ).
fof(f4258,plain,
( spl102_329
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_329])]) ).
fof(f1370,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f1127]) ).
fof(f1127,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| sK90(X0,X1,X2) != X0
| ~ in(sK90(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f4255,plain,
spl102_328,
inference(avatar_split_clause,[],[f1325,f4253]) ).
fof(f1325,plain,
! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f983]) ).
fof(f983,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| empty_set != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f596]) ).
fof(f596,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f4251,plain,
spl102_327,
inference(avatar_split_clause,[],[f1300,f4249]) ).
fof(f4249,plain,
( spl102_327
<=> ! [X5,X1,X0] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_327])]) ).
fof(f1300,plain,
! [X0,X1,X5] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f753]) ).
fof(f753,plain,
! [X0,X1,X4,X5] :
( in(X4,relation_rng(X1))
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f4247,plain,
spl102_326,
inference(avatar_split_clause,[],[f1148,f4245]) ).
fof(f4245,plain,
( spl102_326
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_326])]) ).
fof(f1148,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f4243,plain,
spl102_325,
inference(avatar_split_clause,[],[f1138,f4241]) ).
fof(f4241,plain,
( spl102_325
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_325])]) ).
fof(f1138,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f4239,plain,
spl102_324,
inference(avatar_split_clause,[],[f1132,f4237]) ).
fof(f4237,plain,
( spl102_324
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_324])]) ).
fof(f1132,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f4235,plain,
spl102_323,
inference(avatar_split_clause,[],[f1122,f4233]) ).
fof(f4233,plain,
( spl102_323
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_323])]) ).
fof(f1122,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f4203,plain,
spl102_322,
inference(avatar_split_clause,[],[f1113,f4201]) ).
fof(f4201,plain,
( spl102_322
<=> ! [X0,X8,X2,X1] :
( in(sK89(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_322])]) ).
fof(f1113,plain,
! [X2,X0,X1,X8] :
( in(sK89(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f4199,plain,
spl102_321,
inference(avatar_split_clause,[],[f1112,f4197]) ).
fof(f4197,plain,
( spl102_321
<=> ! [X0,X8,X2,X1] :
( in(sK88(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_321])]) ).
fof(f1112,plain,
! [X2,X0,X1,X8] :
( in(sK88(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f676]) ).
fof(f4195,plain,
spl102_320,
inference(avatar_split_clause,[],[f1093,f4193]) ).
fof(f4193,plain,
( spl102_320
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK81(X0,X1),X0)
| in(sK80(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_320])]) ).
fof(f1093,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK81(X0,X1),X0)
| in(sK80(X0,X1),X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f4191,plain,
spl102_319,
inference(avatar_split_clause,[],[f1079,f4189]) ).
fof(f4189,plain,
( spl102_319
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK78(X0,X1),X1)
| ~ in(sK78(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_319])]) ).
fof(f1079,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK78(X0,X1),X1)
| ~ in(sK78(X0,X1),X0) ),
inference(cnf_transformation,[],[f647]) ).
fof(f647,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK78(X0,X1),X1)
| ~ in(sK78(X0,X1),X0) )
& ( in(sK78(X0,X1),X1)
| in(sK78(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f645,f646]) ).
fof(f646,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK78(X0,X1),X1)
| ~ in(sK78(X0,X1),X0) )
& ( in(sK78(X0,X1),X1)
| in(sK78(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f645,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f425]) ).
fof(f425,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f166]) ).
fof(f166,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f4187,plain,
spl102_318,
inference(avatar_split_clause,[],[f1078,f4185]) ).
fof(f4185,plain,
( spl102_318
<=> ! [X0,X1] :
( X0 = X1
| in(sK78(X0,X1),X1)
| in(sK78(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_318])]) ).
fof(f1078,plain,
! [X0,X1] :
( X0 = X1
| in(sK78(X0,X1),X1)
| in(sK78(X0,X1),X0) ),
inference(cnf_transformation,[],[f647]) ).
fof(f4183,plain,
spl102_317,
inference(avatar_split_clause,[],[f1061,f4181]) ).
fof(f4181,plain,
( spl102_317
<=> ! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP17(X2,X1,X0)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_317])]) ).
fof(f1061,plain,
! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP17(X2,X1,X0)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f639]) ).
fof(f639,plain,
! [X0,X1,X2] :
( ( ( complements_of_subsets(X1,X2) = X0
| ~ sP17(X2,X1,X0) )
& ( sP17(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0 ) )
| ~ sP18(X0,X1,X2) ),
inference(rectify,[],[f638]) ).
fof(f638,plain,
! [X2,X0,X1] :
( ( ( complements_of_subsets(X0,X1) = X2
| ~ sP17(X1,X0,X2) )
& ( sP17(X1,X0,X2)
| complements_of_subsets(X0,X1) != X2 ) )
| ~ sP18(X2,X0,X1) ),
inference(nnf_transformation,[],[f464]) ).
fof(f4179,plain,
spl102_316,
inference(avatar_split_clause,[],[f1038,f4177]) ).
fof(f4177,plain,
( spl102_316
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP15(X2,X1,X0)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_316])]) ).
fof(f1038,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP15(X2,X1,X0)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP15(X2,X1,X0) )
& ( sP15(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP16(X0,X1,X2) ),
inference(rectify,[],[f631]) ).
fof(f631,plain,
! [X2,X0,X1] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP15(X1,X0,X2) )
& ( sP15(X1,X0,X2)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP16(X2,X0,X1) ),
inference(nnf_transformation,[],[f461]) ).
fof(f461,plain,
! [X2,X0,X1] :
( ( relation_rng_restriction(X0,X1) = X2
<=> sP15(X1,X0,X2) )
| ~ sP16(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f4175,plain,
spl102_315,
inference(avatar_split_clause,[],[f1019,f4173]) ).
fof(f4173,plain,
( spl102_315
<=> ! [X0,X1] :
( sP11(X0,X1)
| in(sK71(X0,X1),X0)
| ~ in(sK70(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_315])]) ).
fof(f1019,plain,
! [X0,X1] :
( sP11(X0,X1)
| in(sK71(X0,X1),X0)
| ~ in(sK70(X0,X1),X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f4171,plain,
spl102_314,
inference(avatar_split_clause,[],[f967,f4169]) ).
fof(f4169,plain,
( spl102_314
<=> ! [X0,X6,X2,X1] :
( in(sK61(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_314])]) ).
fof(f967,plain,
! [X2,X0,X1,X6] :
( in(sK61(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f4167,plain,
spl102_313,
inference(avatar_split_clause,[],[f958,f4165]) ).
fof(f4165,plain,
( spl102_313
<=> ! [X0,X6,X2,X1] :
( in(sK58(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_313])]) ).
fof(f958,plain,
! [X2,X0,X1,X6] :
( in(sK58(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f588]) ).
fof(f4163,plain,
( spl102_312
| ~ spl102_148
| ~ spl102_263 ),
inference(avatar_split_clause,[],[f3618,f3572,f2313,f4160]) ).
fof(f2313,plain,
( spl102_148
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK95
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_148])]) ).
fof(f3572,plain,
( spl102_263
<=> subset(relation_rng(sK25),relation_field(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_263])]) ).
fof(f3618,plain,
( sK95 = set_difference(relation_rng(sK25),relation_field(sK25))
| ~ spl102_148
| ~ spl102_263 ),
inference(resolution,[],[f3574,f2314]) ).
fof(f2314,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK95 )
| ~ spl102_148 ),
inference(avatar_component_clause,[],[f2313]) ).
fof(f3574,plain,
( subset(relation_rng(sK25),relation_field(sK25))
| ~ spl102_263 ),
inference(avatar_component_clause,[],[f3572]) ).
fof(f4158,plain,
spl102_311,
inference(avatar_split_clause,[],[f947,f4156]) ).
fof(f4156,plain,
( spl102_311
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP5(X2,X1,X0)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_311])]) ).
fof(f947,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP5(X2,X1,X0)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f576]) ).
fof(f576,plain,
! [X0,X1,X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| ~ sP5(X2,X1,X0) )
& ( sP5(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ sP6(X0,X1,X2) ),
inference(rectify,[],[f575]) ).
fof(f575,plain,
! [X2,X1,X0] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ~ sP5(X0,X1,X2) )
& ( sP5(X0,X1,X2)
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ sP6(X2,X1,X0) ),
inference(nnf_transformation,[],[f446]) ).
fof(f446,plain,
! [X2,X1,X0] :
( ( relation_dom_restriction(X0,X1) = X2
<=> sP5(X0,X1,X2) )
| ~ sP6(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f4154,plain,
spl102_310,
inference(avatar_split_clause,[],[f930,f4152]) ).
fof(f4152,plain,
( spl102_310
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP3(X2,X1,X0)
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_310])]) ).
fof(f930,plain,
! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP3(X2,X1,X0)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f556]) ).
fof(f556,plain,
! [X0,X1,X2] :
( ( ( relation_composition(X1,X2) = X0
| ~ sP3(X2,X1,X0) )
& ( sP3(X2,X1,X0)
| relation_composition(X1,X2) != X0 ) )
| ~ sP4(X0,X1,X2) ),
inference(rectify,[],[f555]) ).
fof(f555,plain,
! [X2,X0,X1] :
( ( ( relation_composition(X0,X1) = X2
| ~ sP3(X1,X0,X2) )
& ( sP3(X1,X0,X2)
| relation_composition(X0,X1) != X2 ) )
| ~ sP4(X2,X0,X1) ),
inference(nnf_transformation,[],[f443]) ).
fof(f443,plain,
! [X2,X0,X1] :
( ( relation_composition(X0,X1) = X2
<=> sP3(X1,X0,X2) )
| ~ sP4(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f4101,plain,
( spl102_309
| ~ spl102_7
| ~ spl102_59
| ~ spl102_304 ),
inference(avatar_split_clause,[],[f3976,f3973,f1661,f1403,f4099]) ).
fof(f4099,plain,
( spl102_309
<=> ! [X0,X1] :
( sK95 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_309])]) ).
fof(f3973,plain,
( spl102_304
<=> ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_304])]) ).
fof(f3976,plain,
( ! [X0,X1] :
( sK95 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_304 ),
inference(forward_demodulation,[],[f3974,f1713]) ).
fof(f3974,plain,
( ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl102_304 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f4018,plain,
( spl102_308
| ~ spl102_7
| ~ spl102_59
| ~ spl102_297 ),
inference(avatar_split_clause,[],[f3946,f3942,f1661,f1403,f4016]) ).
fof(f4016,plain,
( spl102_308
<=> ! [X0,X1] :
( sK95 = X1
| complements_of_subsets(X0,X1) != sK95
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_308])]) ).
fof(f3942,plain,
( spl102_297
<=> ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_297])]) ).
fof(f3946,plain,
( ! [X0,X1] :
( sK95 = X1
| complements_of_subsets(X0,X1) != sK95
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_297 ),
inference(forward_demodulation,[],[f3945,f1713]) ).
fof(f3945,plain,
( ! [X0,X1] :
( complements_of_subsets(X0,X1) != sK95
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_297 ),
inference(forward_demodulation,[],[f3943,f1713]) ).
fof(f3943,plain,
( ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl102_297 ),
inference(avatar_component_clause,[],[f3942]) ).
fof(f3988,plain,
spl102_307,
inference(avatar_split_clause,[],[f1367,f3986]) ).
fof(f3986,plain,
( spl102_307
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK83(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_307])]) ).
fof(f1367,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK83(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f1288]) ).
fof(f1288,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK83(X0,X1) != X0
| ~ in(sK83(X0,X1),X1) ),
inference(definition_unfolding,[],[f1100,f728]) ).
fof(f1100,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK83(X0,X1) != X0
| ~ in(sK83(X0,X1),X1) ),
inference(cnf_transformation,[],[f665]) ).
fof(f3984,plain,
spl102_306,
inference(avatar_split_clause,[],[f1213,f3982]) ).
fof(f3982,plain,
( spl102_306
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_306])]) ).
fof(f1213,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f870,f771]) ).
fof(f870,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f342]) ).
fof(f342,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,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(f3980,plain,
spl102_305,
inference(avatar_split_clause,[],[f1207,f3978]) ).
fof(f3978,plain,
( spl102_305
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_305])]) ).
fof(f1207,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f861,f728]) ).
fof(f861,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f330]) ).
fof(f330,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,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(f3975,plain,
spl102_304,
inference(avatar_split_clause,[],[f1187,f3973]) ).
fof(f1187,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f819,f728,f728]) ).
fof(f819,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f511]) ).
fof(f511,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,[],[f510]) ).
fof(f510,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,[],[f179]) ).
fof(f179,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f3971,plain,
( spl102_303
| ~ spl102_90
| ~ spl102_251 ),
inference(avatar_split_clause,[],[f3446,f3363,f1848,f3968]) ).
fof(f3968,plain,
( spl102_303
<=> sP23(relation_dom(sK25),relation_rng(sK25),relation_field(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_303])]) ).
fof(f3446,plain,
( sP23(relation_dom(sK25),relation_rng(sK25),relation_field(sK25))
| ~ spl102_90
| ~ spl102_251 ),
inference(superposition,[],[f1849,f3365]) ).
fof(f3966,plain,
spl102_302,
inference(avatar_split_clause,[],[f887,f3964]) ).
fof(f3964,plain,
( spl102_302
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_302])]) ).
fof(f887,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,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(f3962,plain,
spl102_301,
inference(avatar_split_clause,[],[f880,f3960]) ).
fof(f3960,plain,
( spl102_301
<=> ! [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,[spl102_301])]) ).
fof(f880,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f348]) ).
fof(f348,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,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(f3958,plain,
spl102_300,
inference(avatar_split_clause,[],[f849,f3956]) ).
fof(f3956,plain,
( spl102_300
<=> ! [X2,X0,X1] :
( in(sK36(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_300])]) ).
fof(f849,plain,
! [X2,X0,X1] :
( in(sK36(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f526]) ).
fof(f3954,plain,
spl102_299,
inference(avatar_split_clause,[],[f845,f3952]) ).
fof(f3952,plain,
( spl102_299
<=> ! [X2,X0,X1] :
( in(sK35(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_299])]) ).
fof(f845,plain,
! [X2,X0,X1] :
( in(sK35(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f522]) ).
fof(f3950,plain,
spl102_298,
inference(avatar_split_clause,[],[f837,f3948]) ).
fof(f837,plain,
! [X2,X0,X1] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f140]) ).
fof(f140,axiom,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f3944,plain,
spl102_297,
inference(avatar_split_clause,[],[f804,f3942]) ).
fof(f804,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f190]) ).
fof(f190,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(f3940,plain,
spl102_296,
inference(avatar_split_clause,[],[f763,f3938]) ).
fof(f3938,plain,
( spl102_296
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_296])]) ).
fof(f763,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f441]) ).
fof(f441,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f269,f440,f439,f438]) ).
fof(f440,plain,
! [X0,X1] :
( ( function_inverse(X0) = X1
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f269,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f3936,plain,
spl102_295,
inference(avatar_split_clause,[],[f742,f3934]) ).
fof(f742,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f3896,plain,
spl102_294,
inference(avatar_split_clause,[],[f1337,f3894]) ).
fof(f3894,plain,
( spl102_294
<=> ! [X2,X1] :
( sP17(X2,X1,complements_of_subsets(X1,X2))
| ~ sP18(complements_of_subsets(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_294])]) ).
fof(f1337,plain,
! [X2,X1] :
( sP17(X2,X1,complements_of_subsets(X1,X2))
| ~ sP18(complements_of_subsets(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1060]) ).
fof(f1060,plain,
! [X2,X0,X1] :
( sP17(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f639]) ).
fof(f3892,plain,
spl102_293,
inference(avatar_split_clause,[],[f1336,f3890]) ).
fof(f3890,plain,
( spl102_293
<=> ! [X2,X1] :
( sP15(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP16(relation_rng_restriction(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_293])]) ).
fof(f1336,plain,
! [X2,X1] :
( sP15(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP16(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1037]) ).
fof(f1037,plain,
! [X2,X0,X1] :
( sP15(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f632]) ).
fof(f3887,plain,
spl102_292,
inference(avatar_split_clause,[],[f1322,f3885]) ).
fof(f3885,plain,
( spl102_292
<=> ! [X2,X1] :
( sP5(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP6(relation_dom_restriction(X2,X1),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_292])]) ).
fof(f1322,plain,
! [X2,X1] :
( sP5(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP6(relation_dom_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f946]) ).
fof(f946,plain,
! [X2,X0,X1] :
( sP5(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f576]) ).
fof(f3883,plain,
spl102_291,
inference(avatar_split_clause,[],[f1317,f3881]) ).
fof(f3881,plain,
( spl102_291
<=> ! [X2,X1] :
( sP3(X2,X1,relation_composition(X1,X2))
| ~ sP4(relation_composition(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_291])]) ).
fof(f1317,plain,
! [X2,X1] :
( sP3(X2,X1,relation_composition(X1,X2))
| ~ sP4(relation_composition(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f929]) ).
fof(f929,plain,
! [X2,X0,X1] :
( sP3(X2,X1,X0)
| relation_composition(X1,X2) != X0
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f556]) ).
fof(f3879,plain,
spl102_290,
inference(avatar_split_clause,[],[f1091,f3877]) ).
fof(f3877,plain,
( spl102_290
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_290])]) ).
fof(f1091,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f3875,plain,
spl102_289,
inference(avatar_split_clause,[],[f1074,f3873]) ).
fof(f3873,plain,
( spl102_289
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_289])]) ).
fof(f1074,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f3871,plain,
spl102_288,
inference(avatar_split_clause,[],[f1059,f3869]) ).
fof(f3869,plain,
( spl102_288
<=> ! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_288])]) ).
fof(f1059,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,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(f3867,plain,
spl102_287,
inference(avatar_split_clause,[],[f1058,f3865]) ).
fof(f3865,plain,
( spl102_287
<=> ! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_287])]) ).
fof(f1058,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,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(f3863,plain,
spl102_286,
inference(avatar_split_clause,[],[f1015,f3861]) ).
fof(f3861,plain,
( spl102_286
<=> ! [X0,X5,X1,X7] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_286])]) ).
fof(f1015,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f3859,plain,
spl102_285,
inference(avatar_split_clause,[],[f996,f3857]) ).
fof(f3857,plain,
( spl102_285
<=> ! [X2,X0,X4] :
( in(X4,sK68(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK67(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_285])]) ).
fof(f996,plain,
! [X2,X0,X4] :
( in(X4,sK68(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK67(X0)) ),
inference(cnf_transformation,[],[f611]) ).
fof(f611,plain,
! [X0] :
( ! [X2] :
( ( ! [X4] :
( in(X4,sK68(X0,X2))
| ~ subset(X4,X2) )
& in(sK68(X0,X2),sK67(X0)) )
| ~ in(X2,sK67(X0)) )
& ! [X5,X6] :
( in(X6,sK67(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK67(X0)) )
& in(X0,sK67(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f608,f610,f609]) ).
fof(f609,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,sK67(X0)) )
| ~ in(X2,sK67(X0)) )
& ! [X6,X5] :
( in(X6,sK67(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK67(X0)) )
& in(X0,sK67(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f610,plain,
! [X0,X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK67(X0)) )
=> ( ! [X4] :
( in(X4,sK68(X0,X2))
| ~ subset(X4,X2) )
& in(sK68(X0,X2),sK67(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f608,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,[],[f386]) ).
fof(f386,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,[],[f385]) ).
fof(f385,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,[],[f243]) ).
fof(f243,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,[],[f236]) ).
fof(f236,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,[],[f231]) ).
fof(f231,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(f3822,plain,
( spl102_283
| ~ spl102_284
| ~ spl102_80
| ~ spl102_251 ),
inference(avatar_split_clause,[],[f3444,f3363,f1808,f3819,f3815]) ).
fof(f3815,plain,
( spl102_283
<=> empty(relation_rng(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_283])]) ).
fof(f3819,plain,
( spl102_284
<=> empty(relation_field(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_284])]) ).
fof(f1808,plain,
( spl102_80
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_80])]) ).
fof(f3444,plain,
( ~ empty(relation_field(sK25))
| empty(relation_rng(sK25))
| ~ spl102_80
| ~ spl102_251 ),
inference(superposition,[],[f1809,f3365]) ).
fof(f1809,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl102_80 ),
inference(avatar_component_clause,[],[f1808]) ).
fof(f3750,plain,
spl102_282,
inference(avatar_split_clause,[],[f1268,f3748]) ).
fof(f3748,plain,
( spl102_282
<=> ! [X2,X0,X3] :
( relation(X0)
| sK62(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_282])]) ).
fof(f1268,plain,
! [X2,X3,X0] :
( relation(X0)
| sK62(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f989,f1170]) ).
fof(f989,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK62(X0) ),
inference(cnf_transformation,[],[f601]) ).
fof(f3746,plain,
spl102_281,
inference(avatar_split_clause,[],[f1176,f3744]) ).
fof(f3744,plain,
( spl102_281
<=> ! [X0,X1] :
( in(sK31(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_281])]) ).
fof(f1176,plain,
! [X0,X1] :
( in(sK31(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f773,f771]) ).
fof(f773,plain,
! [X0,X1] :
( in(sK31(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f496]) ).
fof(f496,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK31(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f272,f495]) ).
fof(f495,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK31(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f272,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,[],[f234]) ).
fof(f234,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,[],[f198]) ).
fof(f198,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(f3742,plain,
spl102_280,
inference(avatar_split_clause,[],[f862,f3740]) ).
fof(f3740,plain,
( spl102_280
<=> ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_280])]) ).
fof(f862,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f332]) ).
fof(f332,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f201]) ).
fof(f201,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(f3738,plain,
spl102_279,
inference(avatar_split_clause,[],[f855,f3736]) ).
fof(f3736,plain,
( spl102_279
<=> ! [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,[spl102_279])]) ).
fof(f855,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f530]) ).
fof(f3734,plain,
spl102_278,
inference(avatar_split_clause,[],[f852,f3732]) ).
fof(f3732,plain,
( spl102_278
<=> ! [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,[spl102_278])]) ).
fof(f852,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f528]) ).
fof(f3730,plain,
spl102_277,
inference(avatar_split_clause,[],[f838,f3728]) ).
fof(f3728,plain,
( spl102_277
<=> ! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_277])]) ).
fof(f838,plain,
! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f317]) ).
fof(f317,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f149]) ).
fof(f149,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f3726,plain,
spl102_276,
inference(avatar_split_clause,[],[f744,f3724]) ).
fof(f3724,plain,
( spl102_276
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_276])]) ).
fof(f744,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,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,[],[f259]) ).
fof(f259,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,[],[f161]) ).
fof(f161,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(f3722,plain,
spl102_275,
inference(avatar_split_clause,[],[f743,f3720]) ).
fof(f3720,plain,
( spl102_275
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_275])]) ).
fof(f743,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f3686,plain,
( ~ spl102_274
| ~ spl102_73
| ~ spl102_263 ),
inference(avatar_split_clause,[],[f3616,f3572,f1762,f3683]) ).
fof(f3683,plain,
( spl102_274
<=> proper_subset(relation_field(sK25),relation_rng(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_274])]) ).
fof(f3616,plain,
( ~ proper_subset(relation_field(sK25),relation_rng(sK25))
| ~ spl102_73
| ~ spl102_263 ),
inference(resolution,[],[f3574,f1763]) ).
fof(f3615,plain,
spl102_273,
inference(avatar_split_clause,[],[f1301,f3613]) ).
fof(f3613,plain,
( spl102_273
<=> ! [X2,X1,X3] :
( sP0(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_273])]) ).
fof(f1301,plain,
! [X2,X3,X1] :
( sP0(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ),
inference(equality_resolution,[],[f762]) ).
fof(f762,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f491]) ).
fof(f3611,plain,
spl102_272,
inference(avatar_split_clause,[],[f1090,f3609]) ).
fof(f3609,plain,
( spl102_272
<=> ! [X5,X0,X1] :
( in(sK82(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_272])]) ).
fof(f1090,plain,
! [X0,X1,X5] :
( in(sK82(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f3607,plain,
spl102_271,
inference(avatar_split_clause,[],[f1089,f3605]) ).
fof(f3605,plain,
( spl102_271
<=> ! [X5,X0,X1] :
( in(X5,sK82(X0,X5))
| ~ in(X5,X1)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_271])]) ).
fof(f1089,plain,
! [X0,X1,X5] :
( in(X5,sK82(X0,X5))
| ~ in(X5,X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f660]) ).
fof(f3603,plain,
spl102_270,
inference(avatar_split_clause,[],[f1064,f3601]) ).
fof(f3601,plain,
( spl102_270
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| element(sK77(X0,X1,X2),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_270])]) ).
fof(f1064,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| element(sK77(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f644]) ).
fof(f3599,plain,
spl102_269,
inference(avatar_split_clause,[],[f1057,f3597]) ).
fof(f3597,plain,
( spl102_269
<=> ! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_269])]) ).
fof(f1057,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f407]) ).
fof(f407,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,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(f3595,plain,
spl102_268,
inference(avatar_split_clause,[],[f1056,f3593]) ).
fof(f3593,plain,
( spl102_268
<=> ! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_268])]) ).
fof(f1056,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f406]) ).
fof(f406,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,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(f3591,plain,
spl102_267,
inference(avatar_split_clause,[],[f1055,f3589]) ).
fof(f3589,plain,
( spl102_267
<=> ! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_267])]) ).
fof(f1055,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,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(f3587,plain,
spl102_266,
inference(avatar_split_clause,[],[f1054,f3585]) ).
fof(f3585,plain,
( spl102_266
<=> ! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_266])]) ).
fof(f1054,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f404]) ).
fof(f404,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,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(f3583,plain,
spl102_265,
inference(avatar_split_clause,[],[f1053,f3581]) ).
fof(f3581,plain,
( spl102_265
<=> ! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_265])]) ).
fof(f1053,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f403]) ).
fof(f403,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,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(f3579,plain,
spl102_264,
inference(avatar_split_clause,[],[f1052,f3577]) ).
fof(f1052,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f402]) ).
fof(f402,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,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(f3575,plain,
( spl102_263
| ~ spl102_50
| ~ spl102_251 ),
inference(avatar_split_clause,[],[f3443,f3363,f1623,f3572]) ).
fof(f3443,plain,
( subset(relation_rng(sK25),relation_field(sK25))
| ~ spl102_50
| ~ spl102_251 ),
inference(superposition,[],[f1624,f3365]) ).
fof(f3570,plain,
spl102_262,
inference(avatar_split_clause,[],[f1017,f3568]) ).
fof(f3568,plain,
( spl102_262
<=> ! [X5,X1,X0] :
( in(X5,X1)
| ~ in(X5,sK72(X0,X5))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_262])]) ).
fof(f1017,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK72(X0,X5))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f3566,plain,
spl102_261,
inference(avatar_split_clause,[],[f1016,f3564]) ).
fof(f3564,plain,
( spl102_261
<=> ! [X5,X1,X0] :
( in(X5,X1)
| in(sK72(X0,X5),X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_261])]) ).
fof(f1016,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK72(X0,X5),X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f622]) ).
fof(f3562,plain,
spl102_260,
inference(avatar_split_clause,[],[f994,f3560]) ).
fof(f3560,plain,
( spl102_260
<=> ! [X6,X0,X5] :
( in(X6,sK67(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK67(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_260])]) ).
fof(f994,plain,
! [X0,X6,X5] :
( in(X6,sK67(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK67(X0)) ),
inference(cnf_transformation,[],[f611]) ).
fof(f3558,plain,
spl102_259,
inference(avatar_split_clause,[],[f979,f3556]) ).
fof(f979,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f378]) ).
fof(f378,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> relation_inverse(X0) = function_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f3554,plain,
spl102_258,
inference(avatar_split_clause,[],[f965,f3552]) ).
fof(f3552,plain,
( spl102_258
<=> ! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP9(X1,X0,X2)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_258])]) ).
fof(f965,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP9(X1,X0,X2)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f589]) ).
fof(f589,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP9(X1,X0,X2) )
& ( sP9(X1,X0,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f452]) ).
fof(f452,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP9(X1,X0,X2) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f3550,plain,
spl102_257,
inference(avatar_split_clause,[],[f956,f3548]) ).
fof(f3548,plain,
( spl102_257
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP7(X1,X0,X2)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_257])]) ).
fof(f956,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP7(X1,X0,X2)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f582,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP7(X1,X0,X2) )
& ( sP7(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f449]) ).
fof(f449,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP7(X1,X0,X2) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f3386,plain,
spl102_256,
inference(avatar_split_clause,[],[f1296,f3384]) ).
fof(f3384,plain,
( spl102_256
<=> ! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP22(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_256])]) ).
fof(f1296,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP22(X1,X0,X2) ),
inference(definition_unfolding,[],[f1137,f771]) ).
fof(f1137,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP22(X1,X0,X2) ),
inference(cnf_transformation,[],[f689]) ).
fof(f689,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP22(X1,X0,X2) )
& ( sP22(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f473]) ).
fof(f473,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP22(X1,X0,X2) ),
inference(definition_folding,[],[f27,f472]) ).
fof(f27,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(f3382,plain,
spl102_255,
inference(avatar_split_clause,[],[f1272,f3380]) ).
fof(f3380,plain,
( spl102_255
<=> ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_255])]) ).
fof(f1272,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f1006,f771,f771]) ).
fof(f1006,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3378,plain,
spl102_254,
inference(avatar_split_clause,[],[f874,f3376]) ).
fof(f3376,plain,
( spl102_254
<=> ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_254])]) ).
fof(f874,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f534]) ).
fof(f534,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,[],[f533]) ).
fof(f533,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,[],[f177]) ).
fof(f177,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(f3374,plain,
spl102_253,
inference(avatar_split_clause,[],[f871,f3372]) ).
fof(f3372,plain,
( spl102_253
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_253])]) ).
fof(f871,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f344]) ).
fof(f344,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f224]) ).
fof(f224,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(f3370,plain,
spl102_252,
inference(avatar_split_clause,[],[f854,f3368]) ).
fof(f3368,plain,
( spl102_252
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_252])]) ).
fof(f854,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f530]) ).
fof(f3366,plain,
( spl102_251
| ~ spl102_1
| ~ spl102_245 ),
inference(avatar_split_clause,[],[f3332,f3283,f1373,f3363]) ).
fof(f3332,plain,
( relation_field(sK25) = set_union2(relation_rng(sK25),relation_dom(sK25))
| ~ spl102_1
| ~ spl102_245 ),
inference(resolution,[],[f3284,f1375]) ).
fof(f3361,plain,
spl102_250,
inference(avatar_split_clause,[],[f851,f3359]) ).
fof(f3359,plain,
( spl102_250
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_250])]) ).
fof(f851,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f528]) ).
fof(f3357,plain,
spl102_249,
inference(avatar_split_clause,[],[f765,f3355]) ).
fof(f3355,plain,
( spl102_249
<=> ! [X4,X0,X3] :
( in(X4,sK30(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_249])]) ).
fof(f765,plain,
! [X3,X0,X4] :
( in(X4,sK30(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK30(X0)) ),
inference(cnf_transformation,[],[f494]) ).
fof(f494,plain,
! [X0] :
( ! [X2] :
( in(powerset(X2),sK30(X0))
| ~ in(X2,sK30(X0)) )
& ! [X3,X4] :
( in(X4,sK30(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK30(X0)) )
& in(X0,sK30(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f492,f493]) ).
fof(f493,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),sK30(X0))
| ~ in(X2,sK30(X0)) )
& ! [X4,X3] :
( in(X4,sK30(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK30(X0)) )
& in(X0,sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f492,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,[],[f271]) ).
fof(f271,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,[],[f270]) ).
fof(f270,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,[],[f242]) ).
fof(f242,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,[],[f233]) ).
fof(f233,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,[],[f139]) ).
fof(f139,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(f3353,plain,
spl102_248,
inference(avatar_split_clause,[],[f741,f3351]) ).
fof(f3351,plain,
( spl102_248
<=> ! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_248])]) ).
fof(f741,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,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(f3349,plain,
spl102_247,
inference(avatar_split_clause,[],[f740,f3347]) ).
fof(f3347,plain,
( spl102_247
<=> ! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_247])]) ).
fof(f740,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,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(f3312,plain,
( spl102_246
| ~ spl102_15
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1603,f1544,f1443,f3309]) ).
fof(f3309,plain,
( spl102_246
<=> sP10(sK100) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_246])]) ).
fof(f1603,plain,
( sP10(sK100)
| ~ spl102_15
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1445]) ).
fof(f3285,plain,
( spl102_245
| ~ spl102_112
| ~ spl102_230 ),
inference(avatar_split_clause,[],[f3223,f3220,f1986,f3283]) ).
fof(f3220,plain,
( spl102_230
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_230])]) ).
fof(f3223,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) )
| ~ spl102_112
| ~ spl102_230 ),
inference(forward_demodulation,[],[f3221,f1987]) ).
fof(f3221,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) )
| ~ spl102_230 ),
inference(avatar_component_clause,[],[f3220]) ).
fof(f3281,plain,
( spl102_244
| ~ spl102_13
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1602,f1544,f1433,f3278]) ).
fof(f3278,plain,
( spl102_244
<=> sP10(sK99) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_244])]) ).
fof(f1602,plain,
( sP10(sK99)
| ~ spl102_13
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1435]) ).
fof(f3276,plain,
spl102_243,
inference(avatar_split_clause,[],[f1147,f3274]) ).
fof(f1147,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f3272,plain,
spl102_242,
inference(avatar_split_clause,[],[f1146,f3270]) ).
fof(f1146,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f700]) ).
fof(f3268,plain,
spl102_241,
inference(avatar_split_clause,[],[f1140,f3266]) ).
fof(f3266,plain,
( spl102_241
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_241])]) ).
fof(f1140,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f3264,plain,
spl102_240,
inference(avatar_split_clause,[],[f1139,f3262]) ).
fof(f3262,plain,
( spl102_240
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_240])]) ).
fof(f1139,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f694]) ).
fof(f3260,plain,
spl102_239,
inference(avatar_split_clause,[],[f1131,f3258]) ).
fof(f3258,plain,
( spl102_239
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_239])]) ).
fof(f1131,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f3256,plain,
spl102_238,
inference(avatar_split_clause,[],[f1130,f3254]) ).
fof(f3254,plain,
( spl102_238
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_238])]) ).
fof(f1130,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f688]) ).
fof(f3252,plain,
spl102_237,
inference(avatar_split_clause,[],[f1109,f3250]) ).
fof(f3250,plain,
( spl102_237
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_237])]) ).
fof(f1109,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f432]) ).
fof(f432,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f431]) ).
fof(f431,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f197]) ).
fof(f197,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f3248,plain,
spl102_236,
inference(avatar_split_clause,[],[f1051,f3246]) ).
fof(f3246,plain,
( spl102_236
<=> ! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_236])]) ).
fof(f1051,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,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(f3244,plain,
spl102_235,
inference(avatar_split_clause,[],[f1029,f3242]) ).
fof(f3242,plain,
( spl102_235
<=> ! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP13(X1,X0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_235])]) ).
fof(f1029,plain,
! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP13(X1,X0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0,X1] :
( ( ( identity_relation(X1) = X0
| ~ sP13(X1,X0) )
& ( sP13(X1,X0)
| identity_relation(X1) != X0 ) )
| ~ sP14(X0,X1) ),
inference(rectify,[],[f624]) ).
fof(f624,plain,
! [X1,X0] :
( ( ( identity_relation(X0) = X1
| ~ sP13(X0,X1) )
& ( sP13(X0,X1)
| identity_relation(X0) != X1 ) )
| ~ sP14(X1,X0) ),
inference(nnf_transformation,[],[f458]) ).
fof(f458,plain,
! [X1,X0] :
( ( identity_relation(X0) = X1
<=> sP13(X0,X1) )
| ~ sP14(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f3240,plain,
spl102_234,
inference(avatar_split_clause,[],[f1014,f3238]) ).
fof(f3238,plain,
( spl102_234
<=> ! [X0,X1] :
( set_meet(X1) = X0
| ~ sP11(X1,X0)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_234])]) ).
fof(f1014,plain,
! [X0,X1] :
( set_meet(X1) = X0
| ~ sP11(X1,X0)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f616]) ).
fof(f616,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP12(X0,X1) ),
inference(rectify,[],[f615]) ).
fof(f615,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP11(X0,X1) )
& ( sP11(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP12(X1,X0) ),
inference(nnf_transformation,[],[f455]) ).
fof(f455,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP11(X0,X1) )
| ~ sP12(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f3236,plain,
( spl102_233
| ~ spl102_12
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1601,f1544,f1428,f3233]) ).
fof(f3233,plain,
( spl102_233
<=> sP10(sK98) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_233])]) ).
fof(f1601,plain,
( sP10(sK98)
| ~ spl102_12
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1430]) ).
fof(f3231,plain,
spl102_232,
inference(avatar_split_clause,[],[f995,f3229]) ).
fof(f3229,plain,
( spl102_232
<=> ! [X2,X0] :
( in(sK68(X0,X2),sK67(X0))
| ~ in(X2,sK67(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_232])]) ).
fof(f995,plain,
! [X2,X0] :
( in(sK68(X0,X2),sK67(X0))
| ~ in(X2,sK67(X0)) ),
inference(cnf_transformation,[],[f611]) ).
fof(f3227,plain,
spl102_231,
inference(avatar_split_clause,[],[f937,f3225]) ).
fof(f3225,plain,
( spl102_231
<=> ! [X2,X0,X1] :
( sP4(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_231])]) ).
fof(f937,plain,
! [X2,X0,X1] :
( sP4(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f444]) ).
fof(f444,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP4(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f364,f443,f442]) ).
fof(f364,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,[],[f39]) ).
fof(f39,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(f3222,plain,
spl102_230,
inference(avatar_split_clause,[],[f917,f3220]) ).
fof(f917,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,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(f3218,plain,
spl102_229,
inference(avatar_split_clause,[],[f761,f3216]) ).
fof(f3216,plain,
( spl102_229
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| apply(X3,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_229])]) ).
fof(f761,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| apply(X3,X0) = X1 ),
inference(cnf_transformation,[],[f491]) ).
fof(f3214,plain,
spl102_228,
inference(avatar_split_clause,[],[f750,f3212]) ).
fof(f3212,plain,
( spl102_228
<=> ! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_228])]) ).
fof(f750,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f483]) ).
fof(f483,plain,
! [X0,X1] :
( ( ( function_inverse(X0) = X1
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| function_inverse(X0) != X1 ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f440]) ).
fof(f3176,plain,
( spl102_227
| ~ spl102_7
| ~ spl102_59
| ~ spl102_222 ),
inference(avatar_split_clause,[],[f2975,f2972,f1661,f1403,f3174]) ).
fof(f3174,plain,
( spl102_227
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK95
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_227])]) ).
fof(f2972,plain,
( spl102_222
<=> ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_222])]) ).
fof(f2975,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK95
| ~ disjoint(X0,X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_222 ),
inference(forward_demodulation,[],[f2973,f1713]) ).
fof(f2973,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl102_222 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f3167,plain,
( spl102_226
| ~ spl102_7
| ~ spl102_59
| ~ spl102_221 ),
inference(avatar_split_clause,[],[f2970,f2967,f1661,f1403,f3165]) ).
fof(f3165,plain,
( spl102_226
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK95
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_226])]) ).
fof(f2967,plain,
( spl102_221
<=> ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_221])]) ).
fof(f2970,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK95
| disjoint(X0,X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_221 ),
inference(forward_demodulation,[],[f2968,f1713]) ).
fof(f2968,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) )
| ~ spl102_221 ),
inference(avatar_component_clause,[],[f2967]) ).
fof(f3054,plain,
( spl102_225
| ~ spl102_1
| ~ spl102_205 ),
inference(avatar_split_clause,[],[f2997,f2900,f1373,f3052]) ).
fof(f3052,plain,
( spl102_225
<=> ! [X0] : relation_dom_restriction(sK25,X0) = relation_composition(identity_relation(X0),sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_225])]) ).
fof(f2900,plain,
( spl102_205
<=> ! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_205])]) ).
fof(f2997,plain,
( ! [X0] : relation_dom_restriction(sK25,X0) = relation_composition(identity_relation(X0),sK25)
| ~ spl102_1
| ~ spl102_205 ),
inference(resolution,[],[f2901,f1375]) ).
fof(f2901,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) )
| ~ spl102_205 ),
inference(avatar_component_clause,[],[f2900]) ).
fof(f2983,plain,
( spl102_224
| ~ spl102_7
| ~ spl102_59
| ~ spl102_204 ),
inference(avatar_split_clause,[],[f2898,f2894,f1661,f1403,f2981]) ).
fof(f2981,plain,
( spl102_224
<=> ! [X0] :
( relation_rng(X0) != sK95
| relation_dom(X0) = sK95
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_224])]) ).
fof(f2894,plain,
( spl102_204
<=> ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_204])]) ).
fof(f2898,plain,
( ! [X0] :
( relation_rng(X0) != sK95
| relation_dom(X0) = sK95
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_204 ),
inference(forward_demodulation,[],[f2897,f1713]) ).
fof(f2897,plain,
( ! [X0] :
( relation_dom(X0) = sK95
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_204 ),
inference(forward_demodulation,[],[f2895,f1713]) ).
fof(f2895,plain,
( ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl102_204 ),
inference(avatar_component_clause,[],[f2894]) ).
fof(f2979,plain,
( spl102_223
| ~ spl102_7
| ~ spl102_59
| ~ spl102_203 ),
inference(avatar_split_clause,[],[f2892,f2888,f1661,f1403,f2977]) ).
fof(f2977,plain,
( spl102_223
<=> ! [X0] :
( relation_dom(X0) != sK95
| relation_rng(X0) = sK95
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_223])]) ).
fof(f2888,plain,
( spl102_203
<=> ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_203])]) ).
fof(f2892,plain,
( ! [X0] :
( relation_dom(X0) != sK95
| relation_rng(X0) = sK95
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_203 ),
inference(forward_demodulation,[],[f2891,f1713]) ).
fof(f2891,plain,
( ! [X0] :
( relation_rng(X0) = sK95
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_203 ),
inference(forward_demodulation,[],[f2889,f1713]) ).
fof(f2889,plain,
( ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl102_203 ),
inference(avatar_component_clause,[],[f2888]) ).
fof(f2974,plain,
spl102_222,
inference(avatar_split_clause,[],[f1287,f2972]) ).
fof(f1287,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1084,f771]) ).
fof(f1084,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f650]) ).
fof(f650,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f2969,plain,
spl102_221,
inference(avatar_split_clause,[],[f1286,f2967]) ).
fof(f1286,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f1085,f771]) ).
fof(f1085,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f650]) ).
fof(f2965,plain,
spl102_220,
inference(avatar_split_clause,[],[f1285,f2963]) ).
fof(f2963,plain,
( spl102_220
<=> ! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_220])]) ).
fof(f1285,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1075,f771]) ).
fof(f1075,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f420]) ).
fof(f420,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f419]) ).
fof(f419,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f2960,plain,
( spl102_219
| ~ spl102_11
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1600,f1544,f1423,f2957]) ).
fof(f2957,plain,
( spl102_219
<=> sP10(sK97) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_219])]) ).
fof(f1423,plain,
( spl102_11
<=> relation(sK97) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_11])]) ).
fof(f1600,plain,
( sP10(sK97)
| ~ spl102_11
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1425]) ).
fof(f1425,plain,
( relation(sK97)
| ~ spl102_11 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f2955,plain,
spl102_218,
inference(avatar_split_clause,[],[f1209,f2953]) ).
fof(f2953,plain,
( spl102_218
<=> ! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_218])]) ).
fof(f1209,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f864,f728]) ).
fof(f864,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f335]) ).
fof(f335,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f232]) ).
fof(f232,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f2951,plain,
spl102_217,
inference(avatar_split_clause,[],[f1208,f2949]) ).
fof(f2949,plain,
( spl102_217
<=> ! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_217])]) ).
fof(f1208,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f863,f728]) ).
fof(f863,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f225]) ).
fof(f225,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f2947,plain,
spl102_216,
inference(avatar_split_clause,[],[f1196,f2945]) ).
fof(f2945,plain,
( spl102_216
<=> ! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_216])]) ).
fof(f1196,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f833,f728]) ).
fof(f833,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f518]) ).
fof(f518,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f211]) ).
fof(f211,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f2943,plain,
spl102_215,
inference(avatar_split_clause,[],[f1195,f2941]) ).
fof(f2941,plain,
( spl102_215
<=> ! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_215])]) ).
fof(f1195,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f834,f728]) ).
fof(f834,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f518]) ).
fof(f2939,plain,
spl102_214,
inference(avatar_split_clause,[],[f1184,f2937]) ).
fof(f2937,plain,
( spl102_214
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_214])]) ).
fof(f1184,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f805,f728,f728]) ).
fof(f805,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f214]) ).
fof(f214,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f2935,plain,
spl102_213,
inference(avatar_split_clause,[],[f1183,f2933]) ).
fof(f2933,plain,
( spl102_213
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_213])]) ).
fof(f1183,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f797,f771]) ).
fof(f797,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f2931,plain,
spl102_212,
inference(avatar_split_clause,[],[f1181,f2929]) ).
fof(f2929,plain,
( spl102_212
<=> ! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_212])]) ).
fof(f1181,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f794,f728]) ).
fof(f794,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f2927,plain,
spl102_211,
inference(avatar_split_clause,[],[f1175,f2925]) ).
fof(f2925,plain,
( spl102_211
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_211])]) ).
fof(f1175,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f774,f771]) ).
fof(f774,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f496]) ).
fof(f2923,plain,
spl102_210,
inference(avatar_split_clause,[],[f860,f2921]) ).
fof(f2921,plain,
( spl102_210
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_210])]) ).
fof(f860,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,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,[],[f135]) ).
fof(f135,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(f2919,plain,
spl102_209,
inference(avatar_split_clause,[],[f859,f2917]) ).
fof(f2917,plain,
( spl102_209
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_209])]) ).
fof(f859,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f329]) ).
fof(f2915,plain,
( spl102_208
| ~ spl102_9
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1599,f1544,f1413,f2912]) ).
fof(f2912,plain,
( spl102_208
<=> sP10(sK96) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_208])]) ).
fof(f1599,plain,
( sP10(sK96)
| ~ spl102_9
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1415]) ).
fof(f2910,plain,
spl102_207,
inference(avatar_split_clause,[],[f858,f2908]) ).
fof(f2908,plain,
( spl102_207
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_207])]) ).
fof(f858,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f169]) ).
fof(f169,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(f2906,plain,
spl102_206,
inference(avatar_split_clause,[],[f799,f2904]) ).
fof(f2904,plain,
( spl102_206
<=> ! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_206])]) ).
fof(f799,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,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(f2902,plain,
spl102_205,
inference(avatar_split_clause,[],[f785,f2900]) ).
fof(f785,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f228]) ).
fof(f228,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(f2896,plain,
spl102_204,
inference(avatar_split_clause,[],[f739,f2894]) ).
fof(f739,plain,
! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f482]) ).
fof(f482,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,[],[f255]) ).
fof(f255,plain,
! [X0] :
( ( empty_set = relation_dom(X0)
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f210]) ).
fof(f210,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(f2890,plain,
spl102_203,
inference(avatar_split_clause,[],[f738,f2888]) ).
fof(f738,plain,
! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f482]) ).
fof(f2874,plain,
( spl102_202
| ~ spl102_5
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1597,f1544,f1393,f2871]) ).
fof(f1597,plain,
( sP10(empty_set)
| ~ spl102_5
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1395]) ).
fof(f2822,plain,
spl102_201,
inference(avatar_split_clause,[],[f1154,f2820]) ).
fof(f2820,plain,
( spl102_201
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_201])]) ).
fof(f1154,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f437]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f205,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f2818,plain,
spl102_200,
inference(avatar_split_clause,[],[f1153,f2816]) ).
fof(f2816,plain,
( spl102_200
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP24(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_200])]) ).
fof(f1153,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP24(X1,X0,X2) ),
inference(cnf_transformation,[],[f701]) ).
fof(f701,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP24(X1,X0,X2) )
& ( sP24(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f477]) ).
fof(f477,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP24(X1,X0,X2) ),
inference(definition_folding,[],[f32,f476]) ).
fof(f32,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(f2814,plain,
spl102_199,
inference(avatar_split_clause,[],[f1145,f2812]) ).
fof(f2812,plain,
( spl102_199
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP23(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_199])]) ).
fof(f1145,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP23(X1,X0,X2) ),
inference(cnf_transformation,[],[f695]) ).
fof(f695,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP23(X1,X0,X2) )
& ( sP23(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f475]) ).
fof(f475,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP23(X1,X0,X2) ),
inference(definition_folding,[],[f23,f474]) ).
fof(f23,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(f2810,plain,
spl102_198,
inference(avatar_split_clause,[],[f1129,f2808]) ).
fof(f2808,plain,
( spl102_198
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP21(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_198])]) ).
fof(f1129,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP21(X1,X0,X2) ),
inference(cnf_transformation,[],[f683]) ).
fof(f683,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP21(X1,X0,X2) )
& ( sP21(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f471]) ).
fof(f471,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP21(X1,X0,X2) ),
inference(definition_folding,[],[f22,f470]) ).
fof(f22,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(f2806,plain,
spl102_197,
inference(avatar_split_clause,[],[f1121,f2804]) ).
fof(f2804,plain,
( spl102_197
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP20(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_197])]) ).
fof(f1121,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP20(X1,X0,X2) ),
inference(cnf_transformation,[],[f677]) ).
fof(f677,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP20(X1,X0,X2) )
& ( sP20(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f469]) ).
fof(f469,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP20(X1,X0,X2) ),
inference(definition_folding,[],[f24,f468]) ).
fof(f24,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(f2801,plain,
( spl102_196
| ~ spl102_18
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1595,f1540,f1458,f2798]) ).
fof(f2798,plain,
( spl102_196
<=> sP8(sK101) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_196])]) ).
fof(f1595,plain,
( sP8(sK101)
| ~ spl102_18
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1460]) ).
fof(f2796,plain,
spl102_195,
inference(avatar_split_clause,[],[f1086,f2794]) ).
fof(f2794,plain,
( spl102_195
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_195])]) ).
fof(f1086,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f654]) ).
fof(f654,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK79(X0,X1),X1)
& in(sK79(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f652,f653]) ).
fof(f653,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK79(X0,X1),X1)
& in(sK79(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f652,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,[],[f651]) ).
fof(f651,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,[],[f428]) ).
fof(f428,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2792,plain,
spl102_194,
inference(avatar_split_clause,[],[f1083,f2790]) ).
fof(f2790,plain,
( spl102_194
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_194])]) ).
fof(f1083,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f427]) ).
fof(f427,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f426]) ).
fof(f426,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f2788,plain,
spl102_193,
inference(avatar_split_clause,[],[f1082,f2786]) ).
fof(f2786,plain,
( spl102_193
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_193])]) ).
fof(f1082,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f649]) ).
fof(f649,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f648]) ).
fof(f648,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2784,plain,
spl102_192,
inference(avatar_split_clause,[],[f976,f2782]) ).
fof(f2782,plain,
( spl102_192
<=> ! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_192])]) ).
fof(f976,plain,
! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f2780,plain,
spl102_191,
inference(avatar_split_clause,[],[f760,f2778]) ).
fof(f2778,plain,
( spl102_191
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_191])]) ).
fof(f760,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f491]) ).
fof(f2685,plain,
( spl102_190
| ~ spl102_7
| ~ spl102_59
| ~ spl102_175 ),
inference(avatar_split_clause,[],[f2582,f2578,f1661,f1403,f2683]) ).
fof(f2578,plain,
( spl102_175
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_175])]) ).
fof(f2582,plain,
( ! [X0] :
( relation_rng(X0) != sK95
| sK95 = X0
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_175 ),
inference(forward_demodulation,[],[f2581,f1713]) ).
fof(f2581,plain,
( ! [X0] :
( sK95 = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_175 ),
inference(forward_demodulation,[],[f2579,f1713]) ).
fof(f2579,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl102_175 ),
inference(avatar_component_clause,[],[f2578]) ).
fof(f2681,plain,
( spl102_189
| ~ spl102_7
| ~ spl102_59
| ~ spl102_174 ),
inference(avatar_split_clause,[],[f2576,f2572,f1661,f1403,f2679]) ).
fof(f2679,plain,
( spl102_189
<=> ! [X0] :
( relation_dom(X0) != sK95
| sK95 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_189])]) ).
fof(f2572,plain,
( spl102_174
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_174])]) ).
fof(f2576,plain,
( ! [X0] :
( relation_dom(X0) != sK95
| sK95 = X0
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_174 ),
inference(forward_demodulation,[],[f2575,f1713]) ).
fof(f2575,plain,
( ! [X0] :
( sK95 = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_174 ),
inference(forward_demodulation,[],[f2573,f1713]) ).
fof(f2573,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl102_174 ),
inference(avatar_component_clause,[],[f2572]) ).
fof(f2677,plain,
( spl102_188
| ~ spl102_1
| ~ spl102_172 ),
inference(avatar_split_clause,[],[f2645,f2564,f1373,f2674]) ).
fof(f2674,plain,
( spl102_188
<=> relation_rng(sK25) = relation_image(sK25,relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_188])]) ).
fof(f2564,plain,
( spl102_172
<=> ! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_172])]) ).
fof(f2645,plain,
( relation_rng(sK25) = relation_image(sK25,relation_dom(sK25))
| ~ spl102_1
| ~ spl102_172 ),
inference(resolution,[],[f2565,f1375]) ).
fof(f2565,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) )
| ~ spl102_172 ),
inference(avatar_component_clause,[],[f2564]) ).
fof(f2631,plain,
spl102_187,
inference(avatar_split_clause,[],[f869,f2629]) ).
fof(f2629,plain,
( spl102_187
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_187])]) ).
fof(f869,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f340]) ).
fof(f340,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f154]) ).
fof(f154,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f2627,plain,
spl102_186,
inference(avatar_split_clause,[],[f868,f2625]) ).
fof(f2625,plain,
( spl102_186
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_186])]) ).
fof(f868,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f339]) ).
fof(f339,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f338]) ).
fof(f338,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f208]) ).
fof(f208,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f2623,plain,
spl102_185,
inference(avatar_split_clause,[],[f816,f2621]) ).
fof(f2621,plain,
( spl102_185
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK34(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_185])]) ).
fof(f816,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK34(X0,X1),X1) ),
inference(cnf_transformation,[],[f508]) ).
fof(f508,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK34(X0,X1),X1)
& in(sK34(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f313,f507]) ).
fof(f507,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK34(X0,X1),X1)
& in(sK34(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,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(f2619,plain,
spl102_184,
inference(avatar_split_clause,[],[f815,f2617]) ).
fof(f815,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK34(X0,X1),X0) ),
inference(cnf_transformation,[],[f508]) ).
fof(f2615,plain,
spl102_183,
inference(avatar_split_clause,[],[f793,f2613]) ).
fof(f2613,plain,
( spl102_183
<=> ! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_183])]) ).
fof(f793,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f2611,plain,
spl102_182,
inference(avatar_split_clause,[],[f784,f2609]) ).
fof(f784,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f229]) ).
fof(f229,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(f2607,plain,
spl102_181,
inference(avatar_split_clause,[],[f783,f2605]) ).
fof(f2605,plain,
( spl102_181
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_181])]) ).
fof(f783,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,axiom,
! [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(f2603,plain,
spl102_180,
inference(avatar_split_clause,[],[f777,f2601]) ).
fof(f2601,plain,
( spl102_180
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_180])]) ).
fof(f777,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f498]) ).
fof(f498,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK32(X0,X1),X1)
& in(sK32(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f273,f497]) ).
fof(f497,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK32(X0,X1),X1)
& in(sK32(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f273,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,[],[f235]) ).
fof(f235,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,[],[f182]) ).
fof(f182,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(f2599,plain,
( spl102_179
| ~ spl102_15
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1594,f1540,f1443,f2596]) ).
fof(f2596,plain,
( spl102_179
<=> sP8(sK100) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_179])]) ).
fof(f1594,plain,
( sP8(sK100)
| ~ spl102_15
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1445]) ).
fof(f2594,plain,
spl102_178,
inference(avatar_split_clause,[],[f772,f2592]) ).
fof(f2592,plain,
( spl102_178
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_178])]) ).
fof(f772,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f184]) ).
fof(f184,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(f2590,plain,
spl102_177,
inference(avatar_split_clause,[],[f770,f2588]) ).
fof(f770,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f178,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(f2586,plain,
spl102_176,
inference(avatar_split_clause,[],[f766,f2584]) ).
fof(f2584,plain,
( spl102_176
<=> ! [X2,X0] :
( in(powerset(X2),sK30(X0))
| ~ in(X2,sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_176])]) ).
fof(f766,plain,
! [X2,X0] :
( in(powerset(X2),sK30(X0))
| ~ in(X2,sK30(X0)) ),
inference(cnf_transformation,[],[f494]) ).
fof(f2580,plain,
spl102_175,
inference(avatar_split_clause,[],[f736,f2578]) ).
fof(f736,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(flattening,[],[f251]) ).
fof(f251,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f209]) ).
fof(f209,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(f2574,plain,
spl102_174,
inference(avatar_split_clause,[],[f735,f2572]) ).
fof(f735,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f2570,plain,
spl102_173,
inference(avatar_split_clause,[],[f732,f2568]) ).
fof(f2568,plain,
( spl102_173
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_173])]) ).
fof(f732,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,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(f2566,plain,
spl102_172,
inference(avatar_split_clause,[],[f731,f2564]) ).
fof(f731,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f144]) ).
fof(f144,axiom,
! [X0] :
( relation(X0)
=> relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f2557,plain,
( spl102_171
| ~ spl102_13
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1593,f1540,f1433,f2554]) ).
fof(f2554,plain,
( spl102_171
<=> sP8(sK99) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_171])]) ).
fof(f1593,plain,
( sP8(sK99)
| ~ spl102_13
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1435]) ).
fof(f2467,plain,
spl102_170,
inference(avatar_split_clause,[],[f1334,f2465]) ).
fof(f2465,plain,
( spl102_170
<=> ! [X1] :
( sP13(X1,identity_relation(X1))
| ~ sP14(identity_relation(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_170])]) ).
fof(f1334,plain,
! [X1] :
( sP13(X1,identity_relation(X1))
| ~ sP14(identity_relation(X1),X1) ),
inference(equality_resolution,[],[f1028]) ).
fof(f1028,plain,
! [X0,X1] :
( sP13(X1,X0)
| identity_relation(X1) != X0
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f625]) ).
fof(f2463,plain,
spl102_169,
inference(avatar_split_clause,[],[f1329,f2461]) ).
fof(f2461,plain,
( spl102_169
<=> ! [X1] :
( sP11(X1,set_meet(X1))
| ~ sP12(set_meet(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_169])]) ).
fof(f1329,plain,
! [X1] :
( sP11(X1,set_meet(X1))
| ~ sP12(set_meet(X1),X1) ),
inference(equality_resolution,[],[f1013]) ).
fof(f1013,plain,
! [X0,X1] :
( sP11(X1,X0)
| set_meet(X1) != X0
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f616]) ).
fof(f2459,plain,
spl102_168,
inference(avatar_split_clause,[],[f1324,f2457]) ).
fof(f2457,plain,
( spl102_168
<=> ! [X0,X1] :
( sP9(X1,X0,relation_image(X0,X1))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_168])]) ).
fof(f1324,plain,
! [X0,X1] :
( sP9(X1,X0,relation_image(X0,X1))
| ~ sP10(X0) ),
inference(equality_resolution,[],[f964]) ).
fof(f964,plain,
! [X2,X0,X1] :
( sP9(X1,X0,X2)
| relation_image(X0,X1) != X2
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f589]) ).
fof(f2451,plain,
spl102_167,
inference(avatar_split_clause,[],[f1323,f2449]) ).
fof(f2449,plain,
( spl102_167
<=> ! [X0,X1] :
( sP7(X1,X0,relation_inverse_image(X0,X1))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_167])]) ).
fof(f1323,plain,
! [X0,X1] :
( sP7(X1,X0,relation_inverse_image(X0,X1))
| ~ sP8(X0) ),
inference(equality_resolution,[],[f955]) ).
fof(f955,plain,
! [X2,X0,X1] :
( sP7(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f2447,plain,
spl102_166,
inference(avatar_split_clause,[],[f1298,f2445]) ).
fof(f2445,plain,
( spl102_166
<=> ! [X0] :
( sP1(function_inverse(X0),X0)
| ~ sP2(X0,function_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_166])]) ).
fof(f1298,plain,
! [X0] :
( sP1(function_inverse(X0),X0)
| ~ sP2(X0,function_inverse(X0)) ),
inference(equality_resolution,[],[f749]) ).
fof(f749,plain,
! [X0,X1] :
( sP1(X1,X0)
| function_inverse(X0) != X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f483]) ).
fof(f2443,plain,
spl102_165,
inference(avatar_split_clause,[],[f1088,f2441]) ).
fof(f2441,plain,
( spl102_165
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK79(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_165])]) ).
fof(f1088,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK79(X0,X1),X1) ),
inference(cnf_transformation,[],[f654]) ).
fof(f2439,plain,
spl102_164,
inference(avatar_split_clause,[],[f1087,f2437]) ).
fof(f1087,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK79(X0,X1),X0) ),
inference(cnf_transformation,[],[f654]) ).
fof(f2435,plain,
spl102_163,
inference(avatar_split_clause,[],[f1077,f2433]) ).
fof(f2433,plain,
( spl102_163
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_163])]) ).
fof(f1077,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f424]) ).
fof(f424,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f423]) ).
fof(f423,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f2431,plain,
spl102_162,
inference(avatar_split_clause,[],[f1076,f2429]) ).
fof(f2429,plain,
( spl102_162
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_162])]) ).
fof(f1076,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f422]) ).
fof(f422,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f421]) ).
fof(f421,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f2427,plain,
spl102_161,
inference(avatar_split_clause,[],[f1072,f2425]) ).
fof(f2425,plain,
( spl102_161
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_161])]) ).
fof(f1072,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f415]) ).
fof(f415,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,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(f2423,plain,
spl102_160,
inference(avatar_split_clause,[],[f1071,f2421]) ).
fof(f2421,plain,
( spl102_160
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_160])]) ).
fof(f1071,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f416]) ).
fof(f2419,plain,
spl102_159,
inference(avatar_split_clause,[],[f1070,f2417]) ).
fof(f2417,plain,
( spl102_159
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_159])]) ).
fof(f1070,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f414]) ).
fof(f414,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f413]) ).
fof(f413,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,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(f2415,plain,
spl102_158,
inference(avatar_split_clause,[],[f1069,f2413]) ).
fof(f2413,plain,
( spl102_158
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_158])]) ).
fof(f1069,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f414]) ).
fof(f2411,plain,
( spl102_157
| ~ spl102_1
| ~ spl102_127 ),
inference(avatar_split_clause,[],[f2247,f2136,f1373,f2408]) ).
fof(f2136,plain,
( spl102_127
<=> ! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_127])]) ).
fof(f2247,plain,
( relation_dom(sK25) = relation_rng(relation_inverse(sK25))
| ~ spl102_1
| ~ spl102_127 ),
inference(resolution,[],[f2137,f1375]) ).
fof(f2137,plain,
( ! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ spl102_127 ),
inference(avatar_component_clause,[],[f2136]) ).
fof(f2406,plain,
spl102_156,
inference(avatar_split_clause,[],[f1068,f2404]) ).
fof(f2404,plain,
( spl102_156
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_156])]) ).
fof(f1068,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f411]) ).
fof(f411,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f2402,plain,
spl102_155,
inference(avatar_split_clause,[],[f1045,f2400]) ).
fof(f2400,plain,
( spl102_155
<=> ! [X2,X0,X1] :
( sP16(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_155])]) ).
fof(f1045,plain,
! [X2,X0,X1] :
( sP16(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f462]) ).
fof(f462,plain,
! [X0,X1] :
( ! [X2] :
( sP16(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f394,f461,f460]) ).
fof(f394,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,[],[f12]) ).
fof(f12,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(f2398,plain,
spl102_154,
inference(avatar_split_clause,[],[f1009,f2396]) ).
fof(f2396,plain,
( spl102_154
<=> ! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_154])]) ).
fof(f1009,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f614]) ).
fof(f614,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,[],[f387]) ).
fof(f387,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,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(f2394,plain,
spl102_153,
inference(avatar_split_clause,[],[f986,f2392]) ).
fof(f2392,plain,
( spl102_153
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_153])]) ).
fof(f986,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f382]) ).
fof(f382,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f2390,plain,
spl102_152,
inference(avatar_split_clause,[],[f954,f2388]) ).
fof(f2388,plain,
( spl102_152
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_152])]) ).
fof(f954,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f447]) ).
fof(f447,plain,
! [X0] :
( ! [X1,X2] :
( sP6(X2,X1,X0)
| ~ relation(X2) )
| ~ relation(X0) ),
inference(definition_folding,[],[f367,f446,f445]) ).
fof(f367,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,[],[f11]) ).
fof(f11,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(f2386,plain,
spl102_151,
inference(avatar_split_clause,[],[f752,f2384]) ).
fof(f2384,plain,
( spl102_151
<=> ! [X4,X0,X5,X1] :
( sP0(X4,X5,X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_151])]) ).
fof(f752,plain,
! [X0,X1,X4,X5] :
( sP0(X4,X5,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f2382,plain,
spl102_150,
inference(avatar_split_clause,[],[f751,f2380]) ).
fof(f2380,plain,
( spl102_150
<=> ! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_150])]) ).
fof(f751,plain,
! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f488]) ).
fof(f2348,plain,
( spl102_149
| ~ spl102_1
| ~ spl102_126 ),
inference(avatar_split_clause,[],[f2227,f2132,f1373,f2345]) ).
fof(f2132,plain,
( spl102_126
<=> ! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_126])]) ).
fof(f2227,plain,
( relation_rng(sK25) = relation_dom(relation_inverse(sK25))
| ~ spl102_1
| ~ spl102_126 ),
inference(resolution,[],[f2133,f1375]) ).
fof(f2133,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ spl102_126 ),
inference(avatar_component_clause,[],[f2132]) ).
fof(f2315,plain,
( spl102_148
| ~ spl102_7
| ~ spl102_59
| ~ spl102_139 ),
inference(avatar_split_clause,[],[f2189,f2186,f1661,f1403,f2313]) ).
fof(f2186,plain,
( spl102_139
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_139])]) ).
fof(f2189,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK95
| ~ subset(X0,X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_139 ),
inference(forward_demodulation,[],[f2187,f1713]) ).
fof(f2187,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl102_139 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f2311,plain,
( spl102_147
| ~ spl102_7
| ~ spl102_59
| ~ spl102_138 ),
inference(avatar_split_clause,[],[f2184,f2181,f1661,f1403,f2309]) ).
fof(f2309,plain,
( spl102_147
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK95
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_147])]) ).
fof(f2181,plain,
( spl102_138
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_138])]) ).
fof(f2184,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK95
| subset(X0,X1) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_138 ),
inference(forward_demodulation,[],[f2182,f1713]) ).
fof(f2182,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl102_138 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f2217,plain,
spl102_146,
inference(avatar_split_clause,[],[f1351,f2215]) ).
fof(f1351,plain,
! [X0,X1] : sP22(X1,X0,set_difference(X0,set_difference(X0,X1))),
inference(equality_resolution,[],[f1297]) ).
fof(f1297,plain,
! [X2,X0,X1] :
( sP22(X1,X0,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f1136,f771]) ).
fof(f1136,plain,
! [X2,X0,X1] :
( sP22(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f689]) ).
fof(f2213,plain,
spl102_145,
inference(avatar_split_clause,[],[f1343,f2211]) ).
fof(f2211,plain,
( spl102_145
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_145])]) ).
fof(f1343,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f1291]) ).
fof(f1291,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1097,f728]) ).
fof(f1097,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f665]) ).
fof(f2209,plain,
spl102_144,
inference(avatar_split_clause,[],[f1197,f2207]) ).
fof(f2207,plain,
( spl102_144
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_144])]) ).
fof(f1197,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f836,f728]) ).
fof(f836,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f2205,plain,
spl102_143,
inference(avatar_split_clause,[],[f1191,f2203]) ).
fof(f2203,plain,
( spl102_143
<=> ! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_143])]) ).
fof(f1191,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f826,f728]) ).
fof(f826,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f514]) ).
fof(f514,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f2201,plain,
spl102_142,
inference(avatar_split_clause,[],[f1180,f2199]) ).
fof(f2199,plain,
( spl102_142
<=> ! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_142])]) ).
fof(f1180,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f790,f728]) ).
fof(f790,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f2197,plain,
spl102_141,
inference(avatar_split_clause,[],[f873,f2195]) ).
fof(f2195,plain,
( spl102_141
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_141])]) ).
fof(f873,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f534]) ).
fof(f2193,plain,
spl102_140,
inference(avatar_split_clause,[],[f872,f2191]) ).
fof(f2191,plain,
( spl102_140
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_140])]) ).
fof(f872,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f534]) ).
fof(f2188,plain,
spl102_139,
inference(avatar_split_clause,[],[f830,f2186]) ).
fof(f830,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f516]) ).
fof(f516,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f2183,plain,
spl102_138,
inference(avatar_split_clause,[],[f829,f2181]) ).
fof(f829,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f516]) ).
fof(f2179,plain,
spl102_137,
inference(avatar_split_clause,[],[f818,f2177]) ).
fof(f2177,plain,
( spl102_137
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_137])]) ).
fof(f818,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f509]) ).
fof(f509,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f219]) ).
fof(f219,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f2175,plain,
spl102_136,
inference(avatar_split_clause,[],[f817,f2173]) ).
fof(f2173,plain,
( spl102_136
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_136])]) ).
fof(f817,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f509]) ).
fof(f2171,plain,
spl102_135,
inference(avatar_split_clause,[],[f796,f2169]) ).
fof(f2169,plain,
( spl102_135
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_135])]) ).
fof(f796,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f2167,plain,
( ~ spl102_133
| spl102_134
| ~ spl102_60
| ~ spl102_125 ),
inference(avatar_split_clause,[],[f2123,f2066,f1665,f2164,f2160]) ).
fof(f2164,plain,
( spl102_134
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_134])]) ).
fof(f2123,plain,
( empty(sK25)
| ~ empty(relation_inverse(sK25))
| ~ spl102_60
| ~ spl102_125 ),
inference(superposition,[],[f1666,f2068]) ).
fof(f2158,plain,
spl102_132,
inference(avatar_split_clause,[],[f782,f2156]) ).
fof(f2156,plain,
( spl102_132
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_132])]) ).
fof(f782,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f132]) ).
fof(f132,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(f2154,plain,
spl102_131,
inference(avatar_split_clause,[],[f781,f2152]) ).
fof(f781,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f2150,plain,
spl102_130,
inference(avatar_split_clause,[],[f780,f2148]) ).
fof(f2148,plain,
( spl102_130
<=> ! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_130])]) ).
fof(f780,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f147]) ).
fof(f147,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f2146,plain,
spl102_129,
inference(avatar_split_clause,[],[f776,f2144]) ).
fof(f776,plain,
! [X0,X1] :
( in(sK32(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f498]) ).
fof(f2142,plain,
spl102_128,
inference(avatar_split_clause,[],[f775,f2140]) ).
fof(f775,plain,
! [X0,X1] :
( in(sK32(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f498]) ).
fof(f2138,plain,
spl102_127,
inference(avatar_split_clause,[],[f734,f2136]) ).
fof(f734,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f174]) ).
fof(f174,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(f2134,plain,
spl102_126,
inference(avatar_split_clause,[],[f733,f2132]) ).
fof(f733,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f2069,plain,
( spl102_125
| ~ spl102_1
| ~ spl102_104 ),
inference(avatar_split_clause,[],[f2042,f1951,f1373,f2066]) ).
fof(f2042,plain,
( sK25 = relation_inverse(relation_inverse(sK25))
| ~ spl102_1
| ~ spl102_104 ),
inference(resolution,[],[f1952,f1375]) ).
fof(f2064,plain,
( spl102_124
| ~ spl102_7
| ~ spl102_59
| ~ spl102_110 ),
inference(avatar_split_clause,[],[f1980,f1977,f1661,f1403,f2062]) ).
fof(f2062,plain,
( spl102_124
<=> ! [X0] :
( sK95 = X0
| in(sK65(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_124])]) ).
fof(f1977,plain,
( spl102_110
<=> ! [X0] :
( empty_set = X0
| in(sK65(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_110])]) ).
fof(f1980,plain,
( ! [X0] :
( sK95 = X0
| in(sK65(X0),X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_110 ),
inference(forward_demodulation,[],[f1978,f1713]) ).
fof(f1978,plain,
( ! [X0] :
( empty_set = X0
| in(sK65(X0),X0) )
| ~ spl102_110 ),
inference(avatar_component_clause,[],[f1977]) ).
fof(f2033,plain,
spl102_123,
inference(avatar_split_clause,[],[f1349,f2031]) ).
fof(f1349,plain,
! [X2,X0,X4] :
( in(X4,X2)
| ~ sP21(X0,X4,X2) ),
inference(equality_resolution,[],[f1123]) ).
fof(f1123,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f2029,plain,
spl102_122,
inference(avatar_split_clause,[],[f1348,f2027]) ).
fof(f1348,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ sP21(X4,X1,X2) ),
inference(equality_resolution,[],[f1124]) ).
fof(f1124,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f682]) ).
fof(f2025,plain,
spl102_121,
inference(avatar_split_clause,[],[f1345,f2023]) ).
fof(f2023,plain,
( spl102_121
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_121])]) ).
fof(f1345,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f1101]) ).
fof(f1101,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f669]) ).
fof(f2021,plain,
( spl102_120
| ~ spl102_12
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1592,f1540,f1428,f2018]) ).
fof(f2018,plain,
( spl102_120
<=> sP8(sK98) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_120])]) ).
fof(f1592,plain,
( sP8(sK98)
| ~ spl102_12
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1430]) ).
fof(f2016,plain,
spl102_119,
inference(avatar_split_clause,[],[f1344,f2014]) ).
fof(f2014,plain,
( spl102_119
<=> ! [X0,X3] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_119])]) ).
fof(f1344,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f1102]) ).
fof(f1102,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f669]) ).
fof(f2012,plain,
spl102_118,
inference(avatar_split_clause,[],[f1107,f2010]) ).
fof(f1107,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f429]) ).
fof(f429,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f222]) ).
fof(f222,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f2008,plain,
spl102_117,
inference(avatar_split_clause,[],[f1106,f2006]) ).
fof(f2006,plain,
( spl102_117
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_117])]) ).
fof(f1106,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f670]) ).
fof(f670,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f181]) ).
fof(f181,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f2004,plain,
spl102_116,
inference(avatar_split_clause,[],[f1105,f2002]) ).
fof(f1105,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f670]) ).
fof(f2000,plain,
spl102_115,
inference(avatar_split_clause,[],[f1096,f1998]) ).
fof(f1998,plain,
( spl102_115
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_115])]) ).
fof(f1096,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f661]) ).
fof(f661,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP19(X0,X1) )
& ( sP19(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f467]) ).
fof(f467,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP19(X0,X1) ),
inference(definition_folding,[],[f31,f466]) ).
fof(f31,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(f1996,plain,
spl102_114,
inference(avatar_split_clause,[],[f1012,f1994]) ).
fof(f1994,plain,
( spl102_114
<=> ! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_114])]) ).
fof(f1012,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f614]) ).
fof(f1992,plain,
spl102_113,
inference(avatar_split_clause,[],[f1011,f1990]) ).
fof(f1011,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f614]) ).
fof(f1988,plain,
spl102_112,
inference(avatar_split_clause,[],[f1007,f1986]) ).
fof(f1007,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1984,plain,
spl102_111,
inference(avatar_split_clause,[],[f1005,f1982]) ).
fof(f1979,plain,
spl102_110,
inference(avatar_split_clause,[],[f991,f1977]) ).
fof(f991,plain,
! [X0] :
( empty_set = X0
| in(sK65(X0),X0) ),
inference(cnf_transformation,[],[f605]) ).
fof(f605,plain,
! [X0] :
( ( empty_set = X0
| in(sK65(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f603,f604]) ).
fof(f604,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK65(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f603,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f602]) ).
fof(f602,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f1974,plain,
( spl102_109
| ~ spl102_11
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1591,f1540,f1423,f1971]) ).
fof(f1971,plain,
( spl102_109
<=> sP8(sK97) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_109])]) ).
fof(f1591,plain,
( sP8(sK97)
| ~ spl102_11
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1425]) ).
fof(f1969,plain,
spl102_108,
inference(avatar_split_clause,[],[f978,f1967]) ).
fof(f1967,plain,
( spl102_108
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_108])]) ).
fof(f978,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f1965,plain,
spl102_107,
inference(avatar_split_clause,[],[f977,f1963]) ).
fof(f1963,plain,
( spl102_107
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_107])]) ).
fof(f977,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1961,plain,
spl102_106,
inference(avatar_split_clause,[],[f974,f1959]) ).
fof(f1959,plain,
( spl102_106
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_106])]) ).
fof(f974,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f1957,plain,
spl102_105,
inference(avatar_split_clause,[],[f973,f1955]) ).
fof(f973,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f1953,plain,
spl102_104,
inference(avatar_split_clause,[],[f916,f1951]) ).
fof(f916,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f1949,plain,
spl102_103,
inference(avatar_split_clause,[],[f904,f1947]) ).
fof(f1947,plain,
( spl102_103
<=> ! [X0] :
( element(sK37(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_103])]) ).
fof(f904,plain,
! [X0] :
( element(sK37(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0] :
( ( ~ empty(sK37(X0))
& element(sK37(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f351,f541]) ).
fof(f541,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK37(X0))
& element(sK37(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f1937,plain,
( spl102_102
| ~ spl102_9
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1590,f1540,f1413,f1934]) ).
fof(f1934,plain,
( spl102_102
<=> sP8(sK96) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_102])]) ).
fof(f1590,plain,
( sP8(sK96)
| ~ spl102_9
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1415]) ).
fof(f1932,plain,
( spl102_101
| ~ spl102_99
| ~ spl102_100 ),
inference(avatar_split_clause,[],[f1928,f1925,f1915,f1930]) ).
fof(f1925,plain,
( spl102_100
<=> ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl102_100])]) ).
fof(f1928,plain,
( ! [X0] : set_difference(X0,sK95) = X0
| ~ spl102_99
| ~ spl102_100 ),
inference(forward_demodulation,[],[f1926,f1916]) ).
fof(f1926,plain,
( ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0
| ~ spl102_100 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f1927,plain,
spl102_100,
inference(avatar_split_clause,[],[f1271,f1925]) ).
fof(f1271,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f1004,f771]) ).
fof(f1004,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f1917,plain,
( spl102_99
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_98 ),
inference(avatar_split_clause,[],[f1913,f1909,f1661,f1653,f1403,f1915]) ).
fof(f1909,plain,
( spl102_98
<=> ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_98])]) ).
fof(f1913,plain,
( ! [X0] : sK95 = set_difference(X0,X0)
| ~ spl102_7
| ~ spl102_57
| ~ spl102_59
| ~ spl102_98 ),
inference(forward_demodulation,[],[f1912,f1713]) ).
fof(f1912,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl102_57
| ~ spl102_98 ),
inference(forward_demodulation,[],[f1910,f1654]) ).
fof(f1910,plain,
( ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set))
| ~ spl102_98 ),
inference(avatar_component_clause,[],[f1909]) ).
fof(f1911,plain,
spl102_98,
inference(avatar_split_clause,[],[f1226,f1909]) ).
fof(f1226,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f897,f771]) ).
fof(f897,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f164]) ).
fof(f164,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f1907,plain,
spl102_97,
inference(avatar_split_clause,[],[f791,f1905]) ).
fof(f1905,plain,
( spl102_97
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_97])]) ).
fof(f791,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f227]) ).
fof(f227,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f1903,plain,
spl102_96,
inference(avatar_split_clause,[],[f779,f1901]) ).
fof(f1901,plain,
( spl102_96
<=> ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_96])]) ).
fof(f779,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f1899,plain,
spl102_95,
inference(avatar_split_clause,[],[f778,f1897]) ).
fof(f1897,plain,
( spl102_95
<=> ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_95])]) ).
fof(f778,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f221]) ).
fof(f221,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f1890,plain,
( spl102_94
| ~ spl102_5
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1588,f1540,f1393,f1887]) ).
fof(f1588,plain,
( sP8(empty_set)
| ~ spl102_5
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1395]) ).
fof(f1867,plain,
( spl102_93
| ~ spl102_7
| ~ spl102_36 ),
inference(avatar_split_clause,[],[f1584,f1536,f1403,f1864]) ).
fof(f1864,plain,
( spl102_93
<=> relation(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_93])]) ).
fof(f1584,plain,
( relation(sK95)
| ~ spl102_7
| ~ spl102_36 ),
inference(resolution,[],[f1537,f1405]) ).
fof(f1860,plain,
( spl102_92
| ~ spl102_7
| ~ spl102_59
| ~ spl102_79 ),
inference(avatar_split_clause,[],[f1806,f1803,f1661,f1403,f1858]) ).
fof(f1858,plain,
( spl102_92
<=> ! [X0,X1] :
( sK95 = X0
| sP12(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_92])]) ).
fof(f1803,plain,
( spl102_79
<=> ! [X0,X1] :
( sP12(X1,X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_79])]) ).
fof(f1806,plain,
( ! [X0,X1] :
( sK95 = X0
| sP12(X1,X0) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_79 ),
inference(forward_demodulation,[],[f1804,f1713]) ).
fof(f1804,plain,
( ! [X0,X1] :
( sP12(X1,X0)
| empty_set = X0 )
| ~ spl102_79 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f1854,plain,
spl102_91,
inference(avatar_split_clause,[],[f1353,f1852]) ).
fof(f1353,plain,
! [X0,X1] : sP24(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f1152]) ).
fof(f1152,plain,
! [X2,X0,X1] :
( sP24(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f701]) ).
fof(f1850,plain,
spl102_90,
inference(avatar_split_clause,[],[f1352,f1848]) ).
fof(f1352,plain,
! [X0,X1] : sP23(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f1144]) ).
fof(f1144,plain,
! [X2,X0,X1] :
( sP23(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f695]) ).
fof(f1846,plain,
spl102_89,
inference(avatar_split_clause,[],[f1350,f1844]) ).
fof(f1350,plain,
! [X0,X1] : sP21(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f1128]) ).
fof(f1128,plain,
! [X2,X0,X1] :
( sP21(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f683]) ).
fof(f1842,plain,
spl102_88,
inference(avatar_split_clause,[],[f1347,f1840]) ).
fof(f1840,plain,
( spl102_88
<=> ! [X0,X1] : sP20(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_88])]) ).
fof(f1347,plain,
! [X0,X1] : sP20(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f1120]) ).
fof(f1120,plain,
! [X2,X0,X1] :
( sP20(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f677]) ).
fof(f1838,plain,
spl102_87,
inference(avatar_split_clause,[],[f1050,f1836]) ).
fof(f1050,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f400]) ).
fof(f400,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f1834,plain,
spl102_86,
inference(avatar_split_clause,[],[f1049,f1832]) ).
fof(f1049,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f399]) ).
fof(f399,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(f1830,plain,
spl102_85,
inference(avatar_split_clause,[],[f1047,f1828]) ).
fof(f1828,plain,
( spl102_85
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_85])]) ).
fof(f1047,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f396]) ).
fof(f396,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f1826,plain,
spl102_84,
inference(avatar_split_clause,[],[f1046,f1824]) ).
fof(f1824,plain,
( spl102_84
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_84])]) ).
fof(f1046,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
fof(f395,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(f1822,plain,
spl102_83,
inference(avatar_split_clause,[],[f1027,f1820]) ).
fof(f1820,plain,
( spl102_83
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_83])]) ).
fof(f1027,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f392]) ).
fof(f392,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f1818,plain,
spl102_82,
inference(avatar_split_clause,[],[f1026,f1816]) ).
fof(f1816,plain,
( spl102_82
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_82])]) ).
fof(f1026,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f1814,plain,
spl102_81,
inference(avatar_split_clause,[],[f1025,f1812]) ).
fof(f1812,plain,
( spl102_81
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_81])]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f390,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f1810,plain,
spl102_80,
inference(avatar_split_clause,[],[f1024,f1808]) ).
fof(f1024,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f1805,plain,
spl102_79,
inference(avatar_split_clause,[],[f1021,f1803]) ).
fof(f1021,plain,
! [X0,X1] :
( sP12(X1,X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP12(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP12(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f388,f455,f454]) ).
fof(f388,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,[],[f16]) ).
fof(f16,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(f1801,plain,
spl102_78,
inference(avatar_split_clause,[],[f988,f1799]) ).
fof(f1799,plain,
( spl102_78
<=> ! [X0] :
( relation(X0)
| in(sK62(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_78])]) ).
fof(f988,plain,
! [X0] :
( relation(X0)
| in(sK62(X0),X0) ),
inference(cnf_transformation,[],[f601]) ).
fof(f1790,plain,
( spl102_77
| ~ spl102_7
| ~ spl102_59
| ~ spl102_74 ),
inference(avatar_split_clause,[],[f1770,f1766,f1661,f1403,f1787]) ).
fof(f1766,plain,
( spl102_74
<=> powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_74])]) ).
fof(f1770,plain,
( powerset(sK95) = unordered_pair(sK95,sK95)
| ~ spl102_7
| ~ spl102_59
| ~ spl102_74 ),
inference(forward_demodulation,[],[f1768,f1713]) ).
fof(f1768,plain,
( powerset(empty_set) = unordered_pair(empty_set,empty_set)
| ~ spl102_74 ),
inference(avatar_component_clause,[],[f1766]) ).
fof(f1784,plain,
( spl102_76
| ~ spl102_10
| ~ spl102_35 ),
inference(avatar_split_clause,[],[f1575,f1532,f1418,f1781]) ).
fof(f1781,plain,
( spl102_76
<=> function(sK97) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_76])]) ).
fof(f1575,plain,
( function(sK97)
| ~ spl102_10
| ~ spl102_35 ),
inference(resolution,[],[f1533,f1420]) ).
fof(f1774,plain,
( spl102_75
| ~ spl102_7
| ~ spl102_59
| ~ spl102_72 ),
inference(avatar_split_clause,[],[f1760,f1756,f1661,f1403,f1772]) ).
fof(f1756,plain,
( spl102_72
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_72])]) ).
fof(f1760,plain,
( ! [X0] :
( ~ subset(X0,sK95)
| sK95 = X0 )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_72 ),
inference(forward_demodulation,[],[f1759,f1713]) ).
fof(f1759,plain,
( ! [X0] :
( sK95 = X0
| ~ subset(X0,empty_set) )
| ~ spl102_7
| ~ spl102_59
| ~ spl102_72 ),
inference(forward_demodulation,[],[f1757,f1713]) ).
fof(f1757,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl102_72 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f1769,plain,
spl102_74,
inference(avatar_split_clause,[],[f1171,f1766]) ).
fof(f1171,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f722,f728]) ).
fof(f722,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f155]) ).
fof(f155,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f1764,plain,
spl102_73,
inference(avatar_split_clause,[],[f835,f1762]) ).
fof(f835,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f207]) ).
fof(f207,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f1758,plain,
spl102_72,
inference(avatar_split_clause,[],[f748,f1756]) ).
fof(f748,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f1748,plain,
( spl102_71
| ~ spl102_7
| ~ spl102_35 ),
inference(avatar_split_clause,[],[f1574,f1532,f1403,f1745]) ).
fof(f1745,plain,
( spl102_71
<=> function(sK95) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_71])]) ).
fof(f1574,plain,
( function(sK95)
| ~ spl102_7
| ~ spl102_35 ),
inference(resolution,[],[f1533,f1405]) ).
fof(f1707,plain,
spl102_70,
inference(avatar_split_clause,[],[f1108,f1705]) ).
fof(f1108,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f1703,plain,
spl102_69,
inference(avatar_split_clause,[],[f1036,f1701]) ).
fof(f1701,plain,
( spl102_69
<=> ! [X0,X1] :
( sP14(X1,X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_69])]) ).
fof(f1036,plain,
! [X0,X1] :
( sP14(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f459]) ).
fof(f459,plain,
! [X0,X1] :
( sP14(X1,X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f393,f458,f457]) ).
fof(f393,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,[],[f9]) ).
fof(f9,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(f1699,plain,
spl102_68,
inference(avatar_split_clause,[],[f1003,f1697]) ).
fof(f1003,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f96]) ).
fof(f96,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f1695,plain,
spl102_67,
inference(avatar_split_clause,[],[f997,f1693]) ).
fof(f997,plain,
! [X0] : element(sK69(X0),powerset(X0)),
inference(cnf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0] :
( empty(sK69(X0))
& element(sK69(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f120,f612]) ).
fof(f612,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK69(X0))
& element(sK69(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f1691,plain,
spl102_66,
inference(avatar_split_clause,[],[f915,f1689]) ).
fof(f915,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f1687,plain,
spl102_65,
inference(avatar_split_clause,[],[f914,f1685]) ).
fof(f914,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f1683,plain,
spl102_64,
inference(avatar_split_clause,[],[f913,f1681]) ).
fof(f913,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1679,plain,
spl102_63,
inference(avatar_split_clause,[],[f912,f1677]) ).
fof(f912,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f1675,plain,
spl102_62,
inference(avatar_split_clause,[],[f911,f1673]) ).
fof(f911,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f1671,plain,
spl102_61,
inference(avatar_split_clause,[],[f910,f1669]) ).
fof(f910,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f1667,plain,
spl102_60,
inference(avatar_split_clause,[],[f909,f1665]) ).
fof(f909,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f1663,plain,
spl102_59,
inference(avatar_split_clause,[],[f908,f1661]) ).
fof(f908,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f213]) ).
fof(f213,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f1659,plain,
spl102_58,
inference(avatar_split_clause,[],[f905,f1657]) ).
fof(f1657,plain,
( spl102_58
<=> ! [X0] :
( ~ empty(sK37(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_58])]) ).
fof(f905,plain,
! [X0] :
( ~ empty(sK37(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f542]) ).
fof(f1655,plain,
spl102_57,
inference(avatar_split_clause,[],[f900,f1653]) ).
fof(f900,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f180]) ).
fof(f180,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f1651,plain,
spl102_56,
inference(avatar_split_clause,[],[f899,f1649]) ).
fof(f899,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f152]) ).
fof(f152,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f1647,plain,
spl102_55,
inference(avatar_split_clause,[],[f898,f1645]) ).
fof(f898,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f196]) ).
fof(f196,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f1643,plain,
( spl102_54
| ~ spl102_1
| ~ spl102_38 ),
inference(avatar_split_clause,[],[f1598,f1544,f1373,f1640]) ).
fof(f1640,plain,
( spl102_54
<=> sP10(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_54])]) ).
fof(f1598,plain,
( sP10(sK25)
| ~ spl102_1
| ~ spl102_38 ),
inference(resolution,[],[f1545,f1375]) ).
fof(f1637,plain,
spl102_53,
inference(avatar_split_clause,[],[f1342,f1635]) ).
fof(f1342,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f1341]) ).
fof(f1341,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f1290]) ).
fof(f1290,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1098,f728]) ).
fof(f1098,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f665]) ).
fof(f1633,plain,
spl102_52,
inference(avatar_split_clause,[],[f1172,f1631]) ).
fof(f1172,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f726,f728]) ).
fof(f726,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f102]) ).
fof(f102,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f1629,plain,
spl102_51,
inference(avatar_split_clause,[],[f769,f1627]) ).
fof(f769,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f173]) ).
fof(f173,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f1625,plain,
spl102_50,
inference(avatar_split_clause,[],[f767,f1623]) ).
fof(f767,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f218]) ).
fof(f218,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f1621,plain,
spl102_49,
inference(avatar_split_clause,[],[f730,f1619]) ).
fof(f730,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f215]) ).
fof(f215,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(f1617,plain,
spl102_48,
inference(avatar_split_clause,[],[f729,f1615]) ).
fof(f729,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f215]) ).
fof(f1613,plain,
( spl102_47
| ~ spl102_1
| ~ spl102_37 ),
inference(avatar_split_clause,[],[f1589,f1540,f1373,f1610]) ).
fof(f1610,plain,
( spl102_47
<=> sP8(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_47])]) ).
fof(f1589,plain,
( sP8(sK25)
| ~ spl102_1
| ~ spl102_37 ),
inference(resolution,[],[f1541,f1375]) ).
fof(f1608,plain,
spl102_46,
inference(avatar_split_clause,[],[f727,f1606]) ).
fof(f727,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f230]) ).
fof(f230,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f1581,plain,
( spl102_45
| ~ spl102_4
| ~ spl102_35 ),
inference(avatar_split_clause,[],[f1572,f1532,f1388,f1578]) ).
fof(f1578,plain,
( spl102_45
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_45])]) ).
fof(f1388,plain,
( spl102_4
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_4])]) ).
fof(f1572,plain,
( function(empty_set)
| ~ spl102_4
| ~ spl102_35 ),
inference(resolution,[],[f1533,f1390]) ).
fof(f1390,plain,
( empty(empty_set)
| ~ spl102_4 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f1571,plain,
spl102_44,
inference(avatar_split_clause,[],[f1357,f1569]) ).
fof(f1357,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f901,f896]) ).
fof(f896,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f901,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f1567,plain,
spl102_43,
inference(avatar_split_clause,[],[f1340,f1565]) ).
fof(f1340,plain,
! [X0] : sP19(X0,union(X0)),
inference(equality_resolution,[],[f1095]) ).
fof(f1095,plain,
! [X0,X1] :
( sP19(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f661]) ).
fof(f1563,plain,
spl102_42,
inference(avatar_split_clause,[],[f1331,f1560]) ).
fof(f1560,plain,
( spl102_42
<=> empty_set = set_meet(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_42])]) ).
fof(f1331,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f1330]) ).
fof(f1330,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f1023]) ).
fof(f1023,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f623]) ).
fof(f1558,plain,
spl102_41,
inference(avatar_split_clause,[],[f1001,f1556]) ).
fof(f1556,plain,
( spl102_41
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_41])]) ).
fof(f1001,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f1554,plain,
spl102_40,
inference(avatar_split_clause,[],[f993,f1552]) ).
fof(f993,plain,
! [X0] : in(X0,sK67(X0)),
inference(cnf_transformation,[],[f611]) ).
fof(f1550,plain,
spl102_39,
inference(avatar_split_clause,[],[f992,f1548]) ).
fof(f992,plain,
! [X0] : element(sK66(X0),X0),
inference(cnf_transformation,[],[f607]) ).
fof(f607,plain,
! [X0] : element(sK66(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f73,f606]) ).
fof(f606,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK66(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f73,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f1546,plain,
spl102_38,
inference(avatar_split_clause,[],[f972,f1544]) ).
fof(f972,plain,
! [X0] :
( sP10(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f453,plain,
! [X0] :
( sP10(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f369,f452,f451]) ).
fof(f369,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f1542,plain,
spl102_37,
inference(avatar_split_clause,[],[f963,f1540]) ).
fof(f963,plain,
! [X0] :
( sP8(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f450]) ).
fof(f450,plain,
! [X0] :
( sP8(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f368,f449,f448]) ).
fof(f368,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f1538,plain,
spl102_36,
inference(avatar_split_clause,[],[f907,f1536]) ).
fof(f907,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f1534,plain,
spl102_35,
inference(avatar_split_clause,[],[f906,f1532]) ).
fof(f906,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f1530,plain,
spl102_34,
inference(avatar_split_clause,[],[f896,f1528]) ).
fof(f1526,plain,
spl102_33,
inference(avatar_split_clause,[],[f764,f1524]) ).
fof(f764,plain,
! [X0] : in(X0,sK30(X0)),
inference(cnf_transformation,[],[f494]) ).
fof(f1522,plain,
spl102_32,
inference(avatar_split_clause,[],[f724,f1519]) ).
fof(f1519,plain,
( spl102_32
<=> empty_set = relation_rng(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_32])]) ).
fof(f724,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f206]) ).
fof(f206,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f1517,plain,
spl102_31,
inference(avatar_split_clause,[],[f723,f1514]) ).
fof(f1514,plain,
( spl102_31
<=> empty_set = relation_dom(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_31])]) ).
fof(f723,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f206]) ).
fof(f1512,plain,
spl102_30,
inference(avatar_split_clause,[],[f1328,f1510]) ).
fof(f1328,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f990]) ).
fof(f990,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f605]) ).
fof(f1508,plain,
spl102_29,
inference(avatar_split_clause,[],[f1000,f1506]) ).
fof(f1506,plain,
( spl102_29
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_29])]) ).
fof(f1000,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f1504,plain,
spl102_28,
inference(avatar_split_clause,[],[f999,f1502]) ).
fof(f1502,plain,
( spl102_28
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_28])]) ).
fof(f999,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f1500,plain,
spl102_27,
inference(avatar_split_clause,[],[f998,f1498]) ).
fof(f998,plain,
! [X0] : empty(sK69(X0)),
inference(cnf_transformation,[],[f613]) ).
fof(f1496,plain,
spl102_26,
inference(avatar_split_clause,[],[f903,f1494]) ).
fof(f1494,plain,
( spl102_26
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_26])]) ).
fof(f903,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f1492,plain,
spl102_25,
inference(avatar_split_clause,[],[f895,f1490]) ).
fof(f895,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f1488,plain,
spl102_24,
inference(avatar_split_clause,[],[f894,f1486]) ).
fof(f1486,plain,
( spl102_24
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_24])]) ).
fof(f894,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f1484,plain,
spl102_23,
inference(avatar_split_clause,[],[f725,f1482]) ).
fof(f725,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f167]) ).
fof(f167,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f1480,plain,
( ~ spl102_21
| ~ spl102_22 ),
inference(avatar_split_clause,[],[f721,f1477,f1473]) ).
fof(f721,plain,
( relation_dom(sK25) != relation_rng(function_inverse(sK25))
| relation_rng(sK25) != relation_dom(function_inverse(sK25)) ),
inference(cnf_transformation,[],[f479]) ).
fof(f479,plain,
( ( relation_dom(sK25) != relation_rng(function_inverse(sK25))
| relation_rng(sK25) != relation_dom(function_inverse(sK25)) )
& one_to_one(sK25)
& function(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f247,f478]) ).
fof(f478,plain,
( ? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ( relation_dom(sK25) != relation_rng(function_inverse(sK25))
| relation_rng(sK25) != relation_dom(function_inverse(sK25)) )
& one_to_one(sK25)
& function(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f246]) ).
fof(f246,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f203]) ).
fof(f203,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
inference(negated_conjecture,[],[f202]) ).
fof(f202,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f1471,plain,
spl102_20,
inference(avatar_split_clause,[],[f1169,f1468]) ).
fof(f1468,plain,
( spl102_20
<=> function(sK101) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_20])]) ).
fof(f1169,plain,
function(sK101),
inference(cnf_transformation,[],[f717]) ).
fof(f717,plain,
( function(sK101)
& empty(sK101)
& relation(sK101) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f118,f716]) ).
fof(f716,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK101)
& empty(sK101)
& relation(sK101) ) ),
introduced(choice_axiom,[]) ).
fof(f118,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f1466,plain,
spl102_19,
inference(avatar_split_clause,[],[f1168,f1463]) ).
fof(f1168,plain,
empty(sK101),
inference(cnf_transformation,[],[f717]) ).
fof(f1461,plain,
spl102_18,
inference(avatar_split_clause,[],[f1167,f1458]) ).
fof(f1167,plain,
relation(sK101),
inference(cnf_transformation,[],[f717]) ).
fof(f1456,plain,
spl102_17,
inference(avatar_split_clause,[],[f1166,f1453]) ).
fof(f1453,plain,
( spl102_17
<=> one_to_one(sK100) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_17])]) ).
fof(f1166,plain,
one_to_one(sK100),
inference(cnf_transformation,[],[f715]) ).
fof(f715,plain,
( one_to_one(sK100)
& function(sK100)
& relation(sK100) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f122,f714]) ).
fof(f714,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK100)
& function(sK100)
& relation(sK100) ) ),
introduced(choice_axiom,[]) ).
fof(f122,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f1451,plain,
spl102_16,
inference(avatar_split_clause,[],[f1165,f1448]) ).
fof(f1448,plain,
( spl102_16
<=> function(sK100) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_16])]) ).
fof(f1165,plain,
function(sK100),
inference(cnf_transformation,[],[f715]) ).
fof(f1446,plain,
spl102_15,
inference(avatar_split_clause,[],[f1164,f1443]) ).
fof(f1164,plain,
relation(sK100),
inference(cnf_transformation,[],[f715]) ).
fof(f1441,plain,
spl102_14,
inference(avatar_split_clause,[],[f1163,f1438]) ).
fof(f1438,plain,
( spl102_14
<=> function(sK99) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_14])]) ).
fof(f1163,plain,
function(sK99),
inference(cnf_transformation,[],[f713]) ).
fof(f713,plain,
( function(sK99)
& relation(sK99) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99])],[f114,f712]) ).
fof(f712,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK99)
& relation(sK99) ) ),
introduced(choice_axiom,[]) ).
fof(f114,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f1436,plain,
spl102_13,
inference(avatar_split_clause,[],[f1162,f1433]) ).
fof(f1162,plain,
relation(sK99),
inference(cnf_transformation,[],[f713]) ).
fof(f1431,plain,
spl102_12,
inference(avatar_split_clause,[],[f1161,f1428]) ).
fof(f1161,plain,
relation(sK98),
inference(cnf_transformation,[],[f711]) ).
fof(f711,plain,
relation(sK98),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98])],[f245,f710]) ).
fof(f710,plain,
( ? [X0] : relation(X0)
=> relation(sK98) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f123]) ).
fof(f123,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f1426,plain,
spl102_11,
inference(avatar_split_clause,[],[f1160,f1423]) ).
fof(f1160,plain,
relation(sK97),
inference(cnf_transformation,[],[f709]) ).
fof(f709,plain,
( relation(sK97)
& empty(sK97) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97])],[f115,f708]) ).
fof(f708,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK97)
& empty(sK97) ) ),
introduced(choice_axiom,[]) ).
fof(f115,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f1421,plain,
spl102_10,
inference(avatar_split_clause,[],[f1159,f1418]) ).
fof(f1159,plain,
empty(sK97),
inference(cnf_transformation,[],[f709]) ).
fof(f1416,plain,
spl102_9,
inference(avatar_split_clause,[],[f1158,f1413]) ).
fof(f1158,plain,
relation(sK96),
inference(cnf_transformation,[],[f707]) ).
fof(f707,plain,
( relation(sK96)
& ~ empty(sK96) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96])],[f119,f706]) ).
fof(f706,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK96)
& ~ empty(sK96) ) ),
introduced(choice_axiom,[]) ).
fof(f119,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f1411,plain,
~ spl102_8,
inference(avatar_split_clause,[],[f1157,f1408]) ).
fof(f1408,plain,
( spl102_8
<=> empty(sK96) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_8])]) ).
fof(f1157,plain,
~ empty(sK96),
inference(cnf_transformation,[],[f707]) ).
fof(f1406,plain,
spl102_7,
inference(avatar_split_clause,[],[f1156,f1403]) ).
fof(f1156,plain,
empty(sK95),
inference(cnf_transformation,[],[f705]) ).
fof(f705,plain,
empty(sK95),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95])],[f117,f704]) ).
fof(f704,plain,
( ? [X0] : empty(X0)
=> empty(sK95) ),
introduced(choice_axiom,[]) ).
fof(f117,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f1401,plain,
~ spl102_6,
inference(avatar_split_clause,[],[f1155,f1398]) ).
fof(f1398,plain,
( spl102_6
<=> empty(sK94) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_6])]) ).
fof(f1155,plain,
~ empty(sK94),
inference(cnf_transformation,[],[f703]) ).
fof(f703,plain,
~ empty(sK94),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94])],[f121,f702]) ).
fof(f702,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK94) ),
introduced(choice_axiom,[]) ).
fof(f121,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f1396,plain,
spl102_5,
inference(avatar_split_clause,[],[f890,f1393]) ).
fof(f890,plain,
relation(empty_set),
inference(cnf_transformation,[],[f89]) ).
fof(f89,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f1391,plain,
spl102_4,
inference(avatar_split_clause,[],[f888,f1388]) ).
fof(f888,plain,
empty(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f1386,plain,
spl102_3,
inference(avatar_split_clause,[],[f720,f1383]) ).
fof(f720,plain,
one_to_one(sK25),
inference(cnf_transformation,[],[f479]) ).
fof(f1381,plain,
spl102_2,
inference(avatar_split_clause,[],[f719,f1378]) ).
fof(f719,plain,
function(sK25),
inference(cnf_transformation,[],[f479]) ).
fof(f1376,plain,
spl102_1,
inference(avatar_split_clause,[],[f718,f1373]) ).
fof(f718,plain,
relation(sK25),
inference(cnf_transformation,[],[f479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n025.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 : Mon Apr 29 20:58:26 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (12780)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (12785)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)
% 0.22/0.38 % (12783)WARNING: value z3 for option sas not known
% 0.22/0.38 % (12781)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (12782)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (12784)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (12783)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)
% 0.22/0.38 % (12786)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)
% 0.22/0.38 % (12787)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)
% 0.22/0.43 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.49 TRYING [1]
% 0.22/0.49 TRYING [3]
% 0.22/0.49 TRYING [2]
% 0.22/0.51 TRYING [3]
% 0.22/0.53 TRYING [1]
% 1.36/0.54 TRYING [2]
% 1.50/0.56 TRYING [4]
% 1.50/0.61 % (12785)First to succeed.
% 1.98/0.64 % (12785)Refutation found. Thanks to Tanya!
% 1.98/0.64 % SZS status Theorem for theBenchmark
% 1.98/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 1.98/0.66 % (12785)------------------------------
% 1.98/0.66 % (12785)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.98/0.66 % (12785)Termination reason: Refutation
% 1.98/0.66
% 1.98/0.66 % (12785)Memory used [KB]: 6813
% 1.98/0.66 % (12785)Time elapsed: 0.268 s
% 1.98/0.66 % (12785)Instructions burned: 695 (million)
% 1.98/0.66 % (12785)------------------------------
% 1.98/0.66 % (12785)------------------------------
% 1.98/0.66 % (12780)Success in time 0.285 s
%------------------------------------------------------------------------------