TSTP Solution File: GRP776+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 12:09:18 EDT 2024
% Result : Theorem 4.39s 0.94s
% Output : Refutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1061
% Syntax : Number of formulae : 3738 ( 24 unt; 0 def)
% Number of atoms : 14322 (2634 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 20092 (9508 ~;9498 |; 17 &)
% (1041 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 1045 (1043 usr;1042 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 5052 (5050 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13722,plain,
$false,
inference(avatar_sat_refutation,[],[f84,f89,f94,f98,f102,f109,f111,f115,f119,f123,f127,f141,f146,f150,f154,f158,f162,f166,f185,f193,f198,f202,f218,f223,f228,f233,f241,f245,f256,f260,f264,f270,f274,f278,f282,f307,f311,f315,f319,f338,f342,f355,f359,f363,f367,f390,f394,f398,f402,f422,f426,f431,f446,f456,f460,f475,f479,f484,f499,f504,f510,f514,f518,f522,f526,f530,f534,f538,f582,f586,f590,f594,f598,f602,f606,f610,f654,f658,f662,f683,f687,f703,f707,f711,f715,f719,f723,f727,f731,f735,f765,f777,f781,f785,f789,f793,f797,f801,f805,f809,f847,f851,f855,f859,f863,f867,f871,f904,f908,f912,f920,f924,f928,f932,f936,f940,f944,f977,f981,f985,f989,f993,f997,f1028,f1032,f1036,f1040,f1044,f1048,f1071,f1075,f1079,f1083,f1087,f1105,f1109,f1117,f1121,f1125,f1129,f1133,f1137,f1159,f1163,f1176,f1182,f1186,f1198,f1204,f1208,f1212,f1216,f1220,f1224,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1361,f1443,f1447,f1451,f1455,f1459,f1463,f1467,f1491,f1498,f1502,f1506,f1510,f1514,f1518,f1531,f1542,f1546,f1550,f1554,f1558,f1562,f1566,f1570,f1574,f1578,f1582,f1586,f1590,f1594,f1598,f1602,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1741,f1745,f1749,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1878,f1916,f1946,f1950,f1954,f1958,f1962,f1966,f1970,f1974,f1978,f1982,f1998,f2002,f2006,f2010,f2014,f2096,f2100,f2104,f2108,f2112,f2116,f2133,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2260,f2305,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2479,f2483,f2487,f2491,f2495,f2499,f2503,f2507,f2511,f2515,f2524,f2528,f2532,f2536,f2540,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2701,f2707,f2711,f2715,f2719,f2723,f2727,f2731,f2735,f2739,f2743,f2747,f2751,f2755,f2784,f2816,f2820,f2824,f2828,f2832,f2836,f2840,f2844,f2848,f2877,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2943,f2958,f3005,f3013,f3019,f3023,f3027,f3031,f3035,f3039,f3045,f3069,f3073,f3077,f3081,f3087,f3097,f3101,f3105,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3137,f3162,f3180,f3184,f3192,f3196,f3202,f3208,f3212,f3220,f3224,f3228,f3232,f3236,f3240,f3258,f3264,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3302,f3306,f3310,f3314,f3318,f3484,f3488,f3492,f3496,f3500,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3552,f3556,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3596,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3812,f3821,f3825,f3829,f3833,f3837,f3841,f3845,f3849,f3853,f3857,f3861,f3865,f3869,f4001,f4040,f4044,f4048,f4052,f4056,f4060,f4064,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4104,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4425,f4429,f4433,f4437,f4441,f4445,f4449,f4453,f4457,f4461,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4687,f4715,f5207,f5212,f5217,f5226,f5231,f5241,f5245,f5261,f5271,f5276,f5281,f5286,f5301,f5306,f5311,f5316,f5328,f5640,f5952,f5956,f5960,f5975,f5983,f5987,f6001,f6010,f6014,f6023,f6034,f6038,f6051,f6056,f6061,f6066,f6089,f6094,f6099,f6104,f6109,f6114,f6133,f6139,f6151,f6157,f6161,f6166,f6170,f6174,f6178,f6182,f6186,f6190,f6194,f6204,f6249,f6253,f6257,f6262,f6266,f6270,f6274,f6278,f6282,f6286,f6290,f6294,f6298,f6308,f6380,f6384,f6388,f6392,f6396,f6400,f6404,f6421,f6460,f6464,f6468,f6472,f6476,f6481,f6505,f6509,f6513,f6517,f6521,f6526,f6530,f6534,f6538,f6588,f6592,f6596,f6600,f6604,f6608,f6612,f6616,f6620,f6626,f6630,f6634,f6638,f6642,f6723,f6728,f6732,f6736,f6740,f6744,f6748,f6752,f6756,f6760,f6764,f6835,f6842,f6846,f6850,f6854,f6858,f6862,f6866,f6870,f6874,f6878,f6885,f6964,f6968,f6972,f6976,f6980,f6984,f6988,f6993,f6997,f7001,f7005,f7052,f7078,f7082,f7086,f7090,f7094,f7098,f7108,f7134,f7138,f7142,f7146,f7150,f7155,f7159,f7163,f7167,f7218,f7228,f7232,f7236,f7240,f7270,f7275,f7279,f7283,f7287,f7291,f7295,f7334,f7344,f7348,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7381,f7385,f7389,f7455,f7459,f7463,f7467,f7471,f7475,f7479,f7484,f7536,f7543,f7557,f7561,f7565,f7569,f7573,f7577,f7626,f7630,f7634,f7638,f7663,f7667,f7671,f7675,f7679,f7683,f7726,f7730,f7748,f7755,f7772,f7776,f7780,f7784,f7788,f7792,f7805,f7809,f7867,f7871,f7876,f7880,f7884,f7890,f7898,f7902,f7906,f7925,f7967,f7972,f7977,f7981,f7985,f8522,f8526,f8531,f8536,f8540,f8544,f8548,f8552,f8556,f8560,f8565,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8606,f8610,f8614,f8618,f8622,f8626,f8630,f8634,f8638,f8642,f8646,f8651,f8655,f8683,f8687,f8702,f10004,f10011,f10015,f10019,f10023,f10027,f10031,f10035,f10039,f10043,f10047,f10048,f10052,f10056,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10091,f10629,f10633,f10637,f10641,f10645,f10649,f10653,f10657,f10661,f10665,f10670,f10870,f10970,f10974,f10978,f10982,f10986,f10990,f10994,f10998,f11002,f11006,f11011,f11015,f11019,f11023,f11027,f11031,f11035,f11039,f11043,f11047,f11051,f11057,f11061,f11065,f11069,f11073,f11077,f11081,f11085,f11112,f11254,f11439,f11443,f11447,f11451,f11458,f11462,f11466,f11470,f11474,f11478,f11482,f11511,f11623,f11628,f11633,f11637,f11641,f11645,f11649,f11653,f11657,f11661,f11665,f11669,f11673,f11677,f11681,f11685,f11689,f11693,f11697,f11701,f11705,f11709,f11713,f11717,f11721,f11725,f11729,f11733,f11737,f11741,f11745,f11749,f11753,f11757,f11761,f11782,f11786,f11790,f11794,f11798,f11802,f11806,f11848,f11852,f11935,f12172,f12252,f12256,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12413,f12417,f12421,f12426,f12430,f12434,f12438,f12442,f12446,f12450,f12454,f12458,f12462,f12466,f12471,f12475,f12479,f12483,f12487,f12491,f12495,f12499,f12503,f12507,f12523,f12527,f12531,f12535,f12670,f12760,f12896,f12900,f12904,f12908,f12912,f12916,f12920,f12924,f12928,f12932,f12937,f12941,f12945,f12949,f12953,f12957,f12961,f12965,f12969,f12973,f12977,f13100,f13104,f13108,f13112,f13116,f13120,f13124,f13128,f13132,f13136,f13141,f13145,f13149,f13153,f13157,f13161,f13165,f13169,f13173,f13177,f13181,f13190,f13194,f13198,f13202,f13260,f13596,f13653,f13657,f13668,f13672,f13676,f13680,f13684,f13688,f13721]) ).
fof(f13721,plain,
( spl1_555
| ~ spl1_576
| ~ spl1_1033 ),
inference(avatar_split_clause,[],[f13658,f13593,f5972,f5204]) ).
fof(f5204,plain,
( spl1_555
<=> f(inv(sK0)) = opp(f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_555])]) ).
fof(f5972,plain,
( spl1_576
<=> f(inv(sK0)) = sum(f(inv(sK0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_576])]) ).
fof(f13593,plain,
( spl1_1033
<=> opp(f(sK0)) = sum(f(inv(sK0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1033])]) ).
fof(f13658,plain,
( f(inv(sK0)) = opp(f(sK0))
| ~ spl1_576
| ~ spl1_1033 ),
inference(superposition,[],[f13595,f5974]) ).
fof(f5974,plain,
( f(inv(sK0)) = sum(f(inv(sK0)),eg)
| ~ spl1_576 ),
inference(avatar_component_clause,[],[f5972]) ).
fof(f13595,plain,
( opp(f(sK0)) = sum(f(inv(sK0)),eg)
| ~ spl1_1033 ),
inference(avatar_component_clause,[],[f13593]) ).
fof(f13688,plain,
( spl1_1041
| ~ spl1_571
| ~ spl1_640 ),
inference(avatar_split_clause,[],[f6557,f6515,f5326,f13686]) ).
fof(f13686,plain,
( spl1_1041
<=> ! [X0] :
( f(product(eh,product(eh,product(eh,X0)))) = f(product(product(eh,product(eh,product(eh,X0))),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1041])]) ).
fof(f5326,plain,
( spl1_571
<=> ! [X0] :
( h(f(product(eh,X0)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_571])]) ).
fof(f6515,plain,
( spl1_640
<=> ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(product(eh,product(eh,X0)),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_640])]) ).
fof(f6557,plain,
( ! [X0] :
( f(product(eh,product(eh,product(eh,X0)))) = f(product(product(eh,product(eh,product(eh,X0))),eh))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_640 ),
inference(resolution,[],[f6516,f5327]) ).
fof(f5327,plain,
( ! [X0] :
( h(f(product(eh,X0)))
| ~ h(f(X0)) )
| ~ spl1_571 ),
inference(avatar_component_clause,[],[f5326]) ).
fof(f6516,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,product(eh,X0))) = f(product(product(eh,product(eh,X0)),eh)) )
| ~ spl1_640 ),
inference(avatar_component_clause,[],[f6515]) ).
fof(f13684,plain,
( spl1_1040
| ~ spl1_572
| ~ spl1_640 ),
inference(avatar_split_clause,[],[f6556,f6515,f5638,f13682]) ).
fof(f13682,plain,
( spl1_1040
<=> ! [X0] :
( f(product(eh,product(eh,product(X0,eh)))) = f(product(product(eh,product(eh,product(X0,eh))),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1040])]) ).
fof(f5638,plain,
( spl1_572
<=> ! [X0] :
( h(f(product(X0,eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_572])]) ).
fof(f6556,plain,
( ! [X0] :
( f(product(eh,product(eh,product(X0,eh)))) = f(product(product(eh,product(eh,product(X0,eh))),eh))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_640 ),
inference(resolution,[],[f6516,f5639]) ).
fof(f5639,plain,
( ! [X0] :
( h(f(product(X0,eh)))
| ~ h(f(X0)) )
| ~ spl1_572 ),
inference(avatar_component_clause,[],[f5638]) ).
fof(f13680,plain,
( spl1_1039
| ~ spl1_571
| ~ spl1_639 ),
inference(avatar_split_clause,[],[f6550,f6511,f5326,f13678]) ).
fof(f13678,plain,
( spl1_1039
<=> ! [X0] :
( f(product(eh,product(eh,product(eh,X0)))) = f(product(eh,product(eh,product(eh,product(eh,X0)))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1039])]) ).
fof(f6511,plain,
( spl1_639
<=> ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(eh,product(eh,product(eh,X0))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_639])]) ).
fof(f6550,plain,
( ! [X0] :
( f(product(eh,product(eh,product(eh,X0)))) = f(product(eh,product(eh,product(eh,product(eh,X0)))))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_639 ),
inference(resolution,[],[f6512,f5327]) ).
fof(f6512,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,product(eh,X0))) = f(product(eh,product(eh,product(eh,X0)))) )
| ~ spl1_639 ),
inference(avatar_component_clause,[],[f6511]) ).
fof(f13676,plain,
( spl1_1038
| ~ spl1_572
| ~ spl1_639 ),
inference(avatar_split_clause,[],[f6549,f6511,f5638,f13674]) ).
fof(f13674,plain,
( spl1_1038
<=> ! [X0] :
( f(product(eh,product(eh,product(X0,eh)))) = f(product(eh,product(eh,product(eh,product(X0,eh)))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1038])]) ).
fof(f6549,plain,
( ! [X0] :
( f(product(eh,product(eh,product(X0,eh)))) = f(product(eh,product(eh,product(eh,product(X0,eh)))))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_639 ),
inference(resolution,[],[f6512,f5639]) ).
fof(f13672,plain,
( spl1_1037
| ~ spl1_42
| ~ spl1_626 ),
inference(avatar_split_clause,[],[f6429,f6390,f340,f13670]) ).
fof(f13670,plain,
( spl1_1037
<=> ! [X0,X1] :
( eg = sum(opp(f(product(product(X0,X1),eh))),f(product(product(X0,X1),eh)))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1037])]) ).
fof(f340,plain,
( spl1_42
<=> ! [X0,X1] :
( h(f(product(X0,X1)))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
fof(f6390,plain,
( spl1_626
<=> ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X0,eh))),f(product(X0,eh))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_626])]) ).
fof(f6429,plain,
( ! [X0,X1] :
( eg = sum(opp(f(product(product(X0,X1),eh))),f(product(product(X0,X1),eh)))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_626 ),
inference(resolution,[],[f6391,f341]) ).
fof(f341,plain,
( ! [X0,X1] :
( h(f(product(X0,X1)))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f6391,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X0,eh))),f(product(X0,eh))) )
| ~ spl1_626 ),
inference(avatar_component_clause,[],[f6390]) ).
fof(f13668,plain,
( spl1_1036
| ~ spl1_42
| ~ spl1_625 ),
inference(avatar_split_clause,[],[f6423,f6386,f340,f13666]) ).
fof(f13666,plain,
( spl1_1036
<=> ! [X0,X1] :
( eg = sum(f(product(product(X0,X1),eh)),opp(f(product(product(X0,X1),eh))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1036])]) ).
fof(f6386,plain,
( spl1_625
<=> ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(X0,eh)),opp(f(product(X0,eh)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_625])]) ).
fof(f6423,plain,
( ! [X0,X1] :
( eg = sum(f(product(product(X0,X1),eh)),opp(f(product(product(X0,X1),eh))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_625 ),
inference(resolution,[],[f6387,f341]) ).
fof(f6387,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(X0,eh)),opp(f(product(X0,eh)))) )
| ~ spl1_625 ),
inference(avatar_component_clause,[],[f6386]) ).
fof(f13657,plain,
( spl1_1035
| ~ spl1_42
| ~ spl1_624 ),
inference(avatar_split_clause,[],[f6412,f6382,f340,f13655]) ).
fof(f13655,plain,
( spl1_1035
<=> ! [X0,X1] :
( eg = sum(opp(f(product(eh,product(X0,X1)))),f(product(eh,product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1035])]) ).
fof(f6382,plain,
( spl1_624
<=> ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(eh,X0))),f(product(eh,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_624])]) ).
fof(f6412,plain,
( ! [X0,X1] :
( eg = sum(opp(f(product(eh,product(X0,X1)))),f(product(eh,product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_624 ),
inference(resolution,[],[f6383,f341]) ).
fof(f6383,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(eh,X0))),f(product(eh,X0))) )
| ~ spl1_624 ),
inference(avatar_component_clause,[],[f6382]) ).
fof(f13653,plain,
( spl1_1034
| ~ spl1_42
| ~ spl1_623 ),
inference(avatar_split_clause,[],[f6406,f6378,f340,f13651]) ).
fof(f13651,plain,
( spl1_1034
<=> ! [X0,X1] :
( eg = sum(f(product(eh,product(X0,X1))),opp(f(product(eh,product(X0,X1)))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1034])]) ).
fof(f6378,plain,
( spl1_623
<=> ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(eh,X0)),opp(f(product(eh,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_623])]) ).
fof(f6406,plain,
( ! [X0,X1] :
( eg = sum(f(product(eh,product(X0,X1))),opp(f(product(eh,product(X0,X1)))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_623 ),
inference(resolution,[],[f6379,f341]) ).
fof(f6379,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(eh,X0)),opp(f(product(eh,X0)))) )
| ~ spl1_623 ),
inference(avatar_component_clause,[],[f6378]) ).
fof(f13596,plain,
( spl1_1033
| ~ spl1_567
| ~ spl1_985 ),
inference(avatar_split_clause,[],[f13434,f12758,f5298,f13593]) ).
fof(f5298,plain,
( spl1_567
<=> eg = sum(f(sK0),opp(f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_567])]) ).
fof(f12758,plain,
( spl1_985
<=> ! [X0] : opp(X0) = sum(f(inv(sK0)),sum(f(sK0),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_985])]) ).
fof(f13434,plain,
( opp(f(sK0)) = sum(f(inv(sK0)),eg)
| ~ spl1_567
| ~ spl1_985 ),
inference(superposition,[],[f12759,f5300]) ).
fof(f5300,plain,
( eg = sum(f(sK0),opp(f(sK0)))
| ~ spl1_567 ),
inference(avatar_component_clause,[],[f5298]) ).
fof(f12759,plain,
( ! [X0] : opp(X0) = sum(f(inv(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_985 ),
inference(avatar_component_clause,[],[f12758]) ).
fof(f13260,plain,
( spl1_1032
| ~ spl1_590
| ~ spl1_996 ),
inference(avatar_split_clause,[],[f12978,f12934,f6091,f13257]) ).
fof(f13257,plain,
( spl1_1032
<=> eg = sum(f(sK0),f(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1032])]) ).
fof(f6091,plain,
( spl1_590
<=> eg = sum(opp(f(inv(sK0))),f(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_590])]) ).
fof(f12934,plain,
( spl1_996
<=> f(sK0) = opp(f(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_996])]) ).
fof(f12978,plain,
( eg = sum(f(sK0),f(inv(sK0)))
| ~ spl1_590
| ~ spl1_996 ),
inference(superposition,[],[f6093,f12936]) ).
fof(f12936,plain,
( f(sK0) = opp(f(inv(sK0)))
| ~ spl1_996 ),
inference(avatar_component_clause,[],[f12934]) ).
fof(f6093,plain,
( eg = sum(opp(f(inv(sK0))),f(inv(sK0)))
| ~ spl1_590 ),
inference(avatar_component_clause,[],[f6091]) ).
fof(f13202,plain,
( spl1_1031
| ~ spl1_2
| ~ spl1_700 ),
inference(avatar_split_clause,[],[f7130,f7096,f81,f13200]) ).
fof(f13200,plain,
( spl1_1031
<=> ! [X0,X1] :
( product(product(sK0,product(X0,inv(X1))),sK0) = product(sK0,product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1031])]) ).
fof(f81,plain,
( spl1_2
<=> g(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f7096,plain,
( spl1_700
<=> ! [X2,X0,X1] :
( product(product(sK0,product(X0,inv(X1))),X2) = product(sK0,product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_700])]) ).
fof(f7130,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,inv(X1))),sK0) = product(sK0,product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_700 ),
inference(resolution,[],[f7097,f83]) ).
fof(f83,plain,
( g(sK0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f7097,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(sK0,product(X0,inv(X1))),X2) = product(sK0,product(product(X0,inv(X1)),X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_700 ),
inference(avatar_component_clause,[],[f7096]) ).
fof(f13198,plain,
( spl1_1030
| ~ spl1_4
| ~ spl1_700 ),
inference(avatar_split_clause,[],[f7129,f7096,f91,f13196]) ).
fof(f13196,plain,
( spl1_1030
<=> ! [X0,X1] :
( product(product(sK0,product(X0,inv(X1))),eh) = product(sK0,product(product(X0,inv(X1)),eh))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1030])]) ).
fof(f91,plain,
( spl1_4
<=> g(eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f7129,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,inv(X1))),eh) = product(sK0,product(product(X0,inv(X1)),eh))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_700 ),
inference(resolution,[],[f7097,f93]) ).
fof(f93,plain,
( g(eh)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f13194,plain,
( spl1_1029
| ~ spl1_2
| ~ spl1_699 ),
inference(avatar_split_clause,[],[f7125,f7092,f81,f13192]) ).
fof(f13192,plain,
( spl1_1029
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X1,sK0),X0),inv(sK0)) = product(product(X1,sK0),product(X0,inv(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1029])]) ).
fof(f7092,plain,
( spl1_699
<=> ! [X2,X0,X1] :
( product(product(product(X0,sK0),X1),inv(X2)) = product(product(X0,sK0),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_699])]) ).
fof(f7125,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X1,sK0),X0),inv(sK0)) = product(product(X1,sK0),product(X0,inv(sK0))) )
| ~ spl1_2
| ~ spl1_699 ),
inference(resolution,[],[f7093,f83]) ).
fof(f7093,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| product(product(product(X0,sK0),X1),inv(X2)) = product(product(X0,sK0),product(X1,inv(X2))) )
| ~ spl1_699 ),
inference(avatar_component_clause,[],[f7092]) ).
fof(f13190,plain,
( spl1_1028
| ~ spl1_2
| ~ spl1_698 ),
inference(avatar_split_clause,[],[f7121,f7088,f81,f13188]) ).
fof(f13188,plain,
( spl1_1028
<=> ! [X0,X1] :
( product(product(sK0,inv(product(X0,X1))),sK0) = product(sK0,product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1028])]) ).
fof(f7088,plain,
( spl1_698
<=> ! [X2,X0,X1] :
( product(product(sK0,inv(product(X0,X1))),X2) = product(sK0,product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_698])]) ).
fof(f7121,plain,
( ! [X0,X1] :
( product(product(sK0,inv(product(X0,X1))),sK0) = product(sK0,product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_698 ),
inference(resolution,[],[f7089,f83]) ).
fof(f7089,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(sK0,inv(product(X0,X1))),X2) = product(sK0,product(inv(product(X0,X1)),X2))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_698 ),
inference(avatar_component_clause,[],[f7088]) ).
fof(f13181,plain,
( spl1_1027
| ~ spl1_4
| ~ spl1_698 ),
inference(avatar_split_clause,[],[f7120,f7088,f91,f13179]) ).
fof(f13179,plain,
( spl1_1027
<=> ! [X0,X1] :
( product(product(sK0,inv(product(X0,X1))),eh) = product(sK0,product(inv(product(X0,X1)),eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1027])]) ).
fof(f7120,plain,
( ! [X0,X1] :
( product(product(sK0,inv(product(X0,X1))),eh) = product(sK0,product(inv(product(X0,X1)),eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_698 ),
inference(resolution,[],[f7089,f93]) ).
fof(f13177,plain,
( spl1_1026
| ~ spl1_2
| ~ spl1_697 ),
inference(avatar_split_clause,[],[f7117,f7084,f81,f13175]) ).
fof(f13175,plain,
( spl1_1026
<=> ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),product(X1,sK0)) = product(inv(sK0),product(X0,product(X1,sK0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1026])]) ).
fof(f7084,plain,
( spl1_697
<=> ! [X2,X0,X1] :
( product(product(inv(sK0),X0),product(X1,X2)) = product(inv(sK0),product(X0,product(X1,X2)))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_697])]) ).
fof(f7117,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),product(X1,sK0)) = product(inv(sK0),product(X0,product(X1,sK0)))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_697 ),
inference(resolution,[],[f7085,f83]) ).
fof(f7085,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| product(product(inv(sK0),X0),product(X1,X2)) = product(inv(sK0),product(X0,product(X1,X2)))
| ~ g(X1) )
| ~ spl1_697 ),
inference(avatar_component_clause,[],[f7084]) ).
fof(f13173,plain,
( spl1_1025
| ~ spl1_4
| ~ spl1_697 ),
inference(avatar_split_clause,[],[f7116,f7084,f91,f13171]) ).
fof(f13171,plain,
( spl1_1025
<=> ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),product(X1,eh)) = product(inv(sK0),product(X0,product(X1,eh)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1025])]) ).
fof(f7116,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),product(X1,eh)) = product(inv(sK0),product(X0,product(X1,eh)))
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_697 ),
inference(resolution,[],[f7085,f93]) ).
fof(f13169,plain,
( spl1_1024
| ~ spl1_2
| ~ spl1_696 ),
inference(avatar_split_clause,[],[f7112,f7080,f81,f13167]) ).
fof(f13167,plain,
( spl1_1024
<=> ! [X0,X1] :
( product(product(product(X0,inv(X1)),sK0),sK0) = product(product(X0,inv(X1)),product(sK0,sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1024])]) ).
fof(f7080,plain,
( spl1_696
<=> ! [X2,X0,X1] :
( product(product(product(X0,inv(X1)),X2),sK0) = product(product(X0,inv(X1)),product(X2,sK0))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_696])]) ).
fof(f7112,plain,
( ! [X0,X1] :
( product(product(product(X0,inv(X1)),sK0),sK0) = product(product(X0,inv(X1)),product(sK0,sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_696 ),
inference(resolution,[],[f7081,f83]) ).
fof(f7081,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(product(X0,inv(X1)),X2),sK0) = product(product(X0,inv(X1)),product(X2,sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_696 ),
inference(avatar_component_clause,[],[f7080]) ).
fof(f13165,plain,
( spl1_1023
| ~ spl1_2
| ~ spl1_695 ),
inference(avatar_split_clause,[],[f7102,f7076,f81,f13163]) ).
fof(f13163,plain,
( spl1_1023
<=> ! [X0,X1] :
( product(product(inv(product(X0,X1)),sK0),sK0) = product(inv(product(X0,X1)),product(sK0,sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1023])]) ).
fof(f7076,plain,
( spl1_695
<=> ! [X2,X0,X1] :
( product(product(inv(product(X0,X1)),X2),sK0) = product(inv(product(X0,X1)),product(X2,sK0))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_695])]) ).
fof(f7102,plain,
( ! [X0,X1] :
( product(product(inv(product(X0,X1)),sK0),sK0) = product(inv(product(X0,X1)),product(sK0,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_695 ),
inference(resolution,[],[f7077,f83]) ).
fof(f7077,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(inv(product(X0,X1)),X2),sK0) = product(inv(product(X0,X1)),product(X2,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_695 ),
inference(avatar_component_clause,[],[f7076]) ).
fof(f13161,plain,
( spl1_1022
| ~ spl1_5
| ~ spl1_693 ),
inference(avatar_split_clause,[],[f7068,f7003,f96,f13159]) ).
fof(f13159,plain,
( spl1_1022
<=> ! [X0,X1] :
( f(product(X0,product(eh,product(X1,eh)))) = f(product(product(X0,eh),product(X1,eh)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1022])]) ).
fof(f96,plain,
( spl1_5
<=> ! [X0] :
( h(f(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f7003,plain,
( spl1_693
<=> ! [X0,X1] :
( f(product(X1,product(eh,product(X0,eh)))) = f(product(product(X1,eh),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_693])]) ).
fof(f7068,plain,
( ! [X0,X1] :
( f(product(X0,product(eh,product(X1,eh)))) = f(product(product(X0,eh),product(X1,eh)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_693 ),
inference(resolution,[],[f7004,f97]) ).
fof(f97,plain,
( ! [X0] :
( h(f(X0))
| ~ g(X0) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f7004,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(eh,product(X0,eh)))) = f(product(product(X1,eh),product(X0,eh)))
| ~ g(X1) )
| ~ spl1_693 ),
inference(avatar_component_clause,[],[f7003]) ).
fof(f13157,plain,
( spl1_1021
| ~ spl1_5
| ~ spl1_692 ),
inference(avatar_split_clause,[],[f7062,f6999,f96,f13155]) ).
fof(f13155,plain,
( spl1_1021
<=> ! [X0,X1] :
( f(product(eh,product(X0,product(X1,eh)))) = f(product(product(eh,X0),product(X1,eh)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1021])]) ).
fof(f6999,plain,
( spl1_692
<=> ! [X0,X1] :
( f(product(eh,product(X1,product(X0,eh)))) = f(product(product(eh,X1),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_692])]) ).
fof(f7062,plain,
( ! [X0,X1] :
( f(product(eh,product(X0,product(X1,eh)))) = f(product(product(eh,X0),product(X1,eh)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_692 ),
inference(resolution,[],[f7000,f97]) ).
fof(f7000,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(eh,product(X1,product(X0,eh)))) = f(product(product(eh,X1),product(X0,eh)))
| ~ g(X1) )
| ~ spl1_692 ),
inference(avatar_component_clause,[],[f6999]) ).
fof(f13153,plain,
( spl1_1020
| ~ spl1_5
| ~ spl1_691 ),
inference(avatar_split_clause,[],[f7053,f6995,f96,f13151]) ).
fof(f13151,plain,
( spl1_1020
<=> ! [X0,X1] :
( sum(eg,sum(f(product(X0,eh)),X1)) = sum(f(product(eh,product(X0,eh))),X1)
| ~ h(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1020])]) ).
fof(f6995,plain,
( spl1_691
<=> ! [X0,X1] :
( sum(eg,sum(f(product(X0,eh)),X1)) = sum(f(product(eh,product(X0,eh))),X1)
| ~ h(f(X0))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_691])]) ).
fof(f7053,plain,
( ! [X0,X1] :
( sum(eg,sum(f(product(X0,eh)),X1)) = sum(f(product(eh,product(X0,eh))),X1)
| ~ h(X1)
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_691 ),
inference(resolution,[],[f6996,f97]) ).
fof(f6996,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(product(X0,eh)),X1)) = sum(f(product(eh,product(X0,eh))),X1)
| ~ h(X1) )
| ~ spl1_691 ),
inference(avatar_component_clause,[],[f6995]) ).
fof(f13149,plain,
( spl1_1019
| ~ spl1_5
| ~ spl1_689 ),
inference(avatar_split_clause,[],[f7043,f6986,f96,f13147]) ).
fof(f13147,plain,
( spl1_1019
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(X0,eh),X1)),opp(f(product(product(X0,eh),X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1019])]) ).
fof(f6986,plain,
( spl1_689
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(product(X0,eh),X1)),opp(f(product(product(X0,eh),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_689])]) ).
fof(f7043,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(X0,eh),X1)),opp(f(product(product(X0,eh),X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_689 ),
inference(resolution,[],[f6987,f97]) ).
fof(f6987,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(f(product(product(X0,eh),X1)),opp(f(product(product(X0,eh),X1)))) )
| ~ spl1_689 ),
inference(avatar_component_clause,[],[f6986]) ).
fof(f13145,plain,
( spl1_1018
| ~ spl1_5
| ~ spl1_688 ),
inference(avatar_split_clause,[],[f7038,f6982,f96,f13143]) ).
fof(f13143,plain,
( spl1_1018
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(X0,eh),X1))),f(product(product(X0,eh),X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1018])]) ).
fof(f6982,plain,
( spl1_688
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(product(X0,eh),X1))),f(product(product(X0,eh),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_688])]) ).
fof(f7038,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(X0,eh),X1))),f(product(product(X0,eh),X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_688 ),
inference(resolution,[],[f6983,f97]) ).
fof(f6983,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(opp(f(product(product(X0,eh),X1))),f(product(product(X0,eh),X1))) )
| ~ spl1_688 ),
inference(avatar_component_clause,[],[f6982]) ).
fof(f13141,plain,
( spl1_1017
| ~ spl1_30
| ~ spl1_582
| ~ spl1_984 ),
inference(avatar_split_clause,[],[f12885,f12668,f6020,f253,f13138]) ).
fof(f13138,plain,
( spl1_1017
<=> eg = sum(f(inv(sK0)),f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1017])]) ).
fof(f253,plain,
( spl1_30
<=> eg = opp(eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f6020,plain,
( spl1_582
<=> f(inv(sK0)) = sum(eg,f(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_582])]) ).
fof(f12668,plain,
( spl1_984
<=> ! [X0] : opp(X0) = sum(sum(opp(X0),f(inv(sK0))),f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_984])]) ).
fof(f12885,plain,
( eg = sum(f(inv(sK0)),f(sK0))
| ~ spl1_30
| ~ spl1_582
| ~ spl1_984 ),
inference(forward_demodulation,[],[f12879,f6022]) ).
fof(f6022,plain,
( f(inv(sK0)) = sum(eg,f(inv(sK0)))
| ~ spl1_582 ),
inference(avatar_component_clause,[],[f6020]) ).
fof(f12879,plain,
( eg = sum(sum(eg,f(inv(sK0))),f(sK0))
| ~ spl1_30
| ~ spl1_984 ),
inference(superposition,[],[f12669,f255]) ).
fof(f255,plain,
( eg = opp(eg)
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f12669,plain,
( ! [X0] : opp(X0) = sum(sum(opp(X0),f(inv(sK0))),f(sK0))
| ~ spl1_984 ),
inference(avatar_component_clause,[],[f12668]) ).
fof(f13136,plain,
( spl1_1016
| ~ spl1_5
| ~ spl1_687 ),
inference(avatar_split_clause,[],[f7031,f6978,f96,f13134]) ).
fof(f13134,plain,
( spl1_1016
<=> ! [X0,X1] :
( f(product(X0,product(eh,product(eh,X1)))) = f(product(product(X0,eh),product(eh,X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1016])]) ).
fof(f6978,plain,
( spl1_687
<=> ! [X0,X1] :
( f(product(X1,product(eh,product(eh,X0)))) = f(product(product(X1,eh),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_687])]) ).
fof(f7031,plain,
( ! [X0,X1] :
( f(product(X0,product(eh,product(eh,X1)))) = f(product(product(X0,eh),product(eh,X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_687 ),
inference(resolution,[],[f6979,f97]) ).
fof(f6979,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(eh,product(eh,X0)))) = f(product(product(X1,eh),product(eh,X0)))
| ~ g(X1) )
| ~ spl1_687 ),
inference(avatar_component_clause,[],[f6978]) ).
fof(f13132,plain,
( spl1_1015
| ~ spl1_5
| ~ spl1_686 ),
inference(avatar_split_clause,[],[f7025,f6974,f96,f13130]) ).
fof(f13130,plain,
( spl1_1015
<=> ! [X0,X1] :
( f(product(eh,product(X0,product(eh,X1)))) = f(product(product(eh,X0),product(eh,X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1015])]) ).
fof(f6974,plain,
( spl1_686
<=> ! [X0,X1] :
( f(product(eh,product(X1,product(eh,X0)))) = f(product(product(eh,X1),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_686])]) ).
fof(f7025,plain,
( ! [X0,X1] :
( f(product(eh,product(X0,product(eh,X1)))) = f(product(product(eh,X0),product(eh,X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_686 ),
inference(resolution,[],[f6975,f97]) ).
fof(f6975,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(eh,product(X1,product(eh,X0)))) = f(product(product(eh,X1),product(eh,X0)))
| ~ g(X1) )
| ~ spl1_686 ),
inference(avatar_component_clause,[],[f6974]) ).
fof(f13128,plain,
( spl1_1014
| ~ spl1_5
| ~ spl1_685 ),
inference(avatar_split_clause,[],[f7016,f6970,f96,f13126]) ).
fof(f13126,plain,
( spl1_1014
<=> ! [X0,X1] :
( sum(eg,sum(f(product(eh,X0)),X1)) = sum(f(product(eh,product(eh,X0))),X1)
| ~ h(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1014])]) ).
fof(f6970,plain,
( spl1_685
<=> ! [X0,X1] :
( sum(eg,sum(f(product(eh,X0)),X1)) = sum(f(product(eh,product(eh,X0))),X1)
| ~ h(f(X0))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_685])]) ).
fof(f7016,plain,
( ! [X0,X1] :
( sum(eg,sum(f(product(eh,X0)),X1)) = sum(f(product(eh,product(eh,X0))),X1)
| ~ h(X1)
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_685 ),
inference(resolution,[],[f6971,f97]) ).
fof(f6971,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(product(eh,X0)),X1)) = sum(f(product(eh,product(eh,X0))),X1)
| ~ h(X1) )
| ~ spl1_685 ),
inference(avatar_component_clause,[],[f6970]) ).
fof(f13124,plain,
( spl1_1013
| ~ spl1_5
| ~ spl1_684 ),
inference(avatar_split_clause,[],[f7011,f6966,f96,f13122]) ).
fof(f13122,plain,
( spl1_1013
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(eh,X0),X1)),opp(f(product(product(eh,X0),X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1013])]) ).
fof(f6966,plain,
( spl1_684
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(product(eh,X0),X1)),opp(f(product(product(eh,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_684])]) ).
fof(f7011,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(eh,X0),X1)),opp(f(product(product(eh,X0),X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_684 ),
inference(resolution,[],[f6967,f97]) ).
fof(f6967,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(f(product(product(eh,X0),X1)),opp(f(product(product(eh,X0),X1)))) )
| ~ spl1_684 ),
inference(avatar_component_clause,[],[f6966]) ).
fof(f13120,plain,
( spl1_1012
| ~ spl1_5
| ~ spl1_683 ),
inference(avatar_split_clause,[],[f7006,f6962,f96,f13118]) ).
fof(f13118,plain,
( spl1_1012
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(eh,X0),X1))),f(product(product(eh,X0),X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1012])]) ).
fof(f6962,plain,
( spl1_683
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(product(eh,X0),X1))),f(product(product(eh,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_683])]) ).
fof(f7006,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(eh,X0),X1))),f(product(product(eh,X0),X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_683 ),
inference(resolution,[],[f6963,f97]) ).
fof(f6963,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(opp(f(product(product(eh,X0),X1))),f(product(product(eh,X0),X1))) )
| ~ spl1_683 ),
inference(avatar_component_clause,[],[f6962]) ).
fof(f13116,plain,
( spl1_1011
| ~ spl1_6
| ~ spl1_659 ),
inference(avatar_split_clause,[],[f6717,f6640,f100,f13114]) ).
fof(f13114,plain,
( spl1_1011
<=> ! [X0,X1] :
( product(product(sK0,product(X0,sK0)),inv(X1)) = product(sK0,product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1011])]) ).
fof(f100,plain,
( spl1_6
<=> ! [X0] :
( g(inv(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f6640,plain,
( spl1_659
<=> ! [X0,X1] :
( product(product(sK0,product(X0,sK0)),X1) = product(sK0,product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_659])]) ).
fof(f6717,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,sK0)),inv(X1)) = product(sK0,product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_659 ),
inference(resolution,[],[f6641,f101]) ).
fof(f101,plain,
( ! [X0] :
( g(inv(X0))
| ~ g(X0) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f6641,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(sK0,product(X0,sK0)),X1) = product(sK0,product(product(X0,sK0),X1))
| ~ g(X0) )
| ~ spl1_659 ),
inference(avatar_component_clause,[],[f6640]) ).
fof(f13112,plain,
( spl1_1010
| ~ spl1_6
| ~ spl1_658 ),
inference(avatar_split_clause,[],[f6713,f6636,f100,f13110]) ).
fof(f13110,plain,
( spl1_1010
<=> ! [X0,X1] :
( product(product(sK0,product(X0,eh)),inv(X1)) = product(sK0,product(product(X0,eh),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1010])]) ).
fof(f6636,plain,
( spl1_658
<=> ! [X0,X1] :
( product(product(sK0,product(X0,eh)),X1) = product(sK0,product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_658])]) ).
fof(f6713,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,eh)),inv(X1)) = product(sK0,product(product(X0,eh),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_658 ),
inference(resolution,[],[f6637,f101]) ).
fof(f6637,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(sK0,product(X0,eh)),X1) = product(sK0,product(product(X0,eh),X1))
| ~ g(X0) )
| ~ spl1_658 ),
inference(avatar_component_clause,[],[f6636]) ).
fof(f13108,plain,
( spl1_1009
| ~ spl1_6
| ~ spl1_657 ),
inference(avatar_split_clause,[],[f6708,f6632,f100,f13106]) ).
fof(f13106,plain,
( spl1_1009
<=> ! [X0,X1] :
( product(product(product(X0,sK0),inv(X1)),sK0) = product(product(X0,sK0),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1009])]) ).
fof(f6632,plain,
( spl1_657
<=> ! [X0,X1] :
( product(product(product(X0,sK0),X1),sK0) = product(product(X0,sK0),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_657])]) ).
fof(f6708,plain,
( ! [X0,X1] :
( product(product(product(X0,sK0),inv(X1)),sK0) = product(product(X0,sK0),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_657 ),
inference(resolution,[],[f6633,f101]) ).
fof(f6633,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(product(X0,sK0),X1),sK0) = product(product(X0,sK0),product(X1,sK0))
| ~ g(X0) )
| ~ spl1_657 ),
inference(avatar_component_clause,[],[f6632]) ).
fof(f13104,plain,
( spl1_1008
| ~ spl1_6
| ~ spl1_656 ),
inference(avatar_split_clause,[],[f6702,f6628,f100,f13102]) ).
fof(f13102,plain,
( spl1_1008
<=> ! [X0,X1] :
( product(product(product(X0,sK0),inv(X1)),eh) = product(product(X0,sK0),product(inv(X1),eh))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1008])]) ).
fof(f6628,plain,
( spl1_656
<=> ! [X0,X1] :
( product(product(product(X0,sK0),X1),eh) = product(product(X0,sK0),product(X1,eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_656])]) ).
fof(f6702,plain,
( ! [X0,X1] :
( product(product(product(X0,sK0),inv(X1)),eh) = product(product(X0,sK0),product(inv(X1),eh))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_656 ),
inference(resolution,[],[f6629,f101]) ).
fof(f6629,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(product(X0,sK0),X1),eh) = product(product(X0,sK0),product(X1,eh))
| ~ g(X0) )
| ~ spl1_656 ),
inference(avatar_component_clause,[],[f6628]) ).
fof(f13100,plain,
( spl1_1007
| ~ spl1_6
| ~ spl1_655 ),
inference(avatar_split_clause,[],[f6698,f6624,f100,f13098]) ).
fof(f13098,plain,
( spl1_1007
<=> ! [X0,X1] :
( product(product(sK0,inv(inv(X0))),inv(X1)) = product(sK0,product(inv(inv(X0)),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1007])]) ).
fof(f6624,plain,
( spl1_655
<=> ! [X0,X1] :
( product(product(sK0,inv(inv(X0))),X1) = product(sK0,product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_655])]) ).
fof(f6698,plain,
( ! [X0,X1] :
( product(product(sK0,inv(inv(X0))),inv(X1)) = product(sK0,product(inv(inv(X0)),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_655 ),
inference(resolution,[],[f6625,f101]) ).
fof(f6625,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(sK0,inv(inv(X0))),X1) = product(sK0,product(inv(inv(X0)),X1))
| ~ g(X0) )
| ~ spl1_655 ),
inference(avatar_component_clause,[],[f6624]) ).
fof(f12977,plain,
( spl1_1006
| ~ spl1_6
| ~ spl1_654 ),
inference(avatar_split_clause,[],[f6693,f6618,f100,f12975]) ).
fof(f12975,plain,
( spl1_1006
<=> ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),inv(inv(X1))) = product(inv(sK0),product(X0,inv(inv(X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1006])]) ).
fof(f6618,plain,
( spl1_654
<=> ! [X0,X1] :
( product(product(inv(sK0),X0),inv(X1)) = product(inv(sK0),product(X0,inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_654])]) ).
fof(f6693,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),inv(inv(X1))) = product(inv(sK0),product(X0,inv(inv(X1))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_654 ),
inference(resolution,[],[f6619,f101]) ).
fof(f6619,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| product(product(inv(sK0),X0),inv(X1)) = product(inv(sK0),product(X0,inv(X1))) )
| ~ spl1_654 ),
inference(avatar_component_clause,[],[f6618]) ).
fof(f12973,plain,
( spl1_1005
| ~ spl1_6
| ~ spl1_653 ),
inference(avatar_split_clause,[],[f6689,f6614,f100,f12971]) ).
fof(f12971,plain,
( spl1_1005
<=> ! [X0,X1] :
( product(product(sK0,sK0),product(X0,inv(X1))) = product(sK0,product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1005])]) ).
fof(f6614,plain,
( spl1_653
<=> ! [X0,X1] :
( product(product(sK0,sK0),product(X0,X1)) = product(sK0,product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_653])]) ).
fof(f6689,plain,
( ! [X0,X1] :
( product(product(sK0,sK0),product(X0,inv(X1))) = product(sK0,product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_653 ),
inference(resolution,[],[f6615,f101]) ).
fof(f6615,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(sK0,sK0),product(X0,X1)) = product(sK0,product(sK0,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_653 ),
inference(avatar_component_clause,[],[f6614]) ).
fof(f12969,plain,
( spl1_1004
| ~ spl1_6
| ~ spl1_648 ),
inference(avatar_split_clause,[],[f6653,f6594,f100,f12967]) ).
fof(f12967,plain,
( spl1_1004
<=> ! [X0,X1] :
( product(product(product(X0,eh),inv(X1)),sK0) = product(product(X0,eh),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1004])]) ).
fof(f6594,plain,
( spl1_648
<=> ! [X0,X1] :
( product(product(product(X0,eh),X1),sK0) = product(product(X0,eh),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_648])]) ).
fof(f6653,plain,
( ! [X0,X1] :
( product(product(product(X0,eh),inv(X1)),sK0) = product(product(X0,eh),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_648 ),
inference(resolution,[],[f6595,f101]) ).
fof(f6595,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(product(X0,eh),X1),sK0) = product(product(X0,eh),product(X1,sK0))
| ~ g(X0) )
| ~ spl1_648 ),
inference(avatar_component_clause,[],[f6594]) ).
fof(f12965,plain,
( spl1_1003
| ~ spl1_6
| ~ spl1_647 ),
inference(avatar_split_clause,[],[f6648,f6590,f100,f12963]) ).
fof(f12963,plain,
( spl1_1003
<=> ! [X0,X1] :
( product(product(inv(inv(X0)),inv(X1)),sK0) = product(inv(inv(X0)),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1003])]) ).
fof(f6590,plain,
( spl1_647
<=> ! [X0,X1] :
( product(product(inv(inv(X0)),X1),sK0) = product(inv(inv(X0)),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_647])]) ).
fof(f6648,plain,
( ! [X0,X1] :
( product(product(inv(inv(X0)),inv(X1)),sK0) = product(inv(inv(X0)),product(inv(X1),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_647 ),
inference(resolution,[],[f6591,f101]) ).
fof(f6591,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(inv(inv(X0)),X1),sK0) = product(inv(inv(X0)),product(X1,sK0))
| ~ g(X0) )
| ~ spl1_647 ),
inference(avatar_component_clause,[],[f6590]) ).
fof(f12961,plain,
( spl1_1002
| ~ spl1_6
| ~ spl1_646 ),
inference(avatar_split_clause,[],[f6644,f6586,f100,f12959]) ).
fof(f12959,plain,
( spl1_1002
<=> ! [X0,X1] :
( product(eh,product(product(X0,sK0),inv(X1))) = product(product(eh,product(X0,sK0)),inv(X1))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1002])]) ).
fof(f6586,plain,
( spl1_646
<=> ! [X0,X1] :
( product(eh,product(product(X0,sK0),X1)) = product(product(eh,product(X0,sK0)),X1)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_646])]) ).
fof(f6644,plain,
( ! [X0,X1] :
( product(eh,product(product(X0,sK0),inv(X1))) = product(product(eh,product(X0,sK0)),inv(X1))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_646 ),
inference(resolution,[],[f6587,f101]) ).
fof(f6587,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(product(X0,sK0),X1)) = product(product(eh,product(X0,sK0)),X1)
| ~ g(X0) )
| ~ spl1_646 ),
inference(avatar_component_clause,[],[f6586]) ).
fof(f12957,plain,
( spl1_1001
| ~ spl1_19
| ~ spl1_629 ),
inference(avatar_split_clause,[],[f6450,f6402,f164,f12955]) ).
fof(f12955,plain,
( spl1_1001
<=> ! [X0,X1] :
( product(product(inv(sK0),product(X0,X1)),sK0) = product(inv(sK0),product(product(X0,X1),sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1001])]) ).
fof(f164,plain,
( spl1_19
<=> ! [X0,X1] :
( g(product(X1,X0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f6402,plain,
( spl1_629
<=> ! [X0] :
( product(product(inv(sK0),X0),sK0) = product(inv(sK0),product(X0,sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_629])]) ).
fof(f6450,plain,
( ! [X0,X1] :
( product(product(inv(sK0),product(X0,X1)),sK0) = product(inv(sK0),product(product(X0,X1),sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_629 ),
inference(resolution,[],[f6403,f165]) ).
fof(f165,plain,
( ! [X0,X1] :
( g(product(X1,X0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f6403,plain,
( ! [X0] :
( ~ g(X0)
| product(product(inv(sK0),X0),sK0) = product(inv(sK0),product(X0,sK0)) )
| ~ spl1_629 ),
inference(avatar_component_clause,[],[f6402]) ).
fof(f12953,plain,
( spl1_1000
| ~ spl1_19
| ~ spl1_628 ),
inference(avatar_split_clause,[],[f6442,f6398,f164,f12951]) ).
fof(f12951,plain,
( spl1_1000
<=> ! [X0,X1] :
( product(product(inv(sK0),product(X0,X1)),eh) = product(inv(sK0),product(product(X0,X1),eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1000])]) ).
fof(f6398,plain,
( spl1_628
<=> ! [X0] :
( product(product(inv(sK0),X0),eh) = product(inv(sK0),product(X0,eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_628])]) ).
fof(f6442,plain,
( ! [X0,X1] :
( product(product(inv(sK0),product(X0,X1)),eh) = product(inv(sK0),product(product(X0,X1),eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_628 ),
inference(resolution,[],[f6399,f165]) ).
fof(f6399,plain,
( ! [X0] :
( ~ g(X0)
| product(product(inv(sK0),X0),eh) = product(inv(sK0),product(X0,eh)) )
| ~ spl1_628 ),
inference(avatar_component_clause,[],[f6398]) ).
fof(f12949,plain,
( spl1_999
| ~ spl1_19
| ~ spl1_627 ),
inference(avatar_split_clause,[],[f6434,f6394,f164,f12947]) ).
fof(f12947,plain,
( spl1_999
<=> ! [X0,X1] :
( product(product(sK0,sK0),inv(product(X0,X1))) = product(sK0,product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_999])]) ).
fof(f6394,plain,
( spl1_627
<=> ! [X0] :
( product(product(sK0,sK0),inv(X0)) = product(sK0,product(sK0,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_627])]) ).
fof(f6434,plain,
( ! [X0,X1] :
( product(product(sK0,sK0),inv(product(X0,X1))) = product(sK0,product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_627 ),
inference(resolution,[],[f6395,f165]) ).
fof(f6395,plain,
( ! [X0] :
( ~ g(X0)
| product(product(sK0,sK0),inv(X0)) = product(sK0,product(sK0,inv(X0))) )
| ~ spl1_627 ),
inference(avatar_component_clause,[],[f6394]) ).
fof(f12945,plain,
( spl1_998
| ~ spl1_42
| ~ spl1_619 ),
inference(avatar_split_clause,[],[f6355,f6288,f340,f12943]) ).
fof(f12943,plain,
( spl1_998
<=> ! [X0,X1] :
( f(product(product(X0,X1),eh)) = f(product(eh,product(product(X0,X1),eh)))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_998])]) ).
fof(f6288,plain,
( spl1_619
<=> ! [X0] :
( f(product(X0,eh)) = f(product(eh,product(X0,eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_619])]) ).
fof(f6355,plain,
( ! [X0,X1] :
( f(product(product(X0,X1),eh)) = f(product(eh,product(product(X0,X1),eh)))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_619 ),
inference(resolution,[],[f6289,f341]) ).
fof(f6289,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(X0,eh)) = f(product(eh,product(X0,eh))) )
| ~ spl1_619 ),
inference(avatar_component_clause,[],[f6288]) ).
fof(f12941,plain,
( spl1_997
| ~ spl1_42
| ~ spl1_618 ),
inference(avatar_split_clause,[],[f6349,f6284,f340,f12939]) ).
fof(f12939,plain,
( spl1_997
<=> ! [X0,X1] :
( f(product(product(X0,X1),eh)) = f(product(product(product(X0,X1),eh),eh))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_997])]) ).
fof(f6284,plain,
( spl1_618
<=> ! [X0] :
( f(product(X0,eh)) = f(product(product(X0,eh),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_618])]) ).
fof(f6349,plain,
( ! [X0,X1] :
( f(product(product(X0,X1),eh)) = f(product(product(product(X0,X1),eh),eh))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_618 ),
inference(resolution,[],[f6285,f341]) ).
fof(f6285,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(X0,eh)) = f(product(product(X0,eh),eh)) )
| ~ spl1_618 ),
inference(avatar_component_clause,[],[f6284]) ).
fof(f12937,plain,
( spl1_996
| ~ spl1_564
| ~ spl1_590
| ~ spl1_984 ),
inference(avatar_split_clause,[],[f12892,f12668,f6091,f5273,f12934]) ).
fof(f5273,plain,
( spl1_564
<=> f(sK0) = sum(eg,f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_564])]) ).
fof(f12892,plain,
( f(sK0) = opp(f(inv(sK0)))
| ~ spl1_564
| ~ spl1_590
| ~ spl1_984 ),
inference(forward_demodulation,[],[f12883,f5275]) ).
fof(f5275,plain,
( f(sK0) = sum(eg,f(sK0))
| ~ spl1_564 ),
inference(avatar_component_clause,[],[f5273]) ).
fof(f12883,plain,
( sum(eg,f(sK0)) = opp(f(inv(sK0)))
| ~ spl1_590
| ~ spl1_984 ),
inference(superposition,[],[f12669,f6093]) ).
fof(f12932,plain,
( spl1_995
| ~ spl1_42
| ~ spl1_617 ),
inference(avatar_split_clause,[],[f6343,f6280,f340,f12930]) ).
fof(f12930,plain,
( spl1_995
<=> ! [X0,X1] :
( f(product(eh,product(X0,X1))) = f(product(eh,product(eh,product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_995])]) ).
fof(f6280,plain,
( spl1_617
<=> ! [X0] :
( f(product(eh,X0)) = f(product(eh,product(eh,X0)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_617])]) ).
fof(f6343,plain,
( ! [X0,X1] :
( f(product(eh,product(X0,X1))) = f(product(eh,product(eh,product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_617 ),
inference(resolution,[],[f6281,f341]) ).
fof(f6281,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,X0)) = f(product(eh,product(eh,X0))) )
| ~ spl1_617 ),
inference(avatar_component_clause,[],[f6280]) ).
fof(f12928,plain,
( spl1_994
| ~ spl1_42
| ~ spl1_616 ),
inference(avatar_split_clause,[],[f6337,f6276,f340,f12926]) ).
fof(f12926,plain,
( spl1_994
<=> ! [X0,X1] :
( f(product(eh,product(X0,X1))) = f(product(product(eh,product(X0,X1)),eh))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_994])]) ).
fof(f6276,plain,
( spl1_616
<=> ! [X0] :
( f(product(eh,X0)) = f(product(product(eh,X0),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_616])]) ).
fof(f6337,plain,
( ! [X0,X1] :
( f(product(eh,product(X0,X1))) = f(product(product(eh,product(X0,X1)),eh))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_616 ),
inference(resolution,[],[f6277,f341]) ).
fof(f6277,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,X0)) = f(product(product(eh,X0),eh)) )
| ~ spl1_616 ),
inference(avatar_component_clause,[],[f6276]) ).
fof(f12924,plain,
( spl1_993
| ~ spl1_206
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5657,f5638,f1616,f12922]) ).
fof(f12922,plain,
( spl1_993
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,product(X0,eh))),opp(f(product(X1,product(X0,eh)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_993])]) ).
fof(f1616,plain,
( spl1_206
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_206])]) ).
fof(f5657,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,product(X0,eh))),opp(f(product(X1,product(X0,eh)))))
| ~ g(X1) )
| ~ spl1_206
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1617]) ).
fof(f1617,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0))))
| ~ g(X1) )
| ~ spl1_206 ),
inference(avatar_component_clause,[],[f1616]) ).
fof(f12920,plain,
( spl1_992
| ~ spl1_204
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5656,f5638,f1608,f12918]) ).
fof(f12918,plain,
( spl1_992
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,product(X0,eh)))),f(product(X1,product(X0,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_992])]) ).
fof(f1608,plain,
( spl1_204
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_204])]) ).
fof(f5656,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,product(X0,eh)))),f(product(X1,product(X0,eh))))
| ~ g(X1) )
| ~ spl1_204
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1609]) ).
fof(f1609,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0)))
| ~ g(X1) )
| ~ spl1_204 ),
inference(avatar_component_clause,[],[f1608]) ).
fof(f12916,plain,
( spl1_991
| ~ spl1_206
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5345,f5326,f1616,f12914]) ).
fof(f12914,plain,
( spl1_991
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,product(eh,X0))),opp(f(product(X1,product(eh,X0)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_991])]) ).
fof(f5345,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,product(eh,X0))),opp(f(product(X1,product(eh,X0)))))
| ~ g(X1) )
| ~ spl1_206
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1617]) ).
fof(f12912,plain,
( spl1_990
| ~ spl1_204
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5344,f5326,f1608,f12910]) ).
fof(f12910,plain,
( spl1_990
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,product(eh,X0)))),f(product(X1,product(eh,X0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_990])]) ).
fof(f5344,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,product(eh,X0)))),f(product(X1,product(eh,X0))))
| ~ g(X1) )
| ~ spl1_204
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1609]) ).
fof(f12908,plain,
( spl1_989
| ~ spl1_2
| ~ spl1_311 ),
inference(avatar_split_clause,[],[f4874,f2501,f81,f12906]) ).
fof(f12906,plain,
( spl1_989
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X1,eh),X0),inv(sK0)) = product(product(X1,eh),product(X0,inv(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_989])]) ).
fof(f2501,plain,
( spl1_311
<=> ! [X2,X0,X1] :
( product(product(product(X0,eh),X1),inv(X2)) = product(product(X0,eh),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_311])]) ).
fof(f4874,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X1,eh),X0),inv(sK0)) = product(product(X1,eh),product(X0,inv(sK0))) )
| ~ spl1_2
| ~ spl1_311 ),
inference(resolution,[],[f83,f2502]) ).
fof(f2502,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| product(product(product(X0,eh),X1),inv(X2)) = product(product(X0,eh),product(X1,inv(X2))) )
| ~ spl1_311 ),
inference(avatar_component_clause,[],[f2501]) ).
fof(f12904,plain,
( spl1_988
| ~ spl1_2
| ~ spl1_309 ),
inference(avatar_split_clause,[],[f4873,f2493,f81,f12902]) ).
fof(f12902,plain,
( spl1_988
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(inv(inv(X1)),X0),inv(sK0)) = product(inv(inv(X1)),product(X0,inv(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_988])]) ).
fof(f2493,plain,
( spl1_309
<=> ! [X2,X0,X1] :
( product(product(inv(inv(X0)),X1),inv(X2)) = product(inv(inv(X0)),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_309])]) ).
fof(f4873,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(inv(inv(X1)),X0),inv(sK0)) = product(inv(inv(X1)),product(X0,inv(sK0))) )
| ~ spl1_2
| ~ spl1_309 ),
inference(resolution,[],[f83,f2494]) ).
fof(f2494,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| product(product(inv(inv(X0)),X1),inv(X2)) = product(inv(inv(X0)),product(X1,inv(X2))) )
| ~ spl1_309 ),
inference(avatar_component_clause,[],[f2493]) ).
fof(f12900,plain,
( spl1_987
| ~ spl1_2
| ~ spl1_308 ),
inference(avatar_split_clause,[],[f4872,f2489,f81,f12898]) ).
fof(f12898,plain,
( spl1_987
<=> ! [X0,X1] :
( product(eh,product(product(X0,inv(X1)),sK0)) = product(product(eh,product(X0,inv(X1))),sK0)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_987])]) ).
fof(f2489,plain,
( spl1_308
<=> ! [X2,X0,X1] :
( product(eh,product(product(X0,inv(X1)),X2)) = product(product(eh,product(X0,inv(X1))),X2)
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_308])]) ).
fof(f4872,plain,
( ! [X0,X1] :
( product(eh,product(product(X0,inv(X1)),sK0)) = product(product(eh,product(X0,inv(X1))),sK0)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_308 ),
inference(resolution,[],[f83,f2490]) ).
fof(f2490,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(eh,product(product(X0,inv(X1)),X2)) = product(product(eh,product(X0,inv(X1))),X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_308 ),
inference(avatar_component_clause,[],[f2489]) ).
fof(f12896,plain,
( spl1_986
| ~ spl1_2
| ~ spl1_304 ),
inference(avatar_split_clause,[],[f4871,f2468,f81,f12894]) ).
fof(f12894,plain,
( spl1_986
<=> ! [X0,X1] :
( product(eh,product(inv(product(X0,X1)),sK0)) = product(product(eh,inv(product(X0,X1))),sK0)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_986])]) ).
fof(f2468,plain,
( spl1_304
<=> ! [X2,X0,X1] :
( product(eh,product(inv(product(X0,X1)),X2)) = product(product(eh,inv(product(X0,X1))),X2)
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_304])]) ).
fof(f4871,plain,
( ! [X0,X1] :
( product(eh,product(inv(product(X0,X1)),sK0)) = product(product(eh,inv(product(X0,X1))),sK0)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_304 ),
inference(resolution,[],[f83,f2469]) ).
fof(f2469,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(eh,product(inv(product(X0,X1)),X2)) = product(product(eh,inv(product(X0,X1))),X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_304 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f12760,plain,
( spl1_985
| ~ spl1_1
| ~ spl1_29
| ~ spl1_559
| ~ spl1_810
| ~ spl1_890 ),
inference(avatar_split_clause,[],[f11500,f11441,f8603,f5228,f243,f77,f12758]) ).
fof(f77,plain,
( spl1_1
<=> eg = f(eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f243,plain,
( spl1_29
<=> ! [X0] : opp(X0) = sum(eg,opp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f5228,plain,
( spl1_559
<=> eh = product(inv(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_559])]) ).
fof(f8603,plain,
( spl1_810
<=> g(inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_810])]) ).
fof(f11441,plain,
( spl1_890
<=> ! [X0,X1] :
( ~ g(X0)
| sum(f(product(X0,sK0)),opp(X1)) = sum(f(X0),sum(f(sK0),opp(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_890])]) ).
fof(f11500,plain,
( ! [X0] : opp(X0) = sum(f(inv(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_1
| ~ spl1_29
| ~ spl1_559
| ~ spl1_810
| ~ spl1_890 ),
inference(forward_demodulation,[],[f11499,f244]) ).
fof(f244,plain,
( ! [X0] : opp(X0) = sum(eg,opp(X0))
| ~ spl1_29 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f11499,plain,
( ! [X0] : sum(eg,opp(X0)) = sum(f(inv(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_1
| ~ spl1_559
| ~ spl1_810
| ~ spl1_890 ),
inference(forward_demodulation,[],[f11498,f78]) ).
fof(f78,plain,
( eg = f(eh)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f11498,plain,
( ! [X0] : sum(f(eh),opp(X0)) = sum(f(inv(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_559
| ~ spl1_810
| ~ spl1_890 ),
inference(forward_demodulation,[],[f11495,f5230]) ).
fof(f5230,plain,
( eh = product(inv(sK0),sK0)
| ~ spl1_559 ),
inference(avatar_component_clause,[],[f5228]) ).
fof(f11495,plain,
( ! [X0] : sum(f(product(inv(sK0),sK0)),opp(X0)) = sum(f(inv(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_810
| ~ spl1_890 ),
inference(resolution,[],[f11442,f8604]) ).
fof(f8604,plain,
( g(inv(sK0))
| ~ spl1_810 ),
inference(avatar_component_clause,[],[f8603]) ).
fof(f11442,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(product(X0,sK0)),opp(X1)) = sum(f(X0),sum(f(sK0),opp(X1))) )
| ~ spl1_890 ),
inference(avatar_component_clause,[],[f11441]) ).
fof(f12670,plain,
( spl1_984
| ~ spl1_1
| ~ spl1_28
| ~ spl1_559
| ~ spl1_810
| ~ spl1_889 ),
inference(avatar_split_clause,[],[f11490,f11437,f8603,f5228,f239,f77,f12668]) ).
fof(f239,plain,
( spl1_28
<=> ! [X0] : opp(X0) = sum(opp(X0),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f11437,plain,
( spl1_889
<=> ! [X0,X1] :
( ~ g(X0)
| sum(opp(X1),f(product(X0,sK0))) = sum(sum(opp(X1),f(X0)),f(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_889])]) ).
fof(f11490,plain,
( ! [X0] : opp(X0) = sum(sum(opp(X0),f(inv(sK0))),f(sK0))
| ~ spl1_1
| ~ spl1_28
| ~ spl1_559
| ~ spl1_810
| ~ spl1_889 ),
inference(forward_demodulation,[],[f11489,f240]) ).
fof(f240,plain,
( ! [X0] : opp(X0) = sum(opp(X0),eg)
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f11489,plain,
( ! [X0] : sum(opp(X0),eg) = sum(sum(opp(X0),f(inv(sK0))),f(sK0))
| ~ spl1_1
| ~ spl1_559
| ~ spl1_810
| ~ spl1_889 ),
inference(forward_demodulation,[],[f11488,f78]) ).
fof(f11488,plain,
( ! [X0] : sum(opp(X0),f(eh)) = sum(sum(opp(X0),f(inv(sK0))),f(sK0))
| ~ spl1_559
| ~ spl1_810
| ~ spl1_889 ),
inference(forward_demodulation,[],[f11485,f5230]) ).
fof(f11485,plain,
( ! [X0] : sum(opp(X0),f(product(inv(sK0),sK0))) = sum(sum(opp(X0),f(inv(sK0))),f(sK0))
| ~ spl1_810
| ~ spl1_889 ),
inference(resolution,[],[f11438,f8604]) ).
fof(f11438,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(opp(X1),f(product(X0,sK0))) = sum(sum(opp(X1),f(X0)),f(sK0)) )
| ~ spl1_889 ),
inference(avatar_component_clause,[],[f11437]) ).
fof(f12535,plain,
( spl1_983
| ~ spl1_5
| ~ spl1_682 ),
inference(avatar_split_clause,[],[f6956,f6883,f96,f12533]) ).
fof(f12533,plain,
( spl1_983
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(product(product(X0,eh),X1),eh))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_983])]) ).
fof(f6883,plain,
( spl1_682
<=> ! [X0,X1] :
( f(product(product(X0,eh),X1)) = f(product(product(product(X0,eh),X1),eh))
| ~ h(f(X0))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_682])]) ).
fof(f6956,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(product(product(X0,eh),X1),eh))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_682 ),
inference(resolution,[],[f6884,f97]) ).
fof(f6884,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(product(product(X0,eh),X1),eh)) )
| ~ spl1_682 ),
inference(avatar_component_clause,[],[f6883]) ).
fof(f12531,plain,
( spl1_982
| ~ spl1_5
| ~ spl1_681 ),
inference(avatar_split_clause,[],[f6951,f6876,f96,f12529]) ).
fof(f12529,plain,
( spl1_982
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(eh,product(product(X0,eh),X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_982])]) ).
fof(f6876,plain,
( spl1_681
<=> ! [X0,X1] :
( f(product(product(X0,eh),X1)) = f(product(eh,product(product(X0,eh),X1)))
| ~ h(f(X0))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_681])]) ).
fof(f6951,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(eh,product(product(X0,eh),X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_681 ),
inference(resolution,[],[f6877,f97]) ).
fof(f6877,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(product(X0,eh),X1)) = f(product(eh,product(product(X0,eh),X1))) )
| ~ spl1_681 ),
inference(avatar_component_clause,[],[f6876]) ).
fof(f12527,plain,
( spl1_981
| ~ spl1_5
| ~ spl1_680 ),
inference(avatar_split_clause,[],[f6945,f6872,f96,f12525]) ).
fof(f12525,plain,
( spl1_981
<=> ! [X0,X1] :
( eg = sum(sum(opp(X0),f(product(X1,eh))),opp(sum(opp(X0),f(product(X1,eh)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_981])]) ).
fof(f6872,plain,
( spl1_680
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(X0,eh))),opp(sum(opp(X1),f(product(X0,eh))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_680])]) ).
fof(f6945,plain,
( ! [X0,X1] :
( eg = sum(sum(opp(X0),f(product(X1,eh))),opp(sum(opp(X0),f(product(X1,eh)))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_680 ),
inference(resolution,[],[f6873,f97]) ).
fof(f6873,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(X0,eh))),opp(sum(opp(X1),f(product(X0,eh))))) )
| ~ spl1_680 ),
inference(avatar_component_clause,[],[f6872]) ).
fof(f12523,plain,
( spl1_980
| ~ spl1_5
| ~ spl1_679 ),
inference(avatar_split_clause,[],[f6936,f6868,f96,f12521]) ).
fof(f12521,plain,
( spl1_980
<=> ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(X1,eh)))),sum(opp(X0),f(product(X1,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_980])]) ).
fof(f6868,plain,
( spl1_679
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(X0,eh)))),sum(opp(X1),f(product(X0,eh)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_679])]) ).
fof(f6936,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(X1,eh)))),sum(opp(X0),f(product(X1,eh))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_679 ),
inference(resolution,[],[f6869,f97]) ).
fof(f6869,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(X0,eh)))),sum(opp(X1),f(product(X0,eh)))) )
| ~ spl1_679 ),
inference(avatar_component_clause,[],[f6868]) ).
fof(f12507,plain,
( spl1_979
| ~ spl1_5
| ~ spl1_678 ),
inference(avatar_split_clause,[],[f6929,f6864,f96,f12505]) ).
fof(f12505,plain,
( spl1_979
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(X1,eh)),X0),opp(sum(f(product(X1,eh)),X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_979])]) ).
fof(f6864,plain,
( spl1_678
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(X0,eh)),X1),opp(sum(f(product(X0,eh)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_678])]) ).
fof(f6929,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(X1,eh)),X0),opp(sum(f(product(X1,eh)),X0)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_678 ),
inference(resolution,[],[f6865,f97]) ).
fof(f6865,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(X0,eh)),X1),opp(sum(f(product(X0,eh)),X1))) )
| ~ spl1_678 ),
inference(avatar_component_clause,[],[f6864]) ).
fof(f12503,plain,
( spl1_978
| ~ spl1_5
| ~ spl1_677 ),
inference(avatar_split_clause,[],[f6922,f6860,f96,f12501]) ).
fof(f12501,plain,
( spl1_978
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(X1,eh)),X0)),sum(f(product(X1,eh)),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_978])]) ).
fof(f6860,plain,
( spl1_677
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(X0,eh)),X1)),sum(f(product(X0,eh)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_677])]) ).
fof(f6922,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(X1,eh)),X0)),sum(f(product(X1,eh)),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_677 ),
inference(resolution,[],[f6861,f97]) ).
fof(f6861,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(X0,eh)),X1)),sum(f(product(X0,eh)),X1)) )
| ~ spl1_677 ),
inference(avatar_component_clause,[],[f6860]) ).
fof(f12499,plain,
( spl1_977
| ~ spl1_5
| ~ spl1_676 ),
inference(avatar_split_clause,[],[f6917,f6856,f96,f12497]) ).
fof(f12497,plain,
( spl1_977
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(product(product(eh,X0),X1),eh))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_977])]) ).
fof(f6856,plain,
( spl1_676
<=> ! [X0,X1] :
( f(product(product(eh,X0),X1)) = f(product(product(product(eh,X0),X1),eh))
| ~ h(f(X0))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_676])]) ).
fof(f6917,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(product(product(eh,X0),X1),eh))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_676 ),
inference(resolution,[],[f6857,f97]) ).
fof(f6857,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(product(product(eh,X0),X1),eh)) )
| ~ spl1_676 ),
inference(avatar_component_clause,[],[f6856]) ).
fof(f12495,plain,
( spl1_976
| ~ spl1_5
| ~ spl1_675 ),
inference(avatar_split_clause,[],[f6912,f6852,f96,f12493]) ).
fof(f12493,plain,
( spl1_976
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(eh,product(product(eh,X0),X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_976])]) ).
fof(f6852,plain,
( spl1_675
<=> ! [X0,X1] :
( f(product(product(eh,X0),X1)) = f(product(eh,product(product(eh,X0),X1)))
| ~ h(f(X0))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_675])]) ).
fof(f6912,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(eh,product(product(eh,X0),X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_675 ),
inference(resolution,[],[f6853,f97]) ).
fof(f6853,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(product(eh,X0),X1)) = f(product(eh,product(product(eh,X0),X1))) )
| ~ spl1_675 ),
inference(avatar_component_clause,[],[f6852]) ).
fof(f12491,plain,
( spl1_975
| ~ spl1_5
| ~ spl1_674 ),
inference(avatar_split_clause,[],[f6906,f6848,f96,f12489]) ).
fof(f12489,plain,
( spl1_975
<=> ! [X0,X1] :
( eg = sum(sum(opp(X0),f(product(eh,X1))),opp(sum(opp(X0),f(product(eh,X1)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_975])]) ).
fof(f6848,plain,
( spl1_674
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(eh,X0))),opp(sum(opp(X1),f(product(eh,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_674])]) ).
fof(f6906,plain,
( ! [X0,X1] :
( eg = sum(sum(opp(X0),f(product(eh,X1))),opp(sum(opp(X0),f(product(eh,X1)))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_674 ),
inference(resolution,[],[f6849,f97]) ).
fof(f6849,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(eh,X0))),opp(sum(opp(X1),f(product(eh,X0))))) )
| ~ spl1_674 ),
inference(avatar_component_clause,[],[f6848]) ).
fof(f12487,plain,
( spl1_974
| ~ spl1_5
| ~ spl1_673 ),
inference(avatar_split_clause,[],[f6900,f6844,f96,f12485]) ).
fof(f12485,plain,
( spl1_974
<=> ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(eh,X1)))),sum(opp(X0),f(product(eh,X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_974])]) ).
fof(f6844,plain,
( spl1_673
<=> ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(eh,X0)))),sum(opp(X1),f(product(eh,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_673])]) ).
fof(f6900,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(eh,X1)))),sum(opp(X0),f(product(eh,X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_673 ),
inference(resolution,[],[f6845,f97]) ).
fof(f6845,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(eh,X0)))),sum(opp(X1),f(product(eh,X0)))) )
| ~ spl1_673 ),
inference(avatar_component_clause,[],[f6844]) ).
fof(f12483,plain,
( spl1_973
| ~ spl1_5
| ~ spl1_672 ),
inference(avatar_split_clause,[],[f6893,f6840,f96,f12481]) ).
fof(f12481,plain,
( spl1_973
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(eh,X1)),X0),opp(sum(f(product(eh,X1)),X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_973])]) ).
fof(f6840,plain,
( spl1_672
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(eh,X0)),X1),opp(sum(f(product(eh,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_672])]) ).
fof(f6893,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(eh,X1)),X0),opp(sum(f(product(eh,X1)),X0)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_672 ),
inference(resolution,[],[f6841,f97]) ).
fof(f6841,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(eh,X0)),X1),opp(sum(f(product(eh,X0)),X1))) )
| ~ spl1_672 ),
inference(avatar_component_clause,[],[f6840]) ).
fof(f12479,plain,
( spl1_972
| ~ spl1_5
| ~ spl1_671 ),
inference(avatar_split_clause,[],[f6886,f6833,f96,f12477]) ).
fof(f12477,plain,
( spl1_972
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(eh,X1)),X0)),sum(f(product(eh,X1)),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_972])]) ).
fof(f6833,plain,
( spl1_671
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(eh,X0)),X1)),sum(f(product(eh,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_671])]) ).
fof(f6886,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(eh,X1)),X0)),sum(f(product(eh,X1)),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_671 ),
inference(resolution,[],[f6834,f97]) ).
fof(f6834,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(eh,X0)),X1)),sum(f(product(eh,X0)),X1)) )
| ~ spl1_671 ),
inference(avatar_component_clause,[],[f6833]) ).
fof(f12475,plain,
( spl1_971
| ~ spl1_6
| ~ spl1_645 ),
inference(avatar_split_clause,[],[f6582,f6536,f100,f12473]) ).
fof(f12473,plain,
( spl1_971
<=> ! [X0,X1] :
( eh = product(product(sK0,product(X0,inv(X1))),inv(product(sK0,product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_971])]) ).
fof(f6536,plain,
( spl1_645
<=> ! [X0,X1] :
( eh = product(product(sK0,product(X0,X1)),inv(product(sK0,product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_645])]) ).
fof(f6582,plain,
( ! [X0,X1] :
( eh = product(product(sK0,product(X0,inv(X1))),inv(product(sK0,product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_645 ),
inference(resolution,[],[f6537,f101]) ).
fof(f6537,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(sK0,product(X0,X1)),inv(product(sK0,product(X0,X1))))
| ~ g(X0) )
| ~ spl1_645 ),
inference(avatar_component_clause,[],[f6536]) ).
fof(f12471,plain,
( spl1_970
| ~ spl1_6
| ~ spl1_644 ),
inference(avatar_split_clause,[],[f6576,f6532,f100,f12469]) ).
fof(f12469,plain,
( spl1_970
<=> ! [X0,X1] :
( eh = product(inv(product(sK0,product(X0,inv(X1)))),product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_970])]) ).
fof(f6532,plain,
( spl1_644
<=> ! [X0,X1] :
( eh = product(inv(product(sK0,product(X0,X1))),product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_644])]) ).
fof(f6576,plain,
( ! [X0,X1] :
( eh = product(inv(product(sK0,product(X0,inv(X1)))),product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_644 ),
inference(resolution,[],[f6533,f101]) ).
fof(f6533,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(sK0,product(X0,X1))),product(sK0,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_644 ),
inference(avatar_component_clause,[],[f6532]) ).
fof(f12466,plain,
( spl1_969
| ~ spl1_6
| ~ spl1_638 ),
inference(avatar_split_clause,[],[f6544,f6507,f100,f12464]) ).
fof(f12464,plain,
( spl1_969
<=> ! [X0,X1] :
( eh = product(product(product(X0,sK0),inv(X1)),inv(product(product(X0,sK0),inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_969])]) ).
fof(f6507,plain,
( spl1_638
<=> ! [X0,X1] :
( eh = product(product(product(X0,sK0),X1),inv(product(product(X0,sK0),X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_638])]) ).
fof(f6544,plain,
( ! [X0,X1] :
( eh = product(product(product(X0,sK0),inv(X1)),inv(product(product(X0,sK0),inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_638 ),
inference(resolution,[],[f6508,f101]) ).
fof(f6508,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(product(X0,sK0),X1),inv(product(product(X0,sK0),X1)))
| ~ g(X0) )
| ~ spl1_638 ),
inference(avatar_component_clause,[],[f6507]) ).
fof(f12462,plain,
( spl1_968
| ~ spl1_6
| ~ spl1_637 ),
inference(avatar_split_clause,[],[f6540,f6503,f100,f12460]) ).
fof(f12460,plain,
( spl1_968
<=> ! [X0,X1] :
( eh = product(inv(product(product(X0,sK0),inv(X1))),product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_968])]) ).
fof(f6503,plain,
( spl1_637
<=> ! [X0,X1] :
( eh = product(inv(product(product(X0,sK0),X1)),product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_637])]) ).
fof(f6540,plain,
( ! [X0,X1] :
( eh = product(inv(product(product(X0,sK0),inv(X1))),product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_637 ),
inference(resolution,[],[f6504,f101]) ).
fof(f6504,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(product(X0,sK0),X1)),product(product(X0,sK0),X1))
| ~ g(X0) )
| ~ spl1_637 ),
inference(avatar_component_clause,[],[f6503]) ).
fof(f12458,plain,
( spl1_967
| ~ spl1_19
| ~ spl1_621 ),
inference(avatar_split_clause,[],[f6370,f6296,f164,f12456]) ).
fof(f12456,plain,
( spl1_967
<=> ! [X0,X1] :
( eh = product(product(sK0,inv(product(X0,X1))),inv(product(sK0,inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_967])]) ).
fof(f6296,plain,
( spl1_621
<=> ! [X0] :
( eh = product(product(sK0,inv(X0)),inv(product(sK0,inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_621])]) ).
fof(f6370,plain,
( ! [X0,X1] :
( eh = product(product(sK0,inv(product(X0,X1))),inv(product(sK0,inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_621 ),
inference(resolution,[],[f6297,f165]) ).
fof(f6297,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(sK0,inv(X0)),inv(product(sK0,inv(X0)))) )
| ~ spl1_621 ),
inference(avatar_component_clause,[],[f6296]) ).
fof(f12454,plain,
( spl1_966
| ~ spl1_19
| ~ spl1_620 ),
inference(avatar_split_clause,[],[f6360,f6292,f164,f12452]) ).
fof(f12452,plain,
( spl1_966
<=> ! [X0,X1] :
( eh = product(inv(product(sK0,inv(product(X0,X1)))),product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_966])]) ).
fof(f6292,plain,
( spl1_620
<=> ! [X0] :
( eh = product(inv(product(sK0,inv(X0))),product(sK0,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_620])]) ).
fof(f6360,plain,
( ! [X0,X1] :
( eh = product(inv(product(sK0,inv(product(X0,X1)))),product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_620 ),
inference(resolution,[],[f6293,f165]) ).
fof(f6293,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(sK0,inv(X0))),product(sK0,inv(X0))) )
| ~ spl1_620 ),
inference(avatar_component_clause,[],[f6292]) ).
fof(f12450,plain,
( spl1_965
| ~ spl1_19
| ~ spl1_615 ),
inference(avatar_split_clause,[],[f6330,f6272,f164,f12448]) ).
fof(f12448,plain,
( spl1_965
<=> ! [X0,X1] :
( eh = product(product(inv(sK0),product(X0,X1)),inv(product(inv(sK0),product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_965])]) ).
fof(f6272,plain,
( spl1_615
<=> ! [X0] :
( eh = product(product(inv(sK0),X0),inv(product(inv(sK0),X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_615])]) ).
fof(f6330,plain,
( ! [X0,X1] :
( eh = product(product(inv(sK0),product(X0,X1)),inv(product(inv(sK0),product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_615 ),
inference(resolution,[],[f6273,f165]) ).
fof(f6273,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(inv(sK0),X0),inv(product(inv(sK0),X0))) )
| ~ spl1_615 ),
inference(avatar_component_clause,[],[f6272]) ).
fof(f12446,plain,
( spl1_964
| ~ spl1_19
| ~ spl1_614 ),
inference(avatar_split_clause,[],[f6324,f6268,f164,f12444]) ).
fof(f12444,plain,
( spl1_964
<=> ! [X0,X1] :
( eh = product(inv(product(inv(sK0),product(X0,X1))),product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_964])]) ).
fof(f6268,plain,
( spl1_614
<=> ! [X0] :
( eh = product(inv(product(inv(sK0),X0)),product(inv(sK0),X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_614])]) ).
fof(f6324,plain,
( ! [X0,X1] :
( eh = product(inv(product(inv(sK0),product(X0,X1))),product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_614 ),
inference(resolution,[],[f6269,f165]) ).
fof(f6269,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(inv(sK0),X0)),product(inv(sK0),X0)) )
| ~ spl1_614 ),
inference(avatar_component_clause,[],[f6268]) ).
fof(f12442,plain,
( spl1_963
| ~ spl1_19
| ~ spl1_613 ),
inference(avatar_split_clause,[],[f6319,f6264,f164,f12440]) ).
fof(f12440,plain,
( spl1_963
<=> ! [X0,X1] :
( eh = product(inv(inv(product(product(X0,X1),sK0))),inv(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_963])]) ).
fof(f6264,plain,
( spl1_613
<=> ! [X0] :
( eh = product(inv(inv(product(X0,sK0))),inv(product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_613])]) ).
fof(f6319,plain,
( ! [X0,X1] :
( eh = product(inv(inv(product(product(X0,X1),sK0))),inv(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_613 ),
inference(resolution,[],[f6265,f165]) ).
fof(f6265,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,sK0))),inv(product(X0,sK0))) )
| ~ spl1_613 ),
inference(avatar_component_clause,[],[f6264]) ).
fof(f12438,plain,
( spl1_962
| ~ spl1_19
| ~ spl1_611 ),
inference(avatar_split_clause,[],[f6314,f6255,f164,f12436]) ).
fof(f12436,plain,
( spl1_962
<=> ! [X0,X1] :
( eh = product(inv(product(product(X0,X1),sK0)),inv(inv(product(product(X0,X1),sK0))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_962])]) ).
fof(f6255,plain,
( spl1_611
<=> ! [X0] :
( eh = product(inv(product(X0,sK0)),inv(inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_611])]) ).
fof(f6314,plain,
( ! [X0,X1] :
( eh = product(inv(product(product(X0,X1),sK0)),inv(inv(product(product(X0,X1),sK0))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_611 ),
inference(resolution,[],[f6256,f165]) ).
fof(f6256,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(X0,sK0)),inv(inv(product(X0,sK0)))) )
| ~ spl1_611 ),
inference(avatar_component_clause,[],[f6255]) ).
fof(f12434,plain,
( spl1_961
| ~ spl1_19
| ~ spl1_610 ),
inference(avatar_split_clause,[],[f6309,f6251,f164,f12432]) ).
fof(f12432,plain,
( spl1_961
<=> ! [X0,X1] :
( eg = sum(opp(f(product(product(X0,X1),sK0))),f(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_961])]) ).
fof(f6251,plain,
( spl1_610
<=> ! [X0] :
( eg = sum(opp(f(product(X0,sK0))),f(product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_610])]) ).
fof(f6309,plain,
( ! [X0,X1] :
( eg = sum(opp(f(product(product(X0,X1),sK0))),f(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_610 ),
inference(resolution,[],[f6252,f165]) ).
fof(f6252,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,sK0))),f(product(X0,sK0))) )
| ~ spl1_610 ),
inference(avatar_component_clause,[],[f6251]) ).
fof(f12430,plain,
( spl1_960
| ~ spl1_19
| ~ spl1_609 ),
inference(avatar_split_clause,[],[f6299,f6247,f164,f12428]) ).
fof(f12428,plain,
( spl1_960
<=> ! [X0,X1] :
( eg = sum(f(product(product(X0,X1),sK0)),opp(f(product(product(X0,X1),sK0))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_960])]) ).
fof(f6247,plain,
( spl1_609
<=> ! [X0] :
( eg = sum(f(product(X0,sK0)),opp(f(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_609])]) ).
fof(f6299,plain,
( ! [X0,X1] :
( eg = sum(f(product(product(X0,X1),sK0)),opp(f(product(product(X0,X1),sK0))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_609 ),
inference(resolution,[],[f6248,f165]) ).
fof(f6248,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(product(X0,sK0)),opp(f(product(X0,sK0)))) )
| ~ spl1_609 ),
inference(avatar_component_clause,[],[f6247]) ).
fof(f12426,plain,
( spl1_959
| ~ spl1_21
| ~ spl1_900
| ~ spl1_946 ),
inference(avatar_split_clause,[],[f12329,f12169,f11509,f191,f12423]) ).
fof(f12423,plain,
( spl1_959
<=> f(sK0) = sum(opp(f(sK0)),f(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_959])]) ).
fof(f191,plain,
( spl1_21
<=> ! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f11509,plain,
( spl1_900
<=> ! [X0] : f(sK0) = sum(opp(X0),sum(opp(opp(X0)),f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_900])]) ).
fof(f12169,plain,
( spl1_946
<=> f(sK0) = opp(opp(f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_946])]) ).
fof(f12329,plain,
( f(sK0) = sum(opp(f(sK0)),f(product(sK0,sK0)))
| ~ spl1_21
| ~ spl1_900
| ~ spl1_946 ),
inference(forward_demodulation,[],[f12264,f192]) ).
fof(f192,plain,
( ! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0))
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f12264,plain,
( f(sK0) = sum(opp(f(sK0)),sum(f(sK0),f(sK0)))
| ~ spl1_900
| ~ spl1_946 ),
inference(superposition,[],[f11510,f12171]) ).
fof(f12171,plain,
( f(sK0) = opp(opp(f(sK0)))
| ~ spl1_946 ),
inference(avatar_component_clause,[],[f12169]) ).
fof(f11510,plain,
( ! [X0] : f(sK0) = sum(opp(X0),sum(opp(opp(X0)),f(sK0)))
| ~ spl1_900 ),
inference(avatar_component_clause,[],[f11509]) ).
fof(f12421,plain,
( spl1_958
| ~ spl1_185
| ~ spl1_561
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5851,f5638,f5243,f1516,f12419]) ).
fof(f12419,plain,
( spl1_958
<=> ! [X0,X1] :
( f(product(X1,product(X0,eh))) = f(product(product(X1,product(X0,eh)),eh))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_958])]) ).
fof(f1516,plain,
( spl1_185
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_185])]) ).
fof(f5243,plain,
( spl1_561
<=> ! [X0] : sum(f(X0),eg) = f(product(X0,eh)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_561])]) ).
fof(f5851,plain,
( ! [X0,X1] :
( f(product(X1,product(X0,eh))) = f(product(product(X1,product(X0,eh)),eh))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_185
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5655,f5244]) ).
fof(f5244,plain,
( ! [X0] : sum(f(X0),eg) = f(product(X0,eh))
| ~ spl1_561 ),
inference(avatar_component_clause,[],[f5243]) ).
fof(f5655,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(X0,eh))) = sum(f(product(X1,product(X0,eh))),eg)
| ~ g(X1) )
| ~ spl1_185
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1517]) ).
fof(f1517,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg)
| ~ g(X1) )
| ~ spl1_185 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f12417,plain,
( spl1_957
| ~ spl1_184
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5850,f5638,f5239,f1512,f12415]) ).
fof(f12415,plain,
( spl1_957
<=> ! [X0,X1] :
( f(product(X1,product(X0,eh))) = f(product(eh,product(X1,product(X0,eh))))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_957])]) ).
fof(f1512,plain,
( spl1_184
<=> ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_184])]) ).
fof(f5239,plain,
( spl1_560
<=> ! [X0] : sum(eg,f(X0)) = f(product(eh,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_560])]) ).
fof(f5850,plain,
( ! [X0,X1] :
( f(product(X1,product(X0,eh))) = f(product(eh,product(X1,product(X0,eh))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_184
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5654,f5240]) ).
fof(f5240,plain,
( ! [X0] : sum(eg,f(X0)) = f(product(eh,X0))
| ~ spl1_560 ),
inference(avatar_component_clause,[],[f5239]) ).
fof(f5654,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(X0,eh))) = sum(eg,f(product(X1,product(X0,eh))))
| ~ g(X1) )
| ~ spl1_184
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1513]) ).
fof(f1513,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0)))
| ~ g(X1) )
| ~ spl1_184 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f12413,plain,
( spl1_956
| ~ spl1_185
| ~ spl1_561
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5539,f5326,f5243,f1516,f12411]) ).
fof(f12411,plain,
( spl1_956
<=> ! [X0,X1] :
( f(product(X1,product(eh,X0))) = f(product(product(X1,product(eh,X0)),eh))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_956])]) ).
fof(f5539,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,X0))) = f(product(product(X1,product(eh,X0)),eh))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_185
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5343,f5244]) ).
fof(f5343,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(eh,X0))) = sum(f(product(X1,product(eh,X0))),eg)
| ~ g(X1) )
| ~ spl1_185
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1517]) ).
fof(f12409,plain,
( spl1_955
| ~ spl1_184
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5538,f5326,f5239,f1512,f12407]) ).
fof(f12407,plain,
( spl1_955
<=> ! [X0,X1] :
( f(product(X1,product(eh,X0))) = f(product(eh,product(X1,product(eh,X0))))
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_955])]) ).
fof(f5538,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,X0))) = f(product(eh,product(X1,product(eh,X0))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_184
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5342,f5240]) ).
fof(f5342,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,product(eh,X0))) = sum(eg,f(product(X1,product(eh,X0))))
| ~ g(X1) )
| ~ spl1_184
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1513]) ).
fof(f12405,plain,
( spl1_954
| ~ spl1_2
| ~ spl1_295 ),
inference(avatar_split_clause,[],[f4870,f2370,f81,f12403]) ).
fof(f12403,plain,
( spl1_954
<=> ! [X0,X1] :
( eh = product(product(product(X0,inv(X1)),sK0),inv(product(product(X0,inv(X1)),sK0)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_954])]) ).
fof(f2370,plain,
( spl1_295
<=> ! [X2,X0,X1] :
( eh = product(product(product(X0,inv(X1)),X2),inv(product(product(X0,inv(X1)),X2)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_295])]) ).
fof(f4870,plain,
( ! [X0,X1] :
( eh = product(product(product(X0,inv(X1)),sK0),inv(product(product(X0,inv(X1)),sK0)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_295 ),
inference(resolution,[],[f83,f2371]) ).
fof(f2371,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(product(product(X0,inv(X1)),X2),inv(product(product(X0,inv(X1)),X2)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_295 ),
inference(avatar_component_clause,[],[f2370]) ).
fof(f12401,plain,
( spl1_953
| ~ spl1_2
| ~ spl1_294 ),
inference(avatar_split_clause,[],[f4869,f2366,f81,f12399]) ).
fof(f12399,plain,
( spl1_953
<=> ! [X0,X1] :
( eh = product(inv(product(product(X0,inv(X1)),sK0)),product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_953])]) ).
fof(f2366,plain,
( spl1_294
<=> ! [X2,X0,X1] :
( eh = product(inv(product(product(X0,inv(X1)),X2)),product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_294])]) ).
fof(f4869,plain,
( ! [X0,X1] :
( eh = product(inv(product(product(X0,inv(X1)),sK0)),product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_294 ),
inference(resolution,[],[f83,f2367]) ).
fof(f2367,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(inv(product(product(X0,inv(X1)),X2)),product(product(X0,inv(X1)),X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_294 ),
inference(avatar_component_clause,[],[f2366]) ).
fof(f12397,plain,
( spl1_952
| ~ spl1_2
| ~ spl1_291 ),
inference(avatar_split_clause,[],[f4868,f2354,f81,f12395]) ).
fof(f12395,plain,
( spl1_952
<=> ! [X0,X1] :
( eh = product(product(inv(product(X0,X1)),sK0),inv(product(inv(product(X0,X1)),sK0)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_952])]) ).
fof(f2354,plain,
( spl1_291
<=> ! [X2,X0,X1] :
( eh = product(product(inv(product(X0,X1)),X2),inv(product(inv(product(X0,X1)),X2)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_291])]) ).
fof(f4868,plain,
( ! [X0,X1] :
( eh = product(product(inv(product(X0,X1)),sK0),inv(product(inv(product(X0,X1)),sK0)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_291 ),
inference(resolution,[],[f83,f2355]) ).
fof(f2355,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(product(inv(product(X0,X1)),X2),inv(product(inv(product(X0,X1)),X2)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_291 ),
inference(avatar_component_clause,[],[f2354]) ).
fof(f12393,plain,
( spl1_951
| ~ spl1_2
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f4866,f2346,f81,f12391]) ).
fof(f12391,plain,
( spl1_951
<=> ! [X0,X1] :
( eh = product(inv(product(inv(product(X0,X1)),sK0)),product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_951])]) ).
fof(f2346,plain,
( spl1_289
<=> ! [X2,X0,X1] :
( eh = product(inv(product(inv(product(X0,X1)),X2)),product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_289])]) ).
fof(f4866,plain,
( ! [X0,X1] :
( eh = product(inv(product(inv(product(X0,X1)),sK0)),product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_289 ),
inference(resolution,[],[f83,f2347]) ).
fof(f2347,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(inv(product(inv(product(X0,X1)),X2)),product(inv(product(X0,X1)),X2))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_289 ),
inference(avatar_component_clause,[],[f2346]) ).
fof(f12389,plain,
( spl1_950
| ~ spl1_2
| ~ spl1_286 ),
inference(avatar_split_clause,[],[f4865,f2334,f81,f12387]) ).
fof(f12387,plain,
( spl1_950
<=> ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,product(X1,sK0)))),inv(product(X0,product(X1,sK0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_950])]) ).
fof(f2334,plain,
( spl1_286
<=> ! [X2,X0,X1] :
( eh = product(inv(inv(product(X0,product(X1,X2)))),inv(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_286])]) ).
fof(f4865,plain,
( ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,product(X1,sK0)))),inv(product(X0,product(X1,sK0))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_286 ),
inference(resolution,[],[f83,f2335]) ).
fof(f2335,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| eh = product(inv(inv(product(X0,product(X1,X2)))),inv(product(X0,product(X1,X2))))
| ~ g(X1) )
| ~ spl1_286 ),
inference(avatar_component_clause,[],[f2334]) ).
fof(f12385,plain,
( spl1_949
| ~ spl1_2
| ~ spl1_285 ),
inference(avatar_split_clause,[],[f4864,f2330,f81,f12383]) ).
fof(f12383,plain,
( spl1_949
<=> ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(product(X0,product(X1,sK0))),inv(inv(product(X0,product(X1,sK0)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_949])]) ).
fof(f2330,plain,
( spl1_285
<=> ! [X2,X0,X1] :
( eh = product(inv(product(X0,product(X1,X2))),inv(inv(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_285])]) ).
fof(f4864,plain,
( ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(product(X0,product(X1,sK0))),inv(inv(product(X0,product(X1,sK0)))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_285 ),
inference(resolution,[],[f83,f2331]) ).
fof(f2331,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| eh = product(inv(product(X0,product(X1,X2))),inv(inv(product(X0,product(X1,X2)))))
| ~ g(X1) )
| ~ spl1_285 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f12256,plain,
( spl1_948
| ~ spl1_2
| ~ spl1_284 ),
inference(avatar_split_clause,[],[f4863,f2326,f81,f12254]) ).
fof(f12254,plain,
( spl1_948
<=> ! [X0,X1] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,product(X1,sK0)))),f(product(X0,product(X1,sK0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_948])]) ).
fof(f2326,plain,
( spl1_284
<=> ! [X2,X0,X1] :
( eg = sum(opp(f(product(X0,product(X1,X2)))),f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_284])]) ).
fof(f4863,plain,
( ! [X0,X1] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,product(X1,sK0)))),f(product(X0,product(X1,sK0))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_284 ),
inference(resolution,[],[f83,f2327]) ).
fof(f2327,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| eg = sum(opp(f(product(X0,product(X1,X2)))),f(product(X0,product(X1,X2))))
| ~ g(X1) )
| ~ spl1_284 ),
inference(avatar_component_clause,[],[f2326]) ).
fof(f12252,plain,
( spl1_947
| ~ spl1_2
| ~ spl1_283 ),
inference(avatar_split_clause,[],[f4862,f2322,f81,f12250]) ).
fof(f12250,plain,
( spl1_947
<=> ! [X0,X1] :
( ~ g(X0)
| eg = sum(f(product(X0,product(X1,sK0))),opp(f(product(X0,product(X1,sK0)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_947])]) ).
fof(f2322,plain,
( spl1_283
<=> ! [X2,X0,X1] :
( eg = sum(f(product(X0,product(X1,X2))),opp(f(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_283])]) ).
fof(f4862,plain,
( ! [X0,X1] :
( ~ g(X0)
| eg = sum(f(product(X0,product(X1,sK0))),opp(f(product(X0,product(X1,sK0)))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_283 ),
inference(resolution,[],[f83,f2323]) ).
fof(f2323,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| eg = sum(f(product(X0,product(X1,X2))),opp(f(product(X0,product(X1,X2)))))
| ~ g(X1) )
| ~ spl1_283 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f12172,plain,
( spl1_946
| ~ spl1_28
| ~ spl1_945 ),
inference(avatar_split_clause,[],[f12032,f11932,f239,f12169]) ).
fof(f11932,plain,
( spl1_945
<=> f(sK0) = sum(opp(opp(f(sK0))),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_945])]) ).
fof(f12032,plain,
( f(sK0) = opp(opp(f(sK0)))
| ~ spl1_28
| ~ spl1_945 ),
inference(superposition,[],[f11934,f240]) ).
fof(f11934,plain,
( f(sK0) = sum(opp(opp(f(sK0))),eg)
| ~ spl1_945 ),
inference(avatar_component_clause,[],[f11932]) ).
fof(f11935,plain,
( spl1_945
| ~ spl1_568
| ~ spl1_903 ),
inference(avatar_split_clause,[],[f11858,f11631,f5303,f11932]) ).
fof(f5303,plain,
( spl1_568
<=> eg = sum(opp(f(sK0)),f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_568])]) ).
fof(f11631,plain,
( spl1_903
<=> ! [X0] : f(sK0) = sum(opp(opp(X0)),sum(opp(X0),f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_903])]) ).
fof(f11858,plain,
( f(sK0) = sum(opp(opp(f(sK0))),eg)
| ~ spl1_568
| ~ spl1_903 ),
inference(superposition,[],[f11632,f5305]) ).
fof(f5305,plain,
( eg = sum(opp(f(sK0)),f(sK0))
| ~ spl1_568 ),
inference(avatar_component_clause,[],[f5303]) ).
fof(f11632,plain,
( ! [X0] : f(sK0) = sum(opp(opp(X0)),sum(opp(X0),f(sK0)))
| ~ spl1_903 ),
inference(avatar_component_clause,[],[f11631]) ).
fof(f11852,plain,
( spl1_944
| ~ spl1_560
| ~ spl1_902 ),
inference(avatar_split_clause,[],[f11629,f11626,f5239,f11850]) ).
fof(f11850,plain,
( spl1_944
<=> ! [X0,X1] :
( f(product(X0,product(X1,sK0))) = f(product(eh,product(X0,product(X1,sK0))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_944])]) ).
fof(f11626,plain,
( spl1_902
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(eg,f(product(X0,product(X1,sK0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_902])]) ).
fof(f11629,plain,
( ! [X0,X1] :
( f(product(X0,product(X1,sK0))) = f(product(eh,product(X0,product(X1,sK0))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_560
| ~ spl1_902 ),
inference(forward_demodulation,[],[f11627,f5240]) ).
fof(f11627,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(eg,f(product(X0,product(X1,sK0))))
| ~ g(X1) )
| ~ spl1_902 ),
inference(avatar_component_clause,[],[f11626]) ).
fof(f11848,plain,
( spl1_943
| ~ spl1_561
| ~ spl1_901 ),
inference(avatar_split_clause,[],[f11624,f11621,f5243,f11846]) ).
fof(f11846,plain,
( spl1_943
<=> ! [X0,X1] :
( f(product(X0,product(X1,sK0))) = f(product(product(X0,product(X1,sK0)),eh))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_943])]) ).
fof(f11621,plain,
( spl1_901
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(f(product(X0,product(X1,sK0))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_901])]) ).
fof(f11624,plain,
( ! [X0,X1] :
( f(product(X0,product(X1,sK0))) = f(product(product(X0,product(X1,sK0)),eh))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_561
| ~ spl1_901 ),
inference(forward_demodulation,[],[f11622,f5244]) ).
fof(f11622,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(f(product(X0,product(X1,sK0))),eg)
| ~ g(X1) )
| ~ spl1_901 ),
inference(avatar_component_clause,[],[f11621]) ).
fof(f11806,plain,
( ~ spl1_3
| spl1_942
| ~ spl1_1
| ~ spl1_20
| ~ spl1_712 ),
inference(avatar_split_clause,[],[f7247,f7226,f182,f77,f11804,f86]) ).
fof(f86,plain,
( spl1_3
<=> h(eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f11804,plain,
( spl1_942
<=> ! [X0,X1] :
( sum(f(X0),sum(eg,X1)) = sum(f(product(X0,eh)),X1)
| ~ g(X0)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_942])]) ).
fof(f182,plain,
( spl1_20
<=> eh = product(eh,eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f7226,plain,
( spl1_712
<=> ! [X2,X0,X1] :
( sum(f(X2),sum(f(product(eh,X0)),X1)) = sum(f(product(X2,product(eh,X0))),X1)
| ~ h(f(X0))
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_712])]) ).
fof(f7247,plain,
( ! [X0,X1] :
( sum(f(X0),sum(eg,X1)) = sum(f(product(X0,eh)),X1)
| ~ h(eg)
| ~ h(X1)
| ~ g(X0) )
| ~ spl1_1
| ~ spl1_20
| ~ spl1_712 ),
inference(forward_demodulation,[],[f7246,f78]) ).
fof(f7246,plain,
( ! [X0,X1] :
( sum(f(product(X0,eh)),X1) = sum(f(X0),sum(f(eh),X1))
| ~ h(eg)
| ~ h(X1)
| ~ g(X0) )
| ~ spl1_1
| ~ spl1_20
| ~ spl1_712 ),
inference(forward_demodulation,[],[f7245,f184]) ).
fof(f184,plain,
( eh = product(eh,eh)
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f7245,plain,
( ! [X0,X1] :
( ~ h(eg)
| sum(f(X0),sum(f(product(eh,eh)),X1)) = sum(f(product(X0,product(eh,eh))),X1)
| ~ h(X1)
| ~ g(X0) )
| ~ spl1_1
| ~ spl1_712 ),
inference(superposition,[],[f7227,f78]) ).
fof(f7227,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(X2),sum(f(product(eh,X0)),X1)) = sum(f(product(X2,product(eh,X0))),X1)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_712 ),
inference(avatar_component_clause,[],[f7226]) ).
fof(f11802,plain,
( spl1_941
| ~ spl1_4
| ~ spl1_557
| ~ spl1_696 ),
inference(avatar_split_clause,[],[f7113,f7080,f5214,f91,f11800]) ).
fof(f11800,plain,
( spl1_941
<=> ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(product(product(X0,inv(X1)),eh),sK0)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_941])]) ).
fof(f5214,plain,
( spl1_557
<=> sK0 = product(eh,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_557])]) ).
fof(f7113,plain,
( ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(product(product(X0,inv(X1)),eh),sK0)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_557
| ~ spl1_696 ),
inference(forward_demodulation,[],[f7111,f5216]) ).
fof(f5216,plain,
( sK0 = product(eh,sK0)
| ~ spl1_557 ),
inference(avatar_component_clause,[],[f5214]) ).
fof(f7111,plain,
( ! [X0,X1] :
( product(product(product(X0,inv(X1)),eh),sK0) = product(product(X0,inv(X1)),product(eh,sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_696 ),
inference(resolution,[],[f7081,f93]) ).
fof(f11798,plain,
( spl1_940
| ~ spl1_4
| ~ spl1_557
| ~ spl1_695 ),
inference(avatar_split_clause,[],[f7103,f7076,f5214,f91,f11796]) ).
fof(f11796,plain,
( spl1_940
<=> ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(product(inv(product(X0,X1)),eh),sK0)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_940])]) ).
fof(f7103,plain,
( ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(product(inv(product(X0,X1)),eh),sK0)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_557
| ~ spl1_695 ),
inference(forward_demodulation,[],[f7101,f5216]) ).
fof(f7101,plain,
( ! [X0,X1] :
( product(product(inv(product(X0,X1)),eh),sK0) = product(inv(product(X0,X1)),product(eh,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_695 ),
inference(resolution,[],[f7077,f93]) ).
fof(f11794,plain,
( spl1_939
| ~ spl1_5
| ~ spl1_670 ),
inference(avatar_split_clause,[],[f6826,f6762,f96,f11792]) ).
fof(f11792,plain,
( spl1_939
<=> ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(opp(X0),f(product(eh,product(X1,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_939])]) ).
fof(f6762,plain,
( spl1_670
<=> ! [X0,X1] :
( sum(opp(X1),f(product(X0,eh))) = sum(opp(X1),f(product(eh,product(X0,eh))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_670])]) ).
fof(f6826,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(opp(X0),f(product(eh,product(X1,eh))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_670 ),
inference(resolution,[],[f6763,f97]) ).
fof(f6763,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(opp(X1),f(product(eh,product(X0,eh)))) )
| ~ spl1_670 ),
inference(avatar_component_clause,[],[f6762]) ).
fof(f11790,plain,
( spl1_938
| ~ spl1_5
| ~ spl1_669 ),
inference(avatar_split_clause,[],[f6820,f6758,f96,f11788]) ).
fof(f11788,plain,
( spl1_938
<=> ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(sum(opp(X0),f(product(X1,eh))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_938])]) ).
fof(f6758,plain,
( spl1_669
<=> ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(sum(opp(X1),f(product(X0,eh))),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_669])]) ).
fof(f6820,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(sum(opp(X0),f(product(X1,eh))),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_669 ),
inference(resolution,[],[f6759,f97]) ).
fof(f6759,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(sum(opp(X1),f(product(X0,eh))),eg) )
| ~ spl1_669 ),
inference(avatar_component_clause,[],[f6758]) ).
fof(f11786,plain,
( spl1_937
| ~ spl1_5
| ~ spl1_668 ),
inference(avatar_split_clause,[],[f6814,f6754,f96,f11784]) ).
fof(f11784,plain,
( spl1_937
<=> ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(eg,sum(opp(X0),f(product(X1,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_937])]) ).
fof(f6754,plain,
( spl1_668
<=> ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(eg,sum(opp(X1),f(product(X0,eh)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_668])]) ).
fof(f6814,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(X1,eh))) = sum(eg,sum(opp(X0),f(product(X1,eh))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_668 ),
inference(resolution,[],[f6755,f97]) ).
fof(f6755,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(eg,sum(opp(X1),f(product(X0,eh)))) )
| ~ spl1_668 ),
inference(avatar_component_clause,[],[f6754]) ).
fof(f11782,plain,
( spl1_936
| ~ spl1_5
| ~ spl1_667 ),
inference(avatar_split_clause,[],[f6807,f6750,f96,f11780]) ).
fof(f11780,plain,
( spl1_936
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(product(X1,eh)),X0) = sum(sum(f(product(X1,eh)),X0),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_936])]) ).
fof(f6750,plain,
( spl1_667
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(sum(f(product(X0,eh)),X1),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_667])]) ).
fof(f6807,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(product(X1,eh)),X0) = sum(sum(f(product(X1,eh)),X0),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_667 ),
inference(resolution,[],[f6751,f97]) ).
fof(f6751,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(sum(f(product(X0,eh)),X1),eg) )
| ~ spl1_667 ),
inference(avatar_component_clause,[],[f6750]) ).
fof(f11761,plain,
( spl1_935
| ~ spl1_5
| ~ spl1_666 ),
inference(avatar_split_clause,[],[f6800,f6746,f96,f11759]) ).
fof(f11759,plain,
( spl1_935
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(product(X1,eh)),X0) = sum(eg,sum(f(product(X1,eh)),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_935])]) ).
fof(f6746,plain,
( spl1_666
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(eg,sum(f(product(X0,eh)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_666])]) ).
fof(f6800,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(product(X1,eh)),X0) = sum(eg,sum(f(product(X1,eh)),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_666 ),
inference(resolution,[],[f6747,f97]) ).
fof(f6747,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(eg,sum(f(product(X0,eh)),X1)) )
| ~ spl1_666 ),
inference(avatar_component_clause,[],[f6746]) ).
fof(f11757,plain,
( spl1_934
| ~ spl1_5
| ~ spl1_665 ),
inference(avatar_split_clause,[],[f6794,f6742,f96,f11755]) ).
fof(f11755,plain,
( spl1_934
<=> ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(opp(X0),f(product(eh,product(eh,X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_934])]) ).
fof(f6742,plain,
( spl1_665
<=> ! [X0,X1] :
( sum(opp(X1),f(product(eh,X0))) = sum(opp(X1),f(product(eh,product(eh,X0))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_665])]) ).
fof(f6794,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(opp(X0),f(product(eh,product(eh,X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_665 ),
inference(resolution,[],[f6743,f97]) ).
fof(f6743,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(opp(X1),f(product(eh,product(eh,X0)))) )
| ~ spl1_665 ),
inference(avatar_component_clause,[],[f6742]) ).
fof(f11753,plain,
( spl1_933
| ~ spl1_5
| ~ spl1_664 ),
inference(avatar_split_clause,[],[f6788,f6738,f96,f11751]) ).
fof(f11751,plain,
( spl1_933
<=> ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(sum(opp(X0),f(product(eh,X1))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_933])]) ).
fof(f6738,plain,
( spl1_664
<=> ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(sum(opp(X1),f(product(eh,X0))),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_664])]) ).
fof(f6788,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(sum(opp(X0),f(product(eh,X1))),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_664 ),
inference(resolution,[],[f6739,f97]) ).
fof(f6739,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(sum(opp(X1),f(product(eh,X0))),eg) )
| ~ spl1_664 ),
inference(avatar_component_clause,[],[f6738]) ).
fof(f11749,plain,
( spl1_932
| ~ spl1_5
| ~ spl1_663 ),
inference(avatar_split_clause,[],[f6782,f6734,f96,f11747]) ).
fof(f11747,plain,
( spl1_932
<=> ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(eg,sum(opp(X0),f(product(eh,X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_932])]) ).
fof(f6734,plain,
( spl1_663
<=> ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(eg,sum(opp(X1),f(product(eh,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_663])]) ).
fof(f6782,plain,
( ! [X0,X1] :
( sum(opp(X0),f(product(eh,X1))) = sum(eg,sum(opp(X0),f(product(eh,X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_663 ),
inference(resolution,[],[f6735,f97]) ).
fof(f6735,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(eg,sum(opp(X1),f(product(eh,X0)))) )
| ~ spl1_663 ),
inference(avatar_component_clause,[],[f6734]) ).
fof(f11745,plain,
( spl1_931
| ~ spl1_5
| ~ spl1_662 ),
inference(avatar_split_clause,[],[f6775,f6730,f96,f11743]) ).
fof(f11743,plain,
( spl1_931
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(product(eh,X1)),X0) = sum(sum(f(product(eh,X1)),X0),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_931])]) ).
fof(f6730,plain,
( spl1_662
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(sum(f(product(eh,X0)),X1),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_662])]) ).
fof(f6775,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(product(eh,X1)),X0) = sum(sum(f(product(eh,X1)),X0),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_662 ),
inference(resolution,[],[f6731,f97]) ).
fof(f6731,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(sum(f(product(eh,X0)),X1),eg) )
| ~ spl1_662 ),
inference(avatar_component_clause,[],[f6730]) ).
fof(f11741,plain,
( spl1_930
| ~ spl1_5
| ~ spl1_660 ),
inference(avatar_split_clause,[],[f6765,f6721,f96,f11739]) ).
fof(f11739,plain,
( spl1_930
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(product(eh,X1)),X0) = sum(eg,sum(f(product(eh,X1)),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_930])]) ).
fof(f6721,plain,
( spl1_660
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(eg,sum(f(product(eh,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_660])]) ).
fof(f6765,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(product(eh,X1)),X0) = sum(eg,sum(f(product(eh,X1)),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_660 ),
inference(resolution,[],[f6722,f97]) ).
fof(f6722,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(eg,sum(f(product(eh,X0)),X1)) )
| ~ spl1_660 ),
inference(avatar_component_clause,[],[f6721]) ).
fof(f11737,plain,
( spl1_929
| ~ spl1_6
| ~ spl1_635 ),
inference(avatar_split_clause,[],[f6499,f6474,f100,f11735]) ).
fof(f11735,plain,
( spl1_929
<=> ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(sK0,product(eh,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_929])]) ).
fof(f6474,plain,
( spl1_635
<=> ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(sK0,product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_635])]) ).
fof(f6499,plain,
( ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(sK0,product(eh,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_635 ),
inference(resolution,[],[f6475,f101]) ).
fof(f6475,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(sK0,product(X0,X1)) = product(sK0,product(eh,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_635 ),
inference(avatar_component_clause,[],[f6474]) ).
fof(f11733,plain,
( spl1_928
| ~ spl1_6
| ~ spl1_634 ),
inference(avatar_split_clause,[],[f6495,f6470,f100,f11731]) ).
fof(f11731,plain,
( spl1_928
<=> ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(product(sK0,product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_928])]) ).
fof(f6470,plain,
( spl1_634
<=> ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(product(sK0,product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_634])]) ).
fof(f6495,plain,
( ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(product(sK0,product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_634 ),
inference(resolution,[],[f6471,f101]) ).
fof(f6471,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(sK0,product(X0,X1)) = product(product(sK0,product(X0,X1)),eh)
| ~ g(X0) )
| ~ spl1_634 ),
inference(avatar_component_clause,[],[f6470]) ).
fof(f11729,plain,
( spl1_927
| ~ spl1_6
| ~ spl1_633 ),
inference(avatar_split_clause,[],[f6491,f6466,f100,f11727]) ).
fof(f11727,plain,
( spl1_927
<=> ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(eh,product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_927])]) ).
fof(f6466,plain,
( spl1_633
<=> ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(eh,product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_633])]) ).
fof(f6491,plain,
( ! [X0,X1] :
( product(sK0,product(X0,inv(X1))) = product(eh,product(sK0,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_633 ),
inference(resolution,[],[f6467,f101]) ).
fof(f6467,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(sK0,product(X0,X1)) = product(eh,product(sK0,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_633 ),
inference(avatar_component_clause,[],[f6466]) ).
fof(f11725,plain,
( spl1_926
| ~ spl1_6
| ~ spl1_632 ),
inference(avatar_split_clause,[],[f6487,f6462,f100,f11723]) ).
fof(f11723,plain,
( spl1_926
<=> ! [X0,X1] :
( product(product(X0,sK0),inv(X1)) = product(product(product(X0,sK0),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_926])]) ).
fof(f6462,plain,
( spl1_632
<=> ! [X0,X1] :
( product(product(X0,sK0),X1) = product(product(product(X0,sK0),X1),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_632])]) ).
fof(f6487,plain,
( ! [X0,X1] :
( product(product(X0,sK0),inv(X1)) = product(product(product(X0,sK0),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_632 ),
inference(resolution,[],[f6463,f101]) ).
fof(f6463,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(X0,sK0),X1) = product(product(product(X0,sK0),X1),eh)
| ~ g(X0) )
| ~ spl1_632 ),
inference(avatar_component_clause,[],[f6462]) ).
fof(f11721,plain,
( spl1_925
| ~ spl1_29
| ~ spl1_567
| ~ spl1_861 ),
inference(avatar_split_clause,[],[f11170,f10980,f5298,f243,f11719]) ).
fof(f11719,plain,
( spl1_925
<=> ! [X0] : opp(X0) = sum(f(sK0),sum(opp(f(sK0)),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_925])]) ).
fof(f10980,plain,
( spl1_861
<=> ! [X0,X1] : sum(sum(f(sK0),opp(X0)),opp(X1)) = sum(f(sK0),sum(opp(X0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_861])]) ).
fof(f11170,plain,
( ! [X0] : opp(X0) = sum(f(sK0),sum(opp(f(sK0)),opp(X0)))
| ~ spl1_29
| ~ spl1_567
| ~ spl1_861 ),
inference(forward_demodulation,[],[f11158,f244]) ).
fof(f11158,plain,
( ! [X0] : sum(eg,opp(X0)) = sum(f(sK0),sum(opp(f(sK0)),opp(X0)))
| ~ spl1_567
| ~ spl1_861 ),
inference(superposition,[],[f10981,f5300]) ).
fof(f10981,plain,
( ! [X0,X1] : sum(sum(f(sK0),opp(X0)),opp(X1)) = sum(f(sK0),sum(opp(X0),opp(X1)))
| ~ spl1_861 ),
inference(avatar_component_clause,[],[f10980]) ).
fof(f11717,plain,
( spl1_924
| ~ spl1_6
| ~ spl1_631 ),
inference(avatar_split_clause,[],[f6483,f6458,f100,f11715]) ).
fof(f11715,plain,
( spl1_924
<=> ! [X0,X1] :
( product(product(X0,sK0),inv(X1)) = product(eh,product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_924])]) ).
fof(f6458,plain,
( spl1_631
<=> ! [X0,X1] :
( product(product(X0,sK0),X1) = product(eh,product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_631])]) ).
fof(f6483,plain,
( ! [X0,X1] :
( product(product(X0,sK0),inv(X1)) = product(eh,product(product(X0,sK0),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_631 ),
inference(resolution,[],[f6459,f101]) ).
fof(f6459,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(X0,sK0),X1) = product(eh,product(product(X0,sK0),X1))
| ~ g(X0) )
| ~ spl1_631 ),
inference(avatar_component_clause,[],[f6458]) ).
fof(f11713,plain,
( spl1_923
| ~ spl1_571
| ~ spl1_626 ),
inference(avatar_split_clause,[],[f6431,f6390,f5326,f11711]) ).
fof(f11711,plain,
( spl1_923
<=> ! [X0] :
( eg = sum(opp(f(product(product(eh,X0),eh))),f(product(product(eh,X0),eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_923])]) ).
fof(f6431,plain,
( ! [X0] :
( eg = sum(opp(f(product(product(eh,X0),eh))),f(product(product(eh,X0),eh)))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_626 ),
inference(resolution,[],[f6391,f5327]) ).
fof(f11709,plain,
( spl1_922
| ~ spl1_572
| ~ spl1_626 ),
inference(avatar_split_clause,[],[f6430,f6390,f5638,f11707]) ).
fof(f11707,plain,
( spl1_922
<=> ! [X0] :
( eg = sum(opp(f(product(product(X0,eh),eh))),f(product(product(X0,eh),eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_922])]) ).
fof(f6430,plain,
( ! [X0] :
( eg = sum(opp(f(product(product(X0,eh),eh))),f(product(product(X0,eh),eh)))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_626 ),
inference(resolution,[],[f6391,f5639]) ).
fof(f11705,plain,
( spl1_921
| ~ spl1_571
| ~ spl1_625 ),
inference(avatar_split_clause,[],[f6425,f6386,f5326,f11703]) ).
fof(f11703,plain,
( spl1_921
<=> ! [X0] :
( eg = sum(f(product(product(eh,X0),eh)),opp(f(product(product(eh,X0),eh))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_921])]) ).
fof(f6425,plain,
( ! [X0] :
( eg = sum(f(product(product(eh,X0),eh)),opp(f(product(product(eh,X0),eh))))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_625 ),
inference(resolution,[],[f6387,f5327]) ).
fof(f11701,plain,
( spl1_920
| ~ spl1_572
| ~ spl1_625 ),
inference(avatar_split_clause,[],[f6424,f6386,f5638,f11699]) ).
fof(f11699,plain,
( spl1_920
<=> ! [X0] :
( eg = sum(f(product(product(X0,eh),eh)),opp(f(product(product(X0,eh),eh))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_920])]) ).
fof(f6424,plain,
( ! [X0] :
( eg = sum(f(product(product(X0,eh),eh)),opp(f(product(product(X0,eh),eh))))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_625 ),
inference(resolution,[],[f6387,f5639]) ).
fof(f11697,plain,
( spl1_919
| ~ spl1_19
| ~ spl1_607 ),
inference(avatar_split_clause,[],[f6241,f6192,f164,f11695]) ).
fof(f11695,plain,
( spl1_919
<=> ! [X0,X1] :
( f(product(product(X0,X1),sK0)) = f(product(eh,product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_919])]) ).
fof(f6192,plain,
( spl1_607
<=> ! [X0] :
( f(product(X0,sK0)) = f(product(eh,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_607])]) ).
fof(f6241,plain,
( ! [X0,X1] :
( f(product(product(X0,X1),sK0)) = f(product(eh,product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_607 ),
inference(resolution,[],[f6193,f165]) ).
fof(f6193,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,sK0)) = f(product(eh,product(X0,sK0))) )
| ~ spl1_607 ),
inference(avatar_component_clause,[],[f6192]) ).
fof(f11693,plain,
( spl1_918
| ~ spl1_19
| ~ spl1_606 ),
inference(avatar_split_clause,[],[f6236,f6188,f164,f11691]) ).
fof(f11691,plain,
( spl1_918
<=> ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(sK0,product(eh,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_918])]) ).
fof(f6188,plain,
( spl1_606
<=> ! [X0] :
( product(sK0,inv(X0)) = product(sK0,product(eh,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_606])]) ).
fof(f6236,plain,
( ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(sK0,product(eh,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_606 ),
inference(resolution,[],[f6189,f165]) ).
fof(f6189,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,inv(X0)) = product(sK0,product(eh,inv(X0))) )
| ~ spl1_606 ),
inference(avatar_component_clause,[],[f6188]) ).
fof(f11689,plain,
( spl1_917
| ~ spl1_19
| ~ spl1_605 ),
inference(avatar_split_clause,[],[f6229,f6184,f164,f11687]) ).
fof(f11687,plain,
( spl1_917
<=> ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(product(sK0,inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_917])]) ).
fof(f6184,plain,
( spl1_605
<=> ! [X0] :
( product(sK0,inv(X0)) = product(product(sK0,inv(X0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_605])]) ).
fof(f6229,plain,
( ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(product(sK0,inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_605 ),
inference(resolution,[],[f6185,f165]) ).
fof(f6185,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,inv(X0)) = product(product(sK0,inv(X0)),eh) )
| ~ spl1_605 ),
inference(avatar_component_clause,[],[f6184]) ).
fof(f11685,plain,
( spl1_916
| ~ spl1_19
| ~ spl1_604 ),
inference(avatar_split_clause,[],[f6222,f6180,f164,f11683]) ).
fof(f11683,plain,
( spl1_916
<=> ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(eh,product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_916])]) ).
fof(f6180,plain,
( spl1_604
<=> ! [X0] :
( product(sK0,inv(X0)) = product(eh,product(sK0,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_604])]) ).
fof(f6222,plain,
( ! [X0,X1] :
( product(sK0,inv(product(X0,X1))) = product(eh,product(sK0,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_604 ),
inference(resolution,[],[f6181,f165]) ).
fof(f6181,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,inv(X0)) = product(eh,product(sK0,inv(X0))) )
| ~ spl1_604 ),
inference(avatar_component_clause,[],[f6180]) ).
fof(f11681,plain,
( spl1_915
| ~ spl1_19
| ~ spl1_603 ),
inference(avatar_split_clause,[],[f6216,f6176,f164,f11679]) ).
fof(f11679,plain,
( spl1_915
<=> ! [X0,X1] :
( product(inv(sK0),product(X0,X1)) = product(product(inv(sK0),product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_915])]) ).
fof(f6176,plain,
( spl1_603
<=> ! [X0] :
( product(inv(sK0),X0) = product(product(inv(sK0),X0),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_603])]) ).
fof(f6216,plain,
( ! [X0,X1] :
( product(inv(sK0),product(X0,X1)) = product(product(inv(sK0),product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_603 ),
inference(resolution,[],[f6177,f165]) ).
fof(f6177,plain,
( ! [X0] :
( ~ g(X0)
| product(inv(sK0),X0) = product(product(inv(sK0),X0),eh) )
| ~ spl1_603 ),
inference(avatar_component_clause,[],[f6176]) ).
fof(f11677,plain,
( spl1_914
| ~ spl1_29
| ~ spl1_568
| ~ spl1_860 ),
inference(avatar_split_clause,[],[f11149,f10976,f5303,f243,f11675]) ).
fof(f11675,plain,
( spl1_914
<=> ! [X0] : opp(X0) = sum(opp(f(sK0)),sum(f(sK0),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_914])]) ).
fof(f10976,plain,
( spl1_860
<=> ! [X0,X1] : sum(sum(opp(X0),f(sK0)),opp(X1)) = sum(opp(X0),sum(f(sK0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_860])]) ).
fof(f11149,plain,
( ! [X0] : opp(X0) = sum(opp(f(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_29
| ~ spl1_568
| ~ spl1_860 ),
inference(forward_demodulation,[],[f11137,f244]) ).
fof(f11137,plain,
( ! [X0] : sum(eg,opp(X0)) = sum(opp(f(sK0)),sum(f(sK0),opp(X0)))
| ~ spl1_568
| ~ spl1_860 ),
inference(superposition,[],[f10977,f5305]) ).
fof(f10977,plain,
( ! [X0,X1] : sum(sum(opp(X0),f(sK0)),opp(X1)) = sum(opp(X0),sum(f(sK0),opp(X1)))
| ~ spl1_860 ),
inference(avatar_component_clause,[],[f10976]) ).
fof(f11673,plain,
( spl1_913
| ~ spl1_19
| ~ spl1_602 ),
inference(avatar_split_clause,[],[f6210,f6172,f164,f11671]) ).
fof(f11671,plain,
( spl1_913
<=> ! [X0,X1] :
( product(inv(sK0),product(X0,X1)) = product(eh,product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_913])]) ).
fof(f6172,plain,
( spl1_602
<=> ! [X0] :
( product(inv(sK0),X0) = product(eh,product(inv(sK0),X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_602])]) ).
fof(f6210,plain,
( ! [X0,X1] :
( product(inv(sK0),product(X0,X1)) = product(eh,product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_602 ),
inference(resolution,[],[f6173,f165]) ).
fof(f6173,plain,
( ! [X0] :
( ~ g(X0)
| product(inv(sK0),X0) = product(eh,product(inv(sK0),X0)) )
| ~ spl1_602 ),
inference(avatar_component_clause,[],[f6172]) ).
fof(f11669,plain,
( spl1_912
| ~ spl1_19
| ~ spl1_601 ),
inference(avatar_split_clause,[],[f6205,f6168,f164,f11667]) ).
fof(f11667,plain,
( spl1_912
<=> ! [X0,X1] :
( inv(product(product(X0,X1),sK0)) = product(eh,inv(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_912])]) ).
fof(f6168,plain,
( spl1_601
<=> ! [X0] :
( inv(product(X0,sK0)) = product(eh,inv(product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_601])]) ).
fof(f6205,plain,
( ! [X0,X1] :
( inv(product(product(X0,X1),sK0)) = product(eh,inv(product(product(X0,X1),sK0)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_601 ),
inference(resolution,[],[f6169,f165]) ).
fof(f6169,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,sK0)) = product(eh,inv(product(X0,sK0))) )
| ~ spl1_601 ),
inference(avatar_component_clause,[],[f6168]) ).
fof(f11665,plain,
( spl1_911
| ~ spl1_19
| ~ spl1_600 ),
inference(avatar_split_clause,[],[f6195,f6164,f164,f11663]) ).
fof(f11663,plain,
( spl1_911
<=> ! [X0,X1] :
( inv(product(product(X0,X1),sK0)) = product(inv(product(product(X0,X1),sK0)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_911])]) ).
fof(f6164,plain,
( spl1_600
<=> ! [X0] :
( inv(product(X0,sK0)) = product(inv(product(X0,sK0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_600])]) ).
fof(f6195,plain,
( ! [X0,X1] :
( inv(product(product(X0,X1),sK0)) = product(inv(product(product(X0,X1),sK0)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_600 ),
inference(resolution,[],[f6165,f165]) ).
fof(f6165,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,sK0)) = product(inv(product(X0,sK0)),eh) )
| ~ spl1_600 ),
inference(avatar_component_clause,[],[f6164]) ).
fof(f11661,plain,
( spl1_910
| ~ spl1_2
| ~ spl1_273 ),
inference(avatar_split_clause,[],[f4861,f2208,f81,f11659]) ).
fof(f11659,plain,
( spl1_910
<=> ! [X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),opp(X1)),f(sK0)) = sum(f(X0),sum(opp(X1),f(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_910])]) ).
fof(f2208,plain,
( spl1_273
<=> ! [X2,X0,X1] :
( sum(sum(f(X0),opp(X1)),f(X2)) = sum(f(X0),sum(opp(X1),f(X2)))
| ~ g(X0)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_273])]) ).
fof(f4861,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),opp(X1)),f(sK0)) = sum(f(X0),sum(opp(X1),f(sK0))) )
| ~ spl1_2
| ~ spl1_273 ),
inference(resolution,[],[f83,f2209]) ).
fof(f2209,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| sum(sum(f(X0),opp(X1)),f(X2)) = sum(f(X0),sum(opp(X1),f(X2))) )
| ~ spl1_273 ),
inference(avatar_component_clause,[],[f2208]) ).
fof(f11657,plain,
( spl1_909
| ~ spl1_2
| ~ spl1_272 ),
inference(avatar_split_clause,[],[f4860,f2204,f81,f11655]) ).
fof(f11655,plain,
( spl1_909
<=> ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(product(product(X0,inv(X1)),sK0),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_909])]) ).
fof(f2204,plain,
( spl1_272
<=> ! [X2,X0,X1] :
( product(product(X0,inv(X1)),X2) = product(product(product(X0,inv(X1)),X2),eh)
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_272])]) ).
fof(f4860,plain,
( ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(product(product(X0,inv(X1)),sK0),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_272 ),
inference(resolution,[],[f83,f2205]) ).
fof(f2205,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(X0,inv(X1)),X2) = product(product(product(X0,inv(X1)),X2),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_272 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f11653,plain,
( spl1_908
| ~ spl1_2
| ~ spl1_271 ),
inference(avatar_split_clause,[],[f4859,f2200,f81,f11651]) ).
fof(f11651,plain,
( spl1_908
<=> ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(eh,product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_908])]) ).
fof(f2200,plain,
( spl1_271
<=> ! [X2,X0,X1] :
( product(product(X0,inv(X1)),X2) = product(eh,product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_271])]) ).
fof(f4859,plain,
( ! [X0,X1] :
( product(product(X0,inv(X1)),sK0) = product(eh,product(product(X0,inv(X1)),sK0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_271 ),
inference(resolution,[],[f83,f2201]) ).
fof(f2201,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(X0,inv(X1)),X2) = product(eh,product(product(X0,inv(X1)),X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_271 ),
inference(avatar_component_clause,[],[f2200]) ).
fof(f11649,plain,
( spl1_907
| ~ spl1_2
| ~ spl1_268 ),
inference(avatar_split_clause,[],[f4858,f2188,f81,f11647]) ).
fof(f11647,plain,
( spl1_907
<=> ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(product(inv(product(X0,X1)),sK0),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_907])]) ).
fof(f2188,plain,
( spl1_268
<=> ! [X2,X0,X1] :
( product(inv(product(X0,X1)),X2) = product(product(inv(product(X0,X1)),X2),eh)
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_268])]) ).
fof(f4858,plain,
( ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(product(inv(product(X0,X1)),sK0),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_268 ),
inference(resolution,[],[f83,f2189]) ).
fof(f2189,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(inv(product(X0,X1)),X2) = product(product(inv(product(X0,X1)),X2),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_268 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f11645,plain,
( spl1_906
| ~ spl1_2
| ~ spl1_267 ),
inference(avatar_split_clause,[],[f4857,f2184,f81,f11643]) ).
fof(f11643,plain,
( spl1_906
<=> ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(eh,product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_906])]) ).
fof(f2184,plain,
( spl1_267
<=> ! [X2,X0,X1] :
( product(inv(product(X0,X1)),X2) = product(eh,product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_267])]) ).
fof(f4857,plain,
( ! [X0,X1] :
( product(inv(product(X0,X1)),sK0) = product(eh,product(inv(product(X0,X1)),sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_267 ),
inference(resolution,[],[f83,f2185]) ).
fof(f2185,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(inv(product(X0,X1)),X2) = product(eh,product(inv(product(X0,X1)),X2))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_267 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f11641,plain,
( spl1_905
| ~ spl1_2
| ~ spl1_263 ),
inference(avatar_split_clause,[],[f4856,f2168,f81,f11639]) ).
fof(f11639,plain,
( spl1_905
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,sK0))) = product(eh,inv(product(X0,product(X1,sK0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_905])]) ).
fof(f2168,plain,
( spl1_263
<=> ! [X2,X0,X1] :
( inv(product(X0,product(X1,X2))) = product(eh,inv(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_263])]) ).
fof(f4856,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,sK0))) = product(eh,inv(product(X0,product(X1,sK0))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_263 ),
inference(resolution,[],[f83,f2169]) ).
fof(f2169,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| inv(product(X0,product(X1,X2))) = product(eh,inv(product(X0,product(X1,X2))))
| ~ g(X1) )
| ~ spl1_263 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f11637,plain,
( spl1_904
| ~ spl1_2
| ~ spl1_262 ),
inference(avatar_split_clause,[],[f4855,f2164,f81,f11635]) ).
fof(f11635,plain,
( spl1_904
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,sK0))) = product(inv(product(X0,product(X1,sK0))),eh)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_904])]) ).
fof(f2164,plain,
( spl1_262
<=> ! [X2,X0,X1] :
( inv(product(X0,product(X1,X2))) = product(inv(product(X0,product(X1,X2))),eh)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_262])]) ).
fof(f4855,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,sK0))) = product(inv(product(X0,product(X1,sK0))),eh)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_262 ),
inference(resolution,[],[f83,f2165]) ).
fof(f2165,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| inv(product(X0,product(X1,X2))) = product(inv(product(X0,product(X1,X2))),eh)
| ~ g(X1) )
| ~ spl1_262 ),
inference(avatar_component_clause,[],[f2164]) ).
fof(f11633,plain,
( spl1_903
| ~ spl1_32
| ~ spl1_557
| ~ spl1_560
| ~ spl1_859 ),
inference(avatar_split_clause,[],[f11133,f10972,f5239,f5214,f262,f11631]) ).
fof(f262,plain,
( spl1_32
<=> ! [X0] : eg = sum(opp(opp(X0)),opp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f10972,plain,
( spl1_859
<=> ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(sK0)) = sum(opp(X0),sum(opp(X1),f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_859])]) ).
fof(f11133,plain,
( ! [X0] : f(sK0) = sum(opp(opp(X0)),sum(opp(X0),f(sK0)))
| ~ spl1_32
| ~ spl1_557
| ~ spl1_560
| ~ spl1_859 ),
inference(forward_demodulation,[],[f11132,f5216]) ).
fof(f11132,plain,
( ! [X0] : f(product(eh,sK0)) = sum(opp(opp(X0)),sum(opp(X0),f(sK0)))
| ~ spl1_32
| ~ spl1_560
| ~ spl1_859 ),
inference(forward_demodulation,[],[f11120,f5240]) ).
fof(f11120,plain,
( ! [X0] : sum(eg,f(sK0)) = sum(opp(opp(X0)),sum(opp(X0),f(sK0)))
| ~ spl1_32
| ~ spl1_859 ),
inference(superposition,[],[f10973,f263]) ).
fof(f263,plain,
( ! [X0] : eg = sum(opp(opp(X0)),opp(X0))
| ~ spl1_32 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f10973,plain,
( ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(sK0)) = sum(opp(X0),sum(opp(X1),f(sK0)))
| ~ spl1_859 ),
inference(avatar_component_clause,[],[f10972]) ).
fof(f11628,plain,
( spl1_902
| ~ spl1_2
| ~ spl1_261 ),
inference(avatar_split_clause,[],[f4854,f2160,f81,f11626]) ).
fof(f2160,plain,
( spl1_261
<=> ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(eg,f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_261])]) ).
fof(f4854,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(eg,f(product(X0,product(X1,sK0))))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_261 ),
inference(resolution,[],[f83,f2161]) ).
fof(f2161,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| f(product(X0,product(X1,X2))) = sum(eg,f(product(X0,product(X1,X2))))
| ~ g(X1) )
| ~ spl1_261 ),
inference(avatar_component_clause,[],[f2160]) ).
fof(f11623,plain,
( spl1_901
| ~ spl1_2
| ~ spl1_260 ),
inference(avatar_split_clause,[],[f4853,f2156,f81,f11621]) ).
fof(f2156,plain,
( spl1_260
<=> ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(f(product(X0,product(X1,X2))),eg)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_260])]) ).
fof(f4853,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,sK0))) = sum(f(product(X0,product(X1,sK0))),eg)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_260 ),
inference(resolution,[],[f83,f2157]) ).
fof(f2157,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| f(product(X0,product(X1,X2))) = sum(f(product(X0,product(X1,X2))),eg)
| ~ g(X1) )
| ~ spl1_260 ),
inference(avatar_component_clause,[],[f2156]) ).
fof(f11511,plain,
( spl1_900
| ~ spl1_31
| ~ spl1_557
| ~ spl1_560
| ~ spl1_859 ),
inference(avatar_split_clause,[],[f11131,f10972,f5239,f5214,f258,f11509]) ).
fof(f258,plain,
( spl1_31
<=> ! [X0] : eg = sum(opp(X0),opp(opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f11131,plain,
( ! [X0] : f(sK0) = sum(opp(X0),sum(opp(opp(X0)),f(sK0)))
| ~ spl1_31
| ~ spl1_557
| ~ spl1_560
| ~ spl1_859 ),
inference(forward_demodulation,[],[f11130,f5216]) ).
fof(f11130,plain,
( ! [X0] : f(product(eh,sK0)) = sum(opp(X0),sum(opp(opp(X0)),f(sK0)))
| ~ spl1_31
| ~ spl1_560
| ~ spl1_859 ),
inference(forward_demodulation,[],[f11119,f5240]) ).
fof(f11119,plain,
( ! [X0] : sum(eg,f(sK0)) = sum(opp(X0),sum(opp(opp(X0)),f(sK0)))
| ~ spl1_31
| ~ spl1_859 ),
inference(superposition,[],[f10973,f259]) ).
fof(f259,plain,
( ! [X0] : eg = sum(opp(X0),opp(opp(X0)))
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f11482,plain,
( spl1_899
| ~ spl1_5
| ~ spl1_652 ),
inference(avatar_split_clause,[],[f6681,f6610,f96,f11480]) ).
fof(f11480,plain,
( spl1_899
<=> ! [X0] :
( eg = sum(f(product(eh,product(X0,eh))),opp(f(product(eh,product(X0,eh)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_899])]) ).
fof(f6610,plain,
( spl1_652
<=> ! [X0] :
( eg = sum(f(product(eh,product(X0,eh))),opp(f(product(eh,product(X0,eh)))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_652])]) ).
fof(f6681,plain,
( ! [X0] :
( eg = sum(f(product(eh,product(X0,eh))),opp(f(product(eh,product(X0,eh)))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_652 ),
inference(resolution,[],[f6611,f97]) ).
fof(f6611,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(eh,product(X0,eh))),opp(f(product(eh,product(X0,eh))))) )
| ~ spl1_652 ),
inference(avatar_component_clause,[],[f6610]) ).
fof(f11478,plain,
( spl1_898
| ~ spl1_5
| ~ spl1_651 ),
inference(avatar_split_clause,[],[f6674,f6606,f96,f11476]) ).
fof(f11476,plain,
( spl1_898
<=> ! [X0] :
( eg = sum(opp(f(product(eh,product(X0,eh)))),f(product(eh,product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_898])]) ).
fof(f6606,plain,
( spl1_651
<=> ! [X0] :
( eg = sum(opp(f(product(eh,product(X0,eh)))),f(product(eh,product(X0,eh))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_651])]) ).
fof(f6674,plain,
( ! [X0] :
( eg = sum(opp(f(product(eh,product(X0,eh)))),f(product(eh,product(X0,eh))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_651 ),
inference(resolution,[],[f6607,f97]) ).
fof(f6607,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(eh,product(X0,eh)))),f(product(eh,product(X0,eh)))) )
| ~ spl1_651 ),
inference(avatar_component_clause,[],[f6606]) ).
fof(f11474,plain,
( spl1_897
| ~ spl1_5
| ~ spl1_650 ),
inference(avatar_split_clause,[],[f6664,f6602,f96,f11472]) ).
fof(f11472,plain,
( spl1_897
<=> ! [X0] :
( eg = sum(f(product(eh,product(eh,X0))),opp(f(product(eh,product(eh,X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_897])]) ).
fof(f6602,plain,
( spl1_650
<=> ! [X0] :
( eg = sum(f(product(eh,product(eh,X0))),opp(f(product(eh,product(eh,X0)))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_650])]) ).
fof(f6664,plain,
( ! [X0] :
( eg = sum(f(product(eh,product(eh,X0))),opp(f(product(eh,product(eh,X0)))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_650 ),
inference(resolution,[],[f6603,f97]) ).
fof(f6603,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(eh,product(eh,X0))),opp(f(product(eh,product(eh,X0))))) )
| ~ spl1_650 ),
inference(avatar_component_clause,[],[f6602]) ).
fof(f11470,plain,
( spl1_896
| ~ spl1_5
| ~ spl1_649 ),
inference(avatar_split_clause,[],[f6657,f6598,f96,f11468]) ).
fof(f11468,plain,
( spl1_896
<=> ! [X0] :
( eg = sum(opp(f(product(eh,product(eh,X0)))),f(product(eh,product(eh,X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_896])]) ).
fof(f6598,plain,
( spl1_649
<=> ! [X0] :
( eg = sum(opp(f(product(eh,product(eh,X0)))),f(product(eh,product(eh,X0))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_649])]) ).
fof(f6657,plain,
( ! [X0] :
( eg = sum(opp(f(product(eh,product(eh,X0)))),f(product(eh,product(eh,X0))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_649 ),
inference(resolution,[],[f6599,f97]) ).
fof(f6599,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(eh,product(eh,X0)))),f(product(eh,product(eh,X0)))) )
| ~ spl1_649 ),
inference(avatar_component_clause,[],[f6598]) ).
fof(f11466,plain,
( spl1_895
| ~ spl1_571
| ~ spl1_619 ),
inference(avatar_split_clause,[],[f6357,f6288,f5326,f11464]) ).
fof(f11464,plain,
( spl1_895
<=> ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(eh,product(product(eh,X0),eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_895])]) ).
fof(f6357,plain,
( ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(eh,product(product(eh,X0),eh)))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_619 ),
inference(resolution,[],[f6289,f5327]) ).
fof(f11462,plain,
( spl1_894
| ~ spl1_572
| ~ spl1_619 ),
inference(avatar_split_clause,[],[f6356,f6288,f5638,f11460]) ).
fof(f11460,plain,
( spl1_894
<=> ! [X0] :
( f(product(product(X0,eh),eh)) = f(product(eh,product(product(X0,eh),eh)))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_894])]) ).
fof(f6356,plain,
( ! [X0] :
( f(product(product(X0,eh),eh)) = f(product(eh,product(product(X0,eh),eh)))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_619 ),
inference(resolution,[],[f6289,f5639]) ).
fof(f11458,plain,
( spl1_893
| ~ spl1_571
| ~ spl1_618 ),
inference(avatar_split_clause,[],[f6351,f6284,f5326,f11456]) ).
fof(f11456,plain,
( spl1_893
<=> ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(product(product(eh,X0),eh),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_893])]) ).
fof(f6351,plain,
( ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(product(product(eh,X0),eh),eh))
| ~ h(f(X0)) )
| ~ spl1_571
| ~ spl1_618 ),
inference(resolution,[],[f6285,f5327]) ).
fof(f11451,plain,
( spl1_892
| ~ spl1_572
| ~ spl1_618 ),
inference(avatar_split_clause,[],[f6350,f6284,f5638,f11449]) ).
fof(f11449,plain,
( spl1_892
<=> ! [X0] :
( f(product(product(X0,eh),eh)) = f(product(product(product(X0,eh),eh),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_892])]) ).
fof(f6350,plain,
( ! [X0] :
( f(product(product(X0,eh),eh)) = f(product(product(product(X0,eh),eh),eh))
| ~ h(f(X0)) )
| ~ spl1_572
| ~ spl1_618 ),
inference(resolution,[],[f6285,f5639]) ).
fof(f11447,plain,
( spl1_891
| ~ spl1_19
| ~ spl1_596 ),
inference(avatar_split_clause,[],[f6140,f6137,f164,f11445]) ).
fof(f11445,plain,
( spl1_891
<=> ! [X0,X1] :
( product(eh,product(X0,X1)) = product(sK0,product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_891])]) ).
fof(f6137,plain,
( spl1_596
<=> ! [X0] :
( product(eh,X0) = product(sK0,product(inv(sK0),X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_596])]) ).
fof(f6140,plain,
( ! [X0,X1] :
( product(eh,product(X0,X1)) = product(sK0,product(inv(sK0),product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_596 ),
inference(resolution,[],[f6138,f165]) ).
fof(f6138,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(sK0,product(inv(sK0),X0)) )
| ~ spl1_596 ),
inference(avatar_component_clause,[],[f6137]) ).
fof(f11443,plain,
( spl1_890
| ~ spl1_2
| ~ spl1_256 ),
inference(avatar_split_clause,[],[f4852,f2114,f81,f11441]) ).
fof(f2114,plain,
( spl1_256
<=> ! [X2,X0,X1] :
( sum(f(product(X0,X1)),opp(X2)) = sum(f(X0),sum(f(X1),opp(X2)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_256])]) ).
fof(f4852,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(product(X0,sK0)),opp(X1)) = sum(f(X0),sum(f(sK0),opp(X1))) )
| ~ spl1_2
| ~ spl1_256 ),
inference(resolution,[],[f83,f2115]) ).
fof(f2115,plain,
( ! [X2,X0,X1] :
( ~ g(X1)
| ~ g(X0)
| sum(f(product(X0,X1)),opp(X2)) = sum(f(X0),sum(f(X1),opp(X2))) )
| ~ spl1_256 ),
inference(avatar_component_clause,[],[f2114]) ).
fof(f11439,plain,
( spl1_889
| ~ spl1_2
| ~ spl1_253 ),
inference(avatar_split_clause,[],[f4851,f2102,f81,f11437]) ).
fof(f2102,plain,
( spl1_253
<=> ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(sum(opp(X0),f(X1)),f(X2))
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_253])]) ).
fof(f4851,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(opp(X1),f(product(X0,sK0))) = sum(sum(opp(X1),f(X0)),f(sK0)) )
| ~ spl1_2
| ~ spl1_253 ),
inference(resolution,[],[f83,f2103]) ).
fof(f2103,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X1)
| sum(opp(X0),f(product(X1,X2))) = sum(sum(opp(X0),f(X1)),f(X2)) )
| ~ spl1_253 ),
inference(avatar_component_clause,[],[f2102]) ).
fof(f11254,plain,
( spl1_888
| ~ spl1_10
| ~ spl1_772 ),
inference(avatar_split_clause,[],[f10266,f7794,f117,f11251]) ).
fof(f11251,plain,
( spl1_888
<=> f(product(sK0,sK0)) = sum(eg,f(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_888])]) ).
fof(f117,plain,
( spl1_10
<=> ! [X0] :
( sum(eg,X0) = X0
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f7794,plain,
( spl1_772
<=> h(f(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_772])]) ).
fof(f10266,plain,
( f(product(sK0,sK0)) = sum(eg,f(product(sK0,sK0)))
| ~ spl1_10
| ~ spl1_772 ),
inference(resolution,[],[f7795,f118]) ).
fof(f118,plain,
( ! [X0] :
( ~ h(X0)
| sum(eg,X0) = X0 )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f7795,plain,
( h(f(product(sK0,sK0)))
| ~ spl1_772 ),
inference(avatar_component_clause,[],[f7794]) ).
fof(f11112,plain,
( spl1_887
| ~ spl1_9
| ~ spl1_772 ),
inference(avatar_split_clause,[],[f10265,f7794,f113,f11109]) ).
fof(f11109,plain,
( spl1_887
<=> f(product(sK0,sK0)) = sum(f(product(sK0,sK0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_887])]) ).
fof(f113,plain,
( spl1_9
<=> ! [X0] :
( sum(X0,eg) = X0
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f10265,plain,
( f(product(sK0,sK0)) = sum(f(product(sK0,sK0)),eg)
| ~ spl1_9
| ~ spl1_772 ),
inference(resolution,[],[f7795,f114]) ).
fof(f114,plain,
( ! [X0] :
( ~ h(X0)
| sum(X0,eg) = X0 )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f11085,plain,
( ~ spl1_3
| spl1_886
| ~ spl1_1
| ~ spl1_20
| ~ spl1_686 ),
inference(avatar_split_clause,[],[f7030,f6974,f182,f77,f11083,f86]) ).
fof(f11083,plain,
( spl1_886
<=> ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(eh,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_886])]) ).
fof(f7030,plain,
( ! [X0] :
( f(product(product(eh,X0),eh)) = f(product(eh,product(X0,eh)))
| ~ h(eg)
| ~ g(X0) )
| ~ spl1_1
| ~ spl1_20
| ~ spl1_686 ),
inference(forward_demodulation,[],[f7029,f184]) ).
fof(f7029,plain,
( ! [X0] :
( ~ h(eg)
| f(product(eh,product(X0,product(eh,eh)))) = f(product(product(eh,X0),product(eh,eh)))
| ~ g(X0) )
| ~ spl1_1
| ~ spl1_686 ),
inference(superposition,[],[f6975,f78]) ).
fof(f11081,plain,
( spl1_885
| ~ spl1_2
| ~ spl1_659 ),
inference(avatar_split_clause,[],[f6719,f6640,f81,f11079]) ).
fof(f11079,plain,
( spl1_885
<=> ! [X0] :
( product(product(sK0,product(X0,sK0)),sK0) = product(sK0,product(product(X0,sK0),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_885])]) ).
fof(f6719,plain,
( ! [X0] :
( product(product(sK0,product(X0,sK0)),sK0) = product(sK0,product(product(X0,sK0),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_659 ),
inference(resolution,[],[f6641,f83]) ).
fof(f11077,plain,
( spl1_884
| ~ spl1_4
| ~ spl1_659 ),
inference(avatar_split_clause,[],[f6718,f6640,f91,f11075]) ).
fof(f11075,plain,
( spl1_884
<=> ! [X0] :
( product(product(sK0,product(X0,sK0)),eh) = product(sK0,product(product(X0,sK0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_884])]) ).
fof(f6718,plain,
( ! [X0] :
( product(product(sK0,product(X0,sK0)),eh) = product(sK0,product(product(X0,sK0),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_659 ),
inference(resolution,[],[f6641,f93]) ).
fof(f11073,plain,
( spl1_883
| ~ spl1_2
| ~ spl1_658 ),
inference(avatar_split_clause,[],[f6715,f6636,f81,f11071]) ).
fof(f11071,plain,
( spl1_883
<=> ! [X0] :
( product(product(sK0,product(X0,eh)),sK0) = product(sK0,product(product(X0,eh),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_883])]) ).
fof(f6715,plain,
( ! [X0] :
( product(product(sK0,product(X0,eh)),sK0) = product(sK0,product(product(X0,eh),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_658 ),
inference(resolution,[],[f6637,f83]) ).
fof(f11069,plain,
( spl1_882
| ~ spl1_4
| ~ spl1_658 ),
inference(avatar_split_clause,[],[f6714,f6636,f91,f11067]) ).
fof(f11067,plain,
( spl1_882
<=> ! [X0] :
( product(product(sK0,product(X0,eh)),eh) = product(sK0,product(product(X0,eh),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_882])]) ).
fof(f6714,plain,
( ! [X0] :
( product(product(sK0,product(X0,eh)),eh) = product(sK0,product(product(X0,eh),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_658 ),
inference(resolution,[],[f6637,f93]) ).
fof(f11065,plain,
( spl1_881
| ~ spl1_2
| ~ spl1_657 ),
inference(avatar_split_clause,[],[f6710,f6632,f81,f11063]) ).
fof(f11063,plain,
( spl1_881
<=> ! [X0] :
( product(product(product(X0,sK0),sK0),sK0) = product(product(X0,sK0),product(sK0,sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_881])]) ).
fof(f6710,plain,
( ! [X0] :
( product(product(product(X0,sK0),sK0),sK0) = product(product(X0,sK0),product(sK0,sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_657 ),
inference(resolution,[],[f6633,f83]) ).
fof(f11061,plain,
( spl1_880
| ~ spl1_2
| ~ spl1_655 ),
inference(avatar_split_clause,[],[f6700,f6624,f81,f11059]) ).
fof(f11059,plain,
( spl1_880
<=> ! [X0] :
( product(product(sK0,inv(inv(X0))),sK0) = product(sK0,product(inv(inv(X0)),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_880])]) ).
fof(f6700,plain,
( ! [X0] :
( product(product(sK0,inv(inv(X0))),sK0) = product(sK0,product(inv(inv(X0)),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_655 ),
inference(resolution,[],[f6625,f83]) ).
fof(f11057,plain,
( spl1_879
| ~ spl1_4
| ~ spl1_655 ),
inference(avatar_split_clause,[],[f6699,f6624,f91,f11055]) ).
fof(f11055,plain,
( spl1_879
<=> ! [X0] :
( product(product(sK0,inv(inv(X0))),eh) = product(sK0,product(inv(inv(X0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_879])]) ).
fof(f6699,plain,
( ! [X0] :
( product(product(sK0,inv(inv(X0))),eh) = product(sK0,product(inv(inv(X0)),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_655 ),
inference(resolution,[],[f6625,f93]) ).
fof(f11051,plain,
( spl1_878
| ~ spl1_2
| ~ spl1_654 ),
inference(avatar_split_clause,[],[f6695,f6618,f81,f11049]) ).
fof(f11049,plain,
( spl1_878
<=> ! [X0] :
( ~ g(X0)
| product(product(inv(sK0),X0),inv(sK0)) = product(inv(sK0),product(X0,inv(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_878])]) ).
fof(f6695,plain,
( ! [X0] :
( ~ g(X0)
| product(product(inv(sK0),X0),inv(sK0)) = product(inv(sK0),product(X0,inv(sK0))) )
| ~ spl1_2
| ~ spl1_654 ),
inference(resolution,[],[f6619,f83]) ).
fof(f11047,plain,
( spl1_877
| ~ spl1_2
| ~ spl1_653 ),
inference(avatar_split_clause,[],[f6691,f6614,f81,f11045]) ).
fof(f11045,plain,
( spl1_877
<=> ! [X0] :
( product(product(sK0,sK0),product(X0,sK0)) = product(sK0,product(sK0,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_877])]) ).
fof(f6691,plain,
( ! [X0] :
( product(product(sK0,sK0),product(X0,sK0)) = product(sK0,product(sK0,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_653 ),
inference(resolution,[],[f6615,f83]) ).
fof(f11043,plain,
( spl1_876
| ~ spl1_4
| ~ spl1_653 ),
inference(avatar_split_clause,[],[f6690,f6614,f91,f11041]) ).
fof(f11041,plain,
( spl1_876
<=> ! [X0] :
( product(product(sK0,sK0),product(X0,eh)) = product(sK0,product(sK0,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_876])]) ).
fof(f6690,plain,
( ! [X0] :
( product(product(sK0,sK0),product(X0,eh)) = product(sK0,product(sK0,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_653 ),
inference(resolution,[],[f6615,f93]) ).
fof(f11039,plain,
( spl1_875
| ~ spl1_2
| ~ spl1_648 ),
inference(avatar_split_clause,[],[f6655,f6594,f81,f11037]) ).
fof(f11037,plain,
( spl1_875
<=> ! [X0] :
( product(product(product(X0,eh),sK0),sK0) = product(product(X0,eh),product(sK0,sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_875])]) ).
fof(f6655,plain,
( ! [X0] :
( product(product(product(X0,eh),sK0),sK0) = product(product(X0,eh),product(sK0,sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_648 ),
inference(resolution,[],[f6595,f83]) ).
fof(f11035,plain,
( spl1_874
| ~ spl1_2
| ~ spl1_647 ),
inference(avatar_split_clause,[],[f6650,f6590,f81,f11033]) ).
fof(f11033,plain,
( spl1_874
<=> ! [X0] :
( product(product(inv(inv(X0)),sK0),sK0) = product(inv(inv(X0)),product(sK0,sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_874])]) ).
fof(f6650,plain,
( ! [X0] :
( product(product(inv(inv(X0)),sK0),sK0) = product(inv(inv(X0)),product(sK0,sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_647 ),
inference(resolution,[],[f6591,f83]) ).
fof(f11031,plain,
( spl1_873
| ~ spl1_2
| ~ spl1_646 ),
inference(avatar_split_clause,[],[f6646,f6586,f81,f11029]) ).
fof(f11029,plain,
( spl1_873
<=> ! [X0] :
( product(eh,product(product(X0,sK0),sK0)) = product(product(eh,product(X0,sK0)),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_873])]) ).
fof(f6646,plain,
( ! [X0] :
( product(eh,product(product(X0,sK0),sK0)) = product(product(eh,product(X0,sK0)),sK0)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_646 ),
inference(resolution,[],[f6587,f83]) ).
fof(f11027,plain,
( spl1_872
| ~ spl1_4
| ~ spl1_646 ),
inference(avatar_split_clause,[],[f6645,f6586,f91,f11025]) ).
fof(f11025,plain,
( spl1_872
<=> ! [X0] :
( product(product(eh,product(X0,sK0)),eh) = product(eh,product(product(X0,sK0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_872])]) ).
fof(f6645,plain,
( ! [X0] :
( product(product(eh,product(X0,sK0)),eh) = product(eh,product(product(X0,sK0),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_646 ),
inference(resolution,[],[f6587,f93]) ).
fof(f11023,plain,
( spl1_871
| ~ spl1_5
| ~ spl1_643 ),
inference(avatar_split_clause,[],[f6568,f6528,f96,f11021]) ).
fof(f11021,plain,
( spl1_871
<=> ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(product(eh,product(X0,eh)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_871])]) ).
fof(f6528,plain,
( spl1_643
<=> ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(product(eh,product(X0,eh)),eh))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_643])]) ).
fof(f6568,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(product(eh,product(X0,eh)),eh))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_643 ),
inference(resolution,[],[f6529,f97]) ).
fof(f6529,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,product(X0,eh))) = f(product(product(eh,product(X0,eh)),eh)) )
| ~ spl1_643 ),
inference(avatar_component_clause,[],[f6528]) ).
fof(f11019,plain,
( spl1_870
| ~ spl1_5
| ~ spl1_641 ),
inference(avatar_split_clause,[],[f6561,f6519,f96,f11017]) ).
fof(f11017,plain,
( spl1_870
<=> ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(eh,product(eh,product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_870])]) ).
fof(f6519,plain,
( spl1_641
<=> ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(eh,product(eh,product(X0,eh))))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_641])]) ).
fof(f6561,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(eh,product(eh,product(X0,eh))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_641 ),
inference(resolution,[],[f6520,f97]) ).
fof(f6520,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,product(X0,eh))) = f(product(eh,product(eh,product(X0,eh)))) )
| ~ spl1_641 ),
inference(avatar_component_clause,[],[f6519]) ).
fof(f11015,plain,
( spl1_869
| ~ spl1_5
| ~ spl1_640 ),
inference(avatar_split_clause,[],[f6554,f6515,f96,f11013]) ).
fof(f11013,plain,
( spl1_869
<=> ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(product(eh,product(eh,X0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_869])]) ).
fof(f6554,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(product(eh,product(eh,X0)),eh))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_640 ),
inference(resolution,[],[f6516,f97]) ).
fof(f11011,plain,
( spl1_868
| ~ spl1_559
| ~ spl1_565
| ~ spl1_629
| ~ spl1_810 ),
inference(avatar_split_clause,[],[f9275,f8603,f6402,f5278,f5228,f11008]) ).
fof(f11008,plain,
( spl1_868
<=> inv(sK0) = product(product(inv(sK0),inv(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_868])]) ).
fof(f5278,plain,
( spl1_565
<=> inv(sK0) = product(inv(sK0),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_565])]) ).
fof(f9275,plain,
( inv(sK0) = product(product(inv(sK0),inv(sK0)),sK0)
| ~ spl1_559
| ~ spl1_565
| ~ spl1_629
| ~ spl1_810 ),
inference(forward_demodulation,[],[f9274,f5280]) ).
fof(f5280,plain,
( inv(sK0) = product(inv(sK0),eh)
| ~ spl1_565 ),
inference(avatar_component_clause,[],[f5278]) ).
fof(f9274,plain,
( product(inv(sK0),eh) = product(product(inv(sK0),inv(sK0)),sK0)
| ~ spl1_559
| ~ spl1_629
| ~ spl1_810 ),
inference(forward_demodulation,[],[f9053,f5230]) ).
fof(f9053,plain,
( product(product(inv(sK0),inv(sK0)),sK0) = product(inv(sK0),product(inv(sK0),sK0))
| ~ spl1_629
| ~ spl1_810 ),
inference(resolution,[],[f8604,f6403]) ).
fof(f11006,plain,
( spl1_867
| ~ spl1_5
| ~ spl1_639 ),
inference(avatar_split_clause,[],[f6547,f6511,f96,f11004]) ).
fof(f11004,plain,
( spl1_867
<=> ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(eh,product(eh,product(eh,X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_867])]) ).
fof(f6547,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(eh,product(eh,product(eh,X0))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_639 ),
inference(resolution,[],[f6512,f97]) ).
fof(f11002,plain,
( spl1_866
| ~ spl1_6
| ~ spl1_629 ),
inference(avatar_split_clause,[],[f6451,f6402,f100,f11000]) ).
fof(f11000,plain,
( spl1_866
<=> ! [X0] :
( product(product(inv(sK0),inv(X0)),sK0) = product(inv(sK0),product(inv(X0),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_866])]) ).
fof(f6451,plain,
( ! [X0] :
( product(product(inv(sK0),inv(X0)),sK0) = product(inv(sK0),product(inv(X0),sK0))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_629 ),
inference(resolution,[],[f6403,f101]) ).
fof(f10998,plain,
( spl1_865
| ~ spl1_6
| ~ spl1_628 ),
inference(avatar_split_clause,[],[f6443,f6398,f100,f10996]) ).
fof(f10996,plain,
( spl1_865
<=> ! [X0] :
( product(product(inv(sK0),inv(X0)),eh) = product(inv(sK0),product(inv(X0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_865])]) ).
fof(f6443,plain,
( ! [X0] :
( product(product(inv(sK0),inv(X0)),eh) = product(inv(sK0),product(inv(X0),eh))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_628 ),
inference(resolution,[],[f6399,f101]) ).
fof(f10994,plain,
( spl1_864
| ~ spl1_6
| ~ spl1_627 ),
inference(avatar_split_clause,[],[f6435,f6394,f100,f10992]) ).
fof(f10992,plain,
( spl1_864
<=> ! [X0] :
( product(product(sK0,sK0),inv(inv(X0))) = product(sK0,product(sK0,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_864])]) ).
fof(f6435,plain,
( ! [X0] :
( product(product(sK0,sK0),inv(inv(X0))) = product(sK0,product(sK0,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_627 ),
inference(resolution,[],[f6395,f101]) ).
fof(f10990,plain,
( spl1_863
| ~ spl1_2
| ~ spl1_247 ),
inference(avatar_split_clause,[],[f4848,f2000,f81,f10988]) ).
fof(f10988,plain,
( spl1_863
<=> ! [X0] :
( product(eh,product(product(X0,eh),sK0)) = product(product(eh,product(X0,eh)),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_863])]) ).
fof(f2000,plain,
( spl1_247
<=> ! [X0,X1] :
( product(eh,product(product(X0,eh),X1)) = product(product(eh,product(X0,eh)),X1)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_247])]) ).
fof(f4848,plain,
( ! [X0] :
( product(eh,product(product(X0,eh),sK0)) = product(product(eh,product(X0,eh)),sK0)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_247 ),
inference(resolution,[],[f83,f2001]) ).
fof(f2001,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(product(X0,eh),X1)) = product(product(eh,product(X0,eh)),X1)
| ~ g(X0) )
| ~ spl1_247 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f10986,plain,
( spl1_862
| ~ spl1_2
| ~ spl1_245 ),
inference(avatar_split_clause,[],[f4847,f1980,f81,f10984]) ).
fof(f10984,plain,
( spl1_862
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| f(product(X0,product(X1,sK0))) = f(product(product(X0,X1),sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_862])]) ).
fof(f1980,plain,
( spl1_245
<=> ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = f(product(product(X0,X1),X2))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_245])]) ).
fof(f4847,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| f(product(X0,product(X1,sK0))) = f(product(product(X0,X1),sK0)) )
| ~ spl1_2
| ~ spl1_245 ),
inference(resolution,[],[f83,f1981]) ).
fof(f1981,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| f(product(X0,product(X1,X2))) = f(product(product(X0,X1),X2)) )
| ~ spl1_245 ),
inference(avatar_component_clause,[],[f1980]) ).
fof(f10982,plain,
( spl1_861
| ~ spl1_2
| ~ spl1_244 ),
inference(avatar_split_clause,[],[f4846,f1976,f81,f10980]) ).
fof(f1976,plain,
( spl1_244
<=> ! [X2,X0,X1] :
( sum(sum(f(X0),opp(X1)),opp(X2)) = sum(f(X0),sum(opp(X1),opp(X2)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_244])]) ).
fof(f4846,plain,
( ! [X0,X1] : sum(sum(f(sK0),opp(X0)),opp(X1)) = sum(f(sK0),sum(opp(X0),opp(X1)))
| ~ spl1_2
| ~ spl1_244 ),
inference(resolution,[],[f83,f1977]) ).
fof(f1977,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),opp(X1)),opp(X2)) = sum(f(X0),sum(opp(X1),opp(X2))) )
| ~ spl1_244 ),
inference(avatar_component_clause,[],[f1976]) ).
fof(f10978,plain,
( spl1_860
| ~ spl1_2
| ~ spl1_243 ),
inference(avatar_split_clause,[],[f4845,f1972,f81,f10976]) ).
fof(f1972,plain,
( spl1_243
<=> ! [X2,X0,X1] :
( sum(sum(opp(X0),f(X1)),opp(X2)) = sum(opp(X0),sum(f(X1),opp(X2)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_243])]) ).
fof(f4845,plain,
( ! [X0,X1] : sum(sum(opp(X0),f(sK0)),opp(X1)) = sum(opp(X0),sum(f(sK0),opp(X1)))
| ~ spl1_2
| ~ spl1_243 ),
inference(resolution,[],[f83,f1973]) ).
fof(f1973,plain,
( ! [X2,X0,X1] :
( ~ g(X1)
| sum(sum(opp(X0),f(X1)),opp(X2)) = sum(opp(X0),sum(f(X1),opp(X2))) )
| ~ spl1_243 ),
inference(avatar_component_clause,[],[f1972]) ).
fof(f10974,plain,
( spl1_859
| ~ spl1_2
| ~ spl1_239 ),
inference(avatar_split_clause,[],[f4843,f1956,f81,f10972]) ).
fof(f1956,plain,
( spl1_239
<=> ! [X2,X0,X1] :
( sum(sum(opp(X0),opp(X1)),f(X2)) = sum(opp(X0),sum(opp(X1),f(X2)))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_239])]) ).
fof(f4843,plain,
( ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(sK0)) = sum(opp(X0),sum(opp(X1),f(sK0)))
| ~ spl1_2
| ~ spl1_239 ),
inference(resolution,[],[f83,f1957]) ).
fof(f1957,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| sum(sum(opp(X0),opp(X1)),f(X2)) = sum(opp(X0),sum(opp(X1),f(X2))) )
| ~ spl1_239 ),
inference(avatar_component_clause,[],[f1956]) ).
fof(f10970,plain,
( spl1_858
| ~ spl1_2
| ~ spl1_238 ),
inference(avatar_split_clause,[],[f4842,f1952,f81,f10968]) ).
fof(f10968,plain,
( spl1_858
<=> ! [X0] :
( product(eh,product(inv(inv(X0)),sK0)) = product(product(eh,inv(inv(X0))),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_858])]) ).
fof(f1952,plain,
( spl1_238
<=> ! [X0,X1] :
( product(eh,product(inv(inv(X0)),X1)) = product(product(eh,inv(inv(X0))),X1)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_238])]) ).
fof(f4842,plain,
( ! [X0] :
( product(eh,product(inv(inv(X0)),sK0)) = product(product(eh,inv(inv(X0))),sK0)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_238 ),
inference(resolution,[],[f83,f1953]) ).
fof(f1953,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(inv(inv(X0)),X1)) = product(product(eh,inv(inv(X0))),X1)
| ~ g(X0) )
| ~ spl1_238 ),
inference(avatar_component_clause,[],[f1952]) ).
fof(f10870,plain,
( spl1_857
| ~ spl1_2
| ~ spl1_566
| ~ spl1_782 ),
inference(avatar_split_clause,[],[f7951,f7896,f5283,f81,f10867]) ).
fof(f10867,plain,
( spl1_857
<=> inv(sK0) = product(sK0,product(inv(sK0),inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_857])]) ).
fof(f5283,plain,
( spl1_566
<=> inv(sK0) = product(eh,inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_566])]) ).
fof(f7896,plain,
( spl1_782
<=> ! [X0] :
( product(eh,inv(X0)) = product(sK0,product(inv(sK0),inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_782])]) ).
fof(f7951,plain,
( inv(sK0) = product(sK0,product(inv(sK0),inv(sK0)))
| ~ spl1_2
| ~ spl1_566
| ~ spl1_782 ),
inference(forward_demodulation,[],[f7947,f5285]) ).
fof(f5285,plain,
( inv(sK0) = product(eh,inv(sK0))
| ~ spl1_566 ),
inference(avatar_component_clause,[],[f5283]) ).
fof(f7947,plain,
( product(eh,inv(sK0)) = product(sK0,product(inv(sK0),inv(sK0)))
| ~ spl1_2
| ~ spl1_782 ),
inference(resolution,[],[f7897,f83]) ).
fof(f7897,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,inv(X0)) = product(sK0,product(inv(sK0),inv(X0))) )
| ~ spl1_782 ),
inference(avatar_component_clause,[],[f7896]) ).
fof(f10670,plain,
( spl1_856
| ~ spl1_556
| ~ spl1_569
| ~ spl1_586
| ~ spl1_782
| ~ spl1_810 ),
inference(avatar_split_clause,[],[f9288,f8603,f7896,f6053,f5308,f5209,f10667]) ).
fof(f10667,plain,
( spl1_856
<=> sK0 = inv(inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_856])]) ).
fof(f5209,plain,
( spl1_556
<=> sK0 = product(sK0,eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_556])]) ).
fof(f5308,plain,
( spl1_569
<=> eh = product(inv(sK0),inv(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_569])]) ).
fof(f6053,plain,
( spl1_586
<=> inv(inv(sK0)) = product(eh,inv(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_586])]) ).
fof(f9288,plain,
( sK0 = inv(inv(sK0))
| ~ spl1_556
| ~ spl1_569
| ~ spl1_586
| ~ spl1_782
| ~ spl1_810 ),
inference(forward_demodulation,[],[f9287,f5211]) ).
fof(f5211,plain,
( sK0 = product(sK0,eh)
| ~ spl1_556 ),
inference(avatar_component_clause,[],[f5209]) ).
fof(f9287,plain,
( product(sK0,eh) = inv(inv(sK0))
| ~ spl1_569
| ~ spl1_586
| ~ spl1_782
| ~ spl1_810 ),
inference(forward_demodulation,[],[f9286,f6055]) ).
fof(f6055,plain,
( inv(inv(sK0)) = product(eh,inv(inv(sK0)))
| ~ spl1_586 ),
inference(avatar_component_clause,[],[f6053]) ).
fof(f9286,plain,
( product(sK0,eh) = product(eh,inv(inv(sK0)))
| ~ spl1_569
| ~ spl1_782
| ~ spl1_810 ),
inference(forward_demodulation,[],[f9086,f5310]) ).
fof(f5310,plain,
( eh = product(inv(sK0),inv(inv(sK0)))
| ~ spl1_569 ),
inference(avatar_component_clause,[],[f5308]) ).
fof(f9086,plain,
( product(eh,inv(inv(sK0))) = product(sK0,product(inv(sK0),inv(inv(sK0))))
| ~ spl1_782
| ~ spl1_810 ),
inference(resolution,[],[f8604,f7897]) ).
fof(f10665,plain,
( spl1_855
| ~ spl1_2
| ~ spl1_645 ),
inference(avatar_split_clause,[],[f6584,f6536,f81,f10663]) ).
fof(f10663,plain,
( spl1_855
<=> ! [X0] :
( eh = product(product(sK0,product(X0,sK0)),inv(product(sK0,product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_855])]) ).
fof(f6584,plain,
( ! [X0] :
( eh = product(product(sK0,product(X0,sK0)),inv(product(sK0,product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_645 ),
inference(resolution,[],[f6537,f83]) ).
fof(f10661,plain,
( spl1_854
| ~ spl1_4
| ~ spl1_645 ),
inference(avatar_split_clause,[],[f6583,f6536,f91,f10659]) ).
fof(f10659,plain,
( spl1_854
<=> ! [X0] :
( eh = product(product(sK0,product(X0,eh)),inv(product(sK0,product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_854])]) ).
fof(f6583,plain,
( ! [X0] :
( eh = product(product(sK0,product(X0,eh)),inv(product(sK0,product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_645 ),
inference(resolution,[],[f6537,f93]) ).
fof(f10657,plain,
( spl1_853
| ~ spl1_2
| ~ spl1_644 ),
inference(avatar_split_clause,[],[f6578,f6532,f81,f10655]) ).
fof(f10655,plain,
( spl1_853
<=> ! [X0] :
( eh = product(inv(product(sK0,product(X0,sK0))),product(sK0,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_853])]) ).
fof(f6578,plain,
( ! [X0] :
( eh = product(inv(product(sK0,product(X0,sK0))),product(sK0,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_644 ),
inference(resolution,[],[f6533,f83]) ).
fof(f10653,plain,
( spl1_852
| ~ spl1_4
| ~ spl1_644 ),
inference(avatar_split_clause,[],[f6577,f6532,f91,f10651]) ).
fof(f10651,plain,
( spl1_852
<=> ! [X0] :
( eh = product(inv(product(sK0,product(X0,eh))),product(sK0,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_852])]) ).
fof(f6577,plain,
( ! [X0] :
( eh = product(inv(product(sK0,product(X0,eh))),product(sK0,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_644 ),
inference(resolution,[],[f6533,f93]) ).
fof(f10649,plain,
( spl1_851
| ~ spl1_2
| ~ spl1_638 ),
inference(avatar_split_clause,[],[f6546,f6507,f81,f10647]) ).
fof(f10647,plain,
( spl1_851
<=> ! [X0] :
( eh = product(product(product(X0,sK0),sK0),inv(product(product(X0,sK0),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_851])]) ).
fof(f6546,plain,
( ! [X0] :
( eh = product(product(product(X0,sK0),sK0),inv(product(product(X0,sK0),sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_638 ),
inference(resolution,[],[f6508,f83]) ).
fof(f10645,plain,
( spl1_850
| ~ spl1_4
| ~ spl1_638 ),
inference(avatar_split_clause,[],[f6545,f6507,f91,f10643]) ).
fof(f10643,plain,
( spl1_850
<=> ! [X0] :
( eh = product(product(product(X0,sK0),eh),inv(product(product(X0,sK0),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_850])]) ).
fof(f6545,plain,
( ! [X0] :
( eh = product(product(product(X0,sK0),eh),inv(product(product(X0,sK0),eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_638 ),
inference(resolution,[],[f6508,f93]) ).
fof(f10641,plain,
( spl1_849
| ~ spl1_2
| ~ spl1_637 ),
inference(avatar_split_clause,[],[f6542,f6503,f81,f10639]) ).
fof(f10639,plain,
( spl1_849
<=> ! [X0] :
( eh = product(inv(product(product(X0,sK0),sK0)),product(product(X0,sK0),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_849])]) ).
fof(f6542,plain,
( ! [X0] :
( eh = product(inv(product(product(X0,sK0),sK0)),product(product(X0,sK0),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_637 ),
inference(resolution,[],[f6504,f83]) ).
fof(f10637,plain,
( spl1_848
| ~ spl1_4
| ~ spl1_637 ),
inference(avatar_split_clause,[],[f6541,f6503,f91,f10635]) ).
fof(f10635,plain,
( spl1_848
<=> ! [X0] :
( eh = product(inv(product(product(X0,sK0),eh)),product(product(X0,sK0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_848])]) ).
fof(f6541,plain,
( ! [X0] :
( eh = product(inv(product(product(X0,sK0),eh)),product(product(X0,sK0),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_637 ),
inference(resolution,[],[f6504,f93]) ).
fof(f10633,plain,
( spl1_847
| ~ spl1_6
| ~ spl1_621 ),
inference(avatar_split_clause,[],[f6371,f6296,f100,f10631]) ).
fof(f10631,plain,
( spl1_847
<=> ! [X0] :
( eh = product(product(sK0,inv(inv(X0))),inv(product(sK0,inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_847])]) ).
fof(f6371,plain,
( ! [X0] :
( eh = product(product(sK0,inv(inv(X0))),inv(product(sK0,inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_621 ),
inference(resolution,[],[f6297,f101]) ).
fof(f10629,plain,
( spl1_846
| ~ spl1_6
| ~ spl1_620 ),
inference(avatar_split_clause,[],[f6361,f6292,f100,f10627]) ).
fof(f10627,plain,
( spl1_846
<=> ! [X0] :
( eh = product(inv(product(sK0,inv(inv(X0)))),product(sK0,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_846])]) ).
fof(f6361,plain,
( ! [X0] :
( eh = product(inv(product(sK0,inv(inv(X0)))),product(sK0,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_620 ),
inference(resolution,[],[f6293,f101]) ).
fof(f10091,plain,
( spl1_845
| ~ spl1_6
| ~ spl1_615 ),
inference(avatar_split_clause,[],[f6331,f6272,f100,f10089]) ).
fof(f10089,plain,
( spl1_845
<=> ! [X0] :
( eh = product(product(inv(sK0),inv(X0)),inv(product(inv(sK0),inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_845])]) ).
fof(f6331,plain,
( ! [X0] :
( eh = product(product(inv(sK0),inv(X0)),inv(product(inv(sK0),inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_615 ),
inference(resolution,[],[f6273,f101]) ).
fof(f10087,plain,
( spl1_844
| ~ spl1_6
| ~ spl1_614 ),
inference(avatar_split_clause,[],[f6325,f6268,f100,f10085]) ).
fof(f10085,plain,
( spl1_844
<=> ! [X0] :
( eh = product(inv(product(inv(sK0),inv(X0))),product(inv(sK0),inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_844])]) ).
fof(f6325,plain,
( ! [X0] :
( eh = product(inv(product(inv(sK0),inv(X0))),product(inv(sK0),inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_614 ),
inference(resolution,[],[f6269,f101]) ).
fof(f10083,plain,
( spl1_843
| ~ spl1_6
| ~ spl1_613 ),
inference(avatar_split_clause,[],[f6320,f6264,f100,f10081]) ).
fof(f10081,plain,
( spl1_843
<=> ! [X0] :
( eh = product(inv(inv(product(inv(X0),sK0))),inv(product(inv(X0),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_843])]) ).
fof(f6320,plain,
( ! [X0] :
( eh = product(inv(inv(product(inv(X0),sK0))),inv(product(inv(X0),sK0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_613 ),
inference(resolution,[],[f6265,f101]) ).
fof(f10079,plain,
( spl1_842
| ~ spl1_6
| ~ spl1_611 ),
inference(avatar_split_clause,[],[f6315,f6255,f100,f10077]) ).
fof(f10077,plain,
( spl1_842
<=> ! [X0] :
( eh = product(inv(product(inv(X0),sK0)),inv(inv(product(inv(X0),sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_842])]) ).
fof(f6315,plain,
( ! [X0] :
( eh = product(inv(product(inv(X0),sK0)),inv(inv(product(inv(X0),sK0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_611 ),
inference(resolution,[],[f6256,f101]) ).
fof(f10075,plain,
( spl1_841
| ~ spl1_6
| ~ spl1_610 ),
inference(avatar_split_clause,[],[f6310,f6251,f100,f10073]) ).
fof(f10073,plain,
( spl1_841
<=> ! [X0] :
( eg = sum(opp(f(product(inv(X0),sK0))),f(product(inv(X0),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_841])]) ).
fof(f6310,plain,
( ! [X0] :
( eg = sum(opp(f(product(inv(X0),sK0))),f(product(inv(X0),sK0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_610 ),
inference(resolution,[],[f6252,f101]) ).
fof(f10071,plain,
( spl1_840
| ~ spl1_6
| ~ spl1_609 ),
inference(avatar_split_clause,[],[f6300,f6247,f100,f10069]) ).
fof(f10069,plain,
( spl1_840
<=> ! [X0] :
( eg = sum(f(product(inv(X0),sK0)),opp(f(product(inv(X0),sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_840])]) ).
fof(f6300,plain,
( ! [X0] :
( eg = sum(f(product(inv(X0),sK0)),opp(f(product(inv(X0),sK0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_609 ),
inference(resolution,[],[f6248,f101]) ).
fof(f10067,plain,
( spl1_839
| ~ spl1_2
| ~ spl1_232 ),
inference(avatar_split_clause,[],[f4840,f1819,f81,f10065]) ).
fof(f10065,plain,
( spl1_839
<=> ! [X0] :
( eh = product(product(product(X0,eh),sK0),inv(product(product(X0,eh),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_839])]) ).
fof(f1819,plain,
( spl1_232
<=> ! [X0,X1] :
( eh = product(product(product(X0,eh),X1),inv(product(product(X0,eh),X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_232])]) ).
fof(f4840,plain,
( ! [X0] :
( eh = product(product(product(X0,eh),sK0),inv(product(product(X0,eh),sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_232 ),
inference(resolution,[],[f83,f1820]) ).
fof(f1820,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(product(X0,eh),X1),inv(product(product(X0,eh),X1)))
| ~ g(X0) )
| ~ spl1_232 ),
inference(avatar_component_clause,[],[f1819]) ).
fof(f10063,plain,
( spl1_838
| ~ spl1_2
| ~ spl1_231 ),
inference(avatar_split_clause,[],[f4839,f1815,f81,f10061]) ).
fof(f10061,plain,
( spl1_838
<=> ! [X0] :
( eh = product(inv(product(product(X0,eh),sK0)),product(product(X0,eh),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_838])]) ).
fof(f1815,plain,
( spl1_231
<=> ! [X0,X1] :
( eh = product(inv(product(product(X0,eh),X1)),product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_231])]) ).
fof(f4839,plain,
( ! [X0] :
( eh = product(inv(product(product(X0,eh),sK0)),product(product(X0,eh),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_231 ),
inference(resolution,[],[f83,f1816]) ).
fof(f1816,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(product(X0,eh),X1)),product(product(X0,eh),X1))
| ~ g(X0) )
| ~ spl1_231 ),
inference(avatar_component_clause,[],[f1815]) ).
fof(f10056,plain,
( spl1_837
| ~ spl1_2
| ~ spl1_228 ),
inference(avatar_split_clause,[],[f4838,f1803,f81,f10054]) ).
fof(f10054,plain,
( spl1_837
<=> ! [X0] :
( ~ g(X0)
| sum(eg,f(product(X0,sK0))) = sum(sum(eg,f(X0)),f(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_837])]) ).
fof(f1803,plain,
( spl1_228
<=> ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(X0)),f(X1))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_228])]) ).
fof(f4838,plain,
( ! [X0] :
( ~ g(X0)
| sum(eg,f(product(X0,sK0))) = sum(sum(eg,f(X0)),f(sK0)) )
| ~ spl1_2
| ~ spl1_228 ),
inference(resolution,[],[f83,f1804]) ).
fof(f1804,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| sum(eg,f(product(X0,X1))) = sum(sum(eg,f(X0)),f(X1)) )
| ~ spl1_228 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f10052,plain,
( spl1_836
| ~ spl1_2
| ~ spl1_227 ),
inference(avatar_split_clause,[],[f4837,f1799,f81,f10050]) ).
fof(f10050,plain,
( spl1_836
<=> ! [X0] :
( eh = product(product(inv(inv(X0)),sK0),inv(product(inv(inv(X0)),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_836])]) ).
fof(f1799,plain,
( spl1_227
<=> ! [X0,X1] :
( eh = product(product(inv(inv(X0)),X1),inv(product(inv(inv(X0)),X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_227])]) ).
fof(f4837,plain,
( ! [X0] :
( eh = product(product(inv(inv(X0)),sK0),inv(product(inv(inv(X0)),sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_227 ),
inference(resolution,[],[f83,f1800]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(inv(inv(X0)),X1),inv(product(inv(inv(X0)),X1)))
| ~ g(X0) )
| ~ spl1_227 ),
inference(avatar_component_clause,[],[f1799]) ).
fof(f10048,plain,
( ~ spl1_774
| ~ spl1_42
| spl1_772 ),
inference(avatar_split_clause,[],[f10007,f7794,f340,f7802]) ).
fof(f7802,plain,
( spl1_774
<=> h(f(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_774])]) ).
fof(f10007,plain,
( ~ h(f(sK0))
| ~ spl1_42
| spl1_772 ),
inference(duplicate_literal_removal,[],[f10005]) ).
fof(f10005,plain,
( ~ h(f(sK0))
| ~ h(f(sK0))
| ~ spl1_42
| spl1_772 ),
inference(resolution,[],[f7796,f341]) ).
fof(f7796,plain,
( ~ h(f(product(sK0,sK0)))
| spl1_772 ),
inference(avatar_component_clause,[],[f7794]) ).
fof(f10047,plain,
( spl1_835
| ~ spl1_2
| ~ spl1_226 ),
inference(avatar_split_clause,[],[f4836,f1795,f81,f10045]) ).
fof(f10045,plain,
( spl1_835
<=> ! [X0] :
( eh = product(inv(product(inv(inv(X0)),sK0)),product(inv(inv(X0)),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_835])]) ).
fof(f1795,plain,
( spl1_226
<=> ! [X0,X1] :
( eh = product(inv(product(inv(inv(X0)),X1)),product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_226])]) ).
fof(f4836,plain,
( ! [X0] :
( eh = product(inv(product(inv(inv(X0)),sK0)),product(inv(inv(X0)),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_226 ),
inference(resolution,[],[f83,f1796]) ).
fof(f1796,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(inv(inv(X0)),X1)),product(inv(inv(X0)),X1))
| ~ g(X0) )
| ~ spl1_226 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f10043,plain,
( spl1_834
| ~ spl1_2
| ~ spl1_225 ),
inference(avatar_split_clause,[],[f4835,f1791,f81,f10041]) ).
fof(f10041,plain,
( spl1_834
<=> ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,inv(sK0)))),inv(product(X0,inv(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_834])]) ).
fof(f1791,plain,
( spl1_225
<=> ! [X0,X1] :
( eh = product(inv(inv(product(X0,inv(X1)))),inv(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_225])]) ).
fof(f4835,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,inv(sK0)))),inv(product(X0,inv(sK0)))) )
| ~ spl1_2
| ~ spl1_225 ),
inference(resolution,[],[f83,f1792]) ).
fof(f1792,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eh = product(inv(inv(product(X0,inv(X1)))),inv(product(X0,inv(X1)))) )
| ~ spl1_225 ),
inference(avatar_component_clause,[],[f1791]) ).
fof(f10039,plain,
( spl1_833
| ~ spl1_2
| ~ spl1_223 ),
inference(avatar_split_clause,[],[f4834,f1783,f81,f10037]) ).
fof(f10037,plain,
( spl1_833
<=> ! [X0] :
( ~ g(X0)
| eh = product(inv(product(X0,inv(sK0))),inv(inv(product(X0,inv(sK0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_833])]) ).
fof(f1783,plain,
( spl1_223
<=> ! [X0,X1] :
( eh = product(inv(product(X0,inv(X1))),inv(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_223])]) ).
fof(f4834,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(X0,inv(sK0))),inv(inv(product(X0,inv(sK0))))) )
| ~ spl1_2
| ~ spl1_223 ),
inference(resolution,[],[f83,f1784]) ).
fof(f1784,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eh = product(inv(product(X0,inv(X1))),inv(inv(product(X0,inv(X1))))) )
| ~ spl1_223 ),
inference(avatar_component_clause,[],[f1783]) ).
fof(f10035,plain,
( spl1_832
| ~ spl1_2
| ~ spl1_222 ),
inference(avatar_split_clause,[],[f4833,f1779,f81,f10033]) ).
fof(f10033,plain,
( spl1_832
<=> ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,inv(sK0)))),f(product(X0,inv(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_832])]) ).
fof(f1779,plain,
( spl1_222
<=> ! [X0,X1] :
( eg = sum(opp(f(product(X0,inv(X1)))),f(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_222])]) ).
fof(f4833,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,inv(sK0)))),f(product(X0,inv(sK0)))) )
| ~ spl1_2
| ~ spl1_222 ),
inference(resolution,[],[f83,f1780]) ).
fof(f1780,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eg = sum(opp(f(product(X0,inv(X1)))),f(product(X0,inv(X1)))) )
| ~ spl1_222 ),
inference(avatar_component_clause,[],[f1779]) ).
fof(f10031,plain,
( spl1_831
| ~ spl1_2
| ~ spl1_221 ),
inference(avatar_split_clause,[],[f4832,f1775,f81,f10029]) ).
fof(f10029,plain,
( spl1_831
<=> ! [X0] :
( ~ g(X0)
| eg = sum(f(product(X0,inv(sK0))),opp(f(product(X0,inv(sK0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_831])]) ).
fof(f1775,plain,
( spl1_221
<=> ! [X0,X1] :
( eg = sum(f(product(X0,inv(X1))),opp(f(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_221])]) ).
fof(f4832,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(product(X0,inv(sK0))),opp(f(product(X0,inv(sK0))))) )
| ~ spl1_2
| ~ spl1_221 ),
inference(resolution,[],[f83,f1776]) ).
fof(f1776,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eg = sum(f(product(X0,inv(X1))),opp(f(product(X0,inv(X1))))) )
| ~ spl1_221 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f10027,plain,
( spl1_830
| ~ spl1_2
| ~ spl1_220 ),
inference(avatar_split_clause,[],[f4831,f1771,f81,f10025]) ).
fof(f10025,plain,
( spl1_830
<=> ! [X0] :
( eh = product(product(eh,product(X0,sK0)),inv(product(eh,product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_830])]) ).
fof(f1771,plain,
( spl1_220
<=> ! [X0,X1] :
( eh = product(product(eh,product(X0,X1)),inv(product(eh,product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_220])]) ).
fof(f4831,plain,
( ! [X0] :
( eh = product(product(eh,product(X0,sK0)),inv(product(eh,product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_220 ),
inference(resolution,[],[f83,f1772]) ).
fof(f1772,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(eh,product(X0,X1)),inv(product(eh,product(X0,X1))))
| ~ g(X0) )
| ~ spl1_220 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f10023,plain,
( spl1_829
| ~ spl1_2
| ~ spl1_219 ),
inference(avatar_split_clause,[],[f4830,f1767,f81,f10021]) ).
fof(f10021,plain,
( spl1_829
<=> ! [X0] :
( eh = product(inv(product(eh,product(X0,sK0))),product(eh,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_829])]) ).
fof(f1767,plain,
( spl1_219
<=> ! [X0,X1] :
( eh = product(inv(product(eh,product(X0,X1))),product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_219])]) ).
fof(f4830,plain,
( ! [X0] :
( eh = product(inv(product(eh,product(X0,sK0))),product(eh,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_219 ),
inference(resolution,[],[f83,f1768]) ).
fof(f1768,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(eh,product(X0,X1))),product(eh,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_219 ),
inference(avatar_component_clause,[],[f1767]) ).
fof(f10019,plain,
( spl1_828
| ~ spl1_2
| ~ spl1_216 ),
inference(avatar_split_clause,[],[f4829,f1755,f81,f10017]) ).
fof(f10017,plain,
( spl1_828
<=> ! [X0] :
( eh = product(inv(inv(inv(product(X0,sK0)))),inv(inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_828])]) ).
fof(f1755,plain,
( spl1_216
<=> ! [X0,X1] :
( eh = product(inv(inv(inv(product(X0,X1)))),inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_216])]) ).
fof(f4829,plain,
( ! [X0] :
( eh = product(inv(inv(inv(product(X0,sK0)))),inv(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_216 ),
inference(resolution,[],[f83,f1756]) ).
fof(f1756,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(inv(inv(product(X0,X1)))),inv(inv(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_216 ),
inference(avatar_component_clause,[],[f1755]) ).
fof(f10015,plain,
( spl1_827
| ~ spl1_2
| ~ spl1_215 ),
inference(avatar_split_clause,[],[f4828,f1751,f81,f10013]) ).
fof(f10013,plain,
( spl1_827
<=> ! [X0] :
( eh = product(inv(inv(product(X0,sK0))),inv(inv(inv(product(X0,sK0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_827])]) ).
fof(f1751,plain,
( spl1_215
<=> ! [X0,X1] :
( eh = product(inv(inv(product(X0,X1))),inv(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_215])]) ).
fof(f4828,plain,
( ! [X0] :
( eh = product(inv(inv(product(X0,sK0))),inv(inv(inv(product(X0,sK0)))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_215 ),
inference(resolution,[],[f83,f1752]) ).
fof(f1752,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(inv(product(X0,X1))),inv(inv(inv(product(X0,X1)))))
| ~ g(X0) )
| ~ spl1_215 ),
inference(avatar_component_clause,[],[f1751]) ).
fof(f10011,plain,
( spl1_826
| ~ spl1_2
| ~ spl1_214 ),
inference(avatar_split_clause,[],[f4827,f1747,f81,f10009]) ).
fof(f10009,plain,
( spl1_826
<=> ! [X0] :
( eg = sum(opp(f(inv(product(X0,sK0)))),f(inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_826])]) ).
fof(f1747,plain,
( spl1_214
<=> ! [X0,X1] :
( eg = sum(opp(f(inv(product(X0,X1)))),f(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_214])]) ).
fof(f4827,plain,
( ! [X0] :
( eg = sum(opp(f(inv(product(X0,sK0)))),f(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_214 ),
inference(resolution,[],[f83,f1748]) ).
fof(f1748,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(opp(f(inv(product(X0,X1)))),f(inv(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_214 ),
inference(avatar_component_clause,[],[f1747]) ).
fof(f10004,plain,
( spl1_825
| ~ spl1_2
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f4826,f1739,f81,f10002]) ).
fof(f10002,plain,
( spl1_825
<=> ! [X0] :
( eg = sum(f(inv(product(X0,sK0))),opp(f(inv(product(X0,sK0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_825])]) ).
fof(f1739,plain,
( spl1_212
<=> ! [X0,X1] :
( eg = sum(f(inv(product(X0,X1))),opp(f(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_212])]) ).
fof(f4826,plain,
( ! [X0] :
( eg = sum(f(inv(product(X0,sK0))),opp(f(inv(product(X0,sK0)))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_212 ),
inference(resolution,[],[f83,f1740]) ).
fof(f1740,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(f(inv(product(X0,X1))),opp(f(inv(product(X0,X1)))))
| ~ g(X0) )
| ~ spl1_212 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f8702,plain,
( ~ spl1_2
| ~ spl1_6
| spl1_810 ),
inference(avatar_split_clause,[],[f8647,f8603,f100,f81]) ).
fof(f8647,plain,
( ~ g(sK0)
| ~ spl1_6
| spl1_810 ),
inference(resolution,[],[f8605,f101]) ).
fof(f8605,plain,
( ~ g(inv(sK0))
| spl1_810 ),
inference(avatar_component_clause,[],[f8603]) ).
fof(f8687,plain,
( spl1_824
| ~ spl1_560
| ~ spl1_792 ),
inference(avatar_split_clause,[],[f8532,f8529,f5239,f8685]) ).
fof(f8685,plain,
( spl1_824
<=> ! [X0] :
( f(product(X0,inv(sK0))) = f(product(eh,product(X0,inv(sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_824])]) ).
fof(f8529,plain,
( spl1_792
<=> ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(eg,f(product(X0,inv(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_792])]) ).
fof(f8532,plain,
( ! [X0] :
( f(product(X0,inv(sK0))) = f(product(eh,product(X0,inv(sK0))))
| ~ g(X0) )
| ~ spl1_560
| ~ spl1_792 ),
inference(forward_demodulation,[],[f8530,f5240]) ).
fof(f8530,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(eg,f(product(X0,inv(sK0)))) )
| ~ spl1_792 ),
inference(avatar_component_clause,[],[f8529]) ).
fof(f8683,plain,
( spl1_823
| ~ spl1_561
| ~ spl1_791 ),
inference(avatar_split_clause,[],[f8527,f8524,f5243,f8681]) ).
fof(f8681,plain,
( spl1_823
<=> ! [X0] :
( f(product(X0,inv(sK0))) = f(product(product(X0,inv(sK0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_823])]) ).
fof(f8524,plain,
( spl1_791
<=> ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(f(product(X0,inv(sK0))),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_791])]) ).
fof(f8527,plain,
( ! [X0] :
( f(product(X0,inv(sK0))) = f(product(product(X0,inv(sK0)),eh))
| ~ g(X0) )
| ~ spl1_561
| ~ spl1_791 ),
inference(forward_demodulation,[],[f8525,f5244]) ).
fof(f8525,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(f(product(X0,inv(sK0))),eg) )
| ~ spl1_791 ),
inference(avatar_component_clause,[],[f8524]) ).
fof(f8655,plain,
( spl1_822
| ~ spl1_560
| ~ spl1_786 ),
inference(avatar_split_clause,[],[f7973,f7970,f5239,f8653]) ).
fof(f8653,plain,
( spl1_822
<=> ! [X0] :
( f(inv(product(X0,sK0))) = f(product(eh,inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_822])]) ).
fof(f7970,plain,
( spl1_786
<=> ! [X0] :
( f(inv(product(X0,sK0))) = sum(eg,f(inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_786])]) ).
fof(f7973,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = f(product(eh,inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_560
| ~ spl1_786 ),
inference(forward_demodulation,[],[f7971,f5240]) ).
fof(f7971,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = sum(eg,f(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_786 ),
inference(avatar_component_clause,[],[f7970]) ).
fof(f8651,plain,
( spl1_821
| ~ spl1_561
| ~ spl1_785 ),
inference(avatar_split_clause,[],[f7968,f7965,f5243,f8649]) ).
fof(f8649,plain,
( spl1_821
<=> ! [X0] :
( f(inv(product(X0,sK0))) = f(product(inv(product(X0,sK0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_821])]) ).
fof(f7965,plain,
( spl1_785
<=> ! [X0] :
( f(inv(product(X0,sK0))) = sum(f(inv(product(X0,sK0))),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_785])]) ).
fof(f7968,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = f(product(inv(product(X0,sK0)),eh))
| ~ g(X0) )
| ~ spl1_561
| ~ spl1_785 ),
inference(forward_demodulation,[],[f7966,f5244]) ).
fof(f7966,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = sum(f(inv(product(X0,sK0))),eg)
| ~ g(X0) )
| ~ spl1_785 ),
inference(avatar_component_clause,[],[f7965]) ).
fof(f8646,plain,
( spl1_820
| ~ spl1_4
| ~ spl1_557
| ~ spl1_657 ),
inference(avatar_split_clause,[],[f6711,f6632,f5214,f91,f8644]) ).
fof(f8644,plain,
( spl1_820
<=> ! [X0] :
( product(product(X0,sK0),sK0) = product(product(product(X0,sK0),eh),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_820])]) ).
fof(f6711,plain,
( ! [X0] :
( product(product(X0,sK0),sK0) = product(product(product(X0,sK0),eh),sK0)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_557
| ~ spl1_657 ),
inference(forward_demodulation,[],[f6709,f5216]) ).
fof(f6709,plain,
( ! [X0] :
( product(product(product(X0,sK0),eh),sK0) = product(product(X0,sK0),product(eh,sK0))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_657 ),
inference(resolution,[],[f6633,f93]) ).
fof(f8642,plain,
( spl1_819
| ~ spl1_4
| ~ spl1_557
| ~ spl1_648 ),
inference(avatar_split_clause,[],[f6656,f6594,f5214,f91,f8640]) ).
fof(f8640,plain,
( spl1_819
<=> ! [X0] :
( product(product(X0,eh),sK0) = product(product(product(X0,eh),eh),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_819])]) ).
fof(f6656,plain,
( ! [X0] :
( product(product(X0,eh),sK0) = product(product(product(X0,eh),eh),sK0)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_557
| ~ spl1_648 ),
inference(forward_demodulation,[],[f6654,f5216]) ).
fof(f6654,plain,
( ! [X0] :
( product(product(product(X0,eh),eh),sK0) = product(product(X0,eh),product(eh,sK0))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_648 ),
inference(resolution,[],[f6595,f93]) ).
fof(f8638,plain,
( spl1_818
| ~ spl1_4
| ~ spl1_557
| ~ spl1_647 ),
inference(avatar_split_clause,[],[f6651,f6590,f5214,f91,f8636]) ).
fof(f8636,plain,
( spl1_818
<=> ! [X0] :
( product(inv(inv(X0)),sK0) = product(product(inv(inv(X0)),eh),sK0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_818])]) ).
fof(f6651,plain,
( ! [X0] :
( product(inv(inv(X0)),sK0) = product(product(inv(inv(X0)),eh),sK0)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_557
| ~ spl1_647 ),
inference(forward_demodulation,[],[f6649,f5216]) ).
fof(f6649,plain,
( ! [X0] :
( product(product(inv(inv(X0)),eh),sK0) = product(inv(inv(X0)),product(eh,sK0))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_647 ),
inference(resolution,[],[f6591,f93]) ).
fof(f8634,plain,
( spl1_817
| ~ spl1_2
| ~ spl1_635 ),
inference(avatar_split_clause,[],[f6501,f6474,f81,f8632]) ).
fof(f8632,plain,
( spl1_817
<=> ! [X0] :
( product(sK0,product(X0,sK0)) = product(sK0,product(eh,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_817])]) ).
fof(f6501,plain,
( ! [X0] :
( product(sK0,product(X0,sK0)) = product(sK0,product(eh,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_635 ),
inference(resolution,[],[f6475,f83]) ).
fof(f8630,plain,
( spl1_816
| ~ spl1_4
| ~ spl1_635 ),
inference(avatar_split_clause,[],[f6500,f6474,f91,f8628]) ).
fof(f8628,plain,
( spl1_816
<=> ! [X0] :
( product(sK0,product(X0,eh)) = product(sK0,product(eh,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_816])]) ).
fof(f6500,plain,
( ! [X0] :
( product(sK0,product(X0,eh)) = product(sK0,product(eh,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_635 ),
inference(resolution,[],[f6475,f93]) ).
fof(f8626,plain,
( spl1_815
| ~ spl1_2
| ~ spl1_634 ),
inference(avatar_split_clause,[],[f6497,f6470,f81,f8624]) ).
fof(f8624,plain,
( spl1_815
<=> ! [X0] :
( product(sK0,product(X0,sK0)) = product(product(sK0,product(X0,sK0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_815])]) ).
fof(f6497,plain,
( ! [X0] :
( product(sK0,product(X0,sK0)) = product(product(sK0,product(X0,sK0)),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_634 ),
inference(resolution,[],[f6471,f83]) ).
fof(f8622,plain,
( spl1_814
| ~ spl1_4
| ~ spl1_634 ),
inference(avatar_split_clause,[],[f6496,f6470,f91,f8620]) ).
fof(f8620,plain,
( spl1_814
<=> ! [X0] :
( product(sK0,product(X0,eh)) = product(product(sK0,product(X0,eh)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_814])]) ).
fof(f6496,plain,
( ! [X0] :
( product(sK0,product(X0,eh)) = product(product(sK0,product(X0,eh)),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_634 ),
inference(resolution,[],[f6471,f93]) ).
fof(f8618,plain,
( spl1_813
| ~ spl1_2
| ~ spl1_633 ),
inference(avatar_split_clause,[],[f6493,f6466,f81,f8616]) ).
fof(f8616,plain,
( spl1_813
<=> ! [X0] :
( product(sK0,product(X0,sK0)) = product(eh,product(sK0,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_813])]) ).
fof(f6493,plain,
( ! [X0] :
( product(sK0,product(X0,sK0)) = product(eh,product(sK0,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_633 ),
inference(resolution,[],[f6467,f83]) ).
fof(f8614,plain,
( spl1_812
| ~ spl1_4
| ~ spl1_633 ),
inference(avatar_split_clause,[],[f6492,f6466,f91,f8612]) ).
fof(f8612,plain,
( spl1_812
<=> ! [X0] :
( product(sK0,product(X0,eh)) = product(eh,product(sK0,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_812])]) ).
fof(f6492,plain,
( ! [X0] :
( product(sK0,product(X0,eh)) = product(eh,product(sK0,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_633 ),
inference(resolution,[],[f6467,f93]) ).
fof(f8610,plain,
( spl1_811
| ~ spl1_2
| ~ spl1_632 ),
inference(avatar_split_clause,[],[f6489,f6462,f81,f8608]) ).
fof(f8608,plain,
( spl1_811
<=> ! [X0] :
( product(product(X0,sK0),sK0) = product(product(product(X0,sK0),sK0),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_811])]) ).
fof(f6489,plain,
( ! [X0] :
( product(product(X0,sK0),sK0) = product(product(product(X0,sK0),sK0),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_632 ),
inference(resolution,[],[f6463,f83]) ).
fof(f8606,plain,
( ~ spl1_810
| ~ spl1_5
| spl1_773 ),
inference(avatar_split_clause,[],[f8561,f7798,f96,f8603]) ).
fof(f7798,plain,
( spl1_773
<=> h(f(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_773])]) ).
fof(f8561,plain,
( ~ g(inv(sK0))
| ~ spl1_5
| spl1_773 ),
inference(resolution,[],[f7800,f97]) ).
fof(f7800,plain,
( ~ h(f(inv(sK0)))
| spl1_773 ),
inference(avatar_component_clause,[],[f7798]) ).
fof(f8601,plain,
( spl1_809
| ~ spl1_4
| ~ spl1_632 ),
inference(avatar_split_clause,[],[f6488,f6462,f91,f8599]) ).
fof(f8599,plain,
( spl1_809
<=> ! [X0] :
( product(product(X0,sK0),eh) = product(product(product(X0,sK0),eh),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_809])]) ).
fof(f6488,plain,
( ! [X0] :
( product(product(X0,sK0),eh) = product(product(product(X0,sK0),eh),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_632 ),
inference(resolution,[],[f6463,f93]) ).
fof(f8597,plain,
( spl1_808
| ~ spl1_2
| ~ spl1_631 ),
inference(avatar_split_clause,[],[f6485,f6458,f81,f8595]) ).
fof(f8595,plain,
( spl1_808
<=> ! [X0] :
( product(product(X0,sK0),sK0) = product(eh,product(product(X0,sK0),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_808])]) ).
fof(f6485,plain,
( ! [X0] :
( product(product(X0,sK0),sK0) = product(eh,product(product(X0,sK0),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_631 ),
inference(resolution,[],[f6459,f83]) ).
fof(f8593,plain,
( spl1_807
| ~ spl1_4
| ~ spl1_631 ),
inference(avatar_split_clause,[],[f6484,f6458,f91,f8591]) ).
fof(f8591,plain,
( spl1_807
<=> ! [X0] :
( product(product(X0,sK0),eh) = product(eh,product(product(X0,sK0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_807])]) ).
fof(f6484,plain,
( ! [X0] :
( product(product(X0,sK0),eh) = product(eh,product(product(X0,sK0),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_631 ),
inference(resolution,[],[f6459,f93]) ).
fof(f8589,plain,
( spl1_806
| ~ spl1_6
| ~ spl1_607 ),
inference(avatar_split_clause,[],[f6242,f6192,f100,f8587]) ).
fof(f8587,plain,
( spl1_806
<=> ! [X0] :
( f(product(inv(X0),sK0)) = f(product(eh,product(inv(X0),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_806])]) ).
fof(f6242,plain,
( ! [X0] :
( f(product(inv(X0),sK0)) = f(product(eh,product(inv(X0),sK0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_607 ),
inference(resolution,[],[f6193,f101]) ).
fof(f8585,plain,
( spl1_805
| ~ spl1_6
| ~ spl1_606 ),
inference(avatar_split_clause,[],[f6237,f6188,f100,f8583]) ).
fof(f8583,plain,
( spl1_805
<=> ! [X0] :
( product(sK0,inv(inv(X0))) = product(sK0,product(eh,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_805])]) ).
fof(f6237,plain,
( ! [X0] :
( product(sK0,inv(inv(X0))) = product(sK0,product(eh,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_606 ),
inference(resolution,[],[f6189,f101]) ).
fof(f8581,plain,
( spl1_804
| ~ spl1_6
| ~ spl1_605 ),
inference(avatar_split_clause,[],[f6230,f6184,f100,f8579]) ).
fof(f8579,plain,
( spl1_804
<=> ! [X0] :
( product(sK0,inv(inv(X0))) = product(product(sK0,inv(inv(X0))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_804])]) ).
fof(f6230,plain,
( ! [X0] :
( product(sK0,inv(inv(X0))) = product(product(sK0,inv(inv(X0))),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_605 ),
inference(resolution,[],[f6185,f101]) ).
fof(f8577,plain,
( spl1_803
| ~ spl1_6
| ~ spl1_604 ),
inference(avatar_split_clause,[],[f6223,f6180,f100,f8575]) ).
fof(f8575,plain,
( spl1_803
<=> ! [X0] :
( product(sK0,inv(inv(X0))) = product(eh,product(sK0,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_803])]) ).
fof(f6223,plain,
( ! [X0] :
( product(sK0,inv(inv(X0))) = product(eh,product(sK0,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_604 ),
inference(resolution,[],[f6181,f101]) ).
fof(f8573,plain,
( spl1_802
| ~ spl1_6
| ~ spl1_603 ),
inference(avatar_split_clause,[],[f6217,f6176,f100,f8571]) ).
fof(f8571,plain,
( spl1_802
<=> ! [X0] :
( product(inv(sK0),inv(X0)) = product(product(inv(sK0),inv(X0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_802])]) ).
fof(f6217,plain,
( ! [X0] :
( product(inv(sK0),inv(X0)) = product(product(inv(sK0),inv(X0)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_603 ),
inference(resolution,[],[f6177,f101]) ).
fof(f8569,plain,
( spl1_801
| ~ spl1_6
| ~ spl1_602 ),
inference(avatar_split_clause,[],[f6211,f6172,f100,f8567]) ).
fof(f8567,plain,
( spl1_801
<=> ! [X0] :
( product(inv(sK0),inv(X0)) = product(eh,product(inv(sK0),inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_801])]) ).
fof(f6211,plain,
( ! [X0] :
( product(inv(sK0),inv(X0)) = product(eh,product(inv(sK0),inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_602 ),
inference(resolution,[],[f6173,f101]) ).
fof(f8565,plain,
( spl1_800
| ~ spl1_6
| ~ spl1_601 ),
inference(avatar_split_clause,[],[f6206,f6168,f100,f8563]) ).
fof(f8563,plain,
( spl1_800
<=> ! [X0] :
( inv(product(inv(X0),sK0)) = product(eh,inv(product(inv(X0),sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_800])]) ).
fof(f6206,plain,
( ! [X0] :
( inv(product(inv(X0),sK0)) = product(eh,inv(product(inv(X0),sK0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_601 ),
inference(resolution,[],[f6169,f101]) ).
fof(f8560,plain,
( spl1_799
| ~ spl1_6
| ~ spl1_600 ),
inference(avatar_split_clause,[],[f6196,f6164,f100,f8558]) ).
fof(f8558,plain,
( spl1_799
<=> ! [X0] :
( inv(product(inv(X0),sK0)) = product(inv(product(inv(X0),sK0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_799])]) ).
fof(f6196,plain,
( ! [X0] :
( inv(product(inv(X0),sK0)) = product(inv(product(inv(X0),sK0)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_600 ),
inference(resolution,[],[f6165,f101]) ).
fof(f8556,plain,
( spl1_798
| ~ spl1_2
| ~ spl1_210 ),
inference(avatar_split_clause,[],[f4824,f1632,f81,f8554]) ).
fof(f8554,plain,
( spl1_798
<=> ! [X0] :
( product(product(X0,eh),sK0) = product(product(product(X0,eh),sK0),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_798])]) ).
fof(f1632,plain,
( spl1_210
<=> ! [X0,X1] :
( product(product(X0,eh),X1) = product(product(product(X0,eh),X1),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_210])]) ).
fof(f4824,plain,
( ! [X0] :
( product(product(X0,eh),sK0) = product(product(product(X0,eh),sK0),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_210 ),
inference(resolution,[],[f83,f1633]) ).
fof(f1633,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(X0,eh),X1) = product(product(product(X0,eh),X1),eh)
| ~ g(X0) )
| ~ spl1_210 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f8552,plain,
( spl1_797
| ~ spl1_2
| ~ spl1_209 ),
inference(avatar_split_clause,[],[f4823,f1628,f81,f8550]) ).
fof(f8550,plain,
( spl1_797
<=> ! [X0] :
( product(product(X0,eh),sK0) = product(eh,product(product(X0,eh),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_797])]) ).
fof(f1628,plain,
( spl1_209
<=> ! [X0,X1] :
( product(product(X0,eh),X1) = product(eh,product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_209])]) ).
fof(f4823,plain,
( ! [X0] :
( product(product(X0,eh),sK0) = product(eh,product(product(X0,eh),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_209 ),
inference(resolution,[],[f83,f1629]) ).
fof(f1629,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(X0,eh),X1) = product(eh,product(product(X0,eh),X1))
| ~ g(X0) )
| ~ spl1_209 ),
inference(avatar_component_clause,[],[f1628]) ).
fof(f8548,plain,
( spl1_796
| ~ spl1_2
| ~ spl1_201 ),
inference(avatar_split_clause,[],[f4821,f1596,f81,f8546]) ).
fof(f8546,plain,
( spl1_796
<=> ! [X0] :
( product(inv(inv(X0)),sK0) = product(product(inv(inv(X0)),sK0),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_796])]) ).
fof(f1596,plain,
( spl1_201
<=> ! [X0,X1] :
( product(inv(inv(X0)),X1) = product(product(inv(inv(X0)),X1),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_201])]) ).
fof(f4821,plain,
( ! [X0] :
( product(inv(inv(X0)),sK0) = product(product(inv(inv(X0)),sK0),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_201 ),
inference(resolution,[],[f83,f1597]) ).
fof(f1597,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(inv(inv(X0)),X1) = product(product(inv(inv(X0)),X1),eh)
| ~ g(X0) )
| ~ spl1_201 ),
inference(avatar_component_clause,[],[f1596]) ).
fof(f8544,plain,
( spl1_795
| ~ spl1_2
| ~ spl1_200 ),
inference(avatar_split_clause,[],[f4820,f1592,f81,f8542]) ).
fof(f8542,plain,
( spl1_795
<=> ! [X0] :
( product(inv(inv(X0)),sK0) = product(eh,product(inv(inv(X0)),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_795])]) ).
fof(f1592,plain,
( spl1_200
<=> ! [X0,X1] :
( product(inv(inv(X0)),X1) = product(eh,product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_200])]) ).
fof(f4820,plain,
( ! [X0] :
( product(inv(inv(X0)),sK0) = product(eh,product(inv(inv(X0)),sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_200 ),
inference(resolution,[],[f83,f1593]) ).
fof(f1593,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(inv(inv(X0)),X1) = product(eh,product(inv(inv(X0)),X1))
| ~ g(X0) )
| ~ spl1_200 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f8540,plain,
( spl1_794
| ~ spl1_2
| ~ spl1_199 ),
inference(avatar_split_clause,[],[f4819,f1588,f81,f8538]) ).
fof(f8538,plain,
( spl1_794
<=> ! [X0] :
( ~ g(X0)
| inv(product(X0,inv(sK0))) = product(eh,inv(product(X0,inv(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_794])]) ).
fof(f1588,plain,
( spl1_199
<=> ! [X0,X1] :
( inv(product(X0,inv(X1))) = product(eh,inv(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_199])]) ).
fof(f4819,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,inv(sK0))) = product(eh,inv(product(X0,inv(sK0)))) )
| ~ spl1_2
| ~ spl1_199 ),
inference(resolution,[],[f83,f1589]) ).
fof(f1589,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| inv(product(X0,inv(X1))) = product(eh,inv(product(X0,inv(X1)))) )
| ~ spl1_199 ),
inference(avatar_component_clause,[],[f1588]) ).
fof(f8536,plain,
( spl1_793
| ~ spl1_2
| ~ spl1_198 ),
inference(avatar_split_clause,[],[f4818,f1584,f81,f8534]) ).
fof(f8534,plain,
( spl1_793
<=> ! [X0] :
( ~ g(X0)
| inv(product(X0,inv(sK0))) = product(inv(product(X0,inv(sK0))),eh) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_793])]) ).
fof(f1584,plain,
( spl1_198
<=> ! [X0,X1] :
( inv(product(X0,inv(X1))) = product(inv(product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_198])]) ).
fof(f4818,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,inv(sK0))) = product(inv(product(X0,inv(sK0))),eh) )
| ~ spl1_2
| ~ spl1_198 ),
inference(resolution,[],[f83,f1585]) ).
fof(f1585,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| inv(product(X0,inv(X1))) = product(inv(product(X0,inv(X1))),eh) )
| ~ spl1_198 ),
inference(avatar_component_clause,[],[f1584]) ).
fof(f8531,plain,
( spl1_792
| ~ spl1_2
| ~ spl1_197 ),
inference(avatar_split_clause,[],[f4817,f1580,f81,f8529]) ).
fof(f1580,plain,
( spl1_197
<=> ! [X0,X1] :
( f(product(X0,inv(X1))) = sum(eg,f(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_197])]) ).
fof(f4817,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(eg,f(product(X0,inv(sK0)))) )
| ~ spl1_2
| ~ spl1_197 ),
inference(resolution,[],[f83,f1581]) ).
fof(f1581,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| f(product(X0,inv(X1))) = sum(eg,f(product(X0,inv(X1)))) )
| ~ spl1_197 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f8526,plain,
( spl1_791
| ~ spl1_2
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f4816,f1576,f81,f8524]) ).
fof(f1576,plain,
( spl1_196
<=> ! [X0,X1] :
( f(product(X0,inv(X1))) = sum(f(product(X0,inv(X1))),eg)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_196])]) ).
fof(f4816,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,inv(sK0))) = sum(f(product(X0,inv(sK0))),eg) )
| ~ spl1_2
| ~ spl1_196 ),
inference(resolution,[],[f83,f1577]) ).
fof(f1577,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| f(product(X0,inv(X1))) = sum(f(product(X0,inv(X1))),eg) )
| ~ spl1_196 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f8522,plain,
( spl1_790
| ~ spl1_2
| ~ spl1_195 ),
inference(avatar_split_clause,[],[f4815,f1572,f81,f8520]) ).
fof(f8520,plain,
( spl1_790
<=> ! [X0] :
( product(eh,product(X0,sK0)) = product(product(eh,product(X0,sK0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_790])]) ).
fof(f1572,plain,
( spl1_195
<=> ! [X0,X1] :
( product(eh,product(X0,X1)) = product(product(eh,product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_195])]) ).
fof(f4815,plain,
( ! [X0] :
( product(eh,product(X0,sK0)) = product(product(eh,product(X0,sK0)),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_195 ),
inference(resolution,[],[f83,f1573]) ).
fof(f1573,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(X0,X1)) = product(product(eh,product(X0,X1)),eh)
| ~ g(X0) )
| ~ spl1_195 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f7985,plain,
( spl1_789
| ~ spl1_2
| ~ spl1_193 ),
inference(avatar_split_clause,[],[f4814,f1564,f81,f7983]) ).
fof(f7983,plain,
( spl1_789
<=> ! [X0] :
( product(eh,product(X0,sK0)) = product(eh,product(eh,product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_789])]) ).
fof(f1564,plain,
( spl1_193
<=> ! [X0,X1] :
( product(eh,product(X0,X1)) = product(eh,product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_193])]) ).
fof(f4814,plain,
( ! [X0] :
( product(eh,product(X0,sK0)) = product(eh,product(eh,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_193 ),
inference(resolution,[],[f83,f1565]) ).
fof(f1565,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(X0,X1)) = product(eh,product(eh,product(X0,X1)))
| ~ g(X0) )
| ~ spl1_193 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f7981,plain,
( spl1_788
| ~ spl1_2
| ~ spl1_190 ),
inference(avatar_split_clause,[],[f4813,f1552,f81,f7979]) ).
fof(f7979,plain,
( spl1_788
<=> ! [X0] :
( inv(inv(product(X0,sK0))) = product(eh,inv(inv(product(X0,sK0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_788])]) ).
fof(f1552,plain,
( spl1_190
<=> ! [X0,X1] :
( inv(inv(product(X0,X1))) = product(eh,inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_190])]) ).
fof(f4813,plain,
( ! [X0] :
( inv(inv(product(X0,sK0))) = product(eh,inv(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_190 ),
inference(resolution,[],[f83,f1553]) ).
fof(f1553,plain,
( ! [X0,X1] :
( ~ g(X1)
| inv(inv(product(X0,X1))) = product(eh,inv(inv(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_190 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f7977,plain,
( spl1_787
| ~ spl1_2
| ~ spl1_189 ),
inference(avatar_split_clause,[],[f4812,f1548,f81,f7975]) ).
fof(f7975,plain,
( spl1_787
<=> ! [X0] :
( inv(inv(product(X0,sK0))) = product(inv(inv(product(X0,sK0))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_787])]) ).
fof(f1548,plain,
( spl1_189
<=> ! [X0,X1] :
( inv(inv(product(X0,X1))) = product(inv(inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_189])]) ).
fof(f4812,plain,
( ! [X0] :
( inv(inv(product(X0,sK0))) = product(inv(inv(product(X0,sK0))),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_189 ),
inference(resolution,[],[f83,f1549]) ).
fof(f1549,plain,
( ! [X0,X1] :
( ~ g(X1)
| inv(inv(product(X0,X1))) = product(inv(inv(product(X0,X1))),eh)
| ~ g(X0) )
| ~ spl1_189 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f7972,plain,
( spl1_786
| ~ spl1_2
| ~ spl1_188 ),
inference(avatar_split_clause,[],[f4811,f1544,f81,f7970]) ).
fof(f1544,plain,
( spl1_188
<=> ! [X0,X1] :
( f(inv(product(X0,X1))) = sum(eg,f(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_188])]) ).
fof(f4811,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = sum(eg,f(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_188 ),
inference(resolution,[],[f83,f1545]) ).
fof(f1545,plain,
( ! [X0,X1] :
( ~ g(X1)
| f(inv(product(X0,X1))) = sum(eg,f(inv(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_188 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f7967,plain,
( spl1_785
| ~ spl1_2
| ~ spl1_187 ),
inference(avatar_split_clause,[],[f4810,f1540,f81,f7965]) ).
fof(f1540,plain,
( spl1_187
<=> ! [X0,X1] :
( f(inv(product(X0,X1))) = sum(f(inv(product(X0,X1))),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_187])]) ).
fof(f4810,plain,
( ! [X0] :
( f(inv(product(X0,sK0))) = sum(f(inv(product(X0,sK0))),eg)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_187 ),
inference(resolution,[],[f83,f1541]) ).
fof(f1541,plain,
( ! [X0,X1] :
( ~ g(X1)
| f(inv(product(X0,X1))) = sum(f(inv(product(X0,X1))),eg)
| ~ g(X0) )
| ~ spl1_187 ),
inference(avatar_component_clause,[],[f1540]) ).
fof(f7925,plain,
( ~ spl1_2
| ~ spl1_5
| spl1_774 ),
inference(avatar_split_clause,[],[f7872,f7802,f96,f81]) ).
fof(f7872,plain,
( ~ g(sK0)
| ~ spl1_5
| spl1_774 ),
inference(resolution,[],[f7803,f97]) ).
fof(f7803,plain,
( ~ h(f(sK0))
| spl1_774 ),
inference(avatar_component_clause,[],[f7802]) ).
fof(f7906,plain,
( spl1_784
| ~ spl1_5
| ~ spl1_624 ),
inference(avatar_split_clause,[],[f6411,f6382,f96,f7904]) ).
fof(f7904,plain,
( spl1_784
<=> ! [X0] :
( eg = sum(opp(f(product(eh,X0))),f(product(eh,X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_784])]) ).
fof(f6411,plain,
( ! [X0] :
( eg = sum(opp(f(product(eh,X0))),f(product(eh,X0)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_624 ),
inference(resolution,[],[f6383,f97]) ).
fof(f7902,plain,
( spl1_783
| ~ spl1_5
| ~ spl1_623 ),
inference(avatar_split_clause,[],[f6405,f6378,f96,f7900]) ).
fof(f7900,plain,
( spl1_783
<=> ! [X0] :
( eg = sum(f(product(eh,X0)),opp(f(product(eh,X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_783])]) ).
fof(f6405,plain,
( ! [X0] :
( eg = sum(f(product(eh,X0)),opp(f(product(eh,X0))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_623 ),
inference(resolution,[],[f6379,f97]) ).
fof(f7898,plain,
( spl1_782
| ~ spl1_6
| ~ spl1_596 ),
inference(avatar_split_clause,[],[f6141,f6137,f100,f7896]) ).
fof(f6141,plain,
( ! [X0] :
( product(eh,inv(X0)) = product(sK0,product(inv(sK0),inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_596 ),
inference(resolution,[],[f6138,f101]) ).
fof(f7890,plain,
( spl1_781
| ~ spl1_21
| ~ spl1_561
| ~ spl1_780 ),
inference(avatar_split_clause,[],[f7886,f7882,f5243,f191,f7888]) ).
fof(f7888,plain,
( spl1_781
<=> ! [X0] :
( f(product(X0,sK0)) = f(product(product(X0,eh),sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_781])]) ).
fof(f7882,plain,
( spl1_780
<=> ! [X0] :
( f(product(X0,sK0)) = sum(sum(f(X0),eg),f(sK0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_780])]) ).
fof(f7886,plain,
( ! [X0] :
( f(product(X0,sK0)) = f(product(product(X0,eh),sK0))
| ~ g(X0) )
| ~ spl1_21
| ~ spl1_561
| ~ spl1_780 ),
inference(forward_demodulation,[],[f7885,f192]) ).
fof(f7885,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(f(product(X0,eh)),f(sK0))
| ~ g(X0) )
| ~ spl1_561
| ~ spl1_780 ),
inference(forward_demodulation,[],[f7883,f5244]) ).
fof(f7883,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(sum(f(X0),eg),f(sK0))
| ~ g(X0) )
| ~ spl1_780 ),
inference(avatar_component_clause,[],[f7882]) ).
fof(f7884,plain,
( spl1_780
| ~ spl1_2
| ~ spl1_21
| ~ spl1_34
| ~ spl1_240 ),
inference(avatar_split_clause,[],[f4999,f1960,f272,f191,f81,f7882]) ).
fof(f272,plain,
( spl1_34
<=> ! [X0] :
( f(X0) = sum(eg,f(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
fof(f1960,plain,
( spl1_240
<=> ! [X0,X1] :
( sum(sum(f(X0),eg),f(X1)) = sum(f(X0),sum(eg,f(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_240])]) ).
fof(f4999,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(sum(f(X0),eg),f(sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_34
| ~ spl1_240 ),
inference(forward_demodulation,[],[f4998,f192]) ).
fof(f4998,plain,
( ! [X0] :
( sum(sum(f(X0),eg),f(sK0)) = sum(f(X0),f(sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_34
| ~ spl1_240 ),
inference(forward_demodulation,[],[f4844,f4722]) ).
fof(f4722,plain,
( f(sK0) = sum(eg,f(sK0))
| ~ spl1_2
| ~ spl1_34 ),
inference(resolution,[],[f83,f273]) ).
fof(f273,plain,
( ! [X0] :
( ~ g(X0)
| f(X0) = sum(eg,f(X0)) )
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f4844,plain,
( ! [X0] :
( ~ g(X0)
| sum(sum(f(X0),eg),f(sK0)) = sum(f(X0),sum(eg,f(sK0))) )
| ~ spl1_2
| ~ spl1_240 ),
inference(resolution,[],[f83,f1961]) ).
fof(f1961,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| sum(sum(f(X0),eg),f(X1)) = sum(f(X0),sum(eg,f(X1))) )
| ~ spl1_240 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f7880,plain,
( spl1_779
| ~ spl1_2
| ~ spl1_183 ),
inference(avatar_split_clause,[],[f4809,f1508,f81,f7878]) ).
fof(f7878,plain,
( spl1_779
<=> ! [X0] : eg = sum(sum(f(sK0),opp(X0)),opp(sum(f(sK0),opp(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_779])]) ).
fof(f1508,plain,
( spl1_183
<=> ! [X0,X1] :
( eg = sum(sum(f(X0),opp(X1)),opp(sum(f(X0),opp(X1))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_183])]) ).
fof(f4809,plain,
( ! [X0] : eg = sum(sum(f(sK0),opp(X0)),opp(sum(f(sK0),opp(X0))))
| ~ spl1_2
| ~ spl1_183 ),
inference(resolution,[],[f83,f1509]) ).
fof(f1509,plain,
( ! [X0,X1] :
( ~ g(X0)
| eg = sum(sum(f(X0),opp(X1)),opp(sum(f(X0),opp(X1)))) )
| ~ spl1_183 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f7876,plain,
( spl1_778
| ~ spl1_2
| ~ spl1_182 ),
inference(avatar_split_clause,[],[f4808,f1504,f81,f7874]) ).
fof(f7874,plain,
( spl1_778
<=> ! [X0] : eg = sum(opp(sum(f(sK0),opp(X0))),sum(f(sK0),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_778])]) ).
fof(f1504,plain,
( spl1_182
<=> ! [X0,X1] :
( eg = sum(opp(sum(f(X0),opp(X1))),sum(f(X0),opp(X1)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_182])]) ).
fof(f4808,plain,
( ! [X0] : eg = sum(opp(sum(f(sK0),opp(X0))),sum(f(sK0),opp(X0)))
| ~ spl1_2
| ~ spl1_182 ),
inference(resolution,[],[f83,f1505]) ).
fof(f1505,plain,
( ! [X0,X1] :
( ~ g(X0)
| eg = sum(opp(sum(f(X0),opp(X1))),sum(f(X0),opp(X1))) )
| ~ spl1_182 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f7871,plain,
( spl1_777
| ~ spl1_2
| ~ spl1_181 ),
inference(avatar_split_clause,[],[f4807,f1500,f81,f7869]) ).
fof(f7869,plain,
( spl1_777
<=> ! [X0] : eg = sum(sum(opp(X0),f(sK0)),opp(sum(opp(X0),f(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_777])]) ).
fof(f1500,plain,
( spl1_181
<=> ! [X0,X1] :
( eg = sum(sum(opp(X0),f(X1)),opp(sum(opp(X0),f(X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_181])]) ).
fof(f4807,plain,
( ! [X0] : eg = sum(sum(opp(X0),f(sK0)),opp(sum(opp(X0),f(sK0))))
| ~ spl1_2
| ~ spl1_181 ),
inference(resolution,[],[f83,f1501]) ).
fof(f1501,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(sum(opp(X0),f(X1)),opp(sum(opp(X0),f(X1)))) )
| ~ spl1_181 ),
inference(avatar_component_clause,[],[f1500]) ).
fof(f7867,plain,
( spl1_776
| ~ spl1_2
| ~ spl1_180 ),
inference(avatar_split_clause,[],[f4806,f1496,f81,f7865]) ).
fof(f7865,plain,
( spl1_776
<=> ! [X0] : eg = sum(opp(sum(opp(X0),f(sK0))),sum(opp(X0),f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_776])]) ).
fof(f1496,plain,
( spl1_180
<=> ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(X1))),sum(opp(X0),f(X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_180])]) ).
fof(f4806,plain,
( ! [X0] : eg = sum(opp(sum(opp(X0),f(sK0))),sum(opp(X0),f(sK0)))
| ~ spl1_2
| ~ spl1_180 ),
inference(resolution,[],[f83,f1497]) ).
fof(f1497,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(opp(sum(opp(X0),f(X1))),sum(opp(X0),f(X1))) )
| ~ spl1_180 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f7809,plain,
( spl1_775
| ~ spl1_5
| ~ spl1_619 ),
inference(avatar_split_clause,[],[f6354,f6288,f96,f7807]) ).
fof(f7807,plain,
( spl1_775
<=> ! [X0] :
( f(product(X0,eh)) = f(product(eh,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_775])]) ).
fof(f6354,plain,
( ! [X0] :
( f(product(X0,eh)) = f(product(eh,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_619 ),
inference(resolution,[],[f6289,f97]) ).
fof(f7805,plain,
( ~ spl1_772
| ~ spl1_773
| spl1_774
| ~ spl1_42
| ~ spl1_636 ),
inference(avatar_split_clause,[],[f6579,f6478,f340,f7802,f7798,f7794]) ).
fof(f6478,plain,
( spl1_636
<=> sK0 = product(product(sK0,sK0),inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_636])]) ).
fof(f6579,plain,
( h(f(sK0))
| ~ h(f(inv(sK0)))
| ~ h(f(product(sK0,sK0)))
| ~ spl1_42
| ~ spl1_636 ),
inference(superposition,[],[f341,f6480]) ).
fof(f6480,plain,
( sK0 = product(product(sK0,sK0),inv(sK0))
| ~ spl1_636 ),
inference(avatar_component_clause,[],[f6478]) ).
fof(f7792,plain,
( spl1_771
| ~ spl1_5
| ~ spl1_617 ),
inference(avatar_split_clause,[],[f6342,f6280,f96,f7790]) ).
fof(f7790,plain,
( spl1_771
<=> ! [X0] :
( f(product(eh,X0)) = f(product(eh,product(eh,X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_771])]) ).
fof(f6342,plain,
( ! [X0] :
( f(product(eh,X0)) = f(product(eh,product(eh,X0)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_617 ),
inference(resolution,[],[f6281,f97]) ).
fof(f7788,plain,
( spl1_770
| ~ spl1_5
| ~ spl1_616 ),
inference(avatar_split_clause,[],[f6336,f6276,f96,f7786]) ).
fof(f7786,plain,
( spl1_770
<=> ! [X0] :
( f(product(eh,X0)) = f(product(product(eh,X0),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_770])]) ).
fof(f6336,plain,
( ! [X0] :
( f(product(eh,X0)) = f(product(product(eh,X0),eh))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_616 ),
inference(resolution,[],[f6277,f97]) ).
fof(f7784,plain,
( spl1_769
| ~ spl1_2
| ~ spl1_176 ),
inference(avatar_split_clause,[],[f4803,f1457,f81,f7782]) ).
fof(f7782,plain,
( spl1_769
<=> ! [X0] : sum(f(sK0),opp(X0)) = sum(sum(f(sK0),opp(X0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_769])]) ).
fof(f1457,plain,
( spl1_176
<=> ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(sum(f(X0),opp(X1)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_176])]) ).
fof(f4803,plain,
( ! [X0] : sum(f(sK0),opp(X0)) = sum(sum(f(sK0),opp(X0)),eg)
| ~ spl1_2
| ~ spl1_176 ),
inference(resolution,[],[f83,f1458]) ).
fof(f1458,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),opp(X1)) = sum(sum(f(X0),opp(X1)),eg) )
| ~ spl1_176 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f7780,plain,
( spl1_768
| ~ spl1_2
| ~ spl1_175 ),
inference(avatar_split_clause,[],[f4802,f1453,f81,f7778]) ).
fof(f7778,plain,
( spl1_768
<=> ! [X0] : sum(f(sK0),opp(X0)) = sum(eg,sum(f(sK0),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_768])]) ).
fof(f1453,plain,
( spl1_175
<=> ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(eg,sum(f(X0),opp(X1)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_175])]) ).
fof(f4802,plain,
( ! [X0] : sum(f(sK0),opp(X0)) = sum(eg,sum(f(sK0),opp(X0)))
| ~ spl1_2
| ~ spl1_175 ),
inference(resolution,[],[f83,f1454]) ).
fof(f1454,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),opp(X1)) = sum(eg,sum(f(X0),opp(X1))) )
| ~ spl1_175 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f7776,plain,
( spl1_767
| ~ spl1_2
| ~ spl1_173 ),
inference(avatar_split_clause,[],[f4800,f1445,f81,f7774]) ).
fof(f7774,plain,
( spl1_767
<=> ! [X0] : sum(opp(X0),f(sK0)) = sum(sum(opp(X0),f(sK0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_767])]) ).
fof(f1445,plain,
( spl1_173
<=> ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(sum(opp(X0),f(X1)),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_173])]) ).
fof(f4800,plain,
( ! [X0] : sum(opp(X0),f(sK0)) = sum(sum(opp(X0),f(sK0)),eg)
| ~ spl1_2
| ~ spl1_173 ),
inference(resolution,[],[f83,f1446]) ).
fof(f1446,plain,
( ! [X0,X1] :
( ~ g(X1)
| sum(opp(X0),f(X1)) = sum(sum(opp(X0),f(X1)),eg) )
| ~ spl1_173 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f7772,plain,
( spl1_766
| ~ spl1_2
| ~ spl1_172 ),
inference(avatar_split_clause,[],[f4799,f1441,f81,f7770]) ).
fof(f7770,plain,
( spl1_766
<=> ! [X0] : sum(opp(X0),f(sK0)) = sum(eg,sum(opp(X0),f(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_766])]) ).
fof(f1441,plain,
( spl1_172
<=> ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(eg,sum(opp(X0),f(X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_172])]) ).
fof(f4799,plain,
( ! [X0] : sum(opp(X0),f(sK0)) = sum(eg,sum(opp(X0),f(sK0)))
| ~ spl1_2
| ~ spl1_172 ),
inference(resolution,[],[f83,f1442]) ).
fof(f1442,plain,
( ! [X0,X1] :
( ~ g(X1)
| sum(opp(X0),f(X1)) = sum(eg,sum(opp(X0),f(X1))) )
| ~ spl1_172 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f7755,plain,
( spl1_765
| ~ spl1_149
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5653,f5638,f1196,f7753]) ).
fof(f7753,plain,
( spl1_765
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(product(X2,product(X0,eh)))),X3),X4) = sum(sum(X1,f(product(X2,product(X0,eh)))),sum(X3,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_765])]) ).
fof(f1196,plain,
( spl1_149
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(sum(X1,f(product(X2,X3))),X0),X4) = sum(sum(X1,f(product(X2,X3))),sum(X0,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
fof(f5653,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(product(X2,product(X0,eh)))),X3),X4) = sum(sum(X1,f(product(X2,product(X0,eh)))),sum(X3,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(f(X2)) )
| ~ spl1_149
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1197]) ).
fof(f1197,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X3))
| sum(sum(sum(X1,f(product(X2,X3))),X0),X4) = sum(sum(X1,f(product(X2,X3))),sum(X0,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X0)
| ~ h(f(X2)) )
| ~ spl1_149 ),
inference(avatar_component_clause,[],[f1196]) ).
fof(f7748,plain,
( spl1_764
| ~ spl1_149
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5341,f5326,f1196,f7746]) ).
fof(f7746,plain,
( spl1_764
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(product(X2,product(eh,X0)))),X3),X4) = sum(sum(X1,f(product(X2,product(eh,X0)))),sum(X3,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_764])]) ).
fof(f5341,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(product(X2,product(eh,X0)))),X3),X4) = sum(sum(X1,f(product(X2,product(eh,X0)))),sum(X3,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(f(X2)) )
| ~ spl1_149
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1197]) ).
fof(f7730,plain,
( spl1_763
| ~ spl1_147
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5752,f5638,f1180,f7728]) ).
fof(f7728,plain,
( spl1_763
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,sum(X2,X3)),X4),f(product(X0,eh))) = sum(sum(X1,sum(X2,X3)),sum(X4,f(product(X0,eh))))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_763])]) ).
fof(f1180,plain,
( spl1_147
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(sum(X1,sum(X2,X3)),X0),X4) = sum(sum(X1,sum(X2,X3)),sum(X0,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
fof(f5752,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X0))
| sum(sum(sum(X1,sum(X2,X3)),X4),f(product(X0,eh))) = sum(sum(X1,sum(X2,X3)),sum(X4,f(product(X0,eh))))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_147
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1181]) ).
fof(f1181,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(X4)
| sum(sum(sum(X1,sum(X2,X3)),X0),X4) = sum(sum(X1,sum(X2,X3)),sum(X0,X4))
| ~ h(X0)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_147 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f7726,plain,
( spl1_762
| ~ spl1_147
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5440,f5326,f1180,f7724]) ).
fof(f7724,plain,
( spl1_762
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,sum(X2,X3)),X4),f(product(eh,X0))) = sum(sum(X1,sum(X2,X3)),sum(X4,f(product(eh,X0))))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_762])]) ).
fof(f5440,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X0))
| sum(sum(sum(X1,sum(X2,X3)),X4),f(product(eh,X0))) = sum(sum(X1,sum(X2,X3)),sum(X4,f(product(eh,X0))))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_147
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1181]) ).
fof(f7683,plain,
( spl1_761
| ~ spl1_142
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5751,f5638,f1131,f7681]) ).
fof(f7681,plain,
( spl1_761
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(X2)),X3),f(product(X0,eh))) = sum(sum(X1,f(X2)),sum(X3,f(product(X0,eh))))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_761])]) ).
fof(f1131,plain,
( spl1_142
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(sum(X1,f(X2)),X0),X3) = sum(sum(X1,f(X2)),sum(X0,X3))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_142])]) ).
fof(f5751,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(X2)),X3),f(product(X0,eh))) = sum(sum(X1,f(X2)),sum(X3,f(product(X0,eh))))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_142
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1132]) ).
fof(f1132,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X3)
| sum(sum(sum(X1,f(X2)),X0),X3) = sum(sum(X1,f(X2)),sum(X0,X3))
| ~ h(X0)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_142 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f7679,plain,
( spl1_760
| ~ spl1_139
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5750,f5638,f1119,f7677]) ).
fof(f7677,plain,
( spl1_760
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),sum(X2,f(product(X0,eh)))),X3) = sum(f(X1),sum(sum(X2,f(product(X0,eh))),X3))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_760])]) ).
fof(f1119,plain,
( spl1_139
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(f(X1),sum(X2,X3)),X0) = sum(f(X1),sum(sum(X2,X3),X0))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
fof(f5750,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),sum(X2,f(product(X0,eh)))),X3) = sum(f(X1),sum(sum(X2,f(product(X0,eh))),X3))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_139
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1120]) ).
fof(f1120,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X3)
| sum(sum(f(X1),sum(X2,X3)),X0) = sum(f(X1),sum(sum(X2,X3),X0))
| ~ g(X1)
| ~ h(X0)
| ~ h(X2) )
| ~ spl1_139 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f7675,plain,
( spl1_759
| ~ spl1_146
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5652,f5638,f1174,f7673]) ).
fof(f7673,plain,
( spl1_759
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ g(X2)
| sum(f(X2),sum(f(product(X3,product(X0,eh))),X1)) = sum(f(product(X2,product(X3,product(X0,eh)))),X1)
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_759])]) ).
fof(f1174,plain,
( spl1_146
<=> ! [X0,X3,X2,X1] :
( sum(f(X1),sum(f(product(X2,X3)),X0)) = sum(f(product(X1,product(X2,X3))),X0)
| ~ h(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
fof(f5652,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ g(X2)
| sum(f(X2),sum(f(product(X3,product(X0,eh))),X1)) = sum(f(product(X2,product(X3,product(X0,eh)))),X1)
| ~ h(f(X3)) )
| ~ spl1_146
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1175]) ).
fof(f1175,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X3))
| ~ h(X0)
| ~ g(X1)
| sum(f(X1),sum(f(product(X2,X3)),X0)) = sum(f(product(X1,product(X2,X3))),X0)
| ~ h(f(X2)) )
| ~ spl1_146 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f7671,plain,
( spl1_758
| ~ spl1_142
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5439,f5326,f1131,f7669]) ).
fof(f7669,plain,
( spl1_758
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(X2)),X3),f(product(eh,X0))) = sum(sum(X1,f(X2)),sum(X3,f(product(eh,X0))))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_758])]) ).
fof(f5439,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,f(X2)),X3),f(product(eh,X0))) = sum(sum(X1,f(X2)),sum(X3,f(product(eh,X0))))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_142
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1132]) ).
fof(f7667,plain,
( spl1_757
| ~ spl1_139
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5438,f5326,f1119,f7665]) ).
fof(f7665,plain,
( spl1_757
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),sum(X2,f(product(eh,X0)))),X3) = sum(f(X1),sum(sum(X2,f(product(eh,X0))),X3))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_757])]) ).
fof(f5438,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),sum(X2,f(product(eh,X0)))),X3) = sum(f(X1),sum(sum(X2,f(product(eh,X0))),X3))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_139
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1120]) ).
fof(f7663,plain,
( spl1_756
| ~ spl1_146
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5340,f5326,f1174,f7661]) ).
fof(f7661,plain,
( spl1_756
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ g(X2)
| sum(f(X2),sum(f(product(X3,product(eh,X0))),X1)) = sum(f(product(X2,product(X3,product(eh,X0)))),X1)
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_756])]) ).
fof(f5340,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ g(X2)
| sum(f(X2),sum(f(product(X3,product(eh,X0))),X1)) = sum(f(product(X2,product(X3,product(eh,X0)))),X1)
| ~ h(f(X3)) )
| ~ spl1_146
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1175]) ).
fof(f7638,plain,
( spl1_755
| ~ spl1_145
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5651,f5638,f1161,f7636]) ).
fof(f7636,plain,
( spl1_755
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(product(X2,product(X0,eh)))),X3) = sum(opp(X1),sum(f(product(X2,product(X0,eh))),X3))
| ~ h(X3)
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_755])]) ).
fof(f1161,plain,
( spl1_145
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(opp(X1),f(product(X2,X3))),X0) = sum(opp(X1),sum(f(product(X2,X3)),X0))
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
fof(f5651,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(product(X2,product(X0,eh)))),X3) = sum(opp(X1),sum(f(product(X2,product(X0,eh))),X3))
| ~ h(X3)
| ~ h(f(X2)) )
| ~ spl1_145
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1162]) ).
fof(f1162,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X3))
| sum(sum(opp(X1),f(product(X2,X3))),X0) = sum(opp(X1),sum(f(product(X2,X3)),X0))
| ~ h(X0)
| ~ h(f(X2)) )
| ~ spl1_145 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f7634,plain,
( spl1_754
| ~ spl1_144
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5650,f5638,f1157,f7632]) ).
fof(f7632,plain,
( spl1_754
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(product(X0,eh),X1)),X3),X2) = sum(f(product(product(X0,eh),X1)),sum(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_754])]) ).
fof(f1157,plain,
( spl1_144
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(X1,X0)),X3),X2) = sum(f(product(X1,X0)),sum(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_144])]) ).
fof(f5650,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(product(X0,eh),X1)),X3),X2) = sum(f(product(product(X0,eh),X1)),sum(X3,X2)) )
| ~ spl1_144
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1158]) ).
fof(f1158,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(X1,X0)),X3),X2) = sum(f(product(X1,X0)),sum(X3,X2)) )
| ~ spl1_144 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f7630,plain,
( spl1_753
| ~ spl1_145
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5339,f5326,f1161,f7628]) ).
fof(f7628,plain,
( spl1_753
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(product(X2,product(eh,X0)))),X3) = sum(opp(X1),sum(f(product(X2,product(eh,X0))),X3))
| ~ h(X3)
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_753])]) ).
fof(f5339,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(product(X2,product(eh,X0)))),X3) = sum(opp(X1),sum(f(product(X2,product(eh,X0))),X3))
| ~ h(X3)
| ~ h(f(X2)) )
| ~ spl1_145
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1162]) ).
fof(f7626,plain,
( spl1_752
| ~ spl1_144
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5338,f5326,f1157,f7624]) ).
fof(f7624,plain,
( spl1_752
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(product(eh,X0),X1)),X3),X2) = sum(f(product(product(eh,X0),X1)),sum(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_752])]) ).
fof(f5338,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(product(eh,X0),X1)),X3),X2) = sum(f(product(product(eh,X0),X1)),sum(X3,X2)) )
| ~ spl1_144
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1158]) ).
fof(f7577,plain,
( spl1_751
| ~ spl1_134
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5749,f5638,f1081,f7575]) ).
fof(f7575,plain,
( spl1_751
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,opp(X2)),X3),f(product(X0,eh))) = sum(sum(X1,opp(X2)),sum(X3,f(product(X0,eh))))
| ~ h(X3)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_751])]) ).
fof(f1081,plain,
( spl1_134
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(sum(X1,opp(X2)),X0),X3) = sum(sum(X1,opp(X2)),sum(X0,X3))
| ~ h(X3)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
fof(f5749,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,opp(X2)),X3),f(product(X0,eh))) = sum(sum(X1,opp(X2)),sum(X3,f(product(X0,eh))))
| ~ h(X3)
| ~ h(X1) )
| ~ spl1_134
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1082]) ).
fof(f1082,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X3)
| sum(sum(sum(X1,opp(X2)),X0),X3) = sum(sum(X1,opp(X2)),sum(X0,X3))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_134 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f7573,plain,
( spl1_750
| ~ spl1_133
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5748,f5638,f1077,f7571]) ).
fof(f7571,plain,
( spl1_750
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),sum(X2,f(product(X0,eh)))),X3) = sum(opp(X1),sum(sum(X2,f(product(X0,eh))),X3))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_750])]) ).
fof(f1077,plain,
( spl1_133
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| sum(sum(opp(X1),sum(X2,X3)),X0) = sum(opp(X1),sum(sum(X2,X3),X0))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
fof(f5748,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),sum(X2,f(product(X0,eh)))),X3) = sum(opp(X1),sum(sum(X2,f(product(X0,eh))),X3))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_133
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1078]) ).
fof(f1078,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X3)
| sum(sum(opp(X1),sum(X2,X3)),X0) = sum(opp(X1),sum(sum(X2,X3),X0))
| ~ h(X0)
| ~ h(X2) )
| ~ spl1_133 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f7569,plain,
( spl1_749
| ~ spl1_57
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5722,f5638,f473,f7567]) ).
fof(f7567,plain,
( spl1_749
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(sum(X2,f(product(X0,eh))),X1),X3) = sum(sum(X2,f(product(X0,eh))),sum(X1,X3))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_749])]) ).
fof(f473,plain,
( spl1_57
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(sum(X2,X3),X1),X0) = sum(sum(X2,X3),sum(X1,X0))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
fof(f5722,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(sum(X2,f(product(X0,eh))),X1),X3) = sum(sum(X2,f(product(X0,eh))),sum(X1,X3))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_57
| ~ spl1_572 ),
inference(resolution,[],[f5639,f474]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X3)
| ~ h(X1)
| sum(sum(sum(X2,X3),X1),X0) = sum(sum(X2,X3),sum(X1,X0))
| ~ h(X0)
| ~ h(X2) )
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f7565,plain,
( spl1_748
| ~ spl1_134
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5437,f5326,f1081,f7563]) ).
fof(f7563,plain,
( spl1_748
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,opp(X2)),X3),f(product(eh,X0))) = sum(sum(X1,opp(X2)),sum(X3,f(product(eh,X0))))
| ~ h(X3)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_748])]) ).
fof(f5437,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,opp(X2)),X3),f(product(eh,X0))) = sum(sum(X1,opp(X2)),sum(X3,f(product(eh,X0))))
| ~ h(X3)
| ~ h(X1) )
| ~ spl1_134
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1082]) ).
fof(f7561,plain,
( spl1_747
| ~ spl1_133
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5436,f5326,f1077,f7559]) ).
fof(f7559,plain,
( spl1_747
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),sum(X2,f(product(eh,X0)))),X3) = sum(opp(X1),sum(sum(X2,f(product(eh,X0))),X3))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_747])]) ).
fof(f5436,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),sum(X2,f(product(eh,X0)))),X3) = sum(opp(X1),sum(sum(X2,f(product(eh,X0))),X3))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_133
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1078]) ).
fof(f7557,plain,
( spl1_746
| ~ spl1_57
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5410,f5326,f473,f7555]) ).
fof(f7555,plain,
( spl1_746
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(sum(X2,f(product(eh,X0))),X1),X3) = sum(sum(X2,f(product(eh,X0))),sum(X1,X3))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_746])]) ).
fof(f5410,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(sum(X2,f(product(eh,X0))),X1),X3) = sum(sum(X2,f(product(eh,X0))),sum(X1,X3))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_57
| ~ spl1_571 ),
inference(resolution,[],[f5327,f474]) ).
fof(f7543,plain,
( spl1_745
| ~ spl1_138
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5849,f5638,f5239,f1115,f7541]) ).
fof(f7541,plain,
( spl1_745
<=> ! [X2,X0,X1] :
( sum(eg,sum(f(product(X1,product(X0,eh))),X2)) = sum(f(product(eh,product(X1,product(X0,eh)))),X2)
| ~ h(f(X0))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_745])]) ).
fof(f1115,plain,
( spl1_138
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(eg,sum(f(product(X1,X2)),X0)) = sum(sum(eg,f(product(X1,X2))),X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
fof(f5849,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(f(product(X1,product(X0,eh))),X2)) = sum(f(product(eh,product(X1,product(X0,eh)))),X2)
| ~ h(f(X0))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_138
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5649,f5240]) ).
fof(f5649,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(product(X1,product(X0,eh))),X2)) = sum(sum(eg,f(product(X1,product(X0,eh)))),X2)
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_138
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1116]) ).
fof(f1116,plain,
( ! [X2,X0,X1] :
( ~ h(f(X2))
| sum(eg,sum(f(product(X1,X2)),X0)) = sum(sum(eg,f(product(X1,X2))),X0)
| ~ h(X0)
| ~ h(f(X1)) )
| ~ spl1_138 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f7536,plain,
( spl1_744
| ~ spl1_138
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5537,f5326,f5239,f1115,f7534]) ).
fof(f7534,plain,
( spl1_744
<=> ! [X2,X0,X1] :
( sum(eg,sum(f(product(X1,product(eh,X0))),X2)) = sum(f(product(eh,product(X1,product(eh,X0)))),X2)
| ~ h(f(X0))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_744])]) ).
fof(f5537,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(f(product(X1,product(eh,X0))),X2)) = sum(f(product(eh,product(X1,product(eh,X0)))),X2)
| ~ h(f(X0))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_138
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5337,f5240]) ).
fof(f5337,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(product(X1,product(eh,X0))),X2)) = sum(sum(eg,f(product(X1,product(eh,X0)))),X2)
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_138
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1116]) ).
fof(f7484,plain,
( spl1_743
| ~ spl1_128
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5747,f5638,f1038,f7482]) ).
fof(f7482,plain,
( spl1_743
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,eg),X2),f(product(X0,eh))) = sum(sum(X1,eg),sum(X2,f(product(X0,eh))))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_743])]) ).
fof(f1038,plain,
( spl1_128
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(sum(X1,eg),X0),X2) = sum(sum(X1,eg),sum(X0,X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
fof(f5747,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,eg),X2),f(product(X0,eh))) = sum(sum(X1,eg),sum(X2,f(product(X0,eh))))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_128
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1039]) ).
fof(f1039,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(sum(X1,eg),X0),X2) = sum(sum(X1,eg),sum(X0,X2))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_128 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f7479,plain,
( spl1_742
| ~ spl1_125
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5746,f5638,f1026,f7477]) ).
fof(f7477,plain,
( spl1_742
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(sum(X1,f(product(X0,eh))),X2)) = sum(sum(eg,sum(X1,f(product(X0,eh)))),X2)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_742])]) ).
fof(f1026,plain,
( spl1_125
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(eg,sum(sum(X1,X2),X0)) = sum(sum(eg,sum(X1,X2)),X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
fof(f5746,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(sum(X1,f(product(X0,eh))),X2)) = sum(sum(eg,sum(X1,f(product(X0,eh)))),X2)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_125
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1027]) ).
fof(f1027,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(eg,sum(sum(X1,X2),X0)) = sum(sum(eg,sum(X1,X2)),X0)
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_125 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f7475,plain,
( spl1_741
| ~ spl1_137
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5648,f5638,f1107,f7473]) ).
fof(f7473,plain,
( spl1_741
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(f(product(X1,product(X0,eh))),X2),opp(sum(f(product(X1,product(X0,eh))),X2)))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_741])]) ).
fof(f1107,plain,
( spl1_137
<=> ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(X1,X2)),X0),opp(sum(f(product(X1,X2)),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
fof(f5648,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(f(product(X1,product(X0,eh))),X2),opp(sum(f(product(X1,product(X0,eh))),X2)))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_137
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1108]) ).
fof(f1108,plain,
( ! [X2,X0,X1] :
( ~ h(f(X2))
| eg = sum(sum(f(product(X1,X2)),X0),opp(sum(f(product(X1,X2)),X0)))
| ~ h(X0)
| ~ h(f(X1)) )
| ~ spl1_137 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f7471,plain,
( spl1_740
| ~ spl1_136
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5647,f5638,f1103,f7469]) ).
fof(f7469,plain,
( spl1_740
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(f(product(X1,product(X0,eh))),X2)),sum(f(product(X1,product(X0,eh))),X2))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_740])]) ).
fof(f1103,plain,
( spl1_136
<=> ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(X1,X2)),X0)),sum(f(product(X1,X2)),X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
fof(f5647,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(f(product(X1,product(X0,eh))),X2)),sum(f(product(X1,product(X0,eh))),X2))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_136
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1104]) ).
fof(f1104,plain,
( ! [X2,X0,X1] :
( ~ h(f(X2))
| eg = sum(opp(sum(f(product(X1,X2)),X0)),sum(f(product(X1,X2)),X0))
| ~ h(X0)
| ~ h(f(X1)) )
| ~ spl1_136 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f7467,plain,
( spl1_739
| ~ spl1_128
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5435,f5326,f1038,f7465]) ).
fof(f7465,plain,
( spl1_739
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,eg),X2),f(product(eh,X0))) = sum(sum(X1,eg),sum(X2,f(product(eh,X0))))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_739])]) ).
fof(f5435,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(sum(X1,eg),X2),f(product(eh,X0))) = sum(sum(X1,eg),sum(X2,f(product(eh,X0))))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_128
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1039]) ).
fof(f7463,plain,
( spl1_738
| ~ spl1_125
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5434,f5326,f1026,f7461]) ).
fof(f7461,plain,
( spl1_738
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(sum(X1,f(product(eh,X0))),X2)) = sum(sum(eg,sum(X1,f(product(eh,X0)))),X2)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_738])]) ).
fof(f5434,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(sum(X1,f(product(eh,X0))),X2)) = sum(sum(eg,sum(X1,f(product(eh,X0)))),X2)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_125
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1027]) ).
fof(f7459,plain,
( spl1_737
| ~ spl1_137
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5336,f5326,f1107,f7457]) ).
fof(f7457,plain,
( spl1_737
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(f(product(X1,product(eh,X0))),X2),opp(sum(f(product(X1,product(eh,X0))),X2)))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_737])]) ).
fof(f5336,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(f(product(X1,product(eh,X0))),X2),opp(sum(f(product(X1,product(eh,X0))),X2)))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_137
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1108]) ).
fof(f7455,plain,
( spl1_736
| ~ spl1_136
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5335,f5326,f1103,f7453]) ).
fof(f7453,plain,
( spl1_736
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(f(product(X1,product(eh,X0))),X2)),sum(f(product(X1,product(eh,X0))),X2))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_736])]) ).
fof(f5335,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(f(product(X1,product(eh,X0))),X2)),sum(f(product(X1,product(eh,X0))),X2))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_136
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1104]) ).
fof(f7389,plain,
( spl1_735
| ~ spl1_19
| ~ spl1_584 ),
inference(avatar_split_clause,[],[f6043,f6036,f164,f7387]) ).
fof(f7387,plain,
( spl1_735
<=> ! [X0,X3,X2,X1] :
( product(product(sK0,product(X0,product(X1,X2))),X3) = product(sK0,product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_735])]) ).
fof(f6036,plain,
( spl1_584
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(sK0,product(X1,X2)),X0) = product(sK0,product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_584])]) ).
fof(f6043,plain,
( ! [X2,X3,X0,X1] :
( product(product(sK0,product(X0,product(X1,X2))),X3) = product(sK0,product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_584 ),
inference(resolution,[],[f6037,f165]) ).
fof(f6037,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(sK0,product(X1,X2)),X0) = product(sK0,product(product(X1,X2),X0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_584 ),
inference(avatar_component_clause,[],[f6036]) ).
fof(f7385,plain,
( spl1_734
| ~ spl1_19
| ~ spl1_583 ),
inference(avatar_split_clause,[],[f6039,f6032,f164,f7383]) ).
fof(f7383,plain,
( spl1_734
<=> ! [X0,X3,X2,X1] :
( product(product(product(X0,sK0),X1),product(X2,X3)) = product(product(X0,sK0),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_734])]) ).
fof(f6032,plain,
( spl1_583
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(product(X1,sK0),X0),X2) = product(product(X1,sK0),product(X0,X2))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_583])]) ).
fof(f6039,plain,
( ! [X2,X3,X0,X1] :
( product(product(product(X0,sK0),X1),product(X2,X3)) = product(product(X0,sK0),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_19
| ~ spl1_583 ),
inference(resolution,[],[f6033,f165]) ).
fof(f6033,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(product(X1,sK0),X0),X2) = product(product(X1,sK0),product(X0,X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_583 ),
inference(avatar_component_clause,[],[f6032]) ).
fof(f7381,plain,
( spl1_733
| ~ spl1_2
| ~ spl1_613 ),
inference(avatar_split_clause,[],[f6322,f6264,f81,f7378]) ).
fof(f7378,plain,
( spl1_733
<=> eh = product(inv(inv(product(sK0,sK0))),inv(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_733])]) ).
fof(f6322,plain,
( eh = product(inv(inv(product(sK0,sK0))),inv(product(sK0,sK0)))
| ~ spl1_2
| ~ spl1_613 ),
inference(resolution,[],[f6265,f83]) ).
fof(f7376,plain,
( spl1_732
| ~ spl1_120
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5744,f5638,f979,f7374]) ).
fof(f7374,plain,
( spl1_732
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(sum(X1,f(product(X0,eh))),X2),opp(sum(sum(X1,f(product(X0,eh))),X2)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_732])]) ).
fof(f979,plain,
( spl1_120
<=> ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(sum(sum(X1,X2),X0),opp(sum(sum(X1,X2),X0)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
fof(f5744,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(sum(X1,f(product(X0,eh))),X2),opp(sum(sum(X1,f(product(X0,eh))),X2)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_120
| ~ spl1_572 ),
inference(resolution,[],[f5639,f980]) ).
fof(f980,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(sum(sum(X1,X2),X0),opp(sum(sum(X1,X2),X0)))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_120 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f7372,plain,
( spl1_731
| ~ spl1_119
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5743,f5638,f975,f7370]) ).
fof(f7370,plain,
( spl1_731
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(sum(X1,f(product(X0,eh))),X2)),sum(sum(X1,f(product(X0,eh))),X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_731])]) ).
fof(f975,plain,
( spl1_119
<=> ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(sum(X1,X2),X0)),sum(sum(X1,X2),X0))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
fof(f5743,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(sum(X1,f(product(X0,eh))),X2)),sum(sum(X1,f(product(X0,eh))),X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_119
| ~ spl1_572 ),
inference(resolution,[],[f5639,f976]) ).
fof(f976,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(opp(sum(sum(X1,X2),X0)),sum(sum(X1,X2),X0))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_119 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f7368,plain,
( spl1_730
| ~ spl1_132
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5646,f5638,f1073,f7366]) ).
fof(f7366,plain,
( spl1_730
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(X0,eh))),X2) = sum(sum(f(product(X1,product(X0,eh))),X2),eg)
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_730])]) ).
fof(f1073,plain,
( spl1_132
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(f(product(X1,X2)),X0) = sum(sum(f(product(X1,X2)),X0),eg)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
fof(f5646,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(X0,eh))),X2) = sum(sum(f(product(X1,product(X0,eh))),X2),eg)
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_132
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1074]) ).
fof(f1074,plain,
( ! [X2,X0,X1] :
( ~ h(f(X2))
| sum(f(product(X1,X2)),X0) = sum(sum(f(product(X1,X2)),X0),eg)
| ~ h(X0)
| ~ h(f(X1)) )
| ~ spl1_132 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f7364,plain,
( spl1_729
| ~ spl1_131
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5645,f5638,f1069,f7362]) ).
fof(f7362,plain,
( spl1_729
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(X0,eh))),X2) = sum(eg,sum(f(product(X1,product(X0,eh))),X2))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_729])]) ).
fof(f1069,plain,
( spl1_131
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(f(product(X1,X2)),X0) = sum(eg,sum(f(product(X1,X2)),X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
fof(f5645,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(X0,eh))),X2) = sum(eg,sum(f(product(X1,product(X0,eh))),X2))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_131
| ~ spl1_572 ),
inference(resolution,[],[f5639,f1070]) ).
fof(f1070,plain,
( ! [X2,X0,X1] :
( ~ h(f(X2))
| sum(f(product(X1,X2)),X0) = sum(eg,sum(f(product(X1,X2)),X0))
| ~ h(X0)
| ~ h(f(X1)) )
| ~ spl1_131 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f7360,plain,
( spl1_728
| ~ spl1_120
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5432,f5326,f979,f7358]) ).
fof(f7358,plain,
( spl1_728
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(sum(X1,f(product(eh,X0))),X2),opp(sum(sum(X1,f(product(eh,X0))),X2)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_728])]) ).
fof(f5432,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(sum(X1,f(product(eh,X0))),X2),opp(sum(sum(X1,f(product(eh,X0))),X2)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_120
| ~ spl1_571 ),
inference(resolution,[],[f5327,f980]) ).
fof(f7356,plain,
( spl1_727
| ~ spl1_119
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5431,f5326,f975,f7354]) ).
fof(f7354,plain,
( spl1_727
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(sum(X1,f(product(eh,X0))),X2)),sum(sum(X1,f(product(eh,X0))),X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_727])]) ).
fof(f5431,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(sum(X1,f(product(eh,X0))),X2)),sum(sum(X1,f(product(eh,X0))),X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_119
| ~ spl1_571 ),
inference(resolution,[],[f5327,f976]) ).
fof(f7352,plain,
( spl1_726
| ~ spl1_132
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5334,f5326,f1073,f7350]) ).
fof(f7350,plain,
( spl1_726
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(eh,X0))),X2) = sum(sum(f(product(X1,product(eh,X0))),X2),eg)
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_726])]) ).
fof(f5334,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(eh,X0))),X2) = sum(sum(f(product(X1,product(eh,X0))),X2),eg)
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_132
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1074]) ).
fof(f7348,plain,
( spl1_725
| ~ spl1_131
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5333,f5326,f1069,f7346]) ).
fof(f7346,plain,
( spl1_725
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(eh,X0))),X2) = sum(eg,sum(f(product(X1,product(eh,X0))),X2))
| ~ h(X2)
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_725])]) ).
fof(f5333,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,product(eh,X0))),X2) = sum(eg,sum(f(product(X1,product(eh,X0))),X2))
| ~ h(X2)
| ~ h(f(X1)) )
| ~ spl1_131
| ~ spl1_571 ),
inference(resolution,[],[f5327,f1070]) ).
fof(f7344,plain,
( spl1_724
| ~ spl1_2
| ~ spl1_148 ),
inference(avatar_split_clause,[],[f4778,f1184,f81,f7342]) ).
fof(f7342,plain,
( spl1_724
<=> ! [X0,X3,X2,X1] :
( product(product(product(X0,product(X1,X2)),X3),sK0) = product(product(X0,product(X1,X2)),product(X3,sK0))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_724])]) ).
fof(f1184,plain,
( spl1_148
<=> ! [X4,X0,X3,X2,X1] :
( ~ g(X0)
| product(product(product(X1,product(X2,X3)),X0),X4) = product(product(X1,product(X2,X3)),product(X0,X4))
| ~ g(X4)
| ~ g(X1)
| ~ g(X3)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
fof(f4778,plain,
( ! [X2,X3,X0,X1] :
( product(product(product(X0,product(X1,X2)),X3),sK0) = product(product(X0,product(X1,X2)),product(X3,sK0))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_148 ),
inference(resolution,[],[f83,f1185]) ).
fof(f1185,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ g(X4)
| product(product(product(X1,product(X2,X3)),X0),X4) = product(product(X1,product(X2,X3)),product(X0,X4))
| ~ g(X0)
| ~ g(X1)
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_148 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f7334,plain,
( spl1_723
| ~ spl1_2
| ~ spl1_611 ),
inference(avatar_split_clause,[],[f6317,f6255,f81,f7331]) ).
fof(f7331,plain,
( spl1_723
<=> eh = product(inv(product(sK0,sK0)),inv(inv(product(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_723])]) ).
fof(f6317,plain,
( eh = product(inv(product(sK0,sK0)),inv(inv(product(sK0,sK0))))
| ~ spl1_2
| ~ spl1_611 ),
inference(resolution,[],[f6256,f83]) ).
fof(f7295,plain,
( spl1_722
| ~ spl1_117
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5742,f5638,f938,f7293]) ).
fof(f7293,plain,
( spl1_722
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),opp(X2)),f(product(X0,eh))) = sum(f(X1),sum(opp(X2),f(product(X0,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_722])]) ).
fof(f938,plain,
( spl1_117
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),opp(X2)),X0) = sum(f(X1),sum(opp(X2),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
fof(f5742,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),opp(X2)),f(product(X0,eh))) = sum(f(X1),sum(opp(X2),f(product(X0,eh))))
| ~ g(X1) )
| ~ spl1_117
| ~ spl1_572 ),
inference(resolution,[],[f5639,f939]) ).
fof(f939,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),opp(X2)),X0) = sum(f(X1),sum(opp(X2),X0))
| ~ g(X1) )
| ~ spl1_117 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f7291,plain,
( spl1_721
| ~ spl1_113
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5740,f5638,f922,f7289]) ).
fof(f7289,plain,
( spl1_721
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(X0,eh))),X2) = sum(sum(sum(X1,f(product(X0,eh))),X2),eg)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_721])]) ).
fof(f922,plain,
( spl1_113
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(X1,X2),X0) = sum(sum(sum(X1,X2),X0),eg)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
fof(f5740,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(X0,eh))),X2) = sum(sum(sum(X1,f(product(X0,eh))),X2),eg)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_113
| ~ spl1_572 ),
inference(resolution,[],[f5639,f923]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X1,X2),X0) = sum(sum(sum(X1,X2),X0),eg)
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_113 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f7287,plain,
( spl1_720
| ~ spl1_112
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5739,f5638,f918,f7285]) ).
fof(f7285,plain,
( spl1_720
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(X0,eh))),X2) = sum(eg,sum(sum(X1,f(product(X0,eh))),X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_720])]) ).
fof(f918,plain,
( spl1_112
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(X1,X2),X0) = sum(eg,sum(sum(X1,X2),X0))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
fof(f5739,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(X0,eh))),X2) = sum(eg,sum(sum(X1,f(product(X0,eh))),X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_112
| ~ spl1_572 ),
inference(resolution,[],[f5639,f919]) ).
fof(f919,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X1,X2),X0) = sum(eg,sum(sum(X1,X2),X0))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_112 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f7283,plain,
( spl1_719
| ~ spl1_117
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5430,f5326,f938,f7281]) ).
fof(f7281,plain,
( spl1_719
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),opp(X2)),f(product(eh,X0))) = sum(f(X1),sum(opp(X2),f(product(eh,X0))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_719])]) ).
fof(f5430,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),opp(X2)),f(product(eh,X0))) = sum(f(X1),sum(opp(X2),f(product(eh,X0))))
| ~ g(X1) )
| ~ spl1_117
| ~ spl1_571 ),
inference(resolution,[],[f5327,f939]) ).
fof(f7279,plain,
( spl1_718
| ~ spl1_113
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5428,f5326,f922,f7277]) ).
fof(f7277,plain,
( spl1_718
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(eh,X0))),X2) = sum(sum(sum(X1,f(product(eh,X0))),X2),eg)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_718])]) ).
fof(f5428,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(eh,X0))),X2) = sum(sum(sum(X1,f(product(eh,X0))),X2),eg)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_113
| ~ spl1_571 ),
inference(resolution,[],[f5327,f923]) ).
fof(f7275,plain,
( spl1_717
| ~ spl1_2
| ~ spl1_610 ),
inference(avatar_split_clause,[],[f6312,f6251,f81,f7272]) ).
fof(f7272,plain,
( spl1_717
<=> eg = sum(opp(f(product(sK0,sK0))),f(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_717])]) ).
fof(f6312,plain,
( eg = sum(opp(f(product(sK0,sK0))),f(product(sK0,sK0)))
| ~ spl1_2
| ~ spl1_610 ),
inference(resolution,[],[f6252,f83]) ).
fof(f7270,plain,
( spl1_716
| ~ spl1_112
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5427,f5326,f918,f7268]) ).
fof(f7268,plain,
( spl1_716
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(eh,X0))),X2) = sum(eg,sum(sum(X1,f(product(eh,X0))),X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_716])]) ).
fof(f5427,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(X1,f(product(eh,X0))),X2) = sum(eg,sum(sum(X1,f(product(eh,X0))),X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_112
| ~ spl1_571 ),
inference(resolution,[],[f5327,f919]) ).
fof(f7240,plain,
( spl1_715
| ~ spl1_21
| ~ spl1_116
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5897,f5638,f934,f191,f7238]) ).
fof(f7238,plain,
( spl1_715
<=> ! [X2,X0,X1] :
( sum(opp(X1),f(product(X2,product(X0,eh)))) = sum(sum(opp(X1),f(X2)),f(product(X0,eh)))
| ~ h(f(X0))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_715])]) ).
fof(f934,plain,
( spl1_116
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),f(X2)),X0) = sum(opp(X1),sum(f(X2),X0))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
fof(f5897,plain,
( ! [X2,X0,X1] :
( sum(opp(X1),f(product(X2,product(X0,eh)))) = sum(sum(opp(X1),f(X2)),f(product(X0,eh)))
| ~ h(f(X0))
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_116
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5741,f192]) ).
fof(f5741,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(X2)),f(product(X0,eh))) = sum(opp(X1),sum(f(X2),f(product(X0,eh))))
| ~ g(X2) )
| ~ spl1_116
| ~ spl1_572 ),
inference(resolution,[],[f5639,f935]) ).
fof(f935,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),f(X2)),X0) = sum(opp(X1),sum(f(X2),X0))
| ~ g(X2) )
| ~ spl1_116 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f7236,plain,
( spl1_714
| ~ spl1_21
| ~ spl1_55
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5875,f5638,f454,f191,f7234]) ).
fof(f7234,plain,
( spl1_714
<=> ! [X2,X0,X1] :
( sum(f(X2),sum(f(product(X0,eh)),X1)) = sum(f(product(X2,product(X0,eh))),X1)
| ~ h(f(X0))
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_714])]) ).
fof(f454,plain,
( spl1_55
<=> ! [X2,X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(f(X2),X1),X0) = sum(f(X2),sum(X1,X0))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
fof(f5875,plain,
( ! [X2,X0,X1] :
( sum(f(X2),sum(f(product(X0,eh)),X1)) = sum(f(product(X2,product(X0,eh))),X1)
| ~ h(f(X0))
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_55
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5721,f192]) ).
fof(f5721,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(f(X2),f(product(X0,eh))),X1) = sum(f(X2),sum(f(product(X0,eh)),X1))
| ~ g(X2) )
| ~ spl1_55
| ~ spl1_572 ),
inference(resolution,[],[f5639,f455]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( ~ h(X1)
| ~ h(X0)
| sum(sum(f(X2),X1),X0) = sum(f(X2),sum(X1,X0))
| ~ g(X2) )
| ~ spl1_55 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f7232,plain,
( spl1_713
| ~ spl1_21
| ~ spl1_116
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5585,f5326,f934,f191,f7230]) ).
fof(f7230,plain,
( spl1_713
<=> ! [X2,X0,X1] :
( sum(opp(X1),f(product(X2,product(eh,X0)))) = sum(sum(opp(X1),f(X2)),f(product(eh,X0)))
| ~ h(f(X0))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_713])]) ).
fof(f5585,plain,
( ! [X2,X0,X1] :
( sum(opp(X1),f(product(X2,product(eh,X0)))) = sum(sum(opp(X1),f(X2)),f(product(eh,X0)))
| ~ h(f(X0))
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_116
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5429,f192]) ).
fof(f5429,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),f(X2)),f(product(eh,X0))) = sum(opp(X1),sum(f(X2),f(product(eh,X0))))
| ~ g(X2) )
| ~ spl1_116
| ~ spl1_571 ),
inference(resolution,[],[f5327,f935]) ).
fof(f7228,plain,
( spl1_712
| ~ spl1_21
| ~ spl1_55
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5563,f5326,f454,f191,f7226]) ).
fof(f5563,plain,
( ! [X2,X0,X1] :
( sum(f(X2),sum(f(product(eh,X0)),X1)) = sum(f(product(X2,product(eh,X0))),X1)
| ~ h(f(X0))
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_55
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5409,f192]) ).
fof(f5409,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(f(X2),f(product(eh,X0))),X1) = sum(f(X2),sum(f(product(eh,X0)),X1))
| ~ g(X2) )
| ~ spl1_55
| ~ spl1_571 ),
inference(resolution,[],[f5327,f455]) ).
fof(f7218,plain,
( spl1_711
| ~ spl1_2
| ~ spl1_609 ),
inference(avatar_split_clause,[],[f6302,f6247,f81,f7215]) ).
fof(f7215,plain,
( spl1_711
<=> eg = sum(f(product(sK0,sK0)),opp(f(product(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_711])]) ).
fof(f6302,plain,
( eg = sum(f(product(sK0,sK0)),opp(f(product(sK0,sK0))))
| ~ spl1_2
| ~ spl1_609 ),
inference(resolution,[],[f6248,f83]) ).
fof(f7167,plain,
( spl1_710
| ~ spl1_21
| ~ spl1_124
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5900,f5638,f995,f191,f7165]) ).
fof(f7165,plain,
( spl1_710
<=> ! [X2,X0,X1] :
( f(product(X1,product(X2,product(X0,eh)))) = f(product(product(X1,X2),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_710])]) ).
fof(f995,plain,
( spl1_124
<=> ! [X2,X0,X1] :
( sum(f(product(X1,X2)),X0) = sum(f(X1),sum(f(X2),X0))
| ~ h(X0)
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
fof(f5900,plain,
( ! [X2,X0,X1] :
( f(product(X1,product(X2,product(X0,eh)))) = f(product(product(X1,X2),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5899,f192]) ).
fof(f5899,plain,
( ! [X2,X0,X1] :
( f(product(X1,product(X2,product(X0,eh)))) = sum(f(product(X1,X2)),f(product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5898,f192]) ).
fof(f5898,plain,
( ! [X2,X0,X1] :
( sum(f(product(X1,X2)),f(product(X0,eh))) = sum(f(X1),f(product(X2,product(X0,eh))))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5745,f192]) ).
fof(f5745,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,X2)),f(product(X0,eh))) = sum(f(X1),sum(f(X2),f(product(X0,eh))))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_124
| ~ spl1_572 ),
inference(resolution,[],[f5639,f996]) ).
fof(f996,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(f(product(X1,X2)),X0) = sum(f(X1),sum(f(X2),X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_124 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f7163,plain,
( spl1_709
| ~ spl1_107
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5737,f5638,f865,f7161]) ).
fof(f7161,plain,
( spl1_709
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),opp(X2)),f(product(X0,eh))) = sum(opp(X1),sum(opp(X2),f(product(X0,eh)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_709])]) ).
fof(f865,plain,
( spl1_107
<=> ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),opp(X2)),X0) = sum(opp(X1),sum(opp(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
fof(f5737,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),opp(X2)),f(product(X0,eh))) = sum(opp(X1),sum(opp(X2),f(product(X0,eh)))) )
| ~ spl1_107
| ~ spl1_572 ),
inference(resolution,[],[f5639,f866]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),opp(X2)),X0) = sum(opp(X1),sum(opp(X2),X0)) )
| ~ spl1_107 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f7159,plain,
( spl1_708
| ~ spl1_54
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5720,f5638,f444,f7157]) ).
fof(f7157,plain,
( spl1_708
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(opp(X2),f(product(X0,eh))),X1) = sum(opp(X2),sum(f(product(X0,eh)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_708])]) ).
fof(f444,plain,
( spl1_54
<=> ! [X2,X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(opp(X2),X1),X0) = sum(opp(X2),sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
fof(f5720,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(opp(X2),f(product(X0,eh))),X1) = sum(opp(X2),sum(f(product(X0,eh)),X1)) )
| ~ spl1_54
| ~ spl1_572 ),
inference(resolution,[],[f5639,f445]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( ~ h(X1)
| ~ h(X0)
| sum(sum(opp(X2),X1),X0) = sum(opp(X2),sum(X1,X0)) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f7155,plain,
( spl1_707
| ~ spl1_2
| ~ spl1_159 ),
inference(avatar_split_clause,[],[f4788,f1311,f81,f7152]) ).
fof(f7152,plain,
( spl1_707
<=> eh = product(inv(inv(inv(inv(sK0)))),inv(inv(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_707])]) ).
fof(f1311,plain,
( spl1_159
<=> ! [X0] :
( eh = product(inv(inv(inv(inv(X0)))),inv(inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_159])]) ).
fof(f4788,plain,
( eh = product(inv(inv(inv(inv(sK0)))),inv(inv(inv(sK0))))
| ~ spl1_2
| ~ spl1_159 ),
inference(resolution,[],[f83,f1312]) ).
fof(f1312,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(inv(inv(X0)))),inv(inv(inv(X0)))) )
| ~ spl1_159 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f7150,plain,
( spl1_706
| ~ spl1_22
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5714,f5638,f196,f7148]) ).
fof(f7148,plain,
( spl1_706
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(X0,eh)),X2),X1) = sum(f(product(X0,eh)),sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_706])]) ).
fof(f196,plain,
( spl1_22
<=> ! [X2,X0,X1] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X0)
| ~ h(X1)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f5714,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(X0,eh)),X2),X1) = sum(f(product(X0,eh)),sum(X2,X1)) )
| ~ spl1_22
| ~ spl1_572 ),
inference(resolution,[],[f5639,f197]) ).
fof(f197,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| ~ h(X0)
| ~ h(X1)
| sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0)) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f7146,plain,
( spl1_705
| ~ spl1_21
| ~ spl1_124
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5588,f5326,f995,f191,f7144]) ).
fof(f7144,plain,
( spl1_705
<=> ! [X2,X0,X1] :
( f(product(X1,product(X2,product(eh,X0)))) = f(product(product(X1,X2),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_705])]) ).
fof(f5588,plain,
( ! [X2,X0,X1] :
( f(product(X1,product(X2,product(eh,X0)))) = f(product(product(X1,X2),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5587,f192]) ).
fof(f5587,plain,
( ! [X2,X0,X1] :
( f(product(X1,product(X2,product(eh,X0)))) = sum(f(product(X1,X2)),f(product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5586,f192]) ).
fof(f5586,plain,
( ! [X2,X0,X1] :
( sum(f(product(X1,X2)),f(product(eh,X0))) = sum(f(X1),f(product(X2,product(eh,X0))))
| ~ h(f(X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_21
| ~ spl1_124
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5433,f192]) ).
fof(f5433,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(f(product(X1,X2)),f(product(eh,X0))) = sum(f(X1),sum(f(X2),f(product(eh,X0))))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_124
| ~ spl1_571 ),
inference(resolution,[],[f5327,f996]) ).
fof(f7142,plain,
( spl1_704
| ~ spl1_107
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5425,f5326,f865,f7140]) ).
fof(f7140,plain,
( spl1_704
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),opp(X2)),f(product(eh,X0))) = sum(opp(X1),sum(opp(X2),f(product(eh,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_704])]) ).
fof(f5425,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| sum(sum(opp(X1),opp(X2)),f(product(eh,X0))) = sum(opp(X1),sum(opp(X2),f(product(eh,X0)))) )
| ~ spl1_107
| ~ spl1_571 ),
inference(resolution,[],[f5327,f866]) ).
fof(f7138,plain,
( spl1_703
| ~ spl1_54
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5408,f5326,f444,f7136]) ).
fof(f7136,plain,
( spl1_703
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(opp(X2),f(product(eh,X0))),X1) = sum(opp(X2),sum(f(product(eh,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_703])]) ).
fof(f5408,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(sum(opp(X2),f(product(eh,X0))),X1) = sum(opp(X2),sum(f(product(eh,X0)),X1)) )
| ~ spl1_54
| ~ spl1_571 ),
inference(resolution,[],[f5327,f445]) ).
fof(f7134,plain,
( spl1_702
| ~ spl1_22
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5402,f5326,f196,f7132]) ).
fof(f7132,plain,
( spl1_702
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(eh,X0)),X2),X1) = sum(f(product(eh,X0)),sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_702])]) ).
fof(f5402,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(eh,X0)),X2),X1) = sum(f(product(eh,X0)),sum(X2,X1)) )
| ~ spl1_22
| ~ spl1_571 ),
inference(resolution,[],[f5327,f197]) ).
fof(f7108,plain,
( spl1_701
| ~ spl1_2
| ~ spl1_158 ),
inference(avatar_split_clause,[],[f4787,f1307,f81,f7105]) ).
fof(f7105,plain,
( spl1_701
<=> eh = product(inv(inv(inv(sK0))),inv(inv(inv(inv(sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_701])]) ).
fof(f1307,plain,
( spl1_158
<=> ! [X0] :
( eh = product(inv(inv(inv(X0))),inv(inv(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
fof(f4787,plain,
( eh = product(inv(inv(inv(sK0))),inv(inv(inv(inv(sK0)))))
| ~ spl1_2
| ~ spl1_158 ),
inference(resolution,[],[f83,f1308]) ).
fof(f1308,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(inv(X0))),inv(inv(inv(inv(X0))))) )
| ~ spl1_158 ),
inference(avatar_component_clause,[],[f1307]) ).
fof(f7098,plain,
( spl1_700
| ~ spl1_6
| ~ spl1_584 ),
inference(avatar_split_clause,[],[f6044,f6036,f100,f7096]) ).
fof(f6044,plain,
( ! [X2,X0,X1] :
( product(product(sK0,product(X0,inv(X1))),X2) = product(sK0,product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_584 ),
inference(resolution,[],[f6037,f101]) ).
fof(f7094,plain,
( spl1_699
| ~ spl1_6
| ~ spl1_583 ),
inference(avatar_split_clause,[],[f6040,f6032,f100,f7092]) ).
fof(f6040,plain,
( ! [X2,X0,X1] :
( product(product(product(X0,sK0),X1),inv(X2)) = product(product(X0,sK0),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) )
| ~ spl1_6
| ~ spl1_583 ),
inference(resolution,[],[f6033,f101]) ).
fof(f7090,plain,
( spl1_698
| ~ spl1_19
| ~ spl1_581 ),
inference(avatar_split_clause,[],[f6024,f6012,f164,f7088]) ).
fof(f6012,plain,
( spl1_581
<=> ! [X0,X1] :
( ~ g(X0)
| product(product(sK0,inv(X1)),X0) = product(sK0,product(inv(X1),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_581])]) ).
fof(f6024,plain,
( ! [X2,X0,X1] :
( product(product(sK0,inv(product(X0,X1))),X2) = product(sK0,product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_581 ),
inference(resolution,[],[f6013,f165]) ).
fof(f6013,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(sK0,inv(X1)),X0) = product(sK0,product(inv(X1),X0))
| ~ g(X0) )
| ~ spl1_581 ),
inference(avatar_component_clause,[],[f6012]) ).
fof(f7086,plain,
( spl1_697
| ~ spl1_19
| ~ spl1_580 ),
inference(avatar_split_clause,[],[f6015,f6008,f164,f7084]) ).
fof(f6008,plain,
( spl1_580
<=> ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),X1) = product(inv(sK0),product(X0,X1))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_580])]) ).
fof(f6015,plain,
( ! [X2,X0,X1] :
( product(product(inv(sK0),X0),product(X1,X2)) = product(inv(sK0),product(X0,product(X1,X2)))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_580 ),
inference(resolution,[],[f6009,f165]) ).
fof(f6009,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(product(inv(sK0),X0),X1) = product(inv(sK0),product(X0,X1))
| ~ g(X0) )
| ~ spl1_580 ),
inference(avatar_component_clause,[],[f6008]) ).
fof(f7082,plain,
( spl1_696
| ~ spl1_2
| ~ spl1_143 ),
inference(avatar_split_clause,[],[f4777,f1135,f81,f7080]) ).
fof(f1135,plain,
( spl1_143
<=> ! [X0,X3,X2,X1] :
( ~ g(X0)
| product(product(product(X1,inv(X2)),X0),X3) = product(product(X1,inv(X2)),product(X0,X3))
| ~ g(X3)
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_143])]) ).
fof(f4777,plain,
( ! [X2,X0,X1] :
( product(product(product(X0,inv(X1)),X2),sK0) = product(product(X0,inv(X1)),product(X2,sK0))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_143 ),
inference(resolution,[],[f83,f1136]) ).
fof(f1136,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X3)
| product(product(product(X1,inv(X2)),X0),X3) = product(product(X1,inv(X2)),product(X0,X3))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_143 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f7078,plain,
( spl1_695
| ~ spl1_2
| ~ spl1_141 ),
inference(avatar_split_clause,[],[f4776,f1127,f81,f7076]) ).
fof(f1127,plain,
( spl1_141
<=> ! [X0,X3,X2,X1] :
( ~ g(X0)
| product(product(inv(product(X1,X2)),X0),X3) = product(inv(product(X1,X2)),product(X0,X3))
| ~ g(X3)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
fof(f4776,plain,
( ! [X2,X0,X1] :
( product(product(inv(product(X0,X1)),X2),sK0) = product(inv(product(X0,X1)),product(X2,sK0))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_141 ),
inference(resolution,[],[f83,f1128]) ).
fof(f1128,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X3)
| product(product(inv(product(X1,X2)),X0),X3) = product(inv(product(X1,X2)),product(X0,X3))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_141 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f7052,plain,
( spl1_694
| ~ spl1_2
| ~ spl1_157 ),
inference(avatar_split_clause,[],[f4786,f1303,f81,f7049]) ).
fof(f7049,plain,
( spl1_694
<=> eg = sum(opp(f(inv(inv(sK0)))),f(inv(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_694])]) ).
fof(f1303,plain,
( spl1_157
<=> ! [X0] :
( eg = sum(opp(f(inv(inv(X0)))),f(inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
fof(f4786,plain,
( eg = sum(opp(f(inv(inv(sK0)))),f(inv(inv(sK0))))
| ~ spl1_2
| ~ spl1_157 ),
inference(resolution,[],[f83,f1304]) ).
fof(f1304,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(inv(inv(X0)))),f(inv(inv(X0)))) )
| ~ spl1_157 ),
inference(avatar_component_clause,[],[f1303]) ).
fof(f7005,plain,
( spl1_693
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5896,f5638,f5243,f5239,f869,f191,f7003]) ).
fof(f869,plain,
( spl1_108
<=> ! [X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),eg),X0) = sum(f(X1),sum(eg,X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
fof(f5896,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,product(X0,eh)))) = f(product(product(X1,eh),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5895,f192]) ).
fof(f5895,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,product(X0,eh)))) = sum(f(product(X1,eh)),f(product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5894,f5244]) ).
fof(f5894,plain,
( ! [X0,X1] :
( sum(sum(f(X1),eg),f(product(X0,eh))) = f(product(X1,product(eh,product(X0,eh))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5893,f192]) ).
fof(f5893,plain,
( ! [X0,X1] :
( sum(sum(f(X1),eg),f(product(X0,eh))) = sum(f(X1),f(product(eh,product(X0,eh))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_108
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5738,f5240]) ).
fof(f5738,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),eg),f(product(X0,eh))) = sum(f(X1),sum(eg,f(product(X0,eh))))
| ~ g(X1) )
| ~ spl1_108
| ~ spl1_572 ),
inference(resolution,[],[f5639,f870]) ).
fof(f870,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),eg),X0) = sum(f(X1),sum(eg,X0))
| ~ g(X1) )
| ~ spl1_108 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f7001,plain,
( spl1_692
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5892,f5638,f5239,f857,f191,f6999]) ).
fof(f857,plain,
( spl1_105
<=> ! [X0,X1] :
( ~ h(X0)
| sum(eg,sum(f(X1),X0)) = sum(sum(eg,f(X1)),X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
fof(f5892,plain,
( ! [X0,X1] :
( f(product(eh,product(X1,product(X0,eh)))) = f(product(product(eh,X1),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5891,f5240]) ).
fof(f5891,plain,
( ! [X0,X1] :
( sum(eg,f(product(X1,product(X0,eh)))) = f(product(product(eh,X1),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5890,f192]) ).
fof(f5890,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X1),f(product(X0,eh)))) = f(product(product(eh,X1),product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5889,f192]) ).
fof(f5889,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X1),f(product(X0,eh)))) = sum(f(product(eh,X1)),f(product(X0,eh)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_105
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5736,f5240]) ).
fof(f5736,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(X1),f(product(X0,eh)))) = sum(sum(eg,f(X1)),f(product(X0,eh)))
| ~ g(X1) )
| ~ spl1_105
| ~ spl1_572 ),
inference(resolution,[],[f5639,f858]) ).
fof(f858,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(eg,sum(f(X1),X0)) = sum(sum(eg,f(X1)),X0)
| ~ g(X1) )
| ~ spl1_105 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f6997,plain,
( spl1_691
| ~ spl1_51
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5874,f5638,f5239,f420,f6995]) ).
fof(f420,plain,
( spl1_51
<=> ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(eg,sum(X1,X0)) = sum(sum(eg,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
fof(f5874,plain,
( ! [X0,X1] :
( sum(eg,sum(f(product(X0,eh)),X1)) = sum(f(product(eh,product(X0,eh))),X1)
| ~ h(f(X0))
| ~ h(X1) )
| ~ spl1_51
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5719,f5240]) ).
fof(f5719,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(eg,sum(f(product(X0,eh)),X1)) = sum(sum(eg,f(product(X0,eh))),X1) )
| ~ spl1_51
| ~ spl1_572 ),
inference(resolution,[],[f5639,f421]) ).
fof(f421,plain,
( ! [X0,X1] :
( ~ h(X1)
| ~ h(X0)
| sum(eg,sum(X1,X0)) = sum(sum(eg,X1),X0) )
| ~ spl1_51 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f6993,plain,
( spl1_690
| ~ spl1_2
| ~ spl1_156 ),
inference(avatar_split_clause,[],[f4785,f1299,f81,f6990]) ).
fof(f6990,plain,
( spl1_690
<=> eg = sum(f(inv(inv(sK0))),opp(f(inv(inv(sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_690])]) ).
fof(f1299,plain,
( spl1_156
<=> ! [X0] :
( eg = sum(f(inv(inv(X0))),opp(f(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
fof(f4785,plain,
( eg = sum(f(inv(inv(sK0))),opp(f(inv(inv(sK0)))))
| ~ spl1_2
| ~ spl1_156 ),
inference(resolution,[],[f83,f1300]) ).
fof(f1300,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(inv(inv(X0))),opp(f(inv(inv(X0))))) )
| ~ spl1_156 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f6988,plain,
( spl1_689
| ~ spl1_111
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5644,f5638,f910,f6986]) ).
fof(f910,plain,
( spl1_111
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
fof(f5644,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(product(X0,eh),X1)),opp(f(product(product(X0,eh),X1)))) )
| ~ spl1_111
| ~ spl1_572 ),
inference(resolution,[],[f5639,f911]) ).
fof(f911,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0)))) )
| ~ spl1_111 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f6984,plain,
( spl1_688
| ~ spl1_110
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5643,f5638,f906,f6982]) ).
fof(f906,plain,
( spl1_110
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
fof(f5643,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(product(X0,eh),X1))),f(product(product(X0,eh),X1))) )
| ~ spl1_110
| ~ spl1_572 ),
inference(resolution,[],[f5639,f907]) ).
fof(f907,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0))) )
| ~ spl1_110 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f6980,plain,
( spl1_687
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5584,f5326,f5243,f5239,f869,f191,f6978]) ).
fof(f5584,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,product(eh,X0)))) = f(product(product(X1,eh),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5583,f192]) ).
fof(f5583,plain,
( ! [X0,X1] :
( f(product(X1,product(eh,product(eh,X0)))) = sum(f(product(X1,eh)),f(product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5582,f5244]) ).
fof(f5582,plain,
( ! [X0,X1] :
( sum(sum(f(X1),eg),f(product(eh,X0))) = f(product(X1,product(eh,product(eh,X0))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_108
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5581,f192]) ).
fof(f5581,plain,
( ! [X0,X1] :
( sum(sum(f(X1),eg),f(product(eh,X0))) = sum(f(X1),f(product(eh,product(eh,X0))))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_108
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5426,f5240]) ).
fof(f5426,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(sum(f(X1),eg),f(product(eh,X0))) = sum(f(X1),sum(eg,f(product(eh,X0))))
| ~ g(X1) )
| ~ spl1_108
| ~ spl1_571 ),
inference(resolution,[],[f5327,f870]) ).
fof(f6976,plain,
( spl1_686
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5580,f5326,f5239,f857,f191,f6974]) ).
fof(f5580,plain,
( ! [X0,X1] :
( f(product(eh,product(X1,product(eh,X0)))) = f(product(product(eh,X1),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5579,f5240]) ).
fof(f5579,plain,
( ! [X0,X1] :
( sum(eg,f(product(X1,product(eh,X0)))) = f(product(product(eh,X1),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5578,f192]) ).
fof(f5578,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X1),f(product(eh,X0)))) = f(product(product(eh,X1),product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_21
| ~ spl1_105
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5577,f192]) ).
fof(f5577,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X1),f(product(eh,X0)))) = sum(f(product(eh,X1)),f(product(eh,X0)))
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_105
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5424,f5240]) ).
fof(f5424,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(eg,sum(f(X1),f(product(eh,X0)))) = sum(sum(eg,f(X1)),f(product(eh,X0)))
| ~ g(X1) )
| ~ spl1_105
| ~ spl1_571 ),
inference(resolution,[],[f5327,f858]) ).
fof(f6972,plain,
( spl1_685
| ~ spl1_51
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5562,f5326,f5239,f420,f6970]) ).
fof(f5562,plain,
( ! [X0,X1] :
( sum(eg,sum(f(product(eh,X0)),X1)) = sum(f(product(eh,product(eh,X0))),X1)
| ~ h(f(X0))
| ~ h(X1) )
| ~ spl1_51
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5407,f5240]) ).
fof(f5407,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(eg,sum(f(product(eh,X0)),X1)) = sum(sum(eg,f(product(eh,X0))),X1) )
| ~ spl1_51
| ~ spl1_571 ),
inference(resolution,[],[f5327,f421]) ).
fof(f6968,plain,
( spl1_684
| ~ spl1_111
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5332,f5326,f910,f6966]) ).
fof(f5332,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(product(eh,X0),X1)),opp(f(product(product(eh,X0),X1)))) )
| ~ spl1_111
| ~ spl1_571 ),
inference(resolution,[],[f5327,f911]) ).
fof(f6964,plain,
( spl1_683
| ~ spl1_110
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5331,f5326,f906,f6962]) ).
fof(f5331,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(product(eh,X0),X1))),f(product(product(eh,X0),X1))) )
| ~ spl1_110
| ~ spl1_571 ),
inference(resolution,[],[f5327,f907]) ).
fof(f6885,plain,
( spl1_682
| ~ spl1_103
| ~ spl1_561
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5848,f5638,f5243,f849,f6883]) ).
fof(f849,plain,
( spl1_103
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
fof(f5848,plain,
( ! [X0,X1] :
( f(product(product(X0,eh),X1)) = f(product(product(product(X0,eh),X1),eh))
| ~ h(f(X0))
| ~ h(f(X1)) )
| ~ spl1_103
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5642,f5244]) ).
fof(f5642,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(product(X0,eh),X1)) = sum(f(product(product(X0,eh),X1)),eg) )
| ~ spl1_103
| ~ spl1_572 ),
inference(resolution,[],[f5639,f850]) ).
fof(f850,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg) )
| ~ spl1_103 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f6878,plain,
( spl1_681
| ~ spl1_102
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5847,f5638,f5239,f845,f6876]) ).
fof(f845,plain,
( spl1_102
<=> ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).
fof(f5847,plain,
( ! [X0,X1] :
( f(product(product(X0,eh),X1)) = f(product(eh,product(product(X0,eh),X1)))
| ~ h(f(X0))
| ~ h(f(X1)) )
| ~ spl1_102
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5641,f5240]) ).
fof(f5641,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(product(X0,eh),X1)) = sum(eg,f(product(product(X0,eh),X1))) )
| ~ spl1_102
| ~ spl1_572 ),
inference(resolution,[],[f5639,f846]) ).
fof(f846,plain,
( ! [X0,X1] :
( ~ h(f(X1))
| ~ h(f(X0))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0))) )
| ~ spl1_102 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f6874,plain,
( spl1_680
| ~ spl1_82
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5731,f5638,f685,f6872]) ).
fof(f685,plain,
( spl1_82
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(opp(X1),X0),opp(sum(opp(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
fof(f5731,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(X0,eh))),opp(sum(opp(X1),f(product(X0,eh))))) )
| ~ spl1_82
| ~ spl1_572 ),
inference(resolution,[],[f5639,f686]) ).
fof(f686,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(opp(X1),X0),opp(sum(opp(X1),X0))) )
| ~ spl1_82 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f6870,plain,
( spl1_679
| ~ spl1_81
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5730,f5638,f681,f6868]) ).
fof(f681,plain,
( spl1_81
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(opp(X1),X0)),sum(opp(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
fof(f5730,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(X0,eh)))),sum(opp(X1),f(product(X0,eh)))) )
| ~ spl1_81
| ~ spl1_572 ),
inference(resolution,[],[f5639,f682]) ).
fof(f682,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(opp(X1),X0)),sum(opp(X1),X0)) )
| ~ spl1_81 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f6866,plain,
( spl1_678
| ~ spl1_48
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5718,f5638,f392,f6864]) ).
fof(f392,plain,
( spl1_48
<=> ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| eg = sum(sum(X1,X0),opp(sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
fof(f5718,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(X0,eh)),X1),opp(sum(f(product(X0,eh)),X1))) )
| ~ spl1_48
| ~ spl1_572 ),
inference(resolution,[],[f5639,f393]) ).
fof(f393,plain,
( ! [X0,X1] :
( ~ h(X1)
| ~ h(X0)
| eg = sum(sum(X1,X0),opp(sum(X1,X0))) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f6862,plain,
( spl1_677
| ~ spl1_47
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5717,f5638,f388,f6860]) ).
fof(f388,plain,
( spl1_47
<=> ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| eg = sum(opp(sum(X1,X0)),sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
fof(f5717,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(X0,eh)),X1)),sum(f(product(X0,eh)),X1)) )
| ~ spl1_47
| ~ spl1_572 ),
inference(resolution,[],[f5639,f389]) ).
fof(f389,plain,
( ! [X0,X1] :
( ~ h(X1)
| ~ h(X0)
| eg = sum(opp(sum(X1,X0)),sum(X1,X0)) )
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f6858,plain,
( spl1_676
| ~ spl1_103
| ~ spl1_561
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5536,f5326,f5243,f849,f6856]) ).
fof(f5536,plain,
( ! [X0,X1] :
( f(product(product(eh,X0),X1)) = f(product(product(product(eh,X0),X1),eh))
| ~ h(f(X0))
| ~ h(f(X1)) )
| ~ spl1_103
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5330,f5244]) ).
fof(f5330,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(product(eh,X0),X1)) = sum(f(product(product(eh,X0),X1)),eg) )
| ~ spl1_103
| ~ spl1_571 ),
inference(resolution,[],[f5327,f850]) ).
fof(f6854,plain,
( spl1_675
| ~ spl1_102
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5535,f5326,f5239,f845,f6852]) ).
fof(f5535,plain,
( ! [X0,X1] :
( f(product(product(eh,X0),X1)) = f(product(eh,product(product(eh,X0),X1)))
| ~ h(f(X0))
| ~ h(f(X1)) )
| ~ spl1_102
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5329,f5240]) ).
fof(f5329,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(product(eh,X0),X1)) = sum(eg,f(product(product(eh,X0),X1))) )
| ~ spl1_102
| ~ spl1_571 ),
inference(resolution,[],[f5327,f846]) ).
fof(f6850,plain,
( spl1_674
| ~ spl1_82
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5419,f5326,f685,f6848]) ).
fof(f5419,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(sum(opp(X1),f(product(eh,X0))),opp(sum(opp(X1),f(product(eh,X0))))) )
| ~ spl1_82
| ~ spl1_571 ),
inference(resolution,[],[f5327,f686]) ).
fof(f6846,plain,
( spl1_673
| ~ spl1_81
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5418,f5326,f681,f6844]) ).
fof(f5418,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(sum(opp(X1),f(product(eh,X0)))),sum(opp(X1),f(product(eh,X0)))) )
| ~ spl1_81
| ~ spl1_571 ),
inference(resolution,[],[f5327,f682]) ).
fof(f6842,plain,
( spl1_672
| ~ spl1_48
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5406,f5326,f392,f6840]) ).
fof(f5406,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(sum(f(product(eh,X0)),X1),opp(sum(f(product(eh,X0)),X1))) )
| ~ spl1_48
| ~ spl1_571 ),
inference(resolution,[],[f5327,f393]) ).
fof(f6835,plain,
( spl1_671
| ~ spl1_47
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5405,f5326,f388,f6833]) ).
fof(f5405,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| eg = sum(opp(sum(f(product(eh,X0)),X1)),sum(f(product(eh,X0)),X1)) )
| ~ spl1_47
| ~ spl1_571 ),
inference(resolution,[],[f5327,f389]) ).
fof(f6764,plain,
( spl1_670
| ~ spl1_80
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5882,f5638,f5239,f660,f6762]) ).
fof(f660,plain,
( spl1_80
<=> ! [X0,X1] :
( sum(opp(X1),X0) = sum(opp(X1),sum(eg,X0))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
fof(f5882,plain,
( ! [X0,X1] :
( sum(opp(X1),f(product(X0,eh))) = sum(opp(X1),f(product(eh,product(X0,eh))))
| ~ h(f(X0)) )
| ~ spl1_80
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5729,f5240]) ).
fof(f5729,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(opp(X1),sum(eg,f(product(X0,eh)))) )
| ~ spl1_80
| ~ spl1_572 ),
inference(resolution,[],[f5639,f661]) ).
fof(f661,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(opp(X1),sum(eg,X0)) )
| ~ spl1_80 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f6760,plain,
( spl1_669
| ~ spl1_79
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5728,f5638,f656,f6758]) ).
fof(f656,plain,
( spl1_79
<=> ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(sum(opp(X1),X0),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
fof(f5728,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(sum(opp(X1),f(product(X0,eh))),eg) )
| ~ spl1_79
| ~ spl1_572 ),
inference(resolution,[],[f5639,f657]) ).
fof(f657,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(sum(opp(X1),X0),eg) )
| ~ spl1_79 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f6756,plain,
( spl1_668
| ~ spl1_78
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5727,f5638,f652,f6754]) ).
fof(f652,plain,
( spl1_78
<=> ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(eg,sum(opp(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
fof(f5727,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(X0,eh))) = sum(eg,sum(opp(X1),f(product(X0,eh)))) )
| ~ spl1_78
| ~ spl1_572 ),
inference(resolution,[],[f5639,f653]) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(eg,sum(opp(X1),X0)) )
| ~ spl1_78 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f6752,plain,
( spl1_667
| ~ spl1_44
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5716,f5638,f357,f6750]) ).
fof(f357,plain,
( spl1_44
<=> ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(X1,X0) = sum(sum(X1,X0),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
fof(f5716,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(sum(f(product(X0,eh)),X1),eg) )
| ~ spl1_44
| ~ spl1_572 ),
inference(resolution,[],[f5639,f358]) ).
fof(f358,plain,
( ! [X0,X1] :
( ~ h(X1)
| ~ h(X0)
| sum(X1,X0) = sum(sum(X1,X0),eg) )
| ~ spl1_44 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f6748,plain,
( spl1_666
| ~ spl1_43
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5715,f5638,f353,f6746]) ).
fof(f353,plain,
( spl1_43
<=> ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(X1,X0) = sum(eg,sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
fof(f5715,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(X0,eh)),X1) = sum(eg,sum(f(product(X0,eh)),X1)) )
| ~ spl1_43
| ~ spl1_572 ),
inference(resolution,[],[f5639,f354]) ).
fof(f354,plain,
( ! [X0,X1] :
( ~ h(X1)
| ~ h(X0)
| sum(X1,X0) = sum(eg,sum(X1,X0)) )
| ~ spl1_43 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f6744,plain,
( spl1_665
| ~ spl1_80
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5570,f5326,f5239,f660,f6742]) ).
fof(f5570,plain,
( ! [X0,X1] :
( sum(opp(X1),f(product(eh,X0))) = sum(opp(X1),f(product(eh,product(eh,X0))))
| ~ h(f(X0)) )
| ~ spl1_80
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5417,f5240]) ).
fof(f5417,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(opp(X1),sum(eg,f(product(eh,X0)))) )
| ~ spl1_80
| ~ spl1_571 ),
inference(resolution,[],[f5327,f661]) ).
fof(f6740,plain,
( spl1_664
| ~ spl1_79
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5416,f5326,f656,f6738]) ).
fof(f5416,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(sum(opp(X1),f(product(eh,X0))),eg) )
| ~ spl1_79
| ~ spl1_571 ),
inference(resolution,[],[f5327,f657]) ).
fof(f6736,plain,
( spl1_663
| ~ spl1_78
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5415,f5326,f652,f6734]) ).
fof(f5415,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| sum(opp(X1),f(product(eh,X0))) = sum(eg,sum(opp(X1),f(product(eh,X0)))) )
| ~ spl1_78
| ~ spl1_571 ),
inference(resolution,[],[f5327,f653]) ).
fof(f6732,plain,
( spl1_662
| ~ spl1_44
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5404,f5326,f357,f6730]) ).
fof(f5404,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(sum(f(product(eh,X0)),X1),eg) )
| ~ spl1_44
| ~ spl1_571 ),
inference(resolution,[],[f5327,f358]) ).
fof(f6728,plain,
( spl1_661
| ~ spl1_2
| ~ spl1_601 ),
inference(avatar_split_clause,[],[f6208,f6168,f81,f6725]) ).
fof(f6725,plain,
( spl1_661
<=> inv(product(sK0,sK0)) = product(eh,inv(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_661])]) ).
fof(f6208,plain,
( inv(product(sK0,sK0)) = product(eh,inv(product(sK0,sK0)))
| ~ spl1_2
| ~ spl1_601 ),
inference(resolution,[],[f6169,f83]) ).
fof(f6723,plain,
( spl1_660
| ~ spl1_43
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5403,f5326,f353,f6721]) ).
fof(f5403,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| sum(f(product(eh,X0)),X1) = sum(eg,sum(f(product(eh,X0)),X1)) )
| ~ spl1_43
| ~ spl1_571 ),
inference(resolution,[],[f5327,f354]) ).
fof(f6642,plain,
( spl1_659
| ~ spl1_2
| ~ spl1_584 ),
inference(avatar_split_clause,[],[f6046,f6036,f81,f6640]) ).
fof(f6046,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,sK0)),X1) = product(sK0,product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_584 ),
inference(resolution,[],[f6037,f83]) ).
fof(f6638,plain,
( spl1_658
| ~ spl1_4
| ~ spl1_584 ),
inference(avatar_split_clause,[],[f6045,f6036,f91,f6636]) ).
fof(f6045,plain,
( ! [X0,X1] :
( product(product(sK0,product(X0,eh)),X1) = product(sK0,product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_584 ),
inference(resolution,[],[f6037,f93]) ).
fof(f6634,plain,
( spl1_657
| ~ spl1_2
| ~ spl1_583 ),
inference(avatar_split_clause,[],[f6042,f6032,f81,f6632]) ).
fof(f6042,plain,
( ! [X0,X1] :
( product(product(product(X0,sK0),X1),sK0) = product(product(X0,sK0),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_583 ),
inference(resolution,[],[f6033,f83]) ).
fof(f6630,plain,
( spl1_656
| ~ spl1_4
| ~ spl1_583 ),
inference(avatar_split_clause,[],[f6041,f6032,f91,f6628]) ).
fof(f6041,plain,
( ! [X0,X1] :
( product(product(product(X0,sK0),X1),eh) = product(product(X0,sK0),product(X1,eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_583 ),
inference(resolution,[],[f6033,f93]) ).
fof(f6626,plain,
( spl1_655
| ~ spl1_6
| ~ spl1_581 ),
inference(avatar_split_clause,[],[f6025,f6012,f100,f6624]) ).
fof(f6025,plain,
( ! [X0,X1] :
( product(product(sK0,inv(inv(X0))),X1) = product(sK0,product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_581 ),
inference(resolution,[],[f6013,f101]) ).
fof(f6620,plain,
( spl1_654
| ~ spl1_6
| ~ spl1_580 ),
inference(avatar_split_clause,[],[f6016,f6008,f100,f6618]) ).
fof(f6016,plain,
( ! [X0,X1] :
( product(product(inv(sK0),X0),inv(X1)) = product(inv(sK0),product(X0,inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_580 ),
inference(resolution,[],[f6009,f101]) ).
fof(f6616,plain,
( spl1_653
| ~ spl1_19
| ~ spl1_579 ),
inference(avatar_split_clause,[],[f6002,f5999,f164,f6614]) ).
fof(f5999,plain,
( spl1_579
<=> ! [X0] :
( ~ g(X0)
| product(product(sK0,sK0),X0) = product(sK0,product(sK0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_579])]) ).
fof(f6002,plain,
( ! [X0,X1] :
( product(product(sK0,sK0),product(X0,X1)) = product(sK0,product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_579 ),
inference(resolution,[],[f6000,f165]) ).
fof(f6000,plain,
( ! [X0] :
( ~ g(X0)
| product(product(sK0,sK0),X0) = product(sK0,product(sK0,X0)) )
| ~ spl1_579 ),
inference(avatar_component_clause,[],[f5999]) ).
fof(f6612,plain,
( spl1_652
| ~ spl1_75
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5881,f5638,f5239,f600,f6610]) ).
fof(f600,plain,
( spl1_75
<=> ! [X0] :
( ~ h(X0)
| eg = sum(sum(eg,X0),opp(sum(eg,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
fof(f5881,plain,
( ! [X0] :
( eg = sum(f(product(eh,product(X0,eh))),opp(f(product(eh,product(X0,eh)))))
| ~ h(f(X0)) )
| ~ spl1_75
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5726,f5240]) ).
fof(f5726,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(sum(eg,f(product(X0,eh))),opp(sum(eg,f(product(X0,eh))))) )
| ~ spl1_75
| ~ spl1_572 ),
inference(resolution,[],[f5639,f601]) ).
fof(f601,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(sum(eg,X0),opp(sum(eg,X0))) )
| ~ spl1_75 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f6608,plain,
( spl1_651
| ~ spl1_74
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5880,f5638,f5239,f596,f6606]) ).
fof(f596,plain,
( spl1_74
<=> ! [X0] :
( ~ h(X0)
| eg = sum(opp(sum(eg,X0)),sum(eg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
fof(f5880,plain,
( ! [X0] :
( eg = sum(opp(f(product(eh,product(X0,eh)))),f(product(eh,product(X0,eh))))
| ~ h(f(X0)) )
| ~ spl1_74
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5725,f5240]) ).
fof(f5725,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(sum(eg,f(product(X0,eh)))),sum(eg,f(product(X0,eh)))) )
| ~ spl1_74
| ~ spl1_572 ),
inference(resolution,[],[f5639,f597]) ).
fof(f597,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(opp(sum(eg,X0)),sum(eg,X0)) )
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f6604,plain,
( spl1_650
| ~ spl1_75
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5569,f5326,f5239,f600,f6602]) ).
fof(f5569,plain,
( ! [X0] :
( eg = sum(f(product(eh,product(eh,X0))),opp(f(product(eh,product(eh,X0)))))
| ~ h(f(X0)) )
| ~ spl1_75
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5414,f5240]) ).
fof(f5414,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(sum(eg,f(product(eh,X0))),opp(sum(eg,f(product(eh,X0))))) )
| ~ spl1_75
| ~ spl1_571 ),
inference(resolution,[],[f5327,f601]) ).
fof(f6600,plain,
( spl1_649
| ~ spl1_74
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5568,f5326,f5239,f596,f6598]) ).
fof(f5568,plain,
( ! [X0] :
( eg = sum(opp(f(product(eh,product(eh,X0)))),f(product(eh,product(eh,X0))))
| ~ h(f(X0)) )
| ~ spl1_74
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5413,f5240]) ).
fof(f5413,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(sum(eg,f(product(eh,X0)))),sum(eg,f(product(eh,X0)))) )
| ~ spl1_74
| ~ spl1_571 ),
inference(resolution,[],[f5327,f597]) ).
fof(f6596,plain,
( spl1_648
| ~ spl1_2
| ~ spl1_130 ),
inference(avatar_split_clause,[],[f4775,f1046,f81,f6594]) ).
fof(f1046,plain,
( spl1_130
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(product(X1,eh),X0),X2) = product(product(X1,eh),product(X0,X2))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
fof(f4775,plain,
( ! [X0,X1] :
( product(product(product(X0,eh),X1),sK0) = product(product(X0,eh),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_130 ),
inference(resolution,[],[f83,f1047]) ).
fof(f1047,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(product(X1,eh),X0),X2) = product(product(X1,eh),product(X0,X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_130 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f6592,plain,
( spl1_647
| ~ spl1_2
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f4773,f1034,f81,f6590]) ).
fof(f1034,plain,
( spl1_127
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(inv(inv(X1)),X0),X2) = product(inv(inv(X1)),product(X0,X2))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
fof(f4773,plain,
( ! [X0,X1] :
( product(product(inv(inv(X0)),X1),sK0) = product(inv(inv(X0)),product(X1,sK0))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_127 ),
inference(resolution,[],[f83,f1035]) ).
fof(f1035,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(inv(inv(X1)),X0),X2) = product(inv(inv(X1)),product(X0,X2))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_127 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f6588,plain,
( spl1_646
| ~ spl1_2
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f4772,f1030,f81,f6586]) ).
fof(f1030,plain,
( spl1_126
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(eh,product(product(X1,X2),X0)) = product(product(eh,product(X1,X2)),X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
fof(f4772,plain,
( ! [X0,X1] :
( product(eh,product(product(X0,sK0),X1)) = product(product(eh,product(X0,sK0)),X1)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_126 ),
inference(resolution,[],[f83,f1031]) ).
fof(f1031,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(eh,product(product(X1,X2),X0)) = product(product(eh,product(X1,X2)),X0)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_126 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f6538,plain,
( spl1_645
| ~ spl1_19
| ~ spl1_578 ),
inference(avatar_split_clause,[],[f5993,f5985,f164,f6536]) ).
fof(f5985,plain,
( spl1_578
<=> ! [X0] :
( ~ g(X0)
| eh = product(product(sK0,X0),inv(product(sK0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_578])]) ).
fof(f5993,plain,
( ! [X0,X1] :
( eh = product(product(sK0,product(X0,X1)),inv(product(sK0,product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_578 ),
inference(resolution,[],[f5986,f165]) ).
fof(f5986,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(sK0,X0),inv(product(sK0,X0))) )
| ~ spl1_578 ),
inference(avatar_component_clause,[],[f5985]) ).
fof(f6534,plain,
( spl1_644
| ~ spl1_19
| ~ spl1_577 ),
inference(avatar_split_clause,[],[f5988,f5981,f164,f6532]) ).
fof(f5981,plain,
( spl1_577
<=> ! [X0] :
( ~ g(X0)
| eh = product(inv(product(sK0,X0)),product(sK0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_577])]) ).
fof(f5988,plain,
( ! [X0,X1] :
( eh = product(inv(product(sK0,product(X0,X1))),product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_577 ),
inference(resolution,[],[f5982,f165]) ).
fof(f5982,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(sK0,X0)),product(sK0,X0)) )
| ~ spl1_577 ),
inference(avatar_component_clause,[],[f5981]) ).
fof(f6530,plain,
( spl1_643
| ~ spl1_67
| ~ spl1_560
| ~ spl1_561
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5879,f5638,f5243,f5239,f528,f6528]) ).
fof(f528,plain,
( spl1_67
<=> ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(sum(eg,X0),eg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
fof(f5879,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(product(eh,product(X0,eh)),eh))
| ~ h(f(X0)) )
| ~ spl1_67
| ~ spl1_560
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5878,f5244]) ).
fof(f5878,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = sum(f(product(eh,product(X0,eh))),eg)
| ~ h(f(X0)) )
| ~ spl1_67
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5724,f5240]) ).
fof(f5724,plain,
( ! [X0] :
( ~ h(f(X0))
| sum(eg,f(product(X0,eh))) = sum(sum(eg,f(product(X0,eh))),eg) )
| ~ spl1_67
| ~ spl1_572 ),
inference(resolution,[],[f5639,f529]) ).
fof(f529,plain,
( ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(sum(eg,X0),eg) )
| ~ spl1_67 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f6526,plain,
( spl1_642
| ~ spl1_2
| ~ spl1_557
| ~ spl1_559
| ~ spl1_629 ),
inference(avatar_split_clause,[],[f6456,f6402,f5228,f5214,f81,f6523]) ).
fof(f6523,plain,
( spl1_642
<=> sK0 = product(inv(sK0),product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_642])]) ).
fof(f6456,plain,
( sK0 = product(inv(sK0),product(sK0,sK0))
| ~ spl1_2
| ~ spl1_557
| ~ spl1_559
| ~ spl1_629 ),
inference(forward_demodulation,[],[f6455,f5216]) ).
fof(f6455,plain,
( product(eh,sK0) = product(inv(sK0),product(sK0,sK0))
| ~ spl1_2
| ~ spl1_559
| ~ spl1_629 ),
inference(forward_demodulation,[],[f6453,f5230]) ).
fof(f6453,plain,
( product(product(inv(sK0),sK0),sK0) = product(inv(sK0),product(sK0,sK0))
| ~ spl1_2
| ~ spl1_629 ),
inference(resolution,[],[f6403,f83]) ).
fof(f6521,plain,
( spl1_641
| ~ spl1_66
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5877,f5638,f5239,f524,f6519]) ).
fof(f524,plain,
( spl1_66
<=> ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(eg,sum(eg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
fof(f5877,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = f(product(eh,product(eh,product(X0,eh))))
| ~ h(f(X0)) )
| ~ spl1_66
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5876,f5240]) ).
fof(f5876,plain,
( ! [X0] :
( f(product(eh,product(X0,eh))) = sum(eg,f(product(eh,product(X0,eh))))
| ~ h(f(X0)) )
| ~ spl1_66
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5723,f5240]) ).
fof(f5723,plain,
( ! [X0] :
( ~ h(f(X0))
| sum(eg,f(product(X0,eh))) = sum(eg,sum(eg,f(product(X0,eh)))) )
| ~ spl1_66
| ~ spl1_572 ),
inference(resolution,[],[f5639,f525]) ).
fof(f525,plain,
( ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(eg,sum(eg,X0)) )
| ~ spl1_66 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f6517,plain,
( spl1_640
| ~ spl1_67
| ~ spl1_560
| ~ spl1_561
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5567,f5326,f5243,f5239,f528,f6515]) ).
fof(f5567,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(product(eh,product(eh,X0)),eh))
| ~ h(f(X0)) )
| ~ spl1_67
| ~ spl1_560
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5566,f5244]) ).
fof(f5566,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = sum(f(product(eh,product(eh,X0))),eg)
| ~ h(f(X0)) )
| ~ spl1_67
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5412,f5240]) ).
fof(f5412,plain,
( ! [X0] :
( ~ h(f(X0))
| sum(eg,f(product(eh,X0))) = sum(sum(eg,f(product(eh,X0))),eg) )
| ~ spl1_67
| ~ spl1_571 ),
inference(resolution,[],[f5327,f529]) ).
fof(f6513,plain,
( spl1_639
| ~ spl1_66
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5565,f5326,f5239,f524,f6511]) ).
fof(f5565,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = f(product(eh,product(eh,product(eh,X0))))
| ~ h(f(X0)) )
| ~ spl1_66
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5564,f5240]) ).
fof(f5564,plain,
( ! [X0] :
( f(product(eh,product(eh,X0))) = sum(eg,f(product(eh,product(eh,X0))))
| ~ h(f(X0)) )
| ~ spl1_66
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5411,f5240]) ).
fof(f5411,plain,
( ! [X0] :
( ~ h(f(X0))
| sum(eg,f(product(eh,X0))) = sum(eg,sum(eg,f(product(eh,X0)))) )
| ~ spl1_66
| ~ spl1_571 ),
inference(resolution,[],[f5327,f525]) ).
fof(f6509,plain,
( spl1_638
| ~ spl1_2
| ~ spl1_122 ),
inference(avatar_split_clause,[],[f4770,f987,f81,f6507]) ).
fof(f987,plain,
( spl1_122
<=> ! [X2,X0,X1] :
( ~ g(X0)
| eh = product(product(product(X1,X2),X0),inv(product(product(X1,X2),X0)))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
fof(f4770,plain,
( ! [X0,X1] :
( eh = product(product(product(X0,sK0),X1),inv(product(product(X0,sK0),X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_122 ),
inference(resolution,[],[f83,f988]) ).
fof(f988,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(product(product(X1,X2),X0),inv(product(product(X1,X2),X0)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_122 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f6505,plain,
( spl1_637
| ~ spl1_2
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f4769,f983,f81,f6503]) ).
fof(f983,plain,
( spl1_121
<=> ! [X2,X0,X1] :
( ~ g(X0)
| eh = product(inv(product(product(X1,X2),X0)),product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).
fof(f4769,plain,
( ! [X0,X1] :
( eh = product(inv(product(product(X0,sK0),X1)),product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_121 ),
inference(resolution,[],[f83,f984]) ).
fof(f984,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| eh = product(inv(product(product(X1,X2),X0)),product(product(X1,X2),X0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_121 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f6481,plain,
( spl1_636
| ~ spl1_2
| ~ spl1_556
| ~ spl1_558
| ~ spl1_627 ),
inference(avatar_split_clause,[],[f6441,f6394,f5223,f5209,f81,f6478]) ).
fof(f5223,plain,
( spl1_558
<=> eh = product(sK0,inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_558])]) ).
fof(f6441,plain,
( sK0 = product(product(sK0,sK0),inv(sK0))
| ~ spl1_2
| ~ spl1_556
| ~ spl1_558
| ~ spl1_627 ),
inference(forward_demodulation,[],[f6440,f5211]) ).
fof(f6440,plain,
( product(sK0,eh) = product(product(sK0,sK0),inv(sK0))
| ~ spl1_2
| ~ spl1_558
| ~ spl1_627 ),
inference(forward_demodulation,[],[f6437,f5225]) ).
fof(f5225,plain,
( eh = product(sK0,inv(sK0))
| ~ spl1_558 ),
inference(avatar_component_clause,[],[f5223]) ).
fof(f6437,plain,
( product(product(sK0,sK0),inv(sK0)) = product(sK0,product(sK0,inv(sK0)))
| ~ spl1_2
| ~ spl1_627 ),
inference(resolution,[],[f6395,f83]) ).
fof(f6476,plain,
( spl1_635
| ~ spl1_19
| ~ spl1_575 ),
inference(avatar_split_clause,[],[f5976,f5958,f164,f6474]) ).
fof(f5958,plain,
( spl1_575
<=> ! [X0] :
( product(sK0,X0) = product(sK0,product(eh,X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_575])]) ).
fof(f5976,plain,
( ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(sK0,product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_575 ),
inference(resolution,[],[f5959,f165]) ).
fof(f5959,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(sK0,product(eh,X0)) )
| ~ spl1_575 ),
inference(avatar_component_clause,[],[f5958]) ).
fof(f6472,plain,
( spl1_634
| ~ spl1_19
| ~ spl1_574 ),
inference(avatar_split_clause,[],[f5966,f5954,f164,f6470]) ).
fof(f5954,plain,
( spl1_574
<=> ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(product(sK0,X0),eh) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_574])]) ).
fof(f5966,plain,
( ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(product(sK0,product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_574 ),
inference(resolution,[],[f5955,f165]) ).
fof(f5955,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(product(sK0,X0),eh) )
| ~ spl1_574 ),
inference(avatar_component_clause,[],[f5954]) ).
fof(f6468,plain,
( spl1_633
| ~ spl1_19
| ~ spl1_573 ),
inference(avatar_split_clause,[],[f5961,f5950,f164,f6466]) ).
fof(f5950,plain,
( spl1_573
<=> ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(eh,product(sK0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_573])]) ).
fof(f5961,plain,
( ! [X0,X1] :
( product(sK0,product(X0,X1)) = product(eh,product(sK0,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_573 ),
inference(resolution,[],[f5951,f165]) ).
fof(f5951,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(eh,product(sK0,X0)) )
| ~ spl1_573 ),
inference(avatar_component_clause,[],[f5950]) ).
fof(f6464,plain,
( spl1_632
| ~ spl1_2
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f4767,f930,f81,f6462]) ).
fof(f930,plain,
( spl1_115
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(X1,X2),X0) = product(product(product(X1,X2),X0),eh)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
fof(f4767,plain,
( ! [X0,X1] :
( product(product(X0,sK0),X1) = product(product(product(X0,sK0),X1),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_115 ),
inference(resolution,[],[f83,f931]) ).
fof(f931,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(X1,X2),X0) = product(product(product(X1,X2),X0),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_115 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f6460,plain,
( spl1_631
| ~ spl1_2
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f4766,f926,f81,f6458]) ).
fof(f926,plain,
( spl1_114
<=> ! [X2,X0,X1] :
( ~ g(X0)
| product(product(X1,X2),X0) = product(eh,product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
fof(f4766,plain,
( ! [X0,X1] :
( product(product(X0,sK0),X1) = product(eh,product(product(X0,sK0),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_114 ),
inference(resolution,[],[f83,f927]) ).
fof(f927,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| product(product(X1,X2),X0) = product(eh,product(product(X1,X2),X0))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_114 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f6421,plain,
( spl1_630
| ~ spl1_2
| ~ spl1_600 ),
inference(avatar_split_clause,[],[f6198,f6164,f81,f6418]) ).
fof(f6418,plain,
( spl1_630
<=> inv(product(sK0,sK0)) = product(inv(product(sK0,sK0)),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_630])]) ).
fof(f6198,plain,
( inv(product(sK0,sK0)) = product(inv(product(sK0,sK0)),eh)
| ~ spl1_2
| ~ spl1_600 ),
inference(resolution,[],[f6165,f83]) ).
fof(f6404,plain,
( spl1_629
| ~ spl1_2
| ~ spl1_580 ),
inference(avatar_split_clause,[],[f6018,f6008,f81,f6402]) ).
fof(f6018,plain,
( ! [X0] :
( product(product(inv(sK0),X0),sK0) = product(inv(sK0),product(X0,sK0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_580 ),
inference(resolution,[],[f6009,f83]) ).
fof(f6400,plain,
( spl1_628
| ~ spl1_4
| ~ spl1_580 ),
inference(avatar_split_clause,[],[f6017,f6008,f91,f6398]) ).
fof(f6017,plain,
( ! [X0] :
( product(product(inv(sK0),X0),eh) = product(inv(sK0),product(X0,eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_580 ),
inference(resolution,[],[f6009,f93]) ).
fof(f6396,plain,
( spl1_627
| ~ spl1_6
| ~ spl1_579 ),
inference(avatar_split_clause,[],[f6003,f5999,f100,f6394]) ).
fof(f6003,plain,
( ! [X0] :
( product(product(sK0,sK0),inv(X0)) = product(sK0,product(sK0,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_579 ),
inference(resolution,[],[f6000,f101]) ).
fof(f6392,plain,
( spl1_626
| ~ spl1_15
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5713,f5638,f148,f6390]) ).
fof(f148,plain,
( spl1_15
<=> ! [X0] :
( eg = sum(opp(X0),X0)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f5713,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X0,eh))),f(product(X0,eh))) )
| ~ spl1_15
| ~ spl1_572 ),
inference(resolution,[],[f5639,f149]) ).
fof(f149,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(opp(X0),X0) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f6388,plain,
( spl1_625
| ~ spl1_13
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5712,f5638,f139,f6386]) ).
fof(f139,plain,
( spl1_13
<=> ! [X0] :
( eg = sum(X0,opp(X0))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f5712,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(X0,eh)),opp(f(product(X0,eh)))) )
| ~ spl1_13
| ~ spl1_572 ),
inference(resolution,[],[f5639,f140]) ).
fof(f140,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(X0,opp(X0)) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f6384,plain,
( spl1_624
| ~ spl1_15
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5401,f5326,f148,f6382]) ).
fof(f5401,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(opp(f(product(eh,X0))),f(product(eh,X0))) )
| ~ spl1_15
| ~ spl1_571 ),
inference(resolution,[],[f5327,f149]) ).
fof(f6380,plain,
( spl1_623
| ~ spl1_13
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5400,f5326,f139,f6378]) ).
fof(f5400,plain,
( ! [X0] :
( ~ h(f(X0))
| eg = sum(f(product(eh,X0)),opp(f(product(eh,X0)))) )
| ~ spl1_13
| ~ spl1_571 ),
inference(resolution,[],[f5327,f140]) ).
fof(f6308,plain,
( spl1_622
| ~ spl1_2
| ~ spl1_104 ),
inference(avatar_split_clause,[],[f4763,f853,f81,f6305]) ).
fof(f6305,plain,
( spl1_622
<=> inv(inv(inv(sK0))) = product(eh,inv(inv(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_622])]) ).
fof(f853,plain,
( spl1_104
<=> ! [X0] :
( inv(inv(inv(X0))) = product(eh,inv(inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
fof(f4763,plain,
( inv(inv(inv(sK0))) = product(eh,inv(inv(inv(sK0))))
| ~ spl1_2
| ~ spl1_104 ),
inference(resolution,[],[f83,f854]) ).
fof(f854,plain,
( ! [X0] :
( ~ g(X0)
| inv(inv(inv(X0))) = product(eh,inv(inv(inv(X0)))) )
| ~ spl1_104 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f6298,plain,
( spl1_621
| ~ spl1_6
| ~ spl1_578 ),
inference(avatar_split_clause,[],[f5994,f5985,f100,f6296]) ).
fof(f5994,plain,
( ! [X0] :
( eh = product(product(sK0,inv(X0)),inv(product(sK0,inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_578 ),
inference(resolution,[],[f5986,f101]) ).
fof(f6294,plain,
( spl1_620
| ~ spl1_6
| ~ spl1_577 ),
inference(avatar_split_clause,[],[f5989,f5981,f100,f6292]) ).
fof(f5989,plain,
( ! [X0] :
( eh = product(inv(product(sK0,inv(X0))),product(sK0,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_577 ),
inference(resolution,[],[f5982,f101]) ).
fof(f6290,plain,
( spl1_619
| ~ spl1_10
| ~ spl1_560
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5873,f5638,f5239,f117,f6288]) ).
fof(f5873,plain,
( ! [X0] :
( f(product(X0,eh)) = f(product(eh,product(X0,eh)))
| ~ h(f(X0)) )
| ~ spl1_10
| ~ spl1_560
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5711,f5240]) ).
fof(f5711,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(X0,eh)) = sum(eg,f(product(X0,eh))) )
| ~ spl1_10
| ~ spl1_572 ),
inference(resolution,[],[f5639,f118]) ).
fof(f6286,plain,
( spl1_618
| ~ spl1_9
| ~ spl1_561
| ~ spl1_572 ),
inference(avatar_split_clause,[],[f5872,f5638,f5243,f113,f6284]) ).
fof(f5872,plain,
( ! [X0] :
( f(product(X0,eh)) = f(product(product(X0,eh),eh))
| ~ h(f(X0)) )
| ~ spl1_9
| ~ spl1_561
| ~ spl1_572 ),
inference(forward_demodulation,[],[f5710,f5244]) ).
fof(f5710,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(X0,eh)) = sum(f(product(X0,eh)),eg) )
| ~ spl1_9
| ~ spl1_572 ),
inference(resolution,[],[f5639,f114]) ).
fof(f6282,plain,
( spl1_617
| ~ spl1_10
| ~ spl1_560
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5561,f5326,f5239,f117,f6280]) ).
fof(f5561,plain,
( ! [X0] :
( f(product(eh,X0)) = f(product(eh,product(eh,X0)))
| ~ h(f(X0)) )
| ~ spl1_10
| ~ spl1_560
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5399,f5240]) ).
fof(f5399,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,X0)) = sum(eg,f(product(eh,X0))) )
| ~ spl1_10
| ~ spl1_571 ),
inference(resolution,[],[f5327,f118]) ).
fof(f6278,plain,
( spl1_616
| ~ spl1_9
| ~ spl1_561
| ~ spl1_571 ),
inference(avatar_split_clause,[],[f5560,f5326,f5243,f113,f6276]) ).
fof(f5560,plain,
( ! [X0] :
( f(product(eh,X0)) = f(product(product(eh,X0),eh))
| ~ h(f(X0)) )
| ~ spl1_9
| ~ spl1_561
| ~ spl1_571 ),
inference(forward_demodulation,[],[f5398,f5244]) ).
fof(f5398,plain,
( ! [X0] :
( ~ h(f(X0))
| f(product(eh,X0)) = sum(f(product(eh,X0)),eg) )
| ~ spl1_9
| ~ spl1_571 ),
inference(resolution,[],[f5327,f114]) ).
fof(f6274,plain,
( spl1_615
| ~ spl1_2
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f4761,f803,f81,f6272]) ).
fof(f803,plain,
( spl1_100
<=> ! [X0,X1] :
( ~ g(X0)
| eh = product(product(inv(X1),X0),inv(product(inv(X1),X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
fof(f4761,plain,
( ! [X0] :
( eh = product(product(inv(sK0),X0),inv(product(inv(sK0),X0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_100 ),
inference(resolution,[],[f83,f804]) ).
fof(f804,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(product(inv(X1),X0),inv(product(inv(X1),X0)))
| ~ g(X0) )
| ~ spl1_100 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f6270,plain,
( spl1_614
| ~ spl1_2
| ~ spl1_99 ),
inference(avatar_split_clause,[],[f4760,f799,f81,f6268]) ).
fof(f799,plain,
( spl1_99
<=> ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(product(inv(X1),X0)),product(inv(X1),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
fof(f4760,plain,
( ! [X0] :
( eh = product(inv(product(inv(sK0),X0)),product(inv(sK0),X0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_99 ),
inference(resolution,[],[f83,f800]) ).
fof(f800,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(inv(X1),X0)),product(inv(X1),X0))
| ~ g(X0) )
| ~ spl1_99 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f6266,plain,
( spl1_613
| ~ spl1_2
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f4759,f787,f81,f6264]) ).
fof(f787,plain,
( spl1_96
<=> ! [X0,X1] :
( eh = product(inv(inv(product(X0,X1))),inv(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
fof(f4759,plain,
( ! [X0] :
( eh = product(inv(inv(product(X0,sK0))),inv(product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_96 ),
inference(resolution,[],[f83,f788]) ).
fof(f788,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(inv(product(X0,X1))),inv(product(X0,X1)))
| ~ g(X0) )
| ~ spl1_96 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f6262,plain,
( spl1_612
| ~ spl1_2
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f4762,f807,f81,f6259]) ).
fof(f6259,plain,
( spl1_612
<=> inv(inv(inv(sK0))) = product(inv(inv(inv(sK0))),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_612])]) ).
fof(f807,plain,
( spl1_101
<=> ! [X0] :
( inv(inv(inv(X0))) = product(inv(inv(inv(X0))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
fof(f4762,plain,
( inv(inv(inv(sK0))) = product(inv(inv(inv(sK0))),eh)
| ~ spl1_2
| ~ spl1_101 ),
inference(resolution,[],[f83,f808]) ).
fof(f808,plain,
( ! [X0] :
( ~ g(X0)
| inv(inv(inv(X0))) = product(inv(inv(inv(X0))),eh) )
| ~ spl1_101 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f6257,plain,
( spl1_611
| ~ spl1_2
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f4758,f783,f81,f6255]) ).
fof(f783,plain,
( spl1_95
<=> ! [X0,X1] :
( eh = product(inv(product(X0,X1)),inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
fof(f4758,plain,
( ! [X0] :
( eh = product(inv(product(X0,sK0)),inv(inv(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_95 ),
inference(resolution,[],[f83,f784]) ).
fof(f784,plain,
( ! [X0,X1] :
( ~ g(X1)
| eh = product(inv(product(X0,X1)),inv(inv(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_95 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f6253,plain,
( spl1_610
| ~ spl1_2
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f4757,f779,f81,f6251]) ).
fof(f779,plain,
( spl1_94
<=> ! [X0,X1] :
( eg = sum(opp(f(product(X0,X1))),f(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
fof(f4757,plain,
( ! [X0] :
( eg = sum(opp(f(product(X0,sK0))),f(product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_94 ),
inference(resolution,[],[f83,f780]) ).
fof(f780,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(opp(f(product(X0,X1))),f(product(X0,X1)))
| ~ g(X0) )
| ~ spl1_94 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f6249,plain,
( spl1_609
| ~ spl1_2
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f4756,f775,f81,f6247]) ).
fof(f775,plain,
( spl1_93
<=> ! [X0,X1] :
( eg = sum(f(product(X0,X1)),opp(f(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).
fof(f4756,plain,
( ! [X0] :
( eg = sum(f(product(X0,sK0)),opp(f(product(X0,sK0))))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_93 ),
inference(resolution,[],[f83,f776]) ).
fof(f776,plain,
( ! [X0,X1] :
( ~ g(X1)
| eg = sum(f(product(X0,X1)),opp(f(product(X0,X1))))
| ~ g(X0) )
| ~ spl1_93 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f6204,plain,
( spl1_608
| ~ spl1_2
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f4755,f763,f81,f6201]) ).
fof(f6201,plain,
( spl1_608
<=> f(inv(inv(sK0))) = sum(eg,f(inv(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_608])]) ).
fof(f763,plain,
( spl1_92
<=> ! [X0] :
( f(inv(inv(X0))) = sum(eg,f(inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
fof(f4755,plain,
( f(inv(inv(sK0))) = sum(eg,f(inv(inv(sK0))))
| ~ spl1_2
| ~ spl1_92 ),
inference(resolution,[],[f83,f764]) ).
fof(f764,plain,
( ! [X0] :
( ~ g(X0)
| f(inv(inv(X0))) = sum(eg,f(inv(inv(X0)))) )
| ~ spl1_92 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f6194,plain,
( spl1_607
| ~ spl1_560
| ~ spl1_599 ),
inference(avatar_split_clause,[],[f6162,f6159,f5239,f6192]) ).
fof(f6159,plain,
( spl1_599
<=> ! [X0] :
( f(product(X0,sK0)) = sum(eg,f(product(X0,sK0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_599])]) ).
fof(f6162,plain,
( ! [X0] :
( f(product(X0,sK0)) = f(product(eh,product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_560
| ~ spl1_599 ),
inference(forward_demodulation,[],[f6160,f5240]) ).
fof(f6160,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(eg,f(product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_599 ),
inference(avatar_component_clause,[],[f6159]) ).
fof(f6190,plain,
( spl1_606
| ~ spl1_6
| ~ spl1_575 ),
inference(avatar_split_clause,[],[f5977,f5958,f100,f6188]) ).
fof(f5977,plain,
( ! [X0] :
( product(sK0,inv(X0)) = product(sK0,product(eh,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_575 ),
inference(resolution,[],[f5959,f101]) ).
fof(f6186,plain,
( spl1_605
| ~ spl1_6
| ~ spl1_574 ),
inference(avatar_split_clause,[],[f5967,f5954,f100,f6184]) ).
fof(f5967,plain,
( ! [X0] :
( product(sK0,inv(X0)) = product(product(sK0,inv(X0)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_574 ),
inference(resolution,[],[f5955,f101]) ).
fof(f6182,plain,
( spl1_604
| ~ spl1_6
| ~ spl1_573 ),
inference(avatar_split_clause,[],[f5962,f5950,f100,f6180]) ).
fof(f5962,plain,
( ! [X0] :
( product(sK0,inv(X0)) = product(eh,product(sK0,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_573 ),
inference(resolution,[],[f5951,f101]) ).
fof(f6178,plain,
( spl1_603
| ~ spl1_2
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f4754,f733,f81,f6176]) ).
fof(f733,plain,
( spl1_91
<=> ! [X0,X1] :
( ~ g(X0)
| product(inv(X1),X0) = product(product(inv(X1),X0),eh)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
fof(f4754,plain,
( ! [X0] :
( product(inv(sK0),X0) = product(product(inv(sK0),X0),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_91 ),
inference(resolution,[],[f83,f734]) ).
fof(f734,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(inv(X1),X0) = product(product(inv(X1),X0),eh)
| ~ g(X0) )
| ~ spl1_91 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f6174,plain,
( spl1_602
| ~ spl1_2
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f4753,f729,f81,f6172]) ).
fof(f729,plain,
( spl1_90
<=> ! [X0,X1] :
( ~ g(X0)
| product(inv(X1),X0) = product(eh,product(inv(X1),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
fof(f4753,plain,
( ! [X0] :
( product(inv(sK0),X0) = product(eh,product(inv(sK0),X0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_90 ),
inference(resolution,[],[f83,f730]) ).
fof(f730,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(inv(X1),X0) = product(eh,product(inv(X1),X0))
| ~ g(X0) )
| ~ spl1_90 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f6170,plain,
( spl1_601
| ~ spl1_2
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f4751,f713,f81,f6168]) ).
fof(f713,plain,
( spl1_86
<=> ! [X0,X1] :
( inv(product(X0,X1)) = product(eh,inv(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
fof(f4751,plain,
( ! [X0] :
( inv(product(X0,sK0)) = product(eh,inv(product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_86 ),
inference(resolution,[],[f83,f714]) ).
fof(f714,plain,
( ! [X0,X1] :
( ~ g(X1)
| inv(product(X0,X1)) = product(eh,inv(product(X0,X1)))
| ~ g(X0) )
| ~ spl1_86 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f6166,plain,
( spl1_600
| ~ spl1_2
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f4750,f709,f81,f6164]) ).
fof(f709,plain,
( spl1_85
<=> ! [X0,X1] :
( inv(product(X0,X1)) = product(inv(product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
fof(f4750,plain,
( ! [X0] :
( inv(product(X0,sK0)) = product(inv(product(X0,sK0)),eh)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_85 ),
inference(resolution,[],[f83,f710]) ).
fof(f710,plain,
( ! [X0,X1] :
( ~ g(X1)
| inv(product(X0,X1)) = product(inv(product(X0,X1)),eh)
| ~ g(X0) )
| ~ spl1_85 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f6161,plain,
( spl1_599
| ~ spl1_2
| ~ spl1_84 ),
inference(avatar_split_clause,[],[f4749,f705,f81,f6159]) ).
fof(f705,plain,
( spl1_84
<=> ! [X0,X1] :
( f(product(X0,X1)) = sum(eg,f(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).
fof(f4749,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(eg,f(product(X0,sK0)))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_84 ),
inference(resolution,[],[f83,f706]) ).
fof(f706,plain,
( ! [X0,X1] :
( ~ g(X1)
| f(product(X0,X1)) = sum(eg,f(product(X0,X1)))
| ~ g(X0) )
| ~ spl1_84 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f6157,plain,
( spl1_598
| ~ spl1_2
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f4752,f717,f81,f6154]) ).
fof(f6154,plain,
( spl1_598
<=> f(inv(inv(sK0))) = sum(f(inv(inv(sK0))),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_598])]) ).
fof(f717,plain,
( spl1_87
<=> ! [X0] :
( f(inv(inv(X0))) = sum(f(inv(inv(X0))),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
fof(f4752,plain,
( f(inv(inv(sK0))) = sum(f(inv(inv(sK0))),eg)
| ~ spl1_2
| ~ spl1_87 ),
inference(resolution,[],[f83,f718]) ).
fof(f718,plain,
( ! [X0] :
( ~ g(X0)
| f(inv(inv(X0))) = sum(f(inv(inv(X0))),eg) )
| ~ spl1_87 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f6151,plain,
( spl1_597
| ~ spl1_2
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f4748,f701,f81,f6149]) ).
fof(f6149,plain,
( spl1_597
<=> ! [X0] :
( f(product(X0,sK0)) = sum(f(product(X0,sK0)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_597])]) ).
fof(f701,plain,
( spl1_83
<=> ! [X0,X1] :
( f(product(X0,X1)) = sum(f(product(X0,X1)),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).
fof(f4748,plain,
( ! [X0] :
( f(product(X0,sK0)) = sum(f(product(X0,sK0)),eg)
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_83 ),
inference(resolution,[],[f83,f702]) ).
fof(f702,plain,
( ! [X0,X1] :
( ~ g(X1)
| f(product(X0,X1)) = sum(f(product(X0,X1)),eg)
| ~ g(X0) )
| ~ spl1_83 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f6139,plain,
( spl1_596
| ~ spl1_2
| ~ spl1_558
| ~ spl1_581 ),
inference(avatar_split_clause,[],[f6030,f6012,f5223,f81,f6137]) ).
fof(f6030,plain,
( ! [X0] :
( product(eh,X0) = product(sK0,product(inv(sK0),X0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_558
| ~ spl1_581 ),
inference(forward_demodulation,[],[f6027,f5225]) ).
fof(f6027,plain,
( ! [X0] :
( product(product(sK0,inv(sK0)),X0) = product(sK0,product(inv(sK0),X0))
| ~ g(X0) )
| ~ spl1_2
| ~ spl1_581 ),
inference(resolution,[],[f6013,f83]) ).
fof(f6133,plain,
( spl1_595
| ~ spl1_2
| ~ spl1_579 ),
inference(avatar_split_clause,[],[f6005,f5999,f81,f6130]) ).
fof(f6130,plain,
( spl1_595
<=> product(product(sK0,sK0),sK0) = product(sK0,product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_595])]) ).
fof(f6005,plain,
( product(product(sK0,sK0),sK0) = product(sK0,product(sK0,sK0))
| ~ spl1_2
| ~ spl1_579 ),
inference(resolution,[],[f6000,f83]) ).
fof(f6114,plain,
( spl1_594
| ~ spl1_2
| ~ spl1_578 ),
inference(avatar_split_clause,[],[f5996,f5985,f81,f6111]) ).
fof(f6111,plain,
( spl1_594
<=> eh = product(product(sK0,sK0),inv(product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_594])]) ).
fof(f5996,plain,
( eh = product(product(sK0,sK0),inv(product(sK0,sK0)))
| ~ spl1_2
| ~ spl1_578 ),
inference(resolution,[],[f5986,f83]) ).
fof(f6109,plain,
( spl1_593
| ~ spl1_2
| ~ spl1_577 ),
inference(avatar_split_clause,[],[f5991,f5981,f81,f6106]) ).
fof(f6106,plain,
( spl1_593
<=> eh = product(inv(product(sK0,sK0)),product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_593])]) ).
fof(f5991,plain,
( eh = product(inv(product(sK0,sK0)),product(sK0,sK0))
| ~ spl1_2
| ~ spl1_577 ),
inference(resolution,[],[f5982,f83]) ).
fof(f6104,plain,
( spl1_592
| ~ spl1_2
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f4745,f592,f81,f6101]) ).
fof(f6101,plain,
( spl1_592
<=> eh = product(inv(inv(inv(sK0))),inv(inv(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_592])]) ).
fof(f592,plain,
( spl1_73
<=> ! [X0] :
( eh = product(inv(inv(inv(X0))),inv(inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
fof(f4745,plain,
( eh = product(inv(inv(inv(sK0))),inv(inv(sK0)))
| ~ spl1_2
| ~ spl1_73 ),
inference(resolution,[],[f83,f593]) ).
fof(f593,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(inv(X0))),inv(inv(X0))) )
| ~ spl1_73 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f6099,plain,
( spl1_591
| ~ spl1_2
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f4744,f588,f81,f6096]) ).
fof(f6096,plain,
( spl1_591
<=> eh = product(inv(inv(sK0)),inv(inv(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_591])]) ).
fof(f588,plain,
( spl1_72
<=> ! [X0] :
( eh = product(inv(inv(X0)),inv(inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
fof(f4744,plain,
( eh = product(inv(inv(sK0)),inv(inv(inv(sK0))))
| ~ spl1_2
| ~ spl1_72 ),
inference(resolution,[],[f83,f589]) ).
fof(f589,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(X0)),inv(inv(inv(X0)))) )
| ~ spl1_72 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f6094,plain,
( spl1_590
| ~ spl1_2
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f4743,f584,f81,f6091]) ).
fof(f584,plain,
( spl1_71
<=> ! [X0] :
( eg = sum(opp(f(inv(X0))),f(inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
fof(f4743,plain,
( eg = sum(opp(f(inv(sK0))),f(inv(sK0)))
| ~ spl1_2
| ~ spl1_71 ),
inference(resolution,[],[f83,f585]) ).
fof(f585,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(inv(X0))),f(inv(X0))) )
| ~ spl1_71 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f6089,plain,
( spl1_589
| ~ spl1_2
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f4742,f580,f81,f6086]) ).
fof(f6086,plain,
( spl1_589
<=> eg = sum(f(inv(sK0)),opp(f(inv(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_589])]) ).
fof(f580,plain,
( spl1_70
<=> ! [X0] :
( eg = sum(f(inv(X0)),opp(f(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
fof(f4742,plain,
( eg = sum(f(inv(sK0)),opp(f(inv(sK0))))
| ~ spl1_2
| ~ spl1_70 ),
inference(resolution,[],[f83,f581]) ).
fof(f581,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(inv(X0)),opp(f(inv(X0)))) )
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f6066,plain,
( spl1_588
| ~ spl1_2
| ~ spl1_574 ),
inference(avatar_split_clause,[],[f5969,f5954,f81,f6063]) ).
fof(f6063,plain,
( spl1_588
<=> product(sK0,sK0) = product(product(sK0,sK0),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_588])]) ).
fof(f5969,plain,
( product(sK0,sK0) = product(product(sK0,sK0),eh)
| ~ spl1_2
| ~ spl1_574 ),
inference(resolution,[],[f5955,f83]) ).
fof(f6061,plain,
( spl1_587
| ~ spl1_2
| ~ spl1_573 ),
inference(avatar_split_clause,[],[f5964,f5950,f81,f6058]) ).
fof(f6058,plain,
( spl1_587
<=> product(sK0,sK0) = product(eh,product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_587])]) ).
fof(f5964,plain,
( product(sK0,sK0) = product(eh,product(sK0,sK0))
| ~ spl1_2
| ~ spl1_573 ),
inference(resolution,[],[f5951,f83]) ).
fof(f6056,plain,
( spl1_586
| ~ spl1_2
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f4739,f520,f81,f6053]) ).
fof(f520,plain,
( spl1_65
<=> ! [X0] :
( inv(inv(X0)) = product(eh,inv(inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
fof(f4739,plain,
( inv(inv(sK0)) = product(eh,inv(inv(sK0)))
| ~ spl1_2
| ~ spl1_65 ),
inference(resolution,[],[f83,f521]) ).
fof(f521,plain,
( ! [X0] :
( ~ g(X0)
| inv(inv(X0)) = product(eh,inv(inv(X0))) )
| ~ spl1_65 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f6051,plain,
( spl1_585
| ~ spl1_2
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f4738,f516,f81,f6048]) ).
fof(f6048,plain,
( spl1_585
<=> inv(inv(sK0)) = product(inv(inv(sK0)),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_585])]) ).
fof(f516,plain,
( spl1_64
<=> ! [X0] :
( inv(inv(X0)) = product(inv(inv(X0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
fof(f4738,plain,
( inv(inv(sK0)) = product(inv(inv(sK0)),eh)
| ~ spl1_2
| ~ spl1_64 ),
inference(resolution,[],[f83,f517]) ).
fof(f517,plain,
( ! [X0] :
( ~ g(X0)
| inv(inv(X0)) = product(inv(inv(X0)),eh) )
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f6038,plain,
( spl1_584
| ~ spl1_19
| ~ spl1_562 ),
inference(avatar_split_clause,[],[f5262,f5259,f164,f6036]) ).
fof(f5259,plain,
( spl1_562
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(sK0,X1),X0) = product(sK0,product(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_562])]) ).
fof(f5262,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(sK0,product(X1,X2)),X0) = product(sK0,product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_562 ),
inference(resolution,[],[f5260,f165]) ).
fof(f5260,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| product(product(sK0,X1),X0) = product(sK0,product(X1,X0)) )
| ~ spl1_562 ),
inference(avatar_component_clause,[],[f5259]) ).
fof(f6034,plain,
( spl1_583
| ~ spl1_2
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f4735,f477,f81,f6032]) ).
fof(f477,plain,
( spl1_58
<=> ! [X0,X3,X2,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X2,X3),X1),X0) = product(product(X2,X3),product(X1,X0))
| ~ g(X3)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
fof(f4735,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(product(X1,sK0),X0),X2) = product(product(X1,sK0),product(X0,X2))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_58 ),
inference(resolution,[],[f83,f478]) ).
fof(f478,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X3)
| ~ g(X1)
| product(product(product(X2,X3),X1),X0) = product(product(X2,X3),product(X1,X0))
| ~ g(X0)
| ~ g(X2) )
| ~ spl1_58 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f6023,plain,
( spl1_582
| ~ spl1_2
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f4737,f512,f81,f6020]) ).
fof(f512,plain,
( spl1_63
<=> ! [X0] :
( f(inv(X0)) = sum(eg,f(inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
fof(f4737,plain,
( f(inv(sK0)) = sum(eg,f(inv(sK0)))
| ~ spl1_2
| ~ spl1_63 ),
inference(resolution,[],[f83,f513]) ).
fof(f513,plain,
( ! [X0] :
( ~ g(X0)
| f(inv(X0)) = sum(eg,f(inv(X0))) )
| ~ spl1_63 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f6014,plain,
( spl1_581
| ~ spl1_6
| ~ spl1_562 ),
inference(avatar_split_clause,[],[f5263,f5259,f100,f6012]) ).
fof(f5263,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(product(sK0,inv(X1)),X0) = product(sK0,product(inv(X1),X0))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_562 ),
inference(resolution,[],[f5260,f101]) ).
fof(f6010,plain,
( spl1_580
| ~ spl1_2
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f4734,f458,f81,f6008]) ).
fof(f458,plain,
( spl1_56
<=> ! [X2,X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(inv(X2),X1),X0) = product(inv(X2),product(X1,X0))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
fof(f4734,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(product(inv(sK0),X0),X1) = product(inv(sK0),product(X0,X1))
| ~ g(X1) )
| ~ spl1_2
| ~ spl1_56 ),
inference(resolution,[],[f83,f459]) ).
fof(f459,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X1)
| product(product(inv(X2),X1),X0) = product(inv(X2),product(X1,X0))
| ~ g(X0) )
| ~ spl1_56 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f6001,plain,
( spl1_579
| ~ spl1_2
| ~ spl1_562 ),
inference(avatar_split_clause,[],[f5265,f5259,f81,f5999]) ).
fof(f5265,plain,
( ! [X0] :
( ~ g(X0)
| product(product(sK0,sK0),X0) = product(sK0,product(sK0,X0)) )
| ~ spl1_2
| ~ spl1_562 ),
inference(resolution,[],[f5260,f83]) ).
fof(f5987,plain,
( spl1_578
| ~ spl1_2
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f4732,f400,f81,f5985]) ).
fof(f400,plain,
( spl1_50
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| eh = product(product(X1,X0),inv(product(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
fof(f4732,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(sK0,X0),inv(product(sK0,X0))) )
| ~ spl1_2
| ~ spl1_50 ),
inference(resolution,[],[f83,f401]) ).
fof(f401,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eh = product(product(X1,X0),inv(product(X1,X0))) )
| ~ spl1_50 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f5983,plain,
( spl1_577
| ~ spl1_2
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f4731,f396,f81,f5981]) ).
fof(f396,plain,
( spl1_49
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| eh = product(inv(product(X1,X0)),product(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
fof(f4731,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(sK0,X0)),product(sK0,X0)) )
| ~ spl1_2
| ~ spl1_49 ),
inference(resolution,[],[f83,f397]) ).
fof(f397,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| eh = product(inv(product(X1,X0)),product(X1,X0)) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f5975,plain,
( spl1_576
| ~ spl1_2
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f4736,f508,f81,f5972]) ).
fof(f508,plain,
( spl1_62
<=> ! [X0] :
( f(inv(X0)) = sum(f(inv(X0)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
fof(f4736,plain,
( f(inv(sK0)) = sum(f(inv(sK0)),eg)
| ~ spl1_2
| ~ spl1_62 ),
inference(resolution,[],[f83,f509]) ).
fof(f509,plain,
( ! [X0] :
( ~ g(X0)
| f(inv(X0)) = sum(f(inv(X0)),eg) )
| ~ spl1_62 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f5960,plain,
( spl1_575
| ~ spl1_4
| ~ spl1_556
| ~ spl1_562 ),
inference(avatar_split_clause,[],[f5266,f5259,f5209,f91,f5958]) ).
fof(f5266,plain,
( ! [X0] :
( product(sK0,X0) = product(sK0,product(eh,X0))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_556
| ~ spl1_562 ),
inference(forward_demodulation,[],[f5264,f5211]) ).
fof(f5264,plain,
( ! [X0] :
( ~ g(X0)
| product(product(sK0,eh),X0) = product(sK0,product(eh,X0)) )
| ~ spl1_4
| ~ spl1_562 ),
inference(resolution,[],[f5260,f93]) ).
fof(f5956,plain,
( spl1_574
| ~ spl1_2
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f4730,f365,f81,f5954]) ).
fof(f365,plain,
( spl1_46
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(X1,X0) = product(product(X1,X0),eh) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
fof(f4730,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(product(sK0,X0),eh) )
| ~ spl1_2
| ~ spl1_46 ),
inference(resolution,[],[f83,f366]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| product(X1,X0) = product(product(X1,X0),eh) )
| ~ spl1_46 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f5952,plain,
( spl1_573
| ~ spl1_2
| ~ spl1_45 ),
inference(avatar_split_clause,[],[f4729,f361,f81,f5950]) ).
fof(f361,plain,
( spl1_45
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(X1,X0) = product(eh,product(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
fof(f4729,plain,
( ! [X0] :
( ~ g(X0)
| product(sK0,X0) = product(eh,product(sK0,X0)) )
| ~ spl1_2
| ~ spl1_45 ),
inference(resolution,[],[f83,f362]) ).
fof(f362,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| product(X1,X0) = product(eh,product(X1,X0)) )
| ~ spl1_45 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f5640,plain,
( ~ spl1_3
| spl1_572
| ~ spl1_18
| ~ spl1_561 ),
inference(avatar_split_clause,[],[f5255,f5243,f160,f5638,f86]) ).
fof(f160,plain,
( spl1_18
<=> ! [X0,X1] :
( h(sum(X1,X0))
| ~ h(X0)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f5255,plain,
( ! [X0] :
( h(f(product(X0,eh)))
| ~ h(eg)
| ~ h(f(X0)) )
| ~ spl1_18
| ~ spl1_561 ),
inference(superposition,[],[f161,f5244]) ).
fof(f161,plain,
( ! [X0,X1] :
( h(sum(X1,X0))
| ~ h(X0)
| ~ h(X1) )
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f5328,plain,
( ~ spl1_3
| spl1_571
| ~ spl1_18
| ~ spl1_560 ),
inference(avatar_split_clause,[],[f5249,f5239,f160,f5326,f86]) ).
fof(f5249,plain,
( ! [X0] :
( h(f(product(eh,X0)))
| ~ h(f(X0))
| ~ h(eg) )
| ~ spl1_18
| ~ spl1_560 ),
inference(superposition,[],[f161,f5240]) ).
fof(f5316,plain,
( spl1_570
| ~ spl1_2
| ~ spl1_40 ),
inference(avatar_split_clause,[],[f4728,f317,f81,f5313]) ).
fof(f5313,plain,
( spl1_570
<=> eh = product(inv(inv(sK0)),inv(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_570])]) ).
fof(f317,plain,
( spl1_40
<=> ! [X0] :
( eh = product(inv(inv(X0)),inv(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
fof(f4728,plain,
( eh = product(inv(inv(sK0)),inv(sK0))
| ~ spl1_2
| ~ spl1_40 ),
inference(resolution,[],[f83,f318]) ).
fof(f318,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(X0)),inv(X0)) )
| ~ spl1_40 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f5311,plain,
( spl1_569
| ~ spl1_2
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f4727,f313,f81,f5308]) ).
fof(f313,plain,
( spl1_39
<=> ! [X0] :
( eh = product(inv(X0),inv(inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
fof(f4727,plain,
( eh = product(inv(sK0),inv(inv(sK0)))
| ~ spl1_2
| ~ spl1_39 ),
inference(resolution,[],[f83,f314]) ).
fof(f314,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(X0),inv(inv(X0))) )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f5306,plain,
( spl1_568
| ~ spl1_2
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f4726,f309,f81,f5303]) ).
fof(f309,plain,
( spl1_38
<=> ! [X0] :
( eg = sum(opp(f(X0)),f(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
fof(f4726,plain,
( eg = sum(opp(f(sK0)),f(sK0))
| ~ spl1_2
| ~ spl1_38 ),
inference(resolution,[],[f83,f310]) ).
fof(f310,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(X0)),f(X0)) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f5301,plain,
( spl1_567
| ~ spl1_2
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f4725,f305,f81,f5298]) ).
fof(f305,plain,
( spl1_37
<=> ! [X0] :
( eg = sum(f(X0),opp(f(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
fof(f4725,plain,
( eg = sum(f(sK0),opp(f(sK0)))
| ~ spl1_2
| ~ spl1_37 ),
inference(resolution,[],[f83,f306]) ).
fof(f306,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(X0),opp(f(X0))) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f5286,plain,
( spl1_566
| ~ spl1_2
| ~ spl1_36 ),
inference(avatar_split_clause,[],[f4724,f280,f81,f5283]) ).
fof(f280,plain,
( spl1_36
<=> ! [X0] :
( inv(X0) = product(eh,inv(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
fof(f4724,plain,
( inv(sK0) = product(eh,inv(sK0))
| ~ spl1_2
| ~ spl1_36 ),
inference(resolution,[],[f83,f281]) ).
fof(f281,plain,
( ! [X0] :
( ~ g(X0)
| inv(X0) = product(eh,inv(X0)) )
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f5281,plain,
( spl1_565
| ~ spl1_2
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f4723,f276,f81,f5278]) ).
fof(f276,plain,
( spl1_35
<=> ! [X0] :
( inv(X0) = product(inv(X0),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
fof(f4723,plain,
( inv(sK0) = product(inv(sK0),eh)
| ~ spl1_2
| ~ spl1_35 ),
inference(resolution,[],[f83,f277]) ).
fof(f277,plain,
( ! [X0] :
( ~ g(X0)
| inv(X0) = product(inv(X0),eh) )
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f5276,plain,
( spl1_564
| ~ spl1_2
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f4722,f272,f81,f5273]) ).
fof(f5271,plain,
( spl1_563
| ~ spl1_2
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f4721,f268,f81,f5268]) ).
fof(f5268,plain,
( spl1_563
<=> f(sK0) = sum(f(sK0),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_563])]) ).
fof(f268,plain,
( spl1_33
<=> ! [X0] :
( f(X0) = sum(f(X0),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f4721,plain,
( f(sK0) = sum(f(sK0),eg)
| ~ spl1_2
| ~ spl1_33 ),
inference(resolution,[],[f83,f269]) ).
fof(f269,plain,
( ! [X0] :
( ~ g(X0)
| f(X0) = sum(f(X0),eg) )
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f5261,plain,
( spl1_562
| ~ spl1_2
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f4720,f200,f81,f5259]) ).
fof(f200,plain,
( spl1_23
<=> ! [X2,X0,X1] :
( product(product(X2,X1),X0) = product(X2,product(X1,X0))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f4720,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(sK0,X1),X0) = product(sK0,product(X1,X0)) )
| ~ spl1_2
| ~ spl1_23 ),
inference(resolution,[],[f83,f201]) ).
fof(f201,plain,
( ! [X2,X0,X1] :
( ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| product(product(X2,X1),X0) = product(X2,product(X1,X0)) )
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f5245,plain,
( spl1_561
| ~ spl1_1
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f5095,f191,f77,f5243]) ).
fof(f5095,plain,
( ! [X0] : sum(f(X0),eg) = f(product(X0,eh))
| ~ spl1_1
| ~ spl1_21 ),
inference(superposition,[],[f192,f78]) ).
fof(f5241,plain,
( spl1_560
| ~ spl1_1
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f5094,f191,f77,f5239]) ).
fof(f5094,plain,
( ! [X0] : sum(eg,f(X0)) = f(product(eh,X0))
| ~ spl1_1
| ~ spl1_21 ),
inference(superposition,[],[f192,f78]) ).
fof(f5231,plain,
( spl1_559
| ~ spl1_2
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f4719,f156,f81,f5228]) ).
fof(f156,plain,
( spl1_17
<=> ! [X0] :
( eh = product(inv(X0),X0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f4719,plain,
( eh = product(inv(sK0),sK0)
| ~ spl1_2
| ~ spl1_17 ),
inference(resolution,[],[f83,f157]) ).
fof(f157,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(X0),X0) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f5226,plain,
( spl1_558
| ~ spl1_2
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f4718,f152,f81,f5223]) ).
fof(f152,plain,
( spl1_16
<=> ! [X0] :
( eh = product(X0,inv(X0))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f4718,plain,
( eh = product(sK0,inv(sK0))
| ~ spl1_2
| ~ spl1_16 ),
inference(resolution,[],[f83,f153]) ).
fof(f153,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(X0,inv(X0)) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f5217,plain,
( spl1_557
| ~ spl1_2
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f4717,f125,f81,f5214]) ).
fof(f125,plain,
( spl1_12
<=> ! [X0] :
( product(eh,X0) = X0
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f4717,plain,
( sK0 = product(eh,sK0)
| ~ spl1_2
| ~ spl1_12 ),
inference(resolution,[],[f83,f126]) ).
fof(f126,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = X0 )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f5212,plain,
( spl1_556
| ~ spl1_2
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f4716,f121,f81,f5209]) ).
fof(f121,plain,
( spl1_11
<=> ! [X0] :
( product(X0,eh) = X0
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f4716,plain,
( sK0 = product(sK0,eh)
| ~ spl1_2
| ~ spl1_11 ),
inference(resolution,[],[f83,f122]) ).
fof(f122,plain,
( ! [X0] :
( ~ g(X0)
| product(X0,eh) = X0 )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f5207,plain,
( ~ spl1_1
| ~ spl1_555 ),
inference(avatar_split_clause,[],[f57,f5204,f77]) ).
fof(f57,plain,
( f(inv(sK0)) != opp(f(sK0))
| eg != f(eh) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
( ( f(inv(sK0)) != opp(f(sK0))
& g(sK0) )
| eg != f(eh) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f34,f54]) ).
fof(f54,plain,
( ? [X0] :
( ( f(inv(X0)) != opp(f(X0))
& g(X0) )
| eg != f(eh) )
=> ( ( f(inv(sK0)) != opp(f(sK0))
& g(sK0) )
| eg != f(eh) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0] :
( ( f(inv(X0)) != opp(f(X0))
& g(X0) )
| eg != f(eh) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] :
( ( f(inv(X0)) = opp(f(X0))
| ~ g(X0) )
& eg = f(eh) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] :
( ( f(inv(X3)) = opp(f(X3))
| ~ g(X3) )
& eg = f(eh) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] :
( ( f(inv(X3)) = opp(f(X3))
| ~ g(X3) )
& eg = f(eh) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f4715,plain,
( spl1_1
| ~ spl1_20
| ~ spl1_21
| ~ spl1_61
| ~ spl1_478
| ~ spl1_543 ),
inference(avatar_split_clause,[],[f4647,f4552,f3999,f501,f191,f182,f77]) ).
fof(f501,plain,
( spl1_61
<=> eg = sum(opp(f(eh)),f(eh)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
fof(f3999,plain,
( spl1_478
<=> ! [X0] : f(eh) = sum(opp(X0),sum(opp(opp(X0)),f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_478])]) ).
fof(f4552,plain,
( spl1_543
<=> f(eh) = opp(opp(f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_543])]) ).
fof(f4647,plain,
( eg = f(eh)
| ~ spl1_20
| ~ spl1_21
| ~ spl1_61
| ~ spl1_478
| ~ spl1_543 ),
inference(forward_demodulation,[],[f4646,f503]) ).
fof(f503,plain,
( eg = sum(opp(f(eh)),f(eh))
| ~ spl1_61 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f4646,plain,
( f(eh) = sum(opp(f(eh)),f(eh))
| ~ spl1_20
| ~ spl1_21
| ~ spl1_478
| ~ spl1_543 ),
inference(forward_demodulation,[],[f4645,f184]) ).
fof(f4645,plain,
( f(eh) = sum(opp(f(eh)),f(product(eh,eh)))
| ~ spl1_21
| ~ spl1_478
| ~ spl1_543 ),
inference(forward_demodulation,[],[f4601,f192]) ).
fof(f4601,plain,
( f(eh) = sum(opp(f(eh)),sum(f(eh),f(eh)))
| ~ spl1_478
| ~ spl1_543 ),
inference(superposition,[],[f4000,f4554]) ).
fof(f4554,plain,
( f(eh) = opp(opp(f(eh)))
| ~ spl1_543 ),
inference(avatar_component_clause,[],[f4552]) ).
fof(f4000,plain,
( ! [X0] : f(eh) = sum(opp(X0),sum(opp(opp(X0)),f(eh)))
| ~ spl1_478 ),
inference(avatar_component_clause,[],[f3999]) ).
fof(f4687,plain,
( spl1_554
| ~ spl1_3
| ~ spl1_29
| ~ spl1_313 ),
inference(avatar_split_clause,[],[f2629,f2509,f243,f86,f4685]) ).
fof(f4685,plain,
( spl1_554
<=> ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(sum(sum(X0,opp(X1)),eg),opp(X2))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_554])]) ).
fof(f2509,plain,
( spl1_313
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,opp(X1)),X2),opp(X3)) = sum(sum(X0,opp(X1)),sum(X2,opp(X3)))
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_313])]) ).
fof(f2629,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(sum(sum(X0,opp(X1)),eg),opp(X2))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_29
| ~ spl1_313 ),
inference(forward_demodulation,[],[f2626,f244]) ).
fof(f2626,plain,
( ! [X2,X0,X1] :
( sum(sum(sum(X0,opp(X1)),eg),opp(X2)) = sum(sum(X0,opp(X1)),sum(eg,opp(X2)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_313 ),
inference(resolution,[],[f2510,f88]) ).
fof(f88,plain,
( h(eg)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f2510,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X2)
| sum(sum(sum(X0,opp(X1)),X2),opp(X3)) = sum(sum(X0,opp(X1)),sum(X2,opp(X3)))
| ~ h(X0) )
| ~ spl1_313 ),
inference(avatar_component_clause,[],[f2509]) ).
fof(f4595,plain,
( spl1_553
| ~ spl1_3
| ~ spl1_277 ),
inference(avatar_split_clause,[],[f2299,f2224,f86,f4593]) ).
fof(f4593,plain,
( spl1_553
<=> ! [X0,X1] :
( sum(sum(opp(X0),sum(X1,eg)),eg) = sum(opp(X0),sum(sum(X1,eg),eg))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_553])]) ).
fof(f2224,plain,
( spl1_277
<=> ! [X2,X0,X1] :
( sum(sum(opp(X0),sum(X1,eg)),X2) = sum(opp(X0),sum(sum(X1,eg),X2))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_277])]) ).
fof(f2299,plain,
( ! [X0,X1] :
( sum(sum(opp(X0),sum(X1,eg)),eg) = sum(opp(X0),sum(sum(X1,eg),eg))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_277 ),
inference(resolution,[],[f2225,f88]) ).
fof(f2225,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(opp(X0),sum(X1,eg)),X2) = sum(opp(X0),sum(sum(X1,eg),X2))
| ~ h(X1) )
| ~ spl1_277 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f4591,plain,
( spl1_552
| ~ spl1_3
| ~ spl1_274 ),
inference(avatar_split_clause,[],[f2288,f2212,f86,f4589]) ).
fof(f4589,plain,
( spl1_552
<=> ! [X0,X1] :
( sum(sum(eg,sum(X0,opp(X1))),eg) = sum(eg,sum(sum(X0,opp(X1)),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_552])]) ).
fof(f2212,plain,
( spl1_274
<=> ! [X2,X0,X1] :
( sum(eg,sum(sum(X0,opp(X1)),X2)) = sum(sum(eg,sum(X0,opp(X1))),X2)
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_274])]) ).
fof(f2288,plain,
( ! [X0,X1] :
( sum(sum(eg,sum(X0,opp(X1))),eg) = sum(eg,sum(sum(X0,opp(X1)),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_274 ),
inference(resolution,[],[f2213,f88]) ).
fof(f2213,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(eg,sum(sum(X0,opp(X1)),X2)) = sum(sum(eg,sum(X0,opp(X1))),X2)
| ~ h(X0) )
| ~ spl1_274 ),
inference(avatar_component_clause,[],[f2212]) ).
fof(f4587,plain,
( spl1_551
| ~ spl1_4
| ~ spl1_273 ),
inference(avatar_split_clause,[],[f2283,f2208,f91,f4585]) ).
fof(f4585,plain,
( spl1_551
<=> ! [X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),opp(X1)),f(eh)) = sum(f(X0),sum(opp(X1),f(eh))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_551])]) ).
fof(f2283,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),opp(X1)),f(eh)) = sum(f(X0),sum(opp(X1),f(eh))) )
| ~ spl1_4
| ~ spl1_273 ),
inference(resolution,[],[f2209,f93]) ).
fof(f4583,plain,
( spl1_550
| ~ spl1_4
| ~ spl1_272 ),
inference(avatar_split_clause,[],[f2280,f2204,f91,f4581]) ).
fof(f4581,plain,
( spl1_550
<=> ! [X0,X1] :
( product(product(X0,inv(X1)),eh) = product(product(product(X0,inv(X1)),eh),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_550])]) ).
fof(f2280,plain,
( ! [X0,X1] :
( product(product(X0,inv(X1)),eh) = product(product(product(X0,inv(X1)),eh),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_272 ),
inference(resolution,[],[f2205,f93]) ).
fof(f4579,plain,
( spl1_549
| ~ spl1_4
| ~ spl1_271 ),
inference(avatar_split_clause,[],[f2277,f2200,f91,f4577]) ).
fof(f4577,plain,
( spl1_549
<=> ! [X0,X1] :
( product(product(X0,inv(X1)),eh) = product(eh,product(product(X0,inv(X1)),eh))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_549])]) ).
fof(f2277,plain,
( ! [X0,X1] :
( product(product(X0,inv(X1)),eh) = product(eh,product(product(X0,inv(X1)),eh))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_271 ),
inference(resolution,[],[f2201,f93]) ).
fof(f4575,plain,
( spl1_548
| ~ spl1_3
| ~ spl1_270 ),
inference(avatar_split_clause,[],[f2274,f2196,f86,f4573]) ).
fof(f4573,plain,
( spl1_548
<=> ! [X0,X1] :
( sum(sum(X0,f(X1)),eg) = sum(sum(sum(X0,f(X1)),eg),eg)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_548])]) ).
fof(f2196,plain,
( spl1_270
<=> ! [X2,X0,X1] :
( sum(sum(X0,f(X1)),X2) = sum(sum(sum(X0,f(X1)),X2),eg)
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_270])]) ).
fof(f2274,plain,
( ! [X0,X1] :
( sum(sum(X0,f(X1)),eg) = sum(sum(sum(X0,f(X1)),eg),eg)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_270 ),
inference(resolution,[],[f2197,f88]) ).
fof(f2197,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X0,f(X1)),X2) = sum(sum(sum(X0,f(X1)),X2),eg)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_270 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f4571,plain,
( spl1_547
| ~ spl1_3
| ~ spl1_269 ),
inference(avatar_split_clause,[],[f2269,f2192,f86,f4569]) ).
fof(f4569,plain,
( spl1_547
<=> ! [X0,X1] :
( sum(sum(X0,f(X1)),eg) = sum(eg,sum(sum(X0,f(X1)),eg))
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_547])]) ).
fof(f2192,plain,
( spl1_269
<=> ! [X2,X0,X1] :
( sum(sum(X0,f(X1)),X2) = sum(eg,sum(sum(X0,f(X1)),X2))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_269])]) ).
fof(f2269,plain,
( ! [X0,X1] :
( sum(sum(X0,f(X1)),eg) = sum(eg,sum(sum(X0,f(X1)),eg))
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_269 ),
inference(resolution,[],[f2193,f88]) ).
fof(f2193,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X0,f(X1)),X2) = sum(eg,sum(sum(X0,f(X1)),X2))
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_269 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f4567,plain,
( spl1_546
| ~ spl1_4
| ~ spl1_268 ),
inference(avatar_split_clause,[],[f2264,f2188,f91,f4565]) ).
fof(f4565,plain,
( spl1_546
<=> ! [X0,X1] :
( product(inv(product(X0,X1)),eh) = product(product(inv(product(X0,X1)),eh),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_546])]) ).
fof(f2264,plain,
( ! [X0,X1] :
( product(inv(product(X0,X1)),eh) = product(product(inv(product(X0,X1)),eh),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_268 ),
inference(resolution,[],[f2189,f93]) ).
fof(f4563,plain,
( spl1_545
| ~ spl1_4
| ~ spl1_267 ),
inference(avatar_split_clause,[],[f2261,f2184,f91,f4561]) ).
fof(f4561,plain,
( spl1_545
<=> ! [X0,X1] :
( product(inv(product(X0,X1)),eh) = product(eh,product(inv(product(X0,X1)),eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_545])]) ).
fof(f2261,plain,
( ! [X0,X1] :
( product(inv(product(X0,X1)),eh) = product(eh,product(inv(product(X0,X1)),eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_267 ),
inference(resolution,[],[f2185,f93]) ).
fof(f4559,plain,
( spl1_544
| ~ spl1_3
| ~ spl1_266 ),
inference(avatar_split_clause,[],[f2254,f2180,f86,f4557]) ).
fof(f4557,plain,
( spl1_544
<=> ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),sum(X1,eg)) = sum(sum(f(X0),sum(X1,eg)),eg)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_544])]) ).
fof(f2180,plain,
( spl1_266
<=> ! [X2,X0,X1] :
( sum(f(X0),sum(X1,X2)) = sum(sum(f(X0),sum(X1,X2)),eg)
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_266])]) ).
fof(f2254,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),sum(X1,eg)) = sum(sum(f(X0),sum(X1,eg)),eg)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_266 ),
inference(resolution,[],[f2181,f88]) ).
fof(f2181,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| ~ g(X0)
| sum(f(X0),sum(X1,X2)) = sum(sum(f(X0),sum(X1,X2)),eg)
| ~ h(X1) )
| ~ spl1_266 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f4555,plain,
( spl1_543
| ~ spl1_28
| ~ spl1_522 ),
inference(avatar_split_clause,[],[f4507,f4463,f239,f4552]) ).
fof(f4463,plain,
( spl1_522
<=> f(eh) = sum(opp(opp(f(eh))),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_522])]) ).
fof(f4507,plain,
( f(eh) = opp(opp(f(eh)))
| ~ spl1_28
| ~ spl1_522 ),
inference(superposition,[],[f4465,f240]) ).
fof(f4465,plain,
( f(eh) = sum(opp(opp(f(eh))),eg)
| ~ spl1_522 ),
inference(avatar_component_clause,[],[f4463]) ).
fof(f4550,plain,
( spl1_542
| ~ spl1_3
| ~ spl1_264 ),
inference(avatar_split_clause,[],[f2249,f2172,f86,f4548]) ).
fof(f4548,plain,
( spl1_542
<=> ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),sum(X1,eg)) = sum(eg,sum(f(X0),sum(X1,eg)))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_542])]) ).
fof(f2172,plain,
( spl1_264
<=> ! [X2,X0,X1] :
( sum(f(X0),sum(X1,X2)) = sum(eg,sum(f(X0),sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_264])]) ).
fof(f2249,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),sum(X1,eg)) = sum(eg,sum(f(X0),sum(X1,eg)))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_264 ),
inference(resolution,[],[f2173,f88]) ).
fof(f2173,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| ~ g(X0)
| sum(f(X0),sum(X1,X2)) = sum(eg,sum(f(X0),sum(X1,X2)))
| ~ h(X1) )
| ~ spl1_264 ),
inference(avatar_component_clause,[],[f2172]) ).
fof(f4546,plain,
( spl1_541
| ~ spl1_4
| ~ spl1_263 ),
inference(avatar_split_clause,[],[f2244,f2168,f91,f4544]) ).
fof(f4544,plain,
( spl1_541
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,eh))) = product(eh,inv(product(X0,product(X1,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_541])]) ).
fof(f2244,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,eh))) = product(eh,inv(product(X0,product(X1,eh))))
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_263 ),
inference(resolution,[],[f2169,f93]) ).
fof(f4542,plain,
( spl1_540
| ~ spl1_4
| ~ spl1_262 ),
inference(avatar_split_clause,[],[f2241,f2164,f91,f4540]) ).
fof(f4540,plain,
( spl1_540
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,eh))) = product(inv(product(X0,product(X1,eh))),eh)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_540])]) ).
fof(f2241,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,product(X1,eh))) = product(inv(product(X0,product(X1,eh))),eh)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_262 ),
inference(resolution,[],[f2165,f93]) ).
fof(f4538,plain,
( spl1_539
| ~ spl1_4
| ~ spl1_261 ),
inference(avatar_split_clause,[],[f2238,f2160,f91,f4536]) ).
fof(f4536,plain,
( spl1_539
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,eh))) = sum(eg,f(product(X0,product(X1,eh))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_539])]) ).
fof(f2238,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,eh))) = sum(eg,f(product(X0,product(X1,eh))))
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_261 ),
inference(resolution,[],[f2161,f93]) ).
fof(f4534,plain,
( spl1_538
| ~ spl1_4
| ~ spl1_260 ),
inference(avatar_split_clause,[],[f2235,f2156,f91,f4532]) ).
fof(f4532,plain,
( spl1_538
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,eh))) = sum(f(product(X0,product(X1,eh))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_538])]) ).
fof(f2235,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,product(X1,eh))) = sum(f(product(X0,product(X1,eh))),eg)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_260 ),
inference(resolution,[],[f2157,f93]) ).
fof(f4530,plain,
( spl1_537
| ~ spl1_8
| ~ spl1_246 ),
inference(avatar_split_clause,[],[f2066,f1996,f107,f4528]) ).
fof(f4528,plain,
( spl1_537
<=> ! [X0,X1] :
( sum(eg,sum(sum(X0,eg),opp(X1))) = sum(sum(eg,sum(X0,eg)),opp(X1))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_537])]) ).
fof(f107,plain,
( spl1_8
<=> ! [X0] : h(opp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f1996,plain,
( spl1_246
<=> ! [X0,X1] :
( sum(eg,sum(sum(X0,eg),X1)) = sum(sum(eg,sum(X0,eg)),X1)
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_246])]) ).
fof(f2066,plain,
( ! [X0,X1] :
( sum(eg,sum(sum(X0,eg),opp(X1))) = sum(sum(eg,sum(X0,eg)),opp(X1))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_246 ),
inference(resolution,[],[f1997,f108]) ).
fof(f108,plain,
( ! [X0] : h(opp(X0))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f1997,plain,
( ! [X0,X1] :
( ~ h(X1)
| sum(eg,sum(sum(X0,eg),X1)) = sum(sum(eg,sum(X0,eg)),X1)
| ~ h(X0) )
| ~ spl1_246 ),
inference(avatar_component_clause,[],[f1996]) ).
fof(f4526,plain,
( spl1_536
| ~ spl1_8
| ~ spl1_242 ),
inference(avatar_split_clause,[],[f2052,f1968,f107,f4524]) ).
fof(f4524,plain,
( spl1_536
<=> ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(sum(sum(X0,opp(X1)),opp(X2)),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_536])]) ).
fof(f1968,plain,
( spl1_242
<=> ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),X2) = sum(sum(sum(X0,opp(X1)),X2),eg)
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_242])]) ).
fof(f2052,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(sum(sum(X0,opp(X1)),opp(X2)),eg)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_242 ),
inference(resolution,[],[f1969,f108]) ).
fof(f1969,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X0,opp(X1)),X2) = sum(sum(sum(X0,opp(X1)),X2),eg)
| ~ h(X0) )
| ~ spl1_242 ),
inference(avatar_component_clause,[],[f1968]) ).
fof(f4522,plain,
( spl1_535
| ~ spl1_8
| ~ spl1_241 ),
inference(avatar_split_clause,[],[f2047,f1964,f107,f4520]) ).
fof(f4520,plain,
( spl1_535
<=> ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(eg,sum(sum(X0,opp(X1)),opp(X2)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_535])]) ).
fof(f1964,plain,
( spl1_241
<=> ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),X2) = sum(eg,sum(sum(X0,opp(X1)),X2))
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_241])]) ).
fof(f2047,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),opp(X2)) = sum(eg,sum(sum(X0,opp(X1)),opp(X2)))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_241 ),
inference(resolution,[],[f1965,f108]) ).
fof(f1965,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X0,opp(X1)),X2) = sum(eg,sum(sum(X0,opp(X1)),X2))
| ~ h(X0) )
| ~ spl1_241 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f4518,plain,
( spl1_534
| ~ spl1_8
| ~ spl1_237 ),
inference(avatar_split_clause,[],[f2026,f1948,f107,f4516]) ).
fof(f4516,plain,
( spl1_534
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(opp(X0),sum(eg,sum(X1,opp(X2))))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_534])]) ).
fof(f1948,plain,
( spl1_237
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(opp(X0),sum(eg,sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_237])]) ).
fof(f2026,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(opp(X0),sum(eg,sum(X1,opp(X2))))
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_237 ),
inference(resolution,[],[f1949,f108]) ).
fof(f1949,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(opp(X0),sum(X1,X2)) = sum(opp(X0),sum(eg,sum(X1,X2)))
| ~ h(X1) )
| ~ spl1_237 ),
inference(avatar_component_clause,[],[f1948]) ).
fof(f4514,plain,
( spl1_533
| ~ spl1_8
| ~ spl1_236 ),
inference(avatar_split_clause,[],[f2021,f1944,f107,f4512]) ).
fof(f4512,plain,
( spl1_533
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(sum(opp(X0),sum(X1,opp(X2))),eg)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_533])]) ).
fof(f1944,plain,
( spl1_236
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(sum(opp(X0),sum(X1,X2)),eg)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_236])]) ).
fof(f2021,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(sum(opp(X0),sum(X1,opp(X2))),eg)
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_236 ),
inference(resolution,[],[f1945,f108]) ).
fof(f1945,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(opp(X0),sum(X1,X2)) = sum(sum(opp(X0),sum(X1,X2)),eg)
| ~ h(X1) )
| ~ spl1_236 ),
inference(avatar_component_clause,[],[f1944]) ).
fof(f4506,plain,
( spl1_532
| ~ spl1_8
| ~ spl1_235 ),
inference(avatar_split_clause,[],[f2016,f1914,f107,f4504]) ).
fof(f4504,plain,
( spl1_532
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(eg,sum(opp(X0),sum(X1,opp(X2))))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_532])]) ).
fof(f1914,plain,
( spl1_235
<=> ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(eg,sum(opp(X0),sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_235])]) ).
fof(f2016,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,opp(X2))) = sum(eg,sum(opp(X0),sum(X1,opp(X2))))
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_235 ),
inference(resolution,[],[f1915,f108]) ).
fof(f1915,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| sum(opp(X0),sum(X1,X2)) = sum(eg,sum(opp(X0),sum(X1,X2)))
| ~ h(X1) )
| ~ spl1_235 ),
inference(avatar_component_clause,[],[f1914]) ).
fof(f4502,plain,
( spl1_531
| ~ spl1_6
| ~ spl1_211 ),
inference(avatar_split_clause,[],[f1735,f1636,f100,f4500]) ).
fof(f4500,plain,
( spl1_531
<=> ! [X0,X1] :
( sum(sum(opp(X0),f(inv(X1))),eg) = sum(opp(X0),sum(f(inv(X1)),eg))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_531])]) ).
fof(f1636,plain,
( spl1_211
<=> ! [X0,X1] :
( sum(sum(opp(X0),f(X1)),eg) = sum(opp(X0),sum(f(X1),eg))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_211])]) ).
fof(f1735,plain,
( ! [X0,X1] :
( sum(sum(opp(X0),f(inv(X1))),eg) = sum(opp(X0),sum(f(inv(X1)),eg))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_211 ),
inference(resolution,[],[f1637,f101]) ).
fof(f1637,plain,
( ! [X0,X1] :
( ~ g(X1)
| sum(sum(opp(X0),f(X1)),eg) = sum(opp(X0),sum(f(X1),eg)) )
| ~ spl1_211 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f4498,plain,
( spl1_530
| ~ spl1_6
| ~ spl1_210 ),
inference(avatar_split_clause,[],[f1732,f1632,f100,f4496]) ).
fof(f4496,plain,
( spl1_530
<=> ! [X0,X1] :
( product(product(X0,eh),inv(X1)) = product(product(product(X0,eh),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_530])]) ).
fof(f1732,plain,
( ! [X0,X1] :
( product(product(X0,eh),inv(X1)) = product(product(product(X0,eh),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_210 ),
inference(resolution,[],[f1633,f101]) ).
fof(f4494,plain,
( spl1_529
| ~ spl1_6
| ~ spl1_209 ),
inference(avatar_split_clause,[],[f1729,f1628,f100,f4492]) ).
fof(f4492,plain,
( spl1_529
<=> ! [X0,X1] :
( product(product(X0,eh),inv(X1)) = product(eh,product(product(X0,eh),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_529])]) ).
fof(f1729,plain,
( ! [X0,X1] :
( product(product(X0,eh),inv(X1)) = product(eh,product(product(X0,eh),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_209 ),
inference(resolution,[],[f1629,f101]) ).
fof(f4490,plain,
( spl1_528
| ~ spl1_5
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f1726,f1624,f96,f4488]) ).
fof(f4488,plain,
( spl1_528
<=> ! [X0,X1] :
( sum(sum(X0,eg),f(X1)) = sum(sum(sum(X0,eg),f(X1)),eg)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_528])]) ).
fof(f1624,plain,
( spl1_208
<=> ! [X0,X1] :
( sum(sum(X0,eg),X1) = sum(sum(sum(X0,eg),X1),eg)
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_208])]) ).
fof(f1726,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),f(X1)) = sum(sum(sum(X0,eg),f(X1)),eg)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_208 ),
inference(resolution,[],[f1625,f97]) ).
fof(f1625,plain,
( ! [X0,X1] :
( ~ h(X1)
| sum(sum(X0,eg),X1) = sum(sum(sum(X0,eg),X1),eg)
| ~ h(X0) )
| ~ spl1_208 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f4486,plain,
( spl1_527
| ~ spl1_5
| ~ spl1_207 ),
inference(avatar_split_clause,[],[f1721,f1620,f96,f4484]) ).
fof(f4484,plain,
( spl1_527
<=> ! [X0,X1] :
( sum(sum(X0,eg),f(X1)) = sum(eg,sum(sum(X0,eg),f(X1)))
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_527])]) ).
fof(f1620,plain,
( spl1_207
<=> ! [X0,X1] :
( sum(sum(X0,eg),X1) = sum(eg,sum(sum(X0,eg),X1))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_207])]) ).
fof(f1721,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),f(X1)) = sum(eg,sum(sum(X0,eg),f(X1)))
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_207 ),
inference(resolution,[],[f1621,f97]) ).
fof(f1621,plain,
( ! [X0,X1] :
( ~ h(X1)
| sum(sum(X0,eg),X1) = sum(eg,sum(sum(X0,eg),X1))
| ~ h(X0) )
| ~ spl1_207 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f4482,plain,
( spl1_526
| ~ spl1_6
| ~ spl1_202 ),
inference(avatar_split_clause,[],[f1698,f1600,f100,f4480]) ).
fof(f4480,plain,
( spl1_526
<=> ! [X0,X1] :
( sum(eg,sum(f(inv(X0)),opp(X1))) = sum(sum(eg,f(inv(X0))),opp(X1))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_526])]) ).
fof(f1600,plain,
( spl1_202
<=> ! [X0,X1] :
( sum(eg,sum(f(X0),opp(X1))) = sum(sum(eg,f(X0)),opp(X1))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_202])]) ).
fof(f1698,plain,
( ! [X0,X1] :
( sum(eg,sum(f(inv(X0)),opp(X1))) = sum(sum(eg,f(inv(X0))),opp(X1))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_202 ),
inference(resolution,[],[f1601,f101]) ).
fof(f1601,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(eg,sum(f(X0),opp(X1))) = sum(sum(eg,f(X0)),opp(X1)) )
| ~ spl1_202 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f4478,plain,
( spl1_525
| ~ spl1_6
| ~ spl1_201 ),
inference(avatar_split_clause,[],[f1691,f1596,f100,f4476]) ).
fof(f4476,plain,
( spl1_525
<=> ! [X0,X1] :
( product(inv(inv(X0)),inv(X1)) = product(product(inv(inv(X0)),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_525])]) ).
fof(f1691,plain,
( ! [X0,X1] :
( product(inv(inv(X0)),inv(X1)) = product(product(inv(inv(X0)),inv(X1)),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_201 ),
inference(resolution,[],[f1597,f101]) ).
fof(f4474,plain,
( spl1_524
| ~ spl1_6
| ~ spl1_200 ),
inference(avatar_split_clause,[],[f1688,f1592,f100,f4472]) ).
fof(f4472,plain,
( spl1_524
<=> ! [X0,X1] :
( product(inv(inv(X0)),inv(X1)) = product(eh,product(inv(inv(X0)),inv(X1)))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_524])]) ).
fof(f1688,plain,
( ! [X0,X1] :
( product(inv(inv(X0)),inv(X1)) = product(eh,product(inv(inv(X0)),inv(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_200 ),
inference(resolution,[],[f1593,f101]) ).
fof(f4470,plain,
( spl1_523
| ~ spl1_6
| ~ spl1_199 ),
inference(avatar_split_clause,[],[f1684,f1588,f100,f4468]) ).
fof(f4468,plain,
( spl1_523
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,inv(inv(X1)))) = product(eh,inv(product(X0,inv(inv(X1)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_523])]) ).
fof(f1684,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,inv(inv(X1)))) = product(eh,inv(product(X0,inv(inv(X1)))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_199 ),
inference(resolution,[],[f1589,f101]) ).
fof(f4466,plain,
( spl1_522
| ~ spl1_61
| ~ spl1_484 ),
inference(avatar_split_clause,[],[f4418,f4058,f501,f4463]) ).
fof(f4058,plain,
( spl1_484
<=> ! [X0] : f(eh) = sum(opp(opp(X0)),sum(opp(X0),f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_484])]) ).
fof(f4418,plain,
( f(eh) = sum(opp(opp(f(eh))),eg)
| ~ spl1_61
| ~ spl1_484 ),
inference(superposition,[],[f4059,f503]) ).
fof(f4059,plain,
( ! [X0] : f(eh) = sum(opp(opp(X0)),sum(opp(X0),f(eh)))
| ~ spl1_484 ),
inference(avatar_component_clause,[],[f4058]) ).
fof(f4461,plain,
( spl1_521
| ~ spl1_6
| ~ spl1_198 ),
inference(avatar_split_clause,[],[f1680,f1584,f100,f4459]) ).
fof(f4459,plain,
( spl1_521
<=> ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,inv(inv(X1)))) = product(inv(product(X0,inv(inv(X1)))),eh)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_521])]) ).
fof(f1680,plain,
( ! [X0,X1] :
( ~ g(X0)
| inv(product(X0,inv(inv(X1)))) = product(inv(product(X0,inv(inv(X1)))),eh)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_198 ),
inference(resolution,[],[f1585,f101]) ).
fof(f4457,plain,
( spl1_520
| ~ spl1_6
| ~ spl1_197 ),
inference(avatar_split_clause,[],[f1676,f1580,f100,f4455]) ).
fof(f4455,plain,
( spl1_520
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,inv(inv(X1)))) = sum(eg,f(product(X0,inv(inv(X1)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_520])]) ).
fof(f1676,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,inv(inv(X1)))) = sum(eg,f(product(X0,inv(inv(X1)))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_197 ),
inference(resolution,[],[f1581,f101]) ).
fof(f4453,plain,
( spl1_519
| ~ spl1_6
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f1672,f1576,f100,f4451]) ).
fof(f4451,plain,
( spl1_519
<=> ! [X0,X1] :
( ~ g(X0)
| f(product(X0,inv(inv(X1)))) = sum(f(product(X0,inv(inv(X1)))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_519])]) ).
fof(f1672,plain,
( ! [X0,X1] :
( ~ g(X0)
| f(product(X0,inv(inv(X1)))) = sum(f(product(X0,inv(inv(X1)))),eg)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_196 ),
inference(resolution,[],[f1577,f101]) ).
fof(f4449,plain,
( spl1_518
| ~ spl1_6
| ~ spl1_195 ),
inference(avatar_split_clause,[],[f1669,f1572,f100,f4447]) ).
fof(f4447,plain,
( spl1_518
<=> ! [X0,X1] :
( product(eh,product(X0,inv(X1))) = product(product(eh,product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_518])]) ).
fof(f1669,plain,
( ! [X0,X1] :
( product(eh,product(X0,inv(X1))) = product(product(eh,product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_195 ),
inference(resolution,[],[f1573,f101]) ).
fof(f4445,plain,
( spl1_517
| ~ spl1_6
| ~ spl1_193 ),
inference(avatar_split_clause,[],[f1666,f1564,f100,f4443]) ).
fof(f4443,plain,
( spl1_517
<=> ! [X0,X1] :
( product(eh,product(X0,inv(X1))) = product(eh,product(eh,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_517])]) ).
fof(f1666,plain,
( ! [X0,X1] :
( product(eh,product(X0,inv(X1))) = product(eh,product(eh,product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_193 ),
inference(resolution,[],[f1565,f101]) ).
fof(f4441,plain,
( spl1_516
| ~ spl1_5
| ~ spl1_192 ),
inference(avatar_split_clause,[],[f1663,f1560,f96,f4439]) ).
fof(f4439,plain,
( spl1_516
<=> ! [X0,X1] :
( sum(eg,sum(X0,f(X1))) = sum(sum(eg,sum(X0,f(X1))),eg)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_516])]) ).
fof(f1560,plain,
( spl1_192
<=> ! [X0,X1] :
( sum(eg,sum(X0,X1)) = sum(sum(eg,sum(X0,X1)),eg)
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_192])]) ).
fof(f1663,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,f(X1))) = sum(sum(eg,sum(X0,f(X1))),eg)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_192 ),
inference(resolution,[],[f1561,f97]) ).
fof(f1561,plain,
( ! [X0,X1] :
( ~ h(X1)
| sum(eg,sum(X0,X1)) = sum(sum(eg,sum(X0,X1)),eg)
| ~ h(X0) )
| ~ spl1_192 ),
inference(avatar_component_clause,[],[f1560]) ).
fof(f4437,plain,
( spl1_515
| ~ spl1_5
| ~ spl1_191 ),
inference(avatar_split_clause,[],[f1658,f1556,f96,f4435]) ).
fof(f4435,plain,
( spl1_515
<=> ! [X0,X1] :
( sum(eg,sum(X0,f(X1))) = sum(eg,sum(eg,sum(X0,f(X1))))
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_515])]) ).
fof(f1556,plain,
( spl1_191
<=> ! [X0,X1] :
( sum(eg,sum(X0,X1)) = sum(eg,sum(eg,sum(X0,X1)))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_191])]) ).
fof(f1658,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,f(X1))) = sum(eg,sum(eg,sum(X0,f(X1))))
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_191 ),
inference(resolution,[],[f1557,f97]) ).
fof(f1557,plain,
( ! [X0,X1] :
( ~ h(X1)
| sum(eg,sum(X0,X1)) = sum(eg,sum(eg,sum(X0,X1)))
| ~ h(X0) )
| ~ spl1_191 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f4433,plain,
( spl1_514
| ~ spl1_6
| ~ spl1_190 ),
inference(avatar_split_clause,[],[f1649,f1552,f100,f4431]) ).
fof(f4431,plain,
( spl1_514
<=> ! [X0,X1] :
( inv(inv(product(X0,inv(X1)))) = product(eh,inv(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_514])]) ).
fof(f1649,plain,
( ! [X0,X1] :
( inv(inv(product(X0,inv(X1)))) = product(eh,inv(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_190 ),
inference(resolution,[],[f1553,f101]) ).
fof(f4429,plain,
( spl1_513
| ~ spl1_6
| ~ spl1_189 ),
inference(avatar_split_clause,[],[f1646,f1548,f100,f4427]) ).
fof(f4427,plain,
( spl1_513
<=> ! [X0,X1] :
( inv(inv(product(X0,inv(X1)))) = product(inv(inv(product(X0,inv(X1)))),eh)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_513])]) ).
fof(f1646,plain,
( ! [X0,X1] :
( inv(inv(product(X0,inv(X1)))) = product(inv(inv(product(X0,inv(X1)))),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_189 ),
inference(resolution,[],[f1549,f101]) ).
fof(f4425,plain,
( spl1_512
| ~ spl1_6
| ~ spl1_188 ),
inference(avatar_split_clause,[],[f1643,f1544,f100,f4423]) ).
fof(f4423,plain,
( spl1_512
<=> ! [X0,X1] :
( f(inv(product(X0,inv(X1)))) = sum(eg,f(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_512])]) ).
fof(f1643,plain,
( ! [X0,X1] :
( f(inv(product(X0,inv(X1)))) = sum(eg,f(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_188 ),
inference(resolution,[],[f1545,f101]) ).
fof(f4414,plain,
( spl1_511
| ~ spl1_6
| ~ spl1_187 ),
inference(avatar_split_clause,[],[f1640,f1540,f100,f4412]) ).
fof(f4412,plain,
( spl1_511
<=> ! [X0,X1] :
( f(inv(product(X0,inv(X1)))) = sum(f(inv(product(X0,inv(X1)))),eg)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_511])]) ).
fof(f1640,plain,
( ! [X0,X1] :
( f(inv(product(X0,inv(X1)))) = sum(f(inv(product(X0,inv(X1)))),eg)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_187 ),
inference(resolution,[],[f1541,f101]) ).
fof(f4410,plain,
( spl1_510
| ~ spl1_19
| ~ spl1_155 ),
inference(avatar_split_clause,[],[f1296,f1222,f164,f4408]) ).
fof(f4408,plain,
( spl1_510
<=> ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(sum(f(product(X0,X1)),eg),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_510])]) ).
fof(f1222,plain,
( spl1_155
<=> ! [X0] :
( sum(f(X0),eg) = sum(sum(f(X0),eg),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
fof(f1296,plain,
( ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(sum(f(product(X0,X1)),eg),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_155 ),
inference(resolution,[],[f1223,f165]) ).
fof(f1223,plain,
( ! [X0] :
( ~ g(X0)
| sum(f(X0),eg) = sum(sum(f(X0),eg),eg) )
| ~ spl1_155 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f4406,plain,
( spl1_509
| ~ spl1_19
| ~ spl1_154 ),
inference(avatar_split_clause,[],[f1292,f1218,f164,f4404]) ).
fof(f4404,plain,
( spl1_509
<=> ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(eg,sum(f(product(X0,X1)),eg))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_509])]) ).
fof(f1218,plain,
( spl1_154
<=> ! [X0] :
( sum(f(X0),eg) = sum(eg,sum(f(X0),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
fof(f1292,plain,
( ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(eg,sum(f(product(X0,X1)),eg))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_154 ),
inference(resolution,[],[f1219,f165]) ).
fof(f1219,plain,
( ! [X0] :
( ~ g(X0)
| sum(f(X0),eg) = sum(eg,sum(f(X0),eg)) )
| ~ spl1_154 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f4402,plain,
( spl1_508
| ~ spl1_19
| ~ spl1_153 ),
inference(avatar_split_clause,[],[f1287,f1214,f164,f4400]) ).
fof(f4400,plain,
( spl1_508
<=> ! [X0,X1] :
( inv(product(product(X0,X1),eh)) = product(eh,inv(product(product(X0,X1),eh)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_508])]) ).
fof(f1214,plain,
( spl1_153
<=> ! [X0] :
( inv(product(X0,eh)) = product(eh,inv(product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
fof(f1287,plain,
( ! [X0,X1] :
( inv(product(product(X0,X1),eh)) = product(eh,inv(product(product(X0,X1),eh)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_153 ),
inference(resolution,[],[f1215,f165]) ).
fof(f1215,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,eh)) = product(eh,inv(product(X0,eh))) )
| ~ spl1_153 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f4398,plain,
( spl1_507
| ~ spl1_19
| ~ spl1_152 ),
inference(avatar_split_clause,[],[f1282,f1210,f164,f4396]) ).
fof(f4396,plain,
( spl1_507
<=> ! [X0,X1] :
( inv(product(product(X0,X1),eh)) = product(inv(product(product(X0,X1),eh)),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_507])]) ).
fof(f1210,plain,
( spl1_152
<=> ! [X0] :
( inv(product(X0,eh)) = product(inv(product(X0,eh)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_152])]) ).
fof(f1282,plain,
( ! [X0,X1] :
( inv(product(product(X0,X1),eh)) = product(inv(product(product(X0,X1),eh)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_152 ),
inference(resolution,[],[f1211,f165]) ).
fof(f1211,plain,
( ! [X0] :
( ~ g(X0)
| inv(product(X0,eh)) = product(inv(product(X0,eh)),eh) )
| ~ spl1_152 ),
inference(avatar_component_clause,[],[f1210]) ).
fof(f4394,plain,
( spl1_506
| ~ spl1_19
| ~ spl1_151 ),
inference(avatar_split_clause,[],[f1278,f1206,f164,f4392]) ).
fof(f4392,plain,
( spl1_506
<=> ! [X0,X1] :
( f(product(product(X0,X1),eh)) = sum(eg,f(product(product(X0,X1),eh)))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_506])]) ).
fof(f1206,plain,
( spl1_151
<=> ! [X0] :
( f(product(X0,eh)) = sum(eg,f(product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
fof(f1278,plain,
( ! [X0,X1] :
( f(product(product(X0,X1),eh)) = sum(eg,f(product(product(X0,X1),eh)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_151 ),
inference(resolution,[],[f1207,f165]) ).
fof(f1207,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,eh)) = sum(eg,f(product(X0,eh))) )
| ~ spl1_151 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f4390,plain,
( spl1_505
| ~ spl1_19
| ~ spl1_150 ),
inference(avatar_split_clause,[],[f1274,f1202,f164,f4388]) ).
fof(f4388,plain,
( spl1_505
<=> ! [X0,X1] :
( f(product(product(X0,X1),eh)) = sum(f(product(product(X0,X1),eh)),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_505])]) ).
fof(f1202,plain,
( spl1_150
<=> ! [X0] :
( f(product(X0,eh)) = sum(f(product(X0,eh)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
fof(f1274,plain,
( ! [X0,X1] :
( f(product(product(X0,X1),eh)) = sum(f(product(product(X0,X1),eh)),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_150 ),
inference(resolution,[],[f1203,f165]) ).
fof(f1203,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,eh)) = sum(f(product(X0,eh)),eg) )
| ~ spl1_150 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f4386,plain,
( spl1_504
| ~ spl1_19
| ~ spl1_129 ),
inference(avatar_split_clause,[],[f1256,f1042,f164,f4384]) ).
fof(f4384,plain,
( spl1_504
<=> ! [X0,X1] :
( product(eh,inv(product(X0,X1))) = product(product(eh,inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_504])]) ).
fof(f1042,plain,
( spl1_129
<=> ! [X0] :
( product(eh,inv(X0)) = product(product(eh,inv(X0)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( product(eh,inv(product(X0,X1))) = product(product(eh,inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_129 ),
inference(resolution,[],[f1043,f165]) ).
fof(f1043,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,inv(X0)) = product(product(eh,inv(X0)),eh) )
| ~ spl1_129 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f4382,plain,
( spl1_503
| ~ spl1_19
| ~ spl1_123 ),
inference(avatar_split_clause,[],[f1252,f991,f164,f4380]) ).
fof(f4380,plain,
( spl1_503
<=> ! [X0,X1] :
( product(eh,inv(product(X0,X1))) = product(eh,product(eh,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_503])]) ).
fof(f991,plain,
( spl1_123
<=> ! [X0] :
( product(eh,inv(X0)) = product(eh,product(eh,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
fof(f1252,plain,
( ! [X0,X1] :
( product(eh,inv(product(X0,X1))) = product(eh,product(eh,inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_123 ),
inference(resolution,[],[f992,f165]) ).
fof(f992,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,inv(X0)) = product(eh,product(eh,inv(X0))) )
| ~ spl1_123 ),
inference(avatar_component_clause,[],[f991]) ).
fof(f4378,plain,
( spl1_502
| ~ spl1_19
| ~ spl1_118 ),
inference(avatar_split_clause,[],[f1248,f942,f164,f4376]) ).
fof(f4376,plain,
( spl1_502
<=> ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(product(X0,X1))),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_502])]) ).
fof(f942,plain,
( spl1_118
<=> ! [X0] :
( sum(eg,f(X0)) = sum(sum(eg,f(X0)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
fof(f1248,plain,
( ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(product(X0,X1))),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_118 ),
inference(resolution,[],[f943,f165]) ).
fof(f943,plain,
( ! [X0] :
( ~ g(X0)
| sum(eg,f(X0)) = sum(sum(eg,f(X0)),eg) )
| ~ spl1_118 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f4374,plain,
( spl1_501
| ~ spl1_29
| ~ spl1_60
| ~ spl1_473 ),
inference(avatar_split_clause,[],[f4011,f3851,f496,f243,f4372]) ).
fof(f4372,plain,
( spl1_501
<=> ! [X0] : opp(X0) = sum(f(eh),sum(opp(f(eh)),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_501])]) ).
fof(f496,plain,
( spl1_60
<=> eg = sum(f(eh),opp(f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
fof(f3851,plain,
( spl1_473
<=> ! [X0,X1] : sum(sum(f(eh),opp(X0)),opp(X1)) = sum(f(eh),sum(opp(X0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_473])]) ).
fof(f4011,plain,
( ! [X0] : opp(X0) = sum(f(eh),sum(opp(f(eh)),opp(X0)))
| ~ spl1_29
| ~ spl1_60
| ~ spl1_473 ),
inference(forward_demodulation,[],[f4004,f244]) ).
fof(f4004,plain,
( ! [X0] : sum(eg,opp(X0)) = sum(f(eh),sum(opp(f(eh)),opp(X0)))
| ~ spl1_60
| ~ spl1_473 ),
inference(superposition,[],[f3852,f498]) ).
fof(f498,plain,
( eg = sum(f(eh),opp(f(eh)))
| ~ spl1_60 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f3852,plain,
( ! [X0,X1] : sum(sum(f(eh),opp(X0)),opp(X1)) = sum(f(eh),sum(opp(X0),opp(X1)))
| ~ spl1_473 ),
inference(avatar_component_clause,[],[f3851]) ).
fof(f4370,plain,
( spl1_500
| ~ spl1_19
| ~ spl1_109 ),
inference(avatar_split_clause,[],[f1244,f902,f164,f4368]) ).
fof(f4368,plain,
( spl1_500
<=> ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(eg,sum(eg,f(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_500])]) ).
fof(f902,plain,
( spl1_109
<=> ! [X0] :
( sum(eg,f(X0)) = sum(eg,sum(eg,f(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
fof(f1244,plain,
( ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(eg,sum(eg,f(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_109 ),
inference(resolution,[],[f903,f165]) ).
fof(f903,plain,
( ! [X0] :
( ~ g(X0)
| sum(eg,f(X0)) = sum(eg,sum(eg,f(X0))) )
| ~ spl1_109 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f4366,plain,
( spl1_499
| ~ spl1_19
| ~ spl1_104 ),
inference(avatar_split_clause,[],[f1238,f853,f164,f4364]) ).
fof(f4364,plain,
( spl1_499
<=> ! [X0,X1] :
( inv(inv(inv(product(X0,X1)))) = product(eh,inv(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_499])]) ).
fof(f1238,plain,
( ! [X0,X1] :
( inv(inv(inv(product(X0,X1)))) = product(eh,inv(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_104 ),
inference(resolution,[],[f854,f165]) ).
fof(f4362,plain,
( spl1_498
| ~ spl1_19
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1232,f807,f164,f4360]) ).
fof(f4360,plain,
( spl1_498
<=> ! [X0,X1] :
( inv(inv(inv(product(X0,X1)))) = product(inv(inv(inv(product(X0,X1)))),eh)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_498])]) ).
fof(f1232,plain,
( ! [X0,X1] :
( inv(inv(inv(product(X0,X1)))) = product(inv(inv(inv(product(X0,X1)))),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_101 ),
inference(resolution,[],[f808,f165]) ).
fof(f4358,plain,
( spl1_497
| ~ spl1_19
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1227,f763,f164,f4356]) ).
fof(f4356,plain,
( spl1_497
<=> ! [X0,X1] :
( f(inv(inv(product(X0,X1)))) = sum(eg,f(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_497])]) ).
fof(f1227,plain,
( ! [X0,X1] :
( f(inv(inv(product(X0,X1)))) = sum(eg,f(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_92 ),
inference(resolution,[],[f764,f165]) ).
fof(f4354,plain,
( spl1_496
| ~ spl1_19
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f1166,f717,f164,f4352]) ).
fof(f4352,plain,
( spl1_496
<=> ! [X0,X1] :
( f(inv(inv(product(X0,X1)))) = sum(f(inv(inv(product(X0,X1)))),eg)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_496])]) ).
fof(f1166,plain,
( ! [X0,X1] :
( f(inv(inv(product(X0,X1)))) = sum(f(inv(inv(product(X0,X1)))),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_87 ),
inference(resolution,[],[f718,f165]) ).
fof(f4104,plain,
( spl1_495
| ~ spl1_29
| ~ spl1_61
| ~ spl1_472 ),
inference(avatar_split_clause,[],[f3996,f3847,f501,f243,f4102]) ).
fof(f4102,plain,
( spl1_495
<=> ! [X0] : opp(X0) = sum(opp(f(eh)),sum(f(eh),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_495])]) ).
fof(f3847,plain,
( spl1_472
<=> ! [X0,X1] : sum(sum(opp(X0),f(eh)),opp(X1)) = sum(opp(X0),sum(f(eh),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_472])]) ).
fof(f3996,plain,
( ! [X0] : opp(X0) = sum(opp(f(eh)),sum(f(eh),opp(X0)))
| ~ spl1_29
| ~ spl1_61
| ~ spl1_472 ),
inference(forward_demodulation,[],[f3989,f244]) ).
fof(f3989,plain,
( ! [X0] : sum(eg,opp(X0)) = sum(opp(f(eh)),sum(f(eh),opp(X0)))
| ~ spl1_61
| ~ spl1_472 ),
inference(superposition,[],[f3848,f503]) ).
fof(f3848,plain,
( ! [X0,X1] : sum(sum(opp(X0),f(eh)),opp(X1)) = sum(opp(X0),sum(f(eh),opp(X1)))
| ~ spl1_472 ),
inference(avatar_component_clause,[],[f3847]) ).
fof(f4100,plain,
( spl1_494
| ~ spl1_4
| ~ spl1_256 ),
inference(avatar_split_clause,[],[f2144,f2114,f91,f4098]) ).
fof(f4098,plain,
( spl1_494
<=> ! [X0,X1] :
( ~ g(X0)
| sum(f(product(X0,eh)),opp(X1)) = sum(f(X0),sum(f(eh),opp(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_494])]) ).
fof(f2144,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(product(X0,eh)),opp(X1)) = sum(f(X0),sum(f(eh),opp(X1))) )
| ~ spl1_4
| ~ spl1_256 ),
inference(resolution,[],[f2115,f93]) ).
fof(f4096,plain,
( spl1_493
| ~ spl1_3
| ~ spl1_255 ),
inference(avatar_split_clause,[],[f2141,f2110,f86,f4094]) ).
fof(f4094,plain,
( spl1_493
<=> ! [X0,X1] :
( eg = sum(sum(sum(X0,opp(X1)),eg),opp(sum(sum(X0,opp(X1)),eg)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_493])]) ).
fof(f2110,plain,
( spl1_255
<=> ! [X2,X0,X1] :
( eg = sum(sum(sum(X0,opp(X1)),X2),opp(sum(sum(X0,opp(X1)),X2)))
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_255])]) ).
fof(f2141,plain,
( ! [X0,X1] :
( eg = sum(sum(sum(X0,opp(X1)),eg),opp(sum(sum(X0,opp(X1)),eg)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_255 ),
inference(resolution,[],[f2111,f88]) ).
fof(f2111,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(sum(sum(X0,opp(X1)),X2),opp(sum(sum(X0,opp(X1)),X2)))
| ~ h(X0) )
| ~ spl1_255 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f4092,plain,
( spl1_492
| ~ spl1_3
| ~ spl1_254 ),
inference(avatar_split_clause,[],[f2136,f2106,f86,f4090]) ).
fof(f4090,plain,
( spl1_492
<=> ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,opp(X1)),eg)),sum(sum(X0,opp(X1)),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_492])]) ).
fof(f2106,plain,
( spl1_254
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(sum(X0,opp(X1)),X2)),sum(sum(X0,opp(X1)),X2))
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_254])]) ).
fof(f2136,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,opp(X1)),eg)),sum(sum(X0,opp(X1)),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_254 ),
inference(resolution,[],[f2107,f88]) ).
fof(f2107,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(opp(sum(sum(X0,opp(X1)),X2)),sum(sum(X0,opp(X1)),X2))
| ~ h(X0) )
| ~ spl1_254 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f4088,plain,
( spl1_491
| ~ spl1_4
| ~ spl1_253 ),
inference(avatar_split_clause,[],[f2127,f2102,f91,f4086]) ).
fof(f4086,plain,
( spl1_491
<=> ! [X0,X1] :
( ~ g(X0)
| sum(opp(X1),f(product(X0,eh))) = sum(sum(opp(X1),f(X0)),f(eh)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_491])]) ).
fof(f2127,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(opp(X1),f(product(X0,eh))) = sum(sum(opp(X1),f(X0)),f(eh)) )
| ~ spl1_4
| ~ spl1_253 ),
inference(resolution,[],[f2103,f93]) ).
fof(f4084,plain,
( spl1_490
| ~ spl1_3
| ~ spl1_252 ),
inference(avatar_split_clause,[],[f2124,f2098,f86,f4082]) ).
fof(f4082,plain,
( spl1_490
<=> ! [X0,X1] :
( eg = sum(sum(opp(X0),sum(X1,eg)),opp(sum(opp(X0),sum(X1,eg))))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_490])]) ).
fof(f2098,plain,
( spl1_252
<=> ! [X2,X0,X1] :
( eg = sum(sum(opp(X0),sum(X1,X2)),opp(sum(opp(X0),sum(X1,X2))))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_252])]) ).
fof(f2124,plain,
( ! [X0,X1] :
( eg = sum(sum(opp(X0),sum(X1,eg)),opp(sum(opp(X0),sum(X1,eg))))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_252 ),
inference(resolution,[],[f2099,f88]) ).
fof(f2099,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(sum(opp(X0),sum(X1,X2)),opp(sum(opp(X0),sum(X1,X2))))
| ~ h(X1) )
| ~ spl1_252 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f4080,plain,
( spl1_489
| ~ spl1_3
| ~ spl1_251 ),
inference(avatar_split_clause,[],[f2119,f2094,f86,f4078]) ).
fof(f4078,plain,
( spl1_489
<=> ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),sum(X1,eg))),sum(opp(X0),sum(X1,eg)))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_489])]) ).
fof(f2094,plain,
( spl1_251
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(opp(X0),sum(X1,X2))),sum(opp(X0),sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_251])]) ).
fof(f2119,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),sum(X1,eg))),sum(opp(X0),sum(X1,eg)))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_251 ),
inference(resolution,[],[f2095,f88]) ).
fof(f2095,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| eg = sum(opp(sum(opp(X0),sum(X1,X2))),sum(opp(X0),sum(X1,X2)))
| ~ h(X1) )
| ~ spl1_251 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f4076,plain,
( spl1_488
| ~ spl1_8
| ~ spl1_230 ),
inference(avatar_split_clause,[],[f1898,f1811,f107,f4074]) ).
fof(f4074,plain,
( spl1_488
<=> ! [X0,X1] :
( eg = sum(sum(sum(X0,eg),opp(X1)),opp(sum(sum(X0,eg),opp(X1))))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_488])]) ).
fof(f1811,plain,
( spl1_230
<=> ! [X0,X1] :
( eg = sum(sum(sum(X0,eg),X1),opp(sum(sum(X0,eg),X1)))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_230])]) ).
fof(f1898,plain,
( ! [X0,X1] :
( eg = sum(sum(sum(X0,eg),opp(X1)),opp(sum(sum(X0,eg),opp(X1))))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_230 ),
inference(resolution,[],[f1812,f108]) ).
fof(f1812,plain,
( ! [X0,X1] :
( ~ h(X1)
| eg = sum(sum(sum(X0,eg),X1),opp(sum(sum(X0,eg),X1)))
| ~ h(X0) )
| ~ spl1_230 ),
inference(avatar_component_clause,[],[f1811]) ).
fof(f4072,plain,
( spl1_487
| ~ spl1_8
| ~ spl1_229 ),
inference(avatar_split_clause,[],[f1893,f1807,f107,f4070]) ).
fof(f4070,plain,
( spl1_487
<=> ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,eg),opp(X1))),sum(sum(X0,eg),opp(X1)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_487])]) ).
fof(f1807,plain,
( spl1_229
<=> ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,eg),X1)),sum(sum(X0,eg),X1))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_229])]) ).
fof(f1893,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,eg),opp(X1))),sum(sum(X0,eg),opp(X1)))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_229 ),
inference(resolution,[],[f1808,f108]) ).
fof(f1808,plain,
( ! [X0,X1] :
( ~ h(X1)
| eg = sum(opp(sum(sum(X0,eg),X1)),sum(sum(X0,eg),X1))
| ~ h(X0) )
| ~ spl1_229 ),
inference(avatar_component_clause,[],[f1807]) ).
fof(f4068,plain,
( spl1_486
| ~ spl1_8
| ~ spl1_218 ),
inference(avatar_split_clause,[],[f1853,f1763,f107,f4066]) ).
fof(f4066,plain,
( spl1_486
<=> ! [X0,X1] :
( eg = sum(sum(eg,sum(X0,opp(X1))),opp(sum(eg,sum(X0,opp(X1)))))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_486])]) ).
fof(f1763,plain,
( spl1_218
<=> ! [X0,X1] :
( eg = sum(sum(eg,sum(X0,X1)),opp(sum(eg,sum(X0,X1))))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_218])]) ).
fof(f1853,plain,
( ! [X0,X1] :
( eg = sum(sum(eg,sum(X0,opp(X1))),opp(sum(eg,sum(X0,opp(X1)))))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_218 ),
inference(resolution,[],[f1764,f108]) ).
fof(f1764,plain,
( ! [X0,X1] :
( ~ h(X1)
| eg = sum(sum(eg,sum(X0,X1)),opp(sum(eg,sum(X0,X1))))
| ~ h(X0) )
| ~ spl1_218 ),
inference(avatar_component_clause,[],[f1763]) ).
fof(f4064,plain,
( spl1_485
| ~ spl1_8
| ~ spl1_217 ),
inference(avatar_split_clause,[],[f1848,f1759,f107,f4062]) ).
fof(f4062,plain,
( spl1_485
<=> ! [X0,X1] :
( eg = sum(opp(sum(eg,sum(X0,opp(X1)))),sum(eg,sum(X0,opp(X1))))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_485])]) ).
fof(f1759,plain,
( spl1_217
<=> ! [X0,X1] :
( eg = sum(opp(sum(eg,sum(X0,X1))),sum(eg,sum(X0,X1)))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_217])]) ).
fof(f1848,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(eg,sum(X0,opp(X1)))),sum(eg,sum(X0,opp(X1))))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_217 ),
inference(resolution,[],[f1760,f108]) ).
fof(f1760,plain,
( ! [X0,X1] :
( ~ h(X1)
| eg = sum(opp(sum(eg,sum(X0,X1))),sum(eg,sum(X0,X1)))
| ~ h(X0) )
| ~ spl1_217 ),
inference(avatar_component_clause,[],[f1759]) ).
fof(f4060,plain,
( spl1_484
| ~ spl1_32
| ~ spl1_59
| ~ spl1_469 ),
inference(avatar_split_clause,[],[f3970,f3835,f481,f262,f4058]) ).
fof(f481,plain,
( spl1_59
<=> f(eh) = sum(eg,f(eh)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
fof(f3835,plain,
( spl1_469
<=> ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(eh)) = sum(opp(X0),sum(opp(X1),f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_469])]) ).
fof(f3970,plain,
( ! [X0] : f(eh) = sum(opp(opp(X0)),sum(opp(X0),f(eh)))
| ~ spl1_32
| ~ spl1_59
| ~ spl1_469 ),
inference(forward_demodulation,[],[f3965,f483]) ).
fof(f483,plain,
( f(eh) = sum(eg,f(eh))
| ~ spl1_59 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f3965,plain,
( ! [X0] : sum(eg,f(eh)) = sum(opp(opp(X0)),sum(opp(X0),f(eh)))
| ~ spl1_32
| ~ spl1_469 ),
inference(superposition,[],[f3836,f263]) ).
fof(f3836,plain,
( ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(eh)) = sum(opp(X0),sum(opp(X1),f(eh)))
| ~ spl1_469 ),
inference(avatar_component_clause,[],[f3835]) ).
fof(f4056,plain,
( spl1_483
| ~ spl1_18
| ~ spl1_203 ),
inference(avatar_split_clause,[],[f1708,f1604,f160,f4054]) ).
fof(f4054,plain,
( spl1_483
<=> ! [X2,X0,X1] :
( h(sum(opp(X0),sum(opp(X1),opp(X2))))
| ~ h(opp(X2))
| ~ h(sum(opp(X0),opp(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_483])]) ).
fof(f1604,plain,
( spl1_203
<=> ! [X2,X0,X1] : sum(sum(opp(X0),opp(X1)),opp(X2)) = sum(opp(X0),sum(opp(X1),opp(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_203])]) ).
fof(f1708,plain,
( ! [X2,X0,X1] :
( h(sum(opp(X0),sum(opp(X1),opp(X2))))
| ~ h(opp(X2))
| ~ h(sum(opp(X0),opp(X1))) )
| ~ spl1_18
| ~ spl1_203 ),
inference(superposition,[],[f161,f1605]) ).
fof(f1605,plain,
( ! [X2,X0,X1] : sum(sum(opp(X0),opp(X1)),opp(X2)) = sum(opp(X0),sum(opp(X1),opp(X2)))
| ~ spl1_203 ),
inference(avatar_component_clause,[],[f1604]) ).
fof(f4052,plain,
( spl1_482
| ~ spl1_6
| ~ spl1_183 ),
inference(avatar_split_clause,[],[f1533,f1508,f100,f4050]) ).
fof(f4050,plain,
( spl1_482
<=> ! [X0,X1] :
( eg = sum(sum(f(inv(X0)),opp(X1)),opp(sum(f(inv(X0)),opp(X1))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_482])]) ).
fof(f1533,plain,
( ! [X0,X1] :
( eg = sum(sum(f(inv(X0)),opp(X1)),opp(sum(f(inv(X0)),opp(X1))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_183 ),
inference(resolution,[],[f1509,f101]) ).
fof(f4048,plain,
( spl1_481
| ~ spl1_6
| ~ spl1_182 ),
inference(avatar_split_clause,[],[f1526,f1504,f100,f4046]) ).
fof(f4046,plain,
( spl1_481
<=> ! [X0,X1] :
( eg = sum(opp(sum(f(inv(X0)),opp(X1))),sum(f(inv(X0)),opp(X1)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_481])]) ).
fof(f1526,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(f(inv(X0)),opp(X1))),sum(f(inv(X0)),opp(X1)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_182 ),
inference(resolution,[],[f1505,f101]) ).
fof(f4044,plain,
( spl1_480
| ~ spl1_6
| ~ spl1_181 ),
inference(avatar_split_clause,[],[f1523,f1500,f100,f4042]) ).
fof(f4042,plain,
( spl1_480
<=> ! [X0,X1] :
( eg = sum(sum(opp(X0),f(inv(X1))),opp(sum(opp(X0),f(inv(X1)))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_480])]) ).
fof(f1523,plain,
( ! [X0,X1] :
( eg = sum(sum(opp(X0),f(inv(X1))),opp(sum(opp(X0),f(inv(X1)))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_181 ),
inference(resolution,[],[f1501,f101]) ).
fof(f4040,plain,
( spl1_479
| ~ spl1_6
| ~ spl1_180 ),
inference(avatar_split_clause,[],[f1520,f1496,f100,f4038]) ).
fof(f4038,plain,
( spl1_479
<=> ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(inv(X1)))),sum(opp(X0),f(inv(X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_479])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(inv(X1)))),sum(opp(X0),f(inv(X1))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_180 ),
inference(resolution,[],[f1497,f101]) ).
fof(f4001,plain,
( spl1_478
| ~ spl1_31
| ~ spl1_59
| ~ spl1_469 ),
inference(avatar_split_clause,[],[f3969,f3835,f481,f258,f3999]) ).
fof(f3969,plain,
( ! [X0] : f(eh) = sum(opp(X0),sum(opp(opp(X0)),f(eh)))
| ~ spl1_31
| ~ spl1_59
| ~ spl1_469 ),
inference(forward_demodulation,[],[f3964,f483]) ).
fof(f3964,plain,
( ! [X0] : sum(eg,f(eh)) = sum(opp(X0),sum(opp(opp(X0)),f(eh)))
| ~ spl1_31
| ~ spl1_469 ),
inference(superposition,[],[f3836,f259]) ).
fof(f3869,plain,
( spl1_477
| ~ spl1_3
| ~ spl1_29
| ~ spl1_275 ),
inference(avatar_split_clause,[],[f2296,f2216,f243,f86,f3867]) ).
fof(f3867,plain,
( spl1_477
<=> ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(sum(sum(X0,eg),eg),opp(X1))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_477])]) ).
fof(f2216,plain,
( spl1_275
<=> ! [X2,X0,X1] :
( sum(sum(sum(X0,eg),X1),opp(X2)) = sum(sum(X0,eg),sum(X1,opp(X2)))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_275])]) ).
fof(f2296,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(sum(sum(X0,eg),eg),opp(X1))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_29
| ~ spl1_275 ),
inference(forward_demodulation,[],[f2293,f244]) ).
fof(f2293,plain,
( ! [X0,X1] :
( sum(sum(sum(X0,eg),eg),opp(X1)) = sum(sum(X0,eg),sum(eg,opp(X1)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_275 ),
inference(resolution,[],[f2217,f88]) ).
fof(f2217,plain,
( ! [X2,X0,X1] :
( ~ h(X1)
| sum(sum(sum(X0,eg),X1),opp(X2)) = sum(sum(X0,eg),sum(X1,opp(X2)))
| ~ h(X0) )
| ~ spl1_275 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f3865,plain,
( spl1_476
| ~ spl1_4
| ~ spl1_247 ),
inference(avatar_split_clause,[],[f2070,f2000,f91,f3863]) ).
fof(f3863,plain,
( spl1_476
<=> ! [X0] :
( product(product(eh,product(X0,eh)),eh) = product(eh,product(product(X0,eh),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_476])]) ).
fof(f2070,plain,
( ! [X0] :
( product(product(eh,product(X0,eh)),eh) = product(eh,product(product(X0,eh),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_247 ),
inference(resolution,[],[f2001,f93]) ).
fof(f3861,plain,
( spl1_475
| ~ spl1_3
| ~ spl1_246 ),
inference(avatar_split_clause,[],[f2067,f1996,f86,f3859]) ).
fof(f3859,plain,
( spl1_475
<=> ! [X0] :
( sum(sum(eg,sum(X0,eg)),eg) = sum(eg,sum(sum(X0,eg),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_475])]) ).
fof(f2067,plain,
( ! [X0] :
( sum(sum(eg,sum(X0,eg)),eg) = sum(eg,sum(sum(X0,eg),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_246 ),
inference(resolution,[],[f1997,f88]) ).
fof(f3857,plain,
( spl1_474
| ~ spl1_4
| ~ spl1_245 ),
inference(avatar_split_clause,[],[f2062,f1980,f91,f3855]) ).
fof(f3855,plain,
( spl1_474
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| f(product(product(X0,X1),eh)) = f(product(X0,product(X1,eh))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_474])]) ).
fof(f2062,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| f(product(product(X0,X1),eh)) = f(product(X0,product(X1,eh))) )
| ~ spl1_4
| ~ spl1_245 ),
inference(resolution,[],[f1981,f93]) ).
fof(f3853,plain,
( spl1_473
| ~ spl1_4
| ~ spl1_244 ),
inference(avatar_split_clause,[],[f2059,f1976,f91,f3851]) ).
fof(f2059,plain,
( ! [X0,X1] : sum(sum(f(eh),opp(X0)),opp(X1)) = sum(f(eh),sum(opp(X0),opp(X1)))
| ~ spl1_4
| ~ spl1_244 ),
inference(resolution,[],[f1977,f93]) ).
fof(f3849,plain,
( spl1_472
| ~ spl1_4
| ~ spl1_243 ),
inference(avatar_split_clause,[],[f2056,f1972,f91,f3847]) ).
fof(f2056,plain,
( ! [X0,X1] : sum(sum(opp(X0),f(eh)),opp(X1)) = sum(opp(X0),sum(f(eh),opp(X1)))
| ~ spl1_4
| ~ spl1_243 ),
inference(resolution,[],[f1973,f93]) ).
fof(f3845,plain,
( spl1_471
| ~ spl1_3
| ~ spl1_242 ),
inference(avatar_split_clause,[],[f2053,f1968,f86,f3843]) ).
fof(f3843,plain,
( spl1_471
<=> ! [X0,X1] :
( sum(sum(X0,opp(X1)),eg) = sum(sum(sum(X0,opp(X1)),eg),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_471])]) ).
fof(f2053,plain,
( ! [X0,X1] :
( sum(sum(X0,opp(X1)),eg) = sum(sum(sum(X0,opp(X1)),eg),eg)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_242 ),
inference(resolution,[],[f1969,f88]) ).
fof(f3841,plain,
( spl1_470
| ~ spl1_3
| ~ spl1_241 ),
inference(avatar_split_clause,[],[f2048,f1964,f86,f3839]) ).
fof(f3839,plain,
( spl1_470
<=> ! [X0,X1] :
( sum(sum(X0,opp(X1)),eg) = sum(eg,sum(sum(X0,opp(X1)),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_470])]) ).
fof(f2048,plain,
( ! [X0,X1] :
( sum(sum(X0,opp(X1)),eg) = sum(eg,sum(sum(X0,opp(X1)),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_241 ),
inference(resolution,[],[f1965,f88]) ).
fof(f3837,plain,
( spl1_469
| ~ spl1_4
| ~ spl1_239 ),
inference(avatar_split_clause,[],[f2033,f1956,f91,f3835]) ).
fof(f2033,plain,
( ! [X0,X1] : sum(sum(opp(X0),opp(X1)),f(eh)) = sum(opp(X0),sum(opp(X1),f(eh)))
| ~ spl1_4
| ~ spl1_239 ),
inference(resolution,[],[f1957,f93]) ).
fof(f3833,plain,
( spl1_468
| ~ spl1_4
| ~ spl1_238 ),
inference(avatar_split_clause,[],[f2030,f1952,f91,f3831]) ).
fof(f3831,plain,
( spl1_468
<=> ! [X0] :
( product(product(eh,inv(inv(X0))),eh) = product(eh,product(inv(inv(X0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_468])]) ).
fof(f2030,plain,
( ! [X0] :
( product(product(eh,inv(inv(X0))),eh) = product(eh,product(inv(inv(X0)),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_238 ),
inference(resolution,[],[f1953,f93]) ).
fof(f3829,plain,
( spl1_467
| ~ spl1_3
| ~ spl1_237 ),
inference(avatar_split_clause,[],[f2027,f1948,f86,f3827]) ).
fof(f3827,plain,
( spl1_467
<=> ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(opp(X0),sum(eg,sum(X1,eg)))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_467])]) ).
fof(f2027,plain,
( ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(opp(X0),sum(eg,sum(X1,eg)))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_237 ),
inference(resolution,[],[f1949,f88]) ).
fof(f3825,plain,
( spl1_466
| ~ spl1_3
| ~ spl1_236 ),
inference(avatar_split_clause,[],[f2022,f1944,f86,f3823]) ).
fof(f3823,plain,
( spl1_466
<=> ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(sum(opp(X0),sum(X1,eg)),eg)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_466])]) ).
fof(f2022,plain,
( ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(sum(opp(X0),sum(X1,eg)),eg)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_236 ),
inference(resolution,[],[f1945,f88]) ).
fof(f3821,plain,
( spl1_465
| ~ spl1_3
| ~ spl1_235 ),
inference(avatar_split_clause,[],[f2017,f1914,f86,f3819]) ).
fof(f3819,plain,
( spl1_465
<=> ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(eg,sum(opp(X0),sum(X1,eg)))
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_465])]) ).
fof(f2017,plain,
( ! [X0,X1] :
( sum(opp(X0),sum(X1,eg)) = sum(eg,sum(opp(X0),sum(X1,eg)))
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_235 ),
inference(resolution,[],[f1915,f88]) ).
fof(f3812,plain,
( spl1_464
| ~ spl1_8
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f1724,f1624,f107,f3810]) ).
fof(f3810,plain,
( spl1_464
<=> ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(sum(sum(X0,eg),opp(X1)),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_464])]) ).
fof(f1724,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(sum(sum(X0,eg),opp(X1)),eg)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_208 ),
inference(resolution,[],[f1625,f108]) ).
fof(f3808,plain,
( spl1_463
| ~ spl1_8
| ~ spl1_207 ),
inference(avatar_split_clause,[],[f1719,f1620,f107,f3806]) ).
fof(f3806,plain,
( spl1_463
<=> ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(eg,sum(sum(X0,eg),opp(X1)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_463])]) ).
fof(f1719,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),opp(X1)) = sum(eg,sum(sum(X0,eg),opp(X1)))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_207 ),
inference(resolution,[],[f1621,f108]) ).
fof(f3804,plain,
( spl1_462
| ~ spl1_8
| ~ spl1_192 ),
inference(avatar_split_clause,[],[f1661,f1560,f107,f3802]) ).
fof(f3802,plain,
( spl1_462
<=> ! [X0,X1] :
( sum(eg,sum(X0,opp(X1))) = sum(sum(eg,sum(X0,opp(X1))),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_462])]) ).
fof(f1661,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,opp(X1))) = sum(sum(eg,sum(X0,opp(X1))),eg)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_192 ),
inference(resolution,[],[f1561,f108]) ).
fof(f3800,plain,
( spl1_461
| ~ spl1_8
| ~ spl1_191 ),
inference(avatar_split_clause,[],[f1656,f1556,f107,f3798]) ).
fof(f3798,plain,
( spl1_461
<=> ! [X0,X1] :
( sum(eg,sum(X0,opp(X1))) = sum(eg,sum(eg,sum(X0,opp(X1))))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_461])]) ).
fof(f1656,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,opp(X1))) = sum(eg,sum(eg,sum(X0,opp(X1))))
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_191 ),
inference(resolution,[],[f1557,f108]) ).
fof(f3796,plain,
( spl1_460
| ~ spl1_6
| ~ spl1_178 ),
inference(avatar_split_clause,[],[f1493,f1465,f100,f3794]) ).
fof(f3794,plain,
( spl1_460
<=> ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(sum(f(inv(X0)),eg),opp(X1))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_460])]) ).
fof(f1465,plain,
( spl1_178
<=> ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(sum(f(X0),eg),opp(X1))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_178])]) ).
fof(f1493,plain,
( ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(sum(f(inv(X0)),eg),opp(X1))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_178 ),
inference(resolution,[],[f1466,f101]) ).
fof(f1466,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(f(X0),opp(X1)) = sum(sum(f(X0),eg),opp(X1)) )
| ~ spl1_178 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f3792,plain,
( spl1_459
| ~ spl1_6
| ~ spl1_177 ),
inference(avatar_split_clause,[],[f1484,f1461,f100,f3790]) ).
fof(f3790,plain,
( spl1_459
<=> ! [X0] :
( sum(sum(eg,f(inv(X0))),eg) = sum(eg,sum(f(inv(X0)),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_459])]) ).
fof(f1461,plain,
( spl1_177
<=> ! [X0] :
( sum(sum(eg,f(X0)),eg) = sum(eg,sum(f(X0),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_177])]) ).
fof(f1484,plain,
( ! [X0] :
( sum(sum(eg,f(inv(X0))),eg) = sum(eg,sum(f(inv(X0)),eg))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_177 ),
inference(resolution,[],[f1462,f101]) ).
fof(f1462,plain,
( ! [X0] :
( ~ g(X0)
| sum(sum(eg,f(X0)),eg) = sum(eg,sum(f(X0),eg)) )
| ~ spl1_177 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f3788,plain,
( spl1_458
| ~ spl1_6
| ~ spl1_176 ),
inference(avatar_split_clause,[],[f1481,f1457,f100,f3786]) ).
fof(f3786,plain,
( spl1_458
<=> ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(sum(f(inv(X0)),opp(X1)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_458])]) ).
fof(f1481,plain,
( ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(sum(f(inv(X0)),opp(X1)),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_176 ),
inference(resolution,[],[f1458,f101]) ).
fof(f3784,plain,
( spl1_457
| ~ spl1_6
| ~ spl1_175 ),
inference(avatar_split_clause,[],[f1478,f1453,f100,f3782]) ).
fof(f3782,plain,
( spl1_457
<=> ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(eg,sum(f(inv(X0)),opp(X1)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_457])]) ).
fof(f1478,plain,
( ! [X0,X1] :
( sum(f(inv(X0)),opp(X1)) = sum(eg,sum(f(inv(X0)),opp(X1)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_175 ),
inference(resolution,[],[f1454,f101]) ).
fof(f3780,plain,
( spl1_456
| ~ spl1_6
| ~ spl1_174 ),
inference(avatar_split_clause,[],[f1475,f1449,f100,f3778]) ).
fof(f3778,plain,
( spl1_456
<=> ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(opp(X0),sum(eg,f(inv(X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_456])]) ).
fof(f1449,plain,
( spl1_174
<=> ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(opp(X0),sum(eg,f(X1)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_174])]) ).
fof(f1475,plain,
( ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(opp(X0),sum(eg,f(inv(X1))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_174 ),
inference(resolution,[],[f1450,f101]) ).
fof(f1450,plain,
( ! [X0,X1] :
( ~ g(X1)
| sum(opp(X0),f(X1)) = sum(opp(X0),sum(eg,f(X1))) )
| ~ spl1_174 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f3776,plain,
( spl1_455
| ~ spl1_6
| ~ spl1_173 ),
inference(avatar_split_clause,[],[f1472,f1445,f100,f3774]) ).
fof(f3774,plain,
( spl1_455
<=> ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(sum(opp(X0),f(inv(X1))),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_455])]) ).
fof(f1472,plain,
( ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(sum(opp(X0),f(inv(X1))),eg)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_173 ),
inference(resolution,[],[f1446,f101]) ).
fof(f3772,plain,
( spl1_454
| ~ spl1_6
| ~ spl1_290 ),
inference(avatar_split_clause,[],[f2621,f2350,f100,f3770]) ).
fof(f3770,plain,
( spl1_454
<=> ! [X0] :
( f(product(inv(X0),eh)) = sum(sum(f(inv(X0)),eg),f(eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_454])]) ).
fof(f2350,plain,
( spl1_290
<=> ! [X0] :
( f(product(X0,eh)) = sum(sum(f(X0),eg),f(eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_290])]) ).
fof(f2621,plain,
( ! [X0] :
( f(product(inv(X0),eh)) = sum(sum(f(inv(X0)),eg),f(eh))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_290 ),
inference(resolution,[],[f2351,f101]) ).
fof(f2351,plain,
( ! [X0] :
( ~ g(X0)
| f(product(X0,eh)) = sum(sum(f(X0),eg),f(eh)) )
| ~ spl1_290 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f3768,plain,
( spl1_453
| ~ spl1_6
| ~ spl1_172 ),
inference(avatar_split_clause,[],[f1469,f1441,f100,f3766]) ).
fof(f3766,plain,
( spl1_453
<=> ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(eg,sum(opp(X0),f(inv(X1))))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_453])]) ).
fof(f1469,plain,
( ! [X0,X1] :
( sum(opp(X0),f(inv(X1))) = sum(eg,sum(opp(X0),f(inv(X1))))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_172 ),
inference(resolution,[],[f1442,f101]) ).
fof(f3596,plain,
( spl1_452
| ~ spl1_4
| ~ spl1_232 ),
inference(avatar_split_clause,[],[f1905,f1819,f91,f3594]) ).
fof(f3594,plain,
( spl1_452
<=> ! [X0] :
( eh = product(product(product(X0,eh),eh),inv(product(product(X0,eh),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_452])]) ).
fof(f1905,plain,
( ! [X0] :
( eh = product(product(product(X0,eh),eh),inv(product(product(X0,eh),eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_232 ),
inference(resolution,[],[f1820,f93]) ).
fof(f3592,plain,
( spl1_451
| ~ spl1_4
| ~ spl1_231 ),
inference(avatar_split_clause,[],[f1902,f1815,f91,f3590]) ).
fof(f3590,plain,
( spl1_451
<=> ! [X0] :
( eh = product(inv(product(product(X0,eh),eh)),product(product(X0,eh),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_451])]) ).
fof(f1902,plain,
( ! [X0] :
( eh = product(inv(product(product(X0,eh),eh)),product(product(X0,eh),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_231 ),
inference(resolution,[],[f1816,f93]) ).
fof(f3588,plain,
( spl1_450
| ~ spl1_3
| ~ spl1_230 ),
inference(avatar_split_clause,[],[f1899,f1811,f86,f3586]) ).
fof(f3586,plain,
( spl1_450
<=> ! [X0] :
( eg = sum(sum(sum(X0,eg),eg),opp(sum(sum(X0,eg),eg)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_450])]) ).
fof(f1899,plain,
( ! [X0] :
( eg = sum(sum(sum(X0,eg),eg),opp(sum(sum(X0,eg),eg)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_230 ),
inference(resolution,[],[f1812,f88]) ).
fof(f3584,plain,
( spl1_449
| ~ spl1_3
| ~ spl1_229 ),
inference(avatar_split_clause,[],[f1894,f1807,f86,f3582]) ).
fof(f3582,plain,
( spl1_449
<=> ! [X0] :
( eg = sum(opp(sum(sum(X0,eg),eg)),sum(sum(X0,eg),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_449])]) ).
fof(f1894,plain,
( ! [X0] :
( eg = sum(opp(sum(sum(X0,eg),eg)),sum(sum(X0,eg),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_229 ),
inference(resolution,[],[f1808,f88]) ).
fof(f3580,plain,
( spl1_448
| ~ spl1_4
| ~ spl1_228 ),
inference(avatar_split_clause,[],[f1889,f1803,f91,f3578]) ).
fof(f3578,plain,
( spl1_448
<=> ! [X0] :
( ~ g(X0)
| sum(eg,f(product(X0,eh))) = sum(sum(eg,f(X0)),f(eh)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_448])]) ).
fof(f1889,plain,
( ! [X0] :
( ~ g(X0)
| sum(eg,f(product(X0,eh))) = sum(sum(eg,f(X0)),f(eh)) )
| ~ spl1_4
| ~ spl1_228 ),
inference(resolution,[],[f1804,f93]) ).
fof(f3576,plain,
( spl1_447
| ~ spl1_4
| ~ spl1_227 ),
inference(avatar_split_clause,[],[f1886,f1799,f91,f3574]) ).
fof(f3574,plain,
( spl1_447
<=> ! [X0] :
( eh = product(product(inv(inv(X0)),eh),inv(product(inv(inv(X0)),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_447])]) ).
fof(f1886,plain,
( ! [X0] :
( eh = product(product(inv(inv(X0)),eh),inv(product(inv(inv(X0)),eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_227 ),
inference(resolution,[],[f1800,f93]) ).
fof(f3572,plain,
( spl1_446
| ~ spl1_4
| ~ spl1_226 ),
inference(avatar_split_clause,[],[f1883,f1795,f91,f3570]) ).
fof(f3570,plain,
( spl1_446
<=> ! [X0] :
( eh = product(inv(product(inv(inv(X0)),eh)),product(inv(inv(X0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_446])]) ).
fof(f1883,plain,
( ! [X0] :
( eh = product(inv(product(inv(inv(X0)),eh)),product(inv(inv(X0)),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_226 ),
inference(resolution,[],[f1796,f93]) ).
fof(f3568,plain,
( spl1_445
| ~ spl1_4
| ~ spl1_220 ),
inference(avatar_split_clause,[],[f1860,f1771,f91,f3566]) ).
fof(f3566,plain,
( spl1_445
<=> ! [X0] :
( eh = product(product(eh,product(X0,eh)),inv(product(eh,product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_445])]) ).
fof(f1860,plain,
( ! [X0] :
( eh = product(product(eh,product(X0,eh)),inv(product(eh,product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_220 ),
inference(resolution,[],[f1772,f93]) ).
fof(f3564,plain,
( spl1_444
| ~ spl1_4
| ~ spl1_219 ),
inference(avatar_split_clause,[],[f1857,f1767,f91,f3562]) ).
fof(f3562,plain,
( spl1_444
<=> ! [X0] :
( eh = product(inv(product(eh,product(X0,eh))),product(eh,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_444])]) ).
fof(f1857,plain,
( ! [X0] :
( eh = product(inv(product(eh,product(X0,eh))),product(eh,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_219 ),
inference(resolution,[],[f1768,f93]) ).
fof(f3560,plain,
( spl1_443
| ~ spl1_3
| ~ spl1_218 ),
inference(avatar_split_clause,[],[f1854,f1763,f86,f3558]) ).
fof(f3558,plain,
( spl1_443
<=> ! [X0] :
( eg = sum(sum(eg,sum(X0,eg)),opp(sum(eg,sum(X0,eg))))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_443])]) ).
fof(f1854,plain,
( ! [X0] :
( eg = sum(sum(eg,sum(X0,eg)),opp(sum(eg,sum(X0,eg))))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_218 ),
inference(resolution,[],[f1764,f88]) ).
fof(f3556,plain,
( spl1_442
| ~ spl1_3
| ~ spl1_217 ),
inference(avatar_split_clause,[],[f1849,f1759,f86,f3554]) ).
fof(f3554,plain,
( spl1_442
<=> ! [X0] :
( eg = sum(opp(sum(eg,sum(X0,eg))),sum(eg,sum(X0,eg)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_442])]) ).
fof(f1849,plain,
( ! [X0] :
( eg = sum(opp(sum(eg,sum(X0,eg))),sum(eg,sum(X0,eg)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_217 ),
inference(resolution,[],[f1760,f88]) ).
fof(f3552,plain,
( spl1_441
| ~ spl1_4
| ~ spl1_216 ),
inference(avatar_split_clause,[],[f1844,f1755,f91,f3550]) ).
fof(f3550,plain,
( spl1_441
<=> ! [X0] :
( eh = product(inv(inv(inv(product(X0,eh)))),inv(inv(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_441])]) ).
fof(f1844,plain,
( ! [X0] :
( eh = product(inv(inv(inv(product(X0,eh)))),inv(inv(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_216 ),
inference(resolution,[],[f1756,f93]) ).
fof(f3548,plain,
( spl1_440
| ~ spl1_4
| ~ spl1_215 ),
inference(avatar_split_clause,[],[f1841,f1751,f91,f3546]) ).
fof(f3546,plain,
( spl1_440
<=> ! [X0] :
( eh = product(inv(inv(product(X0,eh))),inv(inv(inv(product(X0,eh)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_440])]) ).
fof(f1841,plain,
( ! [X0] :
( eh = product(inv(inv(product(X0,eh))),inv(inv(inv(product(X0,eh)))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_215 ),
inference(resolution,[],[f1752,f93]) ).
fof(f3544,plain,
( spl1_439
| ~ spl1_4
| ~ spl1_214 ),
inference(avatar_split_clause,[],[f1838,f1747,f91,f3542]) ).
fof(f3542,plain,
( spl1_439
<=> ! [X0] :
( eg = sum(opp(f(inv(product(X0,eh)))),f(inv(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_439])]) ).
fof(f1838,plain,
( ! [X0] :
( eg = sum(opp(f(inv(product(X0,eh)))),f(inv(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_214 ),
inference(resolution,[],[f1748,f93]) ).
fof(f3540,plain,
( spl1_438
| ~ spl1_4
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f1826,f1739,f91,f3538]) ).
fof(f3538,plain,
( spl1_438
<=> ! [X0] :
( eg = sum(f(inv(product(X0,eh))),opp(f(inv(product(X0,eh)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_438])]) ).
fof(f1826,plain,
( ! [X0] :
( eg = sum(f(inv(product(X0,eh))),opp(f(inv(product(X0,eh)))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_212 ),
inference(resolution,[],[f1740,f93]) ).
fof(f3536,plain,
( spl1_437
| ~ spl1_6
| ~ spl1_171 ),
inference(avatar_split_clause,[],[f1437,f1359,f100,f3534]) ).
fof(f3534,plain,
( spl1_437
<=> ! [X0] :
( eg = sum(sum(f(inv(X0)),eg),opp(sum(f(inv(X0)),eg)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_437])]) ).
fof(f1359,plain,
( spl1_171
<=> ! [X0] :
( eg = sum(sum(f(X0),eg),opp(sum(f(X0),eg)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_171])]) ).
fof(f1437,plain,
( ! [X0] :
( eg = sum(sum(f(inv(X0)),eg),opp(sum(f(inv(X0)),eg)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_171 ),
inference(resolution,[],[f1360,f101]) ).
fof(f1360,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(sum(f(X0),eg),opp(sum(f(X0),eg))) )
| ~ spl1_171 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f3532,plain,
( spl1_436
| ~ spl1_6
| ~ spl1_170 ),
inference(avatar_split_clause,[],[f1433,f1355,f100,f3530]) ).
fof(f3530,plain,
( spl1_436
<=> ! [X0] :
( eg = sum(opp(sum(f(inv(X0)),eg)),sum(f(inv(X0)),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_436])]) ).
fof(f1355,plain,
( spl1_170
<=> ! [X0] :
( eg = sum(opp(sum(f(X0),eg)),sum(f(X0),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_170])]) ).
fof(f1433,plain,
( ! [X0] :
( eg = sum(opp(sum(f(inv(X0)),eg)),sum(f(inv(X0)),eg))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_170 ),
inference(resolution,[],[f1356,f101]) ).
fof(f1356,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(sum(f(X0),eg)),sum(f(X0),eg)) )
| ~ spl1_170 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f3528,plain,
( spl1_435
| ~ spl1_6
| ~ spl1_169 ),
inference(avatar_split_clause,[],[f1428,f1351,f100,f3526]) ).
fof(f3526,plain,
( spl1_435
<=> ! [X0] :
( eh = product(inv(inv(product(inv(X0),eh))),inv(product(inv(X0),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_435])]) ).
fof(f1351,plain,
( spl1_169
<=> ! [X0] :
( eh = product(inv(inv(product(X0,eh))),inv(product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_169])]) ).
fof(f1428,plain,
( ! [X0] :
( eh = product(inv(inv(product(inv(X0),eh))),inv(product(inv(X0),eh)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_169 ),
inference(resolution,[],[f1352,f101]) ).
fof(f1352,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(inv(product(X0,eh))),inv(product(X0,eh))) )
| ~ spl1_169 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f3524,plain,
( spl1_434
| ~ spl1_6
| ~ spl1_168 ),
inference(avatar_split_clause,[],[f1423,f1347,f100,f3522]) ).
fof(f3522,plain,
( spl1_434
<=> ! [X0] :
( eh = product(inv(product(inv(X0),eh)),inv(inv(product(inv(X0),eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_434])]) ).
fof(f1347,plain,
( spl1_168
<=> ! [X0] :
( eh = product(inv(product(X0,eh)),inv(inv(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_168])]) ).
fof(f1423,plain,
( ! [X0] :
( eh = product(inv(product(inv(X0),eh)),inv(inv(product(inv(X0),eh))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_168 ),
inference(resolution,[],[f1348,f101]) ).
fof(f1348,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(X0,eh)),inv(inv(product(X0,eh)))) )
| ~ spl1_168 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f3520,plain,
( spl1_433
| ~ spl1_6
| ~ spl1_167 ),
inference(avatar_split_clause,[],[f1419,f1343,f100,f3518]) ).
fof(f3518,plain,
( spl1_433
<=> ! [X0] :
( eg = sum(opp(f(product(inv(X0),eh))),f(product(inv(X0),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_433])]) ).
fof(f1343,plain,
( spl1_167
<=> ! [X0] :
( eg = sum(opp(f(product(X0,eh))),f(product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_167])]) ).
fof(f1419,plain,
( ! [X0] :
( eg = sum(opp(f(product(inv(X0),eh))),f(product(inv(X0),eh)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_167 ),
inference(resolution,[],[f1344,f101]) ).
fof(f1344,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(f(product(X0,eh))),f(product(X0,eh))) )
| ~ spl1_167 ),
inference(avatar_component_clause,[],[f1343]) ).
fof(f3516,plain,
( spl1_432
| ~ spl1_6
| ~ spl1_166 ),
inference(avatar_split_clause,[],[f1415,f1339,f100,f3514]) ).
fof(f3514,plain,
( spl1_432
<=> ! [X0] :
( eg = sum(f(product(inv(X0),eh)),opp(f(product(inv(X0),eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_432])]) ).
fof(f1339,plain,
( spl1_166
<=> ! [X0] :
( eg = sum(f(product(X0,eh)),opp(f(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
fof(f1415,plain,
( ! [X0] :
( eg = sum(f(product(inv(X0),eh)),opp(f(product(inv(X0),eh))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_166 ),
inference(resolution,[],[f1340,f101]) ).
fof(f1340,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(f(product(X0,eh)),opp(f(product(X0,eh)))) )
| ~ spl1_166 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f3512,plain,
( spl1_431
| ~ spl1_6
| ~ spl1_163 ),
inference(avatar_split_clause,[],[f1397,f1327,f100,f3510]) ).
fof(f3510,plain,
( spl1_431
<=> ! [X0] :
( eh = product(product(eh,inv(inv(X0))),inv(product(eh,inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_431])]) ).
fof(f1327,plain,
( spl1_163
<=> ! [X0] :
( eh = product(product(eh,inv(X0)),inv(product(eh,inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
fof(f1397,plain,
( ! [X0] :
( eh = product(product(eh,inv(inv(X0))),inv(product(eh,inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_163 ),
inference(resolution,[],[f1328,f101]) ).
fof(f1328,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(eh,inv(X0)),inv(product(eh,inv(X0)))) )
| ~ spl1_163 ),
inference(avatar_component_clause,[],[f1327]) ).
fof(f3508,plain,
( spl1_430
| ~ spl1_6
| ~ spl1_162 ),
inference(avatar_split_clause,[],[f1393,f1323,f100,f3506]) ).
fof(f3506,plain,
( spl1_430
<=> ! [X0] :
( eh = product(inv(product(eh,inv(inv(X0)))),product(eh,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_430])]) ).
fof(f1323,plain,
( spl1_162
<=> ! [X0] :
( eh = product(inv(product(eh,inv(X0))),product(eh,inv(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
fof(f1393,plain,
( ! [X0] :
( eh = product(inv(product(eh,inv(inv(X0)))),product(eh,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_162 ),
inference(resolution,[],[f1324,f101]) ).
fof(f1324,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(eh,inv(X0))),product(eh,inv(X0))) )
| ~ spl1_162 ),
inference(avatar_component_clause,[],[f1323]) ).
fof(f3504,plain,
( spl1_429
| ~ spl1_6
| ~ spl1_161 ),
inference(avatar_split_clause,[],[f1389,f1319,f100,f3502]) ).
fof(f3502,plain,
( spl1_429
<=> ! [X0] :
( eg = sum(sum(eg,f(inv(X0))),opp(sum(eg,f(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_429])]) ).
fof(f1319,plain,
( spl1_161
<=> ! [X0] :
( eg = sum(sum(eg,f(X0)),opp(sum(eg,f(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_161])]) ).
fof(f1389,plain,
( ! [X0] :
( eg = sum(sum(eg,f(inv(X0))),opp(sum(eg,f(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_161 ),
inference(resolution,[],[f1320,f101]) ).
fof(f1320,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(sum(eg,f(X0)),opp(sum(eg,f(X0)))) )
| ~ spl1_161 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f3500,plain,
( spl1_428
| ~ spl1_6
| ~ spl1_160 ),
inference(avatar_split_clause,[],[f1385,f1315,f100,f3498]) ).
fof(f3498,plain,
( spl1_428
<=> ! [X0] :
( eg = sum(opp(sum(eg,f(inv(X0)))),sum(eg,f(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_428])]) ).
fof(f1315,plain,
( spl1_160
<=> ! [X0] :
( eg = sum(opp(sum(eg,f(X0))),sum(eg,f(X0)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
fof(f1385,plain,
( ! [X0] :
( eg = sum(opp(sum(eg,f(inv(X0)))),sum(eg,f(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_160 ),
inference(resolution,[],[f1316,f101]) ).
fof(f1316,plain,
( ! [X0] :
( ~ g(X0)
| eg = sum(opp(sum(eg,f(X0))),sum(eg,f(X0))) )
| ~ spl1_160 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f3496,plain,
( spl1_427
| ~ spl1_6
| ~ spl1_159 ),
inference(avatar_split_clause,[],[f1379,f1311,f100,f3494]) ).
fof(f3494,plain,
( spl1_427
<=> ! [X0] :
( eh = product(inv(inv(inv(inv(inv(X0))))),inv(inv(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_427])]) ).
fof(f1379,plain,
( ! [X0] :
( eh = product(inv(inv(inv(inv(inv(X0))))),inv(inv(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_159 ),
inference(resolution,[],[f1312,f101]) ).
fof(f3492,plain,
( spl1_426
| ~ spl1_6
| ~ spl1_158 ),
inference(avatar_split_clause,[],[f1373,f1307,f100,f3490]) ).
fof(f3490,plain,
( spl1_426
<=> ! [X0] :
( eh = product(inv(inv(inv(inv(X0)))),inv(inv(inv(inv(inv(X0))))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_426])]) ).
fof(f1373,plain,
( ! [X0] :
( eh = product(inv(inv(inv(inv(X0)))),inv(inv(inv(inv(inv(X0))))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_158 ),
inference(resolution,[],[f1308,f101]) ).
fof(f3488,plain,
( spl1_425
| ~ spl1_6
| ~ spl1_157 ),
inference(avatar_split_clause,[],[f1368,f1303,f100,f3486]) ).
fof(f3486,plain,
( spl1_425
<=> ! [X0] :
( eg = sum(opp(f(inv(inv(inv(X0))))),f(inv(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_425])]) ).
fof(f1368,plain,
( ! [X0] :
( eg = sum(opp(f(inv(inv(inv(X0))))),f(inv(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_157 ),
inference(resolution,[],[f1304,f101]) ).
fof(f3484,plain,
( spl1_424
| ~ spl1_6
| ~ spl1_156 ),
inference(avatar_split_clause,[],[f1363,f1299,f100,f3482]) ).
fof(f3482,plain,
( spl1_424
<=> ! [X0] :
( eg = sum(f(inv(inv(inv(X0)))),opp(f(inv(inv(inv(X0))))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_424])]) ).
fof(f1363,plain,
( ! [X0] :
( eg = sum(f(inv(inv(inv(X0)))),opp(f(inv(inv(inv(X0))))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_156 ),
inference(resolution,[],[f1300,f101]) ).
fof(f3318,plain,
( spl1_423
| ~ spl1_4
| ~ spl1_210 ),
inference(avatar_split_clause,[],[f1731,f1632,f91,f3316]) ).
fof(f3316,plain,
( spl1_423
<=> ! [X0] :
( product(product(X0,eh),eh) = product(product(product(X0,eh),eh),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_423])]) ).
fof(f1731,plain,
( ! [X0] :
( product(product(X0,eh),eh) = product(product(product(X0,eh),eh),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_210 ),
inference(resolution,[],[f1633,f93]) ).
fof(f3314,plain,
( spl1_422
| ~ spl1_4
| ~ spl1_209 ),
inference(avatar_split_clause,[],[f1728,f1628,f91,f3312]) ).
fof(f3312,plain,
( spl1_422
<=> ! [X0] :
( product(product(X0,eh),eh) = product(eh,product(product(X0,eh),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_422])]) ).
fof(f1728,plain,
( ! [X0] :
( product(product(X0,eh),eh) = product(eh,product(product(X0,eh),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_209 ),
inference(resolution,[],[f1629,f93]) ).
fof(f3310,plain,
( spl1_421
| ~ spl1_3
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f1725,f1624,f86,f3308]) ).
fof(f3308,plain,
( spl1_421
<=> ! [X0] :
( sum(sum(X0,eg),eg) = sum(sum(sum(X0,eg),eg),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_421])]) ).
fof(f1725,plain,
( ! [X0] :
( sum(sum(X0,eg),eg) = sum(sum(sum(X0,eg),eg),eg)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_208 ),
inference(resolution,[],[f1625,f88]) ).
fof(f3306,plain,
( spl1_420
| ~ spl1_3
| ~ spl1_207 ),
inference(avatar_split_clause,[],[f1720,f1620,f86,f3304]) ).
fof(f3304,plain,
( spl1_420
<=> ! [X0] :
( sum(sum(X0,eg),eg) = sum(eg,sum(sum(X0,eg),eg))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_420])]) ).
fof(f1720,plain,
( ! [X0] :
( sum(sum(X0,eg),eg) = sum(eg,sum(sum(X0,eg),eg))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_207 ),
inference(resolution,[],[f1621,f88]) ).
fof(f3302,plain,
( spl1_419
| ~ spl1_4
| ~ spl1_201 ),
inference(avatar_split_clause,[],[f1690,f1596,f91,f3300]) ).
fof(f3300,plain,
( spl1_419
<=> ! [X0] :
( product(inv(inv(X0)),eh) = product(product(inv(inv(X0)),eh),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_419])]) ).
fof(f1690,plain,
( ! [X0] :
( product(inv(inv(X0)),eh) = product(product(inv(inv(X0)),eh),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_201 ),
inference(resolution,[],[f1597,f93]) ).
fof(f3298,plain,
( spl1_418
| ~ spl1_4
| ~ spl1_200 ),
inference(avatar_split_clause,[],[f1687,f1592,f91,f3296]) ).
fof(f3296,plain,
( spl1_418
<=> ! [X0] :
( product(inv(inv(X0)),eh) = product(eh,product(inv(inv(X0)),eh))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_418])]) ).
fof(f1687,plain,
( ! [X0] :
( product(inv(inv(X0)),eh) = product(eh,product(inv(inv(X0)),eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_200 ),
inference(resolution,[],[f1593,f93]) ).
fof(f3294,plain,
( spl1_417
| ~ spl1_4
| ~ spl1_195 ),
inference(avatar_split_clause,[],[f1668,f1572,f91,f3292]) ).
fof(f3292,plain,
( spl1_417
<=> ! [X0] :
( product(eh,product(X0,eh)) = product(product(eh,product(X0,eh)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_417])]) ).
fof(f1668,plain,
( ! [X0] :
( product(eh,product(X0,eh)) = product(product(eh,product(X0,eh)),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_195 ),
inference(resolution,[],[f1573,f93]) ).
fof(f3290,plain,
( spl1_416
| ~ spl1_4
| ~ spl1_193 ),
inference(avatar_split_clause,[],[f1665,f1564,f91,f3288]) ).
fof(f3288,plain,
( spl1_416
<=> ! [X0] :
( product(eh,product(X0,eh)) = product(eh,product(eh,product(X0,eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_416])]) ).
fof(f1665,plain,
( ! [X0] :
( product(eh,product(X0,eh)) = product(eh,product(eh,product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_193 ),
inference(resolution,[],[f1565,f93]) ).
fof(f3286,plain,
( spl1_415
| ~ spl1_3
| ~ spl1_192 ),
inference(avatar_split_clause,[],[f1662,f1560,f86,f3284]) ).
fof(f3284,plain,
( spl1_415
<=> ! [X0] :
( sum(eg,sum(X0,eg)) = sum(sum(eg,sum(X0,eg)),eg)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_415])]) ).
fof(f1662,plain,
( ! [X0] :
( sum(eg,sum(X0,eg)) = sum(sum(eg,sum(X0,eg)),eg)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_192 ),
inference(resolution,[],[f1561,f88]) ).
fof(f3282,plain,
( spl1_414
| ~ spl1_3
| ~ spl1_191 ),
inference(avatar_split_clause,[],[f1657,f1556,f86,f3280]) ).
fof(f3280,plain,
( spl1_414
<=> ! [X0] :
( sum(eg,sum(X0,eg)) = sum(eg,sum(eg,sum(X0,eg)))
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_414])]) ).
fof(f1657,plain,
( ! [X0] :
( sum(eg,sum(X0,eg)) = sum(eg,sum(eg,sum(X0,eg)))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_191 ),
inference(resolution,[],[f1557,f88]) ).
fof(f3278,plain,
( spl1_413
| ~ spl1_4
| ~ spl1_190 ),
inference(avatar_split_clause,[],[f1648,f1552,f91,f3276]) ).
fof(f3276,plain,
( spl1_413
<=> ! [X0] :
( inv(inv(product(X0,eh))) = product(eh,inv(inv(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_413])]) ).
fof(f1648,plain,
( ! [X0] :
( inv(inv(product(X0,eh))) = product(eh,inv(inv(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_190 ),
inference(resolution,[],[f1553,f93]) ).
fof(f3274,plain,
( spl1_412
| ~ spl1_4
| ~ spl1_189 ),
inference(avatar_split_clause,[],[f1645,f1548,f91,f3272]) ).
fof(f3272,plain,
( spl1_412
<=> ! [X0] :
( inv(inv(product(X0,eh))) = product(inv(inv(product(X0,eh))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_412])]) ).
fof(f1645,plain,
( ! [X0] :
( inv(inv(product(X0,eh))) = product(inv(inv(product(X0,eh))),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_189 ),
inference(resolution,[],[f1549,f93]) ).
fof(f3270,plain,
( spl1_411
| ~ spl1_4
| ~ spl1_188 ),
inference(avatar_split_clause,[],[f1642,f1544,f91,f3268]) ).
fof(f3268,plain,
( spl1_411
<=> ! [X0] :
( f(inv(product(X0,eh))) = sum(eg,f(inv(product(X0,eh))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_411])]) ).
fof(f1642,plain,
( ! [X0] :
( f(inv(product(X0,eh))) = sum(eg,f(inv(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_188 ),
inference(resolution,[],[f1545,f93]) ).
fof(f3264,plain,
( spl1_410
| ~ spl1_42
| ~ spl1_149 ),
inference(avatar_split_clause,[],[f1200,f1196,f340,f3262]) ).
fof(f3262,plain,
( spl1_410
<=> ! [X3,X4,X0,X5,X2,X1] :
( sum(sum(sum(X0,f(product(X1,product(X2,X3)))),X4),X5) = sum(sum(X0,f(product(X1,product(X2,X3)))),sum(X4,X5))
| ~ h(X5)
| ~ h(X0)
| ~ h(X4)
| ~ h(f(X1))
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_410])]) ).
fof(f1200,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( sum(sum(sum(X0,f(product(X1,product(X2,X3)))),X4),X5) = sum(sum(X0,f(product(X1,product(X2,X3)))),sum(X4,X5))
| ~ h(X5)
| ~ h(X0)
| ~ h(X4)
| ~ h(f(X1))
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_149 ),
inference(resolution,[],[f1197,f341]) ).
fof(f3258,plain,
( spl1_409
| ~ spl1_42
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1191,f1180,f340,f3256]) ).
fof(f3256,plain,
( spl1_409
<=> ! [X3,X4,X0,X5,X2,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),f(product(X4,X5))) = sum(sum(X0,sum(X1,X2)),sum(X3,f(product(X4,X5))))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ h(f(X5))
| ~ h(f(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_409])]) ).
fof(f1191,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( sum(sum(sum(X0,sum(X1,X2)),X3),f(product(X4,X5))) = sum(sum(X0,sum(X1,X2)),sum(X3,f(product(X4,X5))))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ h(f(X5))
| ~ h(f(X4)) )
| ~ spl1_42
| ~ spl1_147 ),
inference(resolution,[],[f1181,f341]) ).
fof(f3240,plain,
( spl1_408
| ~ spl1_4
| ~ spl1_187 ),
inference(avatar_split_clause,[],[f1639,f1540,f91,f3238]) ).
fof(f3238,plain,
( spl1_408
<=> ! [X0] :
( f(inv(product(X0,eh))) = sum(f(inv(product(X0,eh))),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_408])]) ).
fof(f1639,plain,
( ! [X0] :
( f(inv(product(X0,eh))) = sum(f(inv(product(X0,eh))),eg)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_187 ),
inference(resolution,[],[f1541,f93]) ).
fof(f3236,plain,
( spl1_407
| ~ spl1_19
| ~ spl1_148 ),
inference(avatar_split_clause,[],[f1194,f1184,f164,f3234]) ).
fof(f3234,plain,
( spl1_407
<=> ! [X3,X4,X0,X5,X2,X1] :
( product(product(product(X0,product(X1,X2)),X3),product(X4,X5)) = product(product(X0,product(X1,X2)),product(X3,product(X4,X5)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1)
| ~ g(X5)
| ~ g(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_407])]) ).
fof(f1194,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( product(product(product(X0,product(X1,X2)),X3),product(X4,X5)) = product(product(X0,product(X1,X2)),product(X3,product(X4,X5)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1)
| ~ g(X5)
| ~ g(X4) )
| ~ spl1_19
| ~ spl1_148 ),
inference(resolution,[],[f1185,f165]) ).
fof(f3232,plain,
( spl1_406
| ~ spl1_18
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1187,f1180,f160,f3230]) ).
fof(f3230,plain,
( spl1_406
<=> ! [X3,X4,X0,X5,X2,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),sum(X4,X5)) = sum(sum(X0,sum(X1,X2)),sum(X3,sum(X4,X5)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ h(X5)
| ~ h(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_406])]) ).
fof(f1187,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( sum(sum(sum(X0,sum(X1,X2)),X3),sum(X4,X5)) = sum(sum(X0,sum(X1,X2)),sum(X3,sum(X4,X5)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ h(X5)
| ~ h(X4) )
| ~ spl1_18
| ~ spl1_147 ),
inference(resolution,[],[f1181,f161]) ).
fof(f3228,plain,
( spl1_405
| ~ spl1_42
| ~ spl1_146 ),
inference(avatar_split_clause,[],[f1178,f1174,f340,f3226]) ).
fof(f3226,plain,
( spl1_405
<=> ! [X2,X4,X0,X3,X1] :
( ~ h(X0)
| ~ g(X1)
| sum(f(X1),sum(f(product(X2,product(X3,X4))),X0)) = sum(f(product(X1,product(X2,product(X3,X4)))),X0)
| ~ h(f(X2))
| ~ h(f(X4))
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_405])]) ).
fof(f1178,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(X0)
| ~ g(X1)
| sum(f(X1),sum(f(product(X2,product(X3,X4))),X0)) = sum(f(product(X1,product(X2,product(X3,X4)))),X0)
| ~ h(f(X2))
| ~ h(f(X4))
| ~ h(f(X3)) )
| ~ spl1_42
| ~ spl1_146 ),
inference(resolution,[],[f1175,f341]) ).
fof(f3224,plain,
( spl1_404
| ~ spl1_42
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1152,f1131,f340,f3222]) ).
fof(f3222,plain,
( spl1_404
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,f(X1)),X2),f(product(X3,X4))) = sum(sum(X0,f(X1)),sum(X2,f(product(X3,X4))))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ h(f(X4))
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_404])]) ).
fof(f1152,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,f(X1)),X2),f(product(X3,X4))) = sum(sum(X0,f(X1)),sum(X2,f(product(X3,X4))))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ h(f(X4))
| ~ h(f(X3)) )
| ~ spl1_42
| ~ spl1_142 ),
inference(resolution,[],[f1132,f341]) ).
fof(f3220,plain,
( spl1_403
| ~ spl1_42
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1144,f1119,f340,f3218]) ).
fof(f3218,plain,
( spl1_403
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(f(X0),sum(X1,f(product(X2,X3)))),X4) = sum(f(X0),sum(sum(X1,f(product(X2,X3))),X4))
| ~ g(X0)
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_403])]) ).
fof(f1144,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(f(X0),sum(X1,f(product(X2,X3)))),X4) = sum(f(X0),sum(sum(X1,f(product(X2,X3))),X4))
| ~ g(X0)
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_139 ),
inference(resolution,[],[f1120,f341]) ).
fof(f3212,plain,
( spl1_402
| ~ spl1_42
| ~ spl1_145 ),
inference(avatar_split_clause,[],[f1172,f1161,f340,f3210]) ).
fof(f3210,plain,
( spl1_402
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(opp(X0),f(product(X1,product(X2,X3)))),X4) = sum(opp(X0),sum(f(product(X1,product(X2,X3))),X4))
| ~ h(X4)
| ~ h(f(X1))
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_402])]) ).
fof(f1172,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(opp(X0),f(product(X1,product(X2,X3)))),X4) = sum(opp(X0),sum(f(product(X1,product(X2,X3))),X4))
| ~ h(X4)
| ~ h(f(X1))
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_145 ),
inference(resolution,[],[f1162,f341]) ).
fof(f3208,plain,
( spl1_401
| ~ spl1_42
| ~ spl1_144 ),
inference(avatar_split_clause,[],[f1170,f1157,f340,f3206]) ).
fof(f3206,plain,
( spl1_401
<=> ! [X4,X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(product(X3,X4),X0)),X2),X1) = sum(f(product(product(X3,X4),X0)),sum(X2,X1))
| ~ h(f(X4))
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_401])]) ).
fof(f1170,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(product(X3,X4),X0)),X2),X1) = sum(f(product(product(X3,X4),X0)),sum(X2,X1))
| ~ h(f(X4))
| ~ h(f(X3)) )
| ~ spl1_42
| ~ spl1_144 ),
inference(resolution,[],[f1158,f341]) ).
fof(f3202,plain,
( spl1_400
| ~ spl1_6
| ~ spl1_155 ),
inference(avatar_split_clause,[],[f1295,f1222,f100,f3200]) ).
fof(f3200,plain,
( spl1_400
<=> ! [X0] :
( sum(f(inv(X0)),eg) = sum(sum(f(inv(X0)),eg),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_400])]) ).
fof(f1295,plain,
( ! [X0] :
( sum(f(inv(X0)),eg) = sum(sum(f(inv(X0)),eg),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_155 ),
inference(resolution,[],[f1223,f101]) ).
fof(f3196,plain,
( spl1_399
| ~ spl1_42
| ~ spl1_134 ),
inference(avatar_split_clause,[],[f1101,f1081,f340,f3194]) ).
fof(f3194,plain,
( spl1_399
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,opp(X1)),X2),f(product(X3,X4))) = sum(sum(X0,opp(X1)),sum(X2,f(product(X3,X4))))
| ~ h(X2)
| ~ h(X0)
| ~ h(f(X4))
| ~ h(f(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_399])]) ).
fof(f1101,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,opp(X1)),X2),f(product(X3,X4))) = sum(sum(X0,opp(X1)),sum(X2,f(product(X3,X4))))
| ~ h(X2)
| ~ h(X0)
| ~ h(f(X4))
| ~ h(f(X3)) )
| ~ spl1_42
| ~ spl1_134 ),
inference(resolution,[],[f1082,f341]) ).
fof(f3192,plain,
( spl1_398
| ~ spl1_42
| ~ spl1_133 ),
inference(avatar_split_clause,[],[f1096,f1077,f340,f3190]) ).
fof(f3190,plain,
( spl1_398
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(opp(X0),sum(X1,f(product(X2,X3)))),X4) = sum(opp(X0),sum(sum(X1,f(product(X2,X3))),X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_398])]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(opp(X0),sum(X1,f(product(X2,X3)))),X4) = sum(opp(X0),sum(sum(X1,f(product(X2,X3))),X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_133 ),
inference(resolution,[],[f1078,f341]) ).
fof(f3184,plain,
( spl1_397
| ~ spl1_5
| ~ spl1_149 ),
inference(avatar_split_clause,[],[f1199,f1196,f96,f3182]) ).
fof(f3182,plain,
( spl1_397
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,f(product(X1,X2))),X3),X4) = sum(sum(X0,f(product(X1,X2))),sum(X3,X4))
| ~ h(X4)
| ~ h(X0)
| ~ h(X3)
| ~ h(f(X1))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_397])]) ).
fof(f1199,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,f(product(X1,X2))),X3),X4) = sum(sum(X0,f(product(X1,X2))),sum(X3,X4))
| ~ h(X4)
| ~ h(X0)
| ~ h(X3)
| ~ h(f(X1))
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_149 ),
inference(resolution,[],[f1197,f97]) ).
fof(f3180,plain,
( spl1_396
| ~ spl1_42
| ~ spl1_138 ),
inference(avatar_split_clause,[],[f1139,f1115,f340,f3178]) ).
fof(f3178,plain,
( spl1_396
<=> ! [X0,X3,X2,X1] :
( sum(eg,sum(f(product(X0,product(X1,X2))),X3)) = sum(sum(eg,f(product(X0,product(X1,X2)))),X3)
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_396])]) ).
fof(f1139,plain,
( ! [X2,X3,X0,X1] :
( sum(eg,sum(f(product(X0,product(X1,X2))),X3)) = sum(sum(eg,f(product(X0,product(X1,X2)))),X3)
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_138 ),
inference(resolution,[],[f1116,f341]) ).
fof(f3162,plain,
( spl1_395
| ~ spl1_6
| ~ spl1_154 ),
inference(avatar_split_clause,[],[f1291,f1218,f100,f3160]) ).
fof(f3160,plain,
( spl1_395
<=> ! [X0] :
( sum(f(inv(X0)),eg) = sum(eg,sum(f(inv(X0)),eg))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_395])]) ).
fof(f1291,plain,
( ! [X0] :
( sum(f(inv(X0)),eg) = sum(eg,sum(f(inv(X0)),eg))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_154 ),
inference(resolution,[],[f1219,f101]) ).
fof(f3137,plain,
( spl1_394
| ~ spl1_6
| ~ spl1_148 ),
inference(avatar_split_clause,[],[f1193,f1184,f100,f3135]) ).
fof(f3135,plain,
( spl1_394
<=> ! [X4,X0,X3,X2,X1] :
( product(product(product(X0,product(X1,X2)),X3),inv(X4)) = product(product(X0,product(X1,X2)),product(X3,inv(X4)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1)
| ~ g(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_394])]) ).
fof(f1193,plain,
( ! [X2,X3,X0,X1,X4] :
( product(product(product(X0,product(X1,X2)),X3),inv(X4)) = product(product(X0,product(X1,X2)),product(X3,inv(X4)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1)
| ~ g(X4) )
| ~ spl1_6
| ~ spl1_148 ),
inference(resolution,[],[f1185,f101]) ).
fof(f3133,plain,
( spl1_393
| ~ spl1_5
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1190,f1180,f96,f3131]) ).
fof(f3131,plain,
( spl1_393
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),f(X4)) = sum(sum(X0,sum(X1,X2)),sum(X3,f(X4)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ g(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_393])]) ).
fof(f1190,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,sum(X1,X2)),X3),f(X4)) = sum(sum(X0,sum(X1,X2)),sum(X3,f(X4)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1)
| ~ g(X4) )
| ~ spl1_5
| ~ spl1_147 ),
inference(resolution,[],[f1181,f97]) ).
fof(f3129,plain,
( spl1_392
| ~ spl1_19
| ~ spl1_143 ),
inference(avatar_split_clause,[],[f1155,f1135,f164,f3127]) ).
fof(f3127,plain,
( spl1_392
<=> ! [X4,X0,X3,X2,X1] :
( product(product(product(X0,inv(X1)),X2),product(X3,X4)) = product(product(X0,inv(X1)),product(X2,product(X3,X4)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| ~ g(X4)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_392])]) ).
fof(f1155,plain,
( ! [X2,X3,X0,X1,X4] :
( product(product(product(X0,inv(X1)),X2),product(X3,X4)) = product(product(X0,inv(X1)),product(X2,product(X3,X4)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| ~ g(X4)
| ~ g(X3) )
| ~ spl1_19
| ~ spl1_143 ),
inference(resolution,[],[f1136,f165]) ).
fof(f3125,plain,
( spl1_391
| ~ spl1_6
| ~ spl1_153 ),
inference(avatar_split_clause,[],[f1286,f1214,f100,f3123]) ).
fof(f3123,plain,
( spl1_391
<=> ! [X0] :
( inv(product(inv(X0),eh)) = product(eh,inv(product(inv(X0),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_391])]) ).
fof(f1286,plain,
( ! [X0] :
( inv(product(inv(X0),eh)) = product(eh,inv(product(inv(X0),eh)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_153 ),
inference(resolution,[],[f1215,f101]) ).
fof(f3121,plain,
( spl1_390
| ~ spl1_18
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1148,f1131,f160,f3119]) ).
fof(f3119,plain,
( spl1_390
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,f(X1)),X2),sum(X3,X4)) = sum(sum(X0,f(X1)),sum(X2,sum(X3,X4)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ h(X4)
| ~ h(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_390])]) ).
fof(f1148,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,f(X1)),X2),sum(X3,X4)) = sum(sum(X0,f(X1)),sum(X2,sum(X3,X4)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ h(X4)
| ~ h(X3) )
| ~ spl1_18
| ~ spl1_142 ),
inference(resolution,[],[f1132,f161]) ).
fof(f3117,plain,
( spl1_389
| ~ spl1_19
| ~ spl1_141 ),
inference(avatar_split_clause,[],[f1147,f1127,f164,f3115]) ).
fof(f3115,plain,
( spl1_389
<=> ! [X4,X0,X3,X2,X1] :
( product(product(inv(product(X0,X1)),X2),product(X3,X4)) = product(inv(product(X0,X1)),product(X2,product(X3,X4)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| ~ g(X4)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_389])]) ).
fof(f1147,plain,
( ! [X2,X3,X0,X1,X4] :
( product(product(inv(product(X0,X1)),X2),product(X3,X4)) = product(inv(product(X0,X1)),product(X2,product(X3,X4)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| ~ g(X4)
| ~ g(X3) )
| ~ spl1_19
| ~ spl1_141 ),
inference(resolution,[],[f1128,f165]) ).
fof(f3113,plain,
( spl1_388
| ~ spl1_18
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1140,f1119,f160,f3111]) ).
fof(f3111,plain,
( spl1_388
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(f(X0),sum(X1,sum(X2,X3))),X4) = sum(f(X0),sum(sum(X1,sum(X2,X3)),X4))
| ~ g(X0)
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_388])]) ).
fof(f1140,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(f(X0),sum(X1,sum(X2,X3))),X4) = sum(f(X0),sum(sum(X1,sum(X2,X3)),X4))
| ~ g(X0)
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_139 ),
inference(resolution,[],[f1120,f161]) ).
fof(f3109,plain,
( spl1_387
| ~ spl1_42
| ~ spl1_137 ),
inference(avatar_split_clause,[],[f1113,f1107,f340,f3107]) ).
fof(f3107,plain,
( spl1_387
<=> ! [X0,X3,X2,X1] :
( eg = sum(sum(f(product(X0,product(X1,X2))),X3),opp(sum(f(product(X0,product(X1,X2))),X3)))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_387])]) ).
fof(f1113,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(sum(f(product(X0,product(X1,X2))),X3),opp(sum(f(product(X0,product(X1,X2))),X3)))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_137 ),
inference(resolution,[],[f1108,f341]) ).
fof(f3105,plain,
( spl1_386
| ~ spl1_42
| ~ spl1_136 ),
inference(avatar_split_clause,[],[f1111,f1103,f340,f3103]) ).
fof(f3103,plain,
( spl1_386
<=> ! [X0,X3,X2,X1] :
( eg = sum(opp(sum(f(product(X0,product(X1,X2))),X3)),sum(f(product(X0,product(X1,X2))),X3))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_386])]) ).
fof(f1111,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(opp(sum(f(product(X0,product(X1,X2))),X3)),sum(f(product(X0,product(X1,X2))),X3))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_136 ),
inference(resolution,[],[f1104,f341]) ).
fof(f3101,plain,
( spl1_385
| ~ spl1_42
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1064,f1038,f340,f3099]) ).
fof(f3099,plain,
( spl1_385
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,eg),X1),f(product(X2,X3))) = sum(sum(X0,eg),sum(X1,f(product(X2,X3))))
| ~ h(X1)
| ~ h(X0)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_385])]) ).
fof(f1064,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,eg),X1),f(product(X2,X3))) = sum(sum(X0,eg),sum(X1,f(product(X2,X3))))
| ~ h(X1)
| ~ h(X0)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_128 ),
inference(resolution,[],[f1039,f341]) ).
fof(f3097,plain,
( spl1_384
| ~ spl1_42
| ~ spl1_125 ),
inference(avatar_split_clause,[],[f1053,f1026,f340,f3095]) ).
fof(f3095,plain,
( spl1_384
<=> ! [X0,X3,X2,X1] :
( sum(eg,sum(sum(X0,f(product(X1,X2))),X3)) = sum(sum(eg,sum(X0,f(product(X1,X2)))),X3)
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_384])]) ).
fof(f1053,plain,
( ! [X2,X3,X0,X1] :
( sum(eg,sum(sum(X0,f(product(X1,X2))),X3)) = sum(sum(eg,sum(X0,f(product(X1,X2)))),X3)
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_125 ),
inference(resolution,[],[f1027,f341]) ).
fof(f3087,plain,
( spl1_383
| ~ spl1_6
| ~ spl1_152 ),
inference(avatar_split_clause,[],[f1281,f1210,f100,f3085]) ).
fof(f3085,plain,
( spl1_383
<=> ! [X0] :
( inv(product(inv(X0),eh)) = product(inv(product(inv(X0),eh)),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_383])]) ).
fof(f1281,plain,
( ! [X0] :
( inv(product(inv(X0),eh)) = product(inv(product(inv(X0),eh)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_152 ),
inference(resolution,[],[f1211,f101]) ).
fof(f3081,plain,
( spl1_382
| ~ spl1_42
| ~ spl1_132 ),
inference(avatar_split_clause,[],[f1091,f1073,f340,f3079]) ).
fof(f3079,plain,
( spl1_382
<=> ! [X0,X3,X2,X1] :
( sum(f(product(X0,product(X1,X2))),X3) = sum(sum(f(product(X0,product(X1,X2))),X3),eg)
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_382])]) ).
fof(f1091,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,product(X1,X2))),X3) = sum(sum(f(product(X0,product(X1,X2))),X3),eg)
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_132 ),
inference(resolution,[],[f1074,f341]) ).
fof(f3077,plain,
( spl1_381
| ~ spl1_42
| ~ spl1_131 ),
inference(avatar_split_clause,[],[f1089,f1069,f340,f3075]) ).
fof(f3075,plain,
( spl1_381
<=> ! [X0,X3,X2,X1] :
( sum(f(product(X0,product(X1,X2))),X3) = sum(eg,sum(f(product(X0,product(X1,X2))),X3))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_381])]) ).
fof(f1089,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,product(X1,X2))),X3) = sum(eg,sum(f(product(X0,product(X1,X2))),X3))
| ~ h(X3)
| ~ h(f(X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_131 ),
inference(resolution,[],[f1070,f341]) ).
fof(f3073,plain,
( spl1_380
| ~ spl1_42
| ~ spl1_120 ),
inference(avatar_split_clause,[],[f1007,f979,f340,f3071]) ).
fof(f3071,plain,
( spl1_380
<=> ! [X0,X3,X2,X1] :
( eg = sum(sum(sum(X0,f(product(X1,X2))),X3),opp(sum(sum(X0,f(product(X1,X2))),X3)))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_380])]) ).
fof(f1007,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(sum(sum(X0,f(product(X1,X2))),X3),opp(sum(sum(X0,f(product(X1,X2))),X3)))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_120 ),
inference(resolution,[],[f980,f341]) ).
fof(f3069,plain,
( spl1_379
| ~ spl1_42
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f1002,f975,f340,f3067]) ).
fof(f3067,plain,
( spl1_379
<=> ! [X0,X3,X2,X1] :
( eg = sum(opp(sum(sum(X0,f(product(X1,X2))),X3)),sum(sum(X0,f(product(X1,X2))),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_379])]) ).
fof(f1002,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(opp(sum(sum(X0,f(product(X1,X2))),X3)),sum(sum(X0,f(product(X1,X2))),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_119 ),
inference(resolution,[],[f976,f341]) ).
fof(f3045,plain,
( spl1_378
| ~ spl1_6
| ~ spl1_151 ),
inference(avatar_split_clause,[],[f1277,f1206,f100,f3043]) ).
fof(f3043,plain,
( spl1_378
<=> ! [X0] :
( f(product(inv(X0),eh)) = sum(eg,f(product(inv(X0),eh)))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_378])]) ).
fof(f1277,plain,
( ! [X0] :
( f(product(inv(X0),eh)) = sum(eg,f(product(inv(X0),eh)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_151 ),
inference(resolution,[],[f1207,f101]) ).
fof(f3039,plain,
( spl1_377
| ~ spl1_8
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1188,f1180,f107,f3037]) ).
fof(f3037,plain,
( spl1_377
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),opp(X4)) = sum(sum(X0,sum(X1,X2)),sum(X3,opp(X4)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_377])]) ).
fof(f1188,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,sum(X1,X2)),X3),opp(X4)) = sum(sum(X0,sum(X1,X2)),sum(X3,opp(X4)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_147 ),
inference(resolution,[],[f1181,f108]) ).
fof(f3035,plain,
( spl1_376
| ~ spl1_18
| ~ spl1_134 ),
inference(avatar_split_clause,[],[f1097,f1081,f160,f3033]) ).
fof(f3033,plain,
( spl1_376
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(sum(X0,opp(X1)),X2),sum(X3,X4)) = sum(sum(X0,opp(X1)),sum(X2,sum(X3,X4)))
| ~ h(X2)
| ~ h(X0)
| ~ h(X4)
| ~ h(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_376])]) ).
fof(f1097,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(sum(X0,opp(X1)),X2),sum(X3,X4)) = sum(sum(X0,opp(X1)),sum(X2,sum(X3,X4)))
| ~ h(X2)
| ~ h(X0)
| ~ h(X4)
| ~ h(X3) )
| ~ spl1_18
| ~ spl1_134 ),
inference(resolution,[],[f1082,f161]) ).
fof(f3031,plain,
( spl1_375
| ~ spl1_18
| ~ spl1_133 ),
inference(avatar_split_clause,[],[f1092,f1077,f160,f3029]) ).
fof(f3029,plain,
( spl1_375
<=> ! [X4,X0,X3,X2,X1] :
( sum(sum(opp(X0),sum(X1,sum(X2,X3))),X4) = sum(opp(X0),sum(sum(X1,sum(X2,X3)),X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_375])]) ).
fof(f1092,plain,
( ! [X2,X3,X0,X1,X4] :
( sum(sum(opp(X0),sum(X1,sum(X2,X3))),X4) = sum(opp(X0),sum(sum(X1,sum(X2,X3)),X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_133 ),
inference(resolution,[],[f1078,f161]) ).
fof(f3027,plain,
( spl1_374
| ~ spl1_42
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f972,f938,f340,f3025]) ).
fof(f3025,plain,
( spl1_374
<=> ! [X0,X3,X2,X1] :
( sum(sum(f(X0),opp(X1)),f(product(X2,X3))) = sum(f(X0),sum(opp(X1),f(product(X2,X3))))
| ~ g(X0)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_374])]) ).
fof(f972,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(f(X0),opp(X1)),f(product(X2,X3))) = sum(f(X0),sum(opp(X1),f(product(X2,X3))))
| ~ g(X0)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_117 ),
inference(resolution,[],[f939,f341]) ).
fof(f3023,plain,
( spl1_373
| ~ spl1_42
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f954,f922,f340,f3021]) ).
fof(f3021,plain,
( spl1_373
<=> ! [X0,X3,X2,X1] :
( sum(sum(X0,f(product(X1,X2))),X3) = sum(sum(sum(X0,f(product(X1,X2))),X3),eg)
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_373])]) ).
fof(f954,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(X0,f(product(X1,X2))),X3) = sum(sum(sum(X0,f(product(X1,X2))),X3),eg)
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_113 ),
inference(resolution,[],[f923,f341]) ).
fof(f3019,plain,
( spl1_372
| ~ spl1_42
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f949,f918,f340,f3017]) ).
fof(f3017,plain,
( spl1_372
<=> ! [X0,X3,X2,X1] :
( sum(sum(X0,f(product(X1,X2))),X3) = sum(eg,sum(sum(X0,f(product(X1,X2))),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_372])]) ).
fof(f949,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(X0,f(product(X1,X2))),X3) = sum(eg,sum(sum(X0,f(product(X1,X2))),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_112 ),
inference(resolution,[],[f919,f341]) ).
fof(f3013,plain,
( spl1_371
| ~ spl1_21
| ~ spl1_42
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f967,f934,f340,f191,f3011]) ).
fof(f3011,plain,
( spl1_371
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),f(X1)),f(product(X2,X3))) = sum(opp(X0),f(product(X1,product(X2,X3))))
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_371])]) ).
fof(f967,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),f(X1)),f(product(X2,X3))) = sum(opp(X0),f(product(X1,product(X2,X3))))
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_116 ),
inference(forward_demodulation,[],[f965,f192]) ).
fof(f965,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),f(X1)),f(product(X2,X3))) = sum(opp(X0),sum(f(X1),f(product(X2,X3))))
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_116 ),
inference(resolution,[],[f935,f341]) ).
fof(f3005,plain,
( spl1_370
| ~ spl1_6
| ~ spl1_150 ),
inference(avatar_split_clause,[],[f1273,f1202,f100,f3003]) ).
fof(f3003,plain,
( spl1_370
<=> ! [X0] :
( f(product(inv(X0),eh)) = sum(f(product(inv(X0),eh)),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_370])]) ).
fof(f1273,plain,
( ! [X0] :
( f(product(inv(X0),eh)) = sum(f(product(inv(X0),eh)),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_150 ),
inference(resolution,[],[f1203,f101]) ).
fof(f2958,plain,
( spl1_369
| ~ spl1_6
| ~ spl1_129 ),
inference(avatar_split_clause,[],[f1255,f1042,f100,f2956]) ).
fof(f2956,plain,
( spl1_369
<=> ! [X0] :
( product(eh,inv(inv(X0))) = product(product(eh,inv(inv(X0))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_369])]) ).
fof(f1255,plain,
( ! [X0] :
( product(eh,inv(inv(X0))) = product(product(eh,inv(inv(X0))),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_129 ),
inference(resolution,[],[f1043,f101]) ).
fof(f2943,plain,
( spl1_368
| ~ spl1_4
| ~ spl1_148 ),
inference(avatar_split_clause,[],[f1192,f1184,f91,f2941]) ).
fof(f2941,plain,
( spl1_368
<=> ! [X0,X3,X2,X1] :
( product(product(product(X0,product(X1,X2)),X3),eh) = product(product(X0,product(X1,X2)),product(X3,eh))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_368])]) ).
fof(f1192,plain,
( ! [X2,X3,X0,X1] :
( product(product(product(X0,product(X1,X2)),X3),eh) = product(product(X0,product(X1,X2)),product(X3,eh))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_148 ),
inference(resolution,[],[f1185,f93]) ).
fof(f2939,plain,
( spl1_367
| ~ spl1_3
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1189,f1180,f86,f2937]) ).
fof(f2937,plain,
( spl1_367
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),eg) = sum(sum(X0,sum(X1,X2)),sum(X3,eg))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_367])]) ).
fof(f1189,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,sum(X1,X2)),X3),eg) = sum(sum(X0,sum(X1,X2)),sum(X3,eg))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_147 ),
inference(resolution,[],[f1181,f88]) ).
fof(f2935,plain,
( spl1_366
| ~ spl1_5
| ~ spl1_146 ),
inference(avatar_split_clause,[],[f1177,f1174,f96,f2933]) ).
fof(f2933,plain,
( spl1_366
<=> ! [X0,X3,X2,X1] :
( ~ h(X0)
| ~ g(X1)
| sum(f(X1),sum(f(product(X2,X3)),X0)) = sum(f(product(X1,product(X2,X3))),X0)
| ~ h(f(X2))
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_366])]) ).
fof(f1177,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| ~ g(X1)
| sum(f(X1),sum(f(product(X2,X3)),X0)) = sum(f(product(X1,product(X2,X3))),X0)
| ~ h(f(X2))
| ~ g(X3) )
| ~ spl1_5
| ~ spl1_146 ),
inference(resolution,[],[f1175,f97]) ).
fof(f2931,plain,
( spl1_365
| ~ spl1_6
| ~ spl1_143 ),
inference(avatar_split_clause,[],[f1154,f1135,f100,f2929]) ).
fof(f2929,plain,
( spl1_365
<=> ! [X0,X3,X2,X1] :
( product(product(product(X0,inv(X1)),X2),inv(X3)) = product(product(X0,inv(X1)),product(X2,inv(X3)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_365])]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1] :
( product(product(product(X0,inv(X1)),X2),inv(X3)) = product(product(X0,inv(X1)),product(X2,inv(X3)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1)
| ~ g(X3) )
| ~ spl1_6
| ~ spl1_143 ),
inference(resolution,[],[f1136,f101]) ).
fof(f2927,plain,
( spl1_364
| ~ spl1_5
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1151,f1131,f96,f2925]) ).
fof(f2925,plain,
( spl1_364
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,f(X1)),X2),f(X3)) = sum(sum(X0,f(X1)),sum(X2,f(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_364])]) ).
fof(f1151,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,f(X1)),X2),f(X3)) = sum(sum(X0,f(X1)),sum(X2,f(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1)
| ~ g(X3) )
| ~ spl1_5
| ~ spl1_142 ),
inference(resolution,[],[f1132,f97]) ).
fof(f2923,plain,
( spl1_363
| ~ spl1_6
| ~ spl1_141 ),
inference(avatar_split_clause,[],[f1146,f1127,f100,f2921]) ).
fof(f2921,plain,
( spl1_363
<=> ! [X0,X3,X2,X1] :
( product(product(inv(product(X0,X1)),X2),inv(X3)) = product(inv(product(X0,X1)),product(X2,inv(X3)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_363])]) ).
fof(f1146,plain,
( ! [X2,X3,X0,X1] :
( product(product(inv(product(X0,X1)),X2),inv(X3)) = product(inv(product(X0,X1)),product(X2,inv(X3)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0)
| ~ g(X3) )
| ~ spl1_6
| ~ spl1_141 ),
inference(resolution,[],[f1128,f101]) ).
fof(f2919,plain,
( spl1_362
| ~ spl1_6
| ~ spl1_123 ),
inference(avatar_split_clause,[],[f1251,f991,f100,f2917]) ).
fof(f2917,plain,
( spl1_362
<=> ! [X0] :
( product(eh,inv(inv(X0))) = product(eh,product(eh,inv(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_362])]) ).
fof(f1251,plain,
( ! [X0] :
( product(eh,inv(inv(X0))) = product(eh,product(eh,inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_123 ),
inference(resolution,[],[f992,f101]) ).
fof(f2915,plain,
( spl1_361
| ~ spl1_5
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1143,f1119,f96,f2913]) ).
fof(f2913,plain,
( spl1_361
<=> ! [X0,X3,X2,X1] :
( sum(sum(f(X0),sum(X1,f(X2))),X3) = sum(f(X0),sum(sum(X1,f(X2)),X3))
| ~ g(X0)
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_361])]) ).
fof(f1143,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(f(X0),sum(X1,f(X2))),X3) = sum(f(X0),sum(sum(X1,f(X2)),X3))
| ~ g(X0)
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_139 ),
inference(resolution,[],[f1120,f97]) ).
fof(f2911,plain,
( spl1_360
| ~ spl1_19
| ~ spl1_130 ),
inference(avatar_split_clause,[],[f1067,f1046,f164,f2909]) ).
fof(f2909,plain,
( spl1_360
<=> ! [X0,X3,X2,X1] :
( product(product(product(X0,eh),X1),product(X2,X3)) = product(product(X0,eh),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_360])]) ).
fof(f1067,plain,
( ! [X2,X3,X0,X1] :
( product(product(product(X0,eh),X1),product(X2,X3)) = product(product(X0,eh),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_19
| ~ spl1_130 ),
inference(resolution,[],[f1047,f165]) ).
fof(f2907,plain,
( spl1_359
| ~ spl1_18
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1060,f1038,f160,f2905]) ).
fof(f2905,plain,
( spl1_359
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,eg),X1),sum(X2,X3)) = sum(sum(X0,eg),sum(X1,sum(X2,X3)))
| ~ h(X1)
| ~ h(X0)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_359])]) ).
fof(f1060,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,eg),X1),sum(X2,X3)) = sum(sum(X0,eg),sum(X1,sum(X2,X3)))
| ~ h(X1)
| ~ h(X0)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_128 ),
inference(resolution,[],[f1039,f161]) ).
fof(f2903,plain,
( spl1_358
| ~ spl1_19
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1059,f1034,f164,f2901]) ).
fof(f2901,plain,
( spl1_358
<=> ! [X0,X3,X2,X1] :
( product(product(inv(inv(X0)),X1),product(X2,X3)) = product(inv(inv(X0)),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_358])]) ).
fof(f1059,plain,
( ! [X2,X3,X0,X1] :
( product(product(inv(inv(X0)),X1),product(X2,X3)) = product(inv(inv(X0)),product(X1,product(X2,X3)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_19
| ~ spl1_127 ),
inference(resolution,[],[f1035,f165]) ).
fof(f2899,plain,
( spl1_357
| ~ spl1_19
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f1056,f1030,f164,f2897]) ).
fof(f2897,plain,
( spl1_357
<=> ! [X0,X3,X2,X1] :
( product(eh,product(product(X0,product(X1,X2)),X3)) = product(product(eh,product(X0,product(X1,X2))),X3)
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_357])]) ).
fof(f1056,plain,
( ! [X2,X3,X0,X1] :
( product(eh,product(product(X0,product(X1,X2)),X3)) = product(product(eh,product(X0,product(X1,X2))),X3)
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_126 ),
inference(resolution,[],[f1031,f165]) ).
fof(f2895,plain,
( spl1_356
| ~ spl1_18
| ~ spl1_125 ),
inference(avatar_split_clause,[],[f1049,f1026,f160,f2893]) ).
fof(f2893,plain,
( spl1_356
<=> ! [X0,X3,X2,X1] :
( sum(eg,sum(sum(X0,sum(X1,X2)),X3)) = sum(sum(eg,sum(X0,sum(X1,X2))),X3)
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_356])]) ).
fof(f1049,plain,
( ! [X2,X3,X0,X1] :
( sum(eg,sum(sum(X0,sum(X1,X2)),X3)) = sum(sum(eg,sum(X0,sum(X1,X2))),X3)
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_125 ),
inference(resolution,[],[f1027,f161]) ).
fof(f2891,plain,
( spl1_355
| ~ spl1_21
| ~ spl1_42
| ~ spl1_124 ),
inference(avatar_split_clause,[],[f1024,f995,f340,f191,f2889]) ).
fof(f2889,plain,
( spl1_355
<=> ! [X0,X3,X2,X1] :
( f(product(X0,product(X1,product(X2,X3)))) = f(product(product(X0,X1),product(X2,X3)))
| ~ g(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_355])]) ).
fof(f1024,plain,
( ! [X2,X3,X0,X1] :
( f(product(X0,product(X1,product(X2,X3)))) = f(product(product(X0,X1),product(X2,X3)))
| ~ g(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1023,f192]) ).
fof(f1023,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,X1)),f(product(X2,X3))) = f(product(X0,product(X1,product(X2,X3))))
| ~ g(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1022,f192]) ).
fof(f1022,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,X1)),f(product(X2,X3))) = sum(f(X0),f(product(X1,product(X2,X3))))
| ~ g(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1018,f192]) ).
fof(f1018,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,X1)),f(product(X2,X3))) = sum(f(X0),sum(f(X1),f(product(X2,X3))))
| ~ g(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_124 ),
inference(resolution,[],[f996,f341]) ).
fof(f2887,plain,
( spl1_354
| ~ spl1_42
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f898,f869,f340,f2885]) ).
fof(f2885,plain,
( spl1_354
<=> ! [X2,X0,X1] :
( sum(sum(f(X0),eg),f(product(X1,X2))) = sum(f(X0),sum(eg,f(product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_354])]) ).
fof(f898,plain,
( ! [X2,X0,X1] :
( sum(sum(f(X0),eg),f(product(X1,X2))) = sum(f(X0),sum(eg,f(product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_108 ),
inference(resolution,[],[f870,f341]) ).
fof(f2883,plain,
( spl1_353
| ~ spl1_42
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f892,f865,f340,f2881]) ).
fof(f2881,plain,
( spl1_353
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),opp(X1)),f(product(X2,X3))) = sum(opp(X0),sum(opp(X1),f(product(X2,X3))))
| ~ h(f(X3))
| ~ h(f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_353])]) ).
fof(f892,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),opp(X1)),f(product(X2,X3))) = sum(opp(X0),sum(opp(X1),f(product(X2,X3))))
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_107 ),
inference(resolution,[],[f866,f341]) ).
fof(f2877,plain,
( spl1_352
| ~ spl1_6
| ~ spl1_118 ),
inference(avatar_split_clause,[],[f1247,f942,f100,f2875]) ).
fof(f2875,plain,
( spl1_352
<=> ! [X0] :
( sum(eg,f(inv(X0))) = sum(sum(eg,f(inv(X0))),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_352])]) ).
fof(f1247,plain,
( ! [X0] :
( sum(eg,f(inv(X0))) = sum(sum(eg,f(inv(X0))),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_118 ),
inference(resolution,[],[f943,f101]) ).
fof(f2848,plain,
( spl1_351
| ~ spl1_5
| ~ spl1_145 ),
inference(avatar_split_clause,[],[f1171,f1161,f96,f2846]) ).
fof(f2846,plain,
( spl1_351
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),f(product(X1,X2))),X3) = sum(opp(X0),sum(f(product(X1,X2)),X3))
| ~ h(X3)
| ~ h(f(X1))
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_351])]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),f(product(X1,X2))),X3) = sum(opp(X0),sum(f(product(X1,X2)),X3))
| ~ h(X3)
| ~ h(f(X1))
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_145 ),
inference(resolution,[],[f1162,f97]) ).
fof(f2844,plain,
( spl1_350
| ~ spl1_5
| ~ spl1_144 ),
inference(avatar_split_clause,[],[f1169,f1157,f96,f2842]) ).
fof(f2842,plain,
( spl1_350
<=> ! [X0,X3,X2,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(X3,X0)),X2),X1) = sum(f(product(X3,X0)),sum(X2,X1))
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_350])]) ).
fof(f1169,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(X1)
| ~ h(X2)
| sum(sum(f(product(X3,X0)),X2),X1) = sum(f(product(X3,X0)),sum(X2,X1))
| ~ g(X3) )
| ~ spl1_5
| ~ spl1_144 ),
inference(resolution,[],[f1158,f97]) ).
fof(f2840,plain,
( spl1_349
| ~ spl1_18
| ~ spl1_124 ),
inference(avatar_split_clause,[],[f1014,f995,f160,f2838]) ).
fof(f2838,plain,
( spl1_349
<=> ! [X0,X3,X2,X1] :
( sum(f(product(X0,X1)),sum(X2,X3)) = sum(f(X0),sum(f(X1),sum(X2,X3)))
| ~ g(X0)
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_349])]) ).
fof(f1014,plain,
( ! [X2,X3,X0,X1] :
( sum(f(product(X0,X1)),sum(X2,X3)) = sum(f(X0),sum(f(X1),sum(X2,X3)))
| ~ g(X0)
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_124 ),
inference(resolution,[],[f996,f161]) ).
fof(f2836,plain,
( spl1_348
| ~ spl1_6
| ~ spl1_109 ),
inference(avatar_split_clause,[],[f1243,f902,f100,f2834]) ).
fof(f2834,plain,
( spl1_348
<=> ! [X0] :
( sum(eg,f(inv(X0))) = sum(eg,sum(eg,f(inv(X0))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_348])]) ).
fof(f1243,plain,
( ! [X0] :
( sum(eg,f(inv(X0))) = sum(eg,sum(eg,f(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_109 ),
inference(resolution,[],[f903,f101]) ).
fof(f2832,plain,
( spl1_347
| ~ spl1_19
| ~ spl1_122 ),
inference(avatar_split_clause,[],[f1013,f987,f164,f2830]) ).
fof(f2830,plain,
( spl1_347
<=> ! [X0,X3,X2,X1] :
( eh = product(product(product(X0,product(X1,X2)),X3),inv(product(product(X0,product(X1,X2)),X3)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_347])]) ).
fof(f1013,plain,
( ! [X2,X3,X0,X1] :
( eh = product(product(product(X0,product(X1,X2)),X3),inv(product(product(X0,product(X1,X2)),X3)))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_122 ),
inference(resolution,[],[f988,f165]) ).
fof(f2828,plain,
( spl1_346
| ~ spl1_19
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f1010,f983,f164,f2826]) ).
fof(f2826,plain,
( spl1_346
<=> ! [X0,X3,X2,X1] :
( eh = product(inv(product(product(X0,product(X1,X2)),X3)),product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_346])]) ).
fof(f1010,plain,
( ! [X2,X3,X0,X1] :
( eh = product(inv(product(product(X0,product(X1,X2)),X3)),product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_121 ),
inference(resolution,[],[f984,f165]) ).
fof(f2824,plain,
( spl1_345
| ~ spl1_18
| ~ spl1_120 ),
inference(avatar_split_clause,[],[f1003,f979,f160,f2822]) ).
fof(f2822,plain,
( spl1_345
<=> ! [X0,X3,X2,X1] :
( eg = sum(sum(sum(X0,sum(X1,X2)),X3),opp(sum(sum(X0,sum(X1,X2)),X3)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_345])]) ).
fof(f1003,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(sum(sum(X0,sum(X1,X2)),X3),opp(sum(sum(X0,sum(X1,X2)),X3)))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_120 ),
inference(resolution,[],[f980,f161]) ).
fof(f2820,plain,
( spl1_344
| ~ spl1_18
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f998,f975,f160,f2818]) ).
fof(f2818,plain,
( spl1_344
<=> ! [X0,X3,X2,X1] :
( eg = sum(opp(sum(sum(X0,sum(X1,X2)),X3)),sum(sum(X0,sum(X1,X2)),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_344])]) ).
fof(f998,plain,
( ! [X2,X3,X0,X1] :
( eg = sum(opp(sum(sum(X0,sum(X1,X2)),X3)),sum(sum(X0,sum(X1,X2)),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_119 ),
inference(resolution,[],[f976,f161]) ).
fof(f2816,plain,
( spl1_343
| ~ spl1_21
| ~ spl1_42
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f882,f857,f340,f191,f2814]) ).
fof(f2814,plain,
( spl1_343
<=> ! [X2,X0,X1] :
( sum(eg,f(product(X0,product(X1,X2)))) = sum(sum(eg,f(X0)),f(product(X1,X2)))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_343])]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( sum(eg,f(product(X0,product(X1,X2)))) = sum(sum(eg,f(X0)),f(product(X1,X2)))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_105 ),
inference(forward_demodulation,[],[f880,f192]) ).
fof(f880,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(f(X0),f(product(X1,X2)))) = sum(sum(eg,f(X0)),f(product(X1,X2)))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_105 ),
inference(resolution,[],[f858,f341]) ).
fof(f2784,plain,
( spl1_342
| ~ spl1_6
| ~ spl1_104 ),
inference(avatar_split_clause,[],[f1237,f853,f100,f2782]) ).
fof(f2782,plain,
( spl1_342
<=> ! [X0] :
( inv(inv(inv(inv(X0)))) = product(eh,inv(inv(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_342])]) ).
fof(f1237,plain,
( ! [X0] :
( inv(inv(inv(inv(X0)))) = product(eh,inv(inv(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_104 ),
inference(resolution,[],[f854,f101]) ).
fof(f2755,plain,
( spl1_341
| ~ spl1_8
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1149,f1131,f107,f2753]) ).
fof(f2753,plain,
( spl1_341
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,f(X1)),X2),opp(X3)) = sum(sum(X0,f(X1)),sum(X2,opp(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_341])]) ).
fof(f1149,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,f(X1)),X2),opp(X3)) = sum(sum(X0,f(X1)),sum(X2,opp(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_8
| ~ spl1_142 ),
inference(resolution,[],[f1132,f108]) ).
fof(f2751,plain,
( spl1_340
| ~ spl1_8
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1141,f1119,f107,f2749]) ).
fof(f2749,plain,
( spl1_340
<=> ! [X0,X3,X2,X1] :
( sum(sum(f(X0),sum(X1,opp(X2))),X3) = sum(f(X0),sum(sum(X1,opp(X2)),X3))
| ~ g(X0)
| ~ h(X3)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_340])]) ).
fof(f1141,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(f(X0),sum(X1,opp(X2))),X3) = sum(f(X0),sum(sum(X1,opp(X2)),X3))
| ~ g(X0)
| ~ h(X3)
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_139 ),
inference(resolution,[],[f1120,f108]) ).
fof(f2747,plain,
( spl1_339
| ~ spl1_5
| ~ spl1_134 ),
inference(avatar_split_clause,[],[f1100,f1081,f96,f2745]) ).
fof(f2745,plain,
( spl1_339
<=> ! [X0,X3,X2,X1] :
( sum(sum(sum(X0,opp(X1)),X2),f(X3)) = sum(sum(X0,opp(X1)),sum(X2,f(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_339])]) ).
fof(f1100,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,opp(X1)),X2),f(X3)) = sum(sum(X0,opp(X1)),sum(X2,f(X3)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X3) )
| ~ spl1_5
| ~ spl1_134 ),
inference(resolution,[],[f1082,f97]) ).
fof(f2743,plain,
( spl1_338
| ~ spl1_6
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1231,f807,f100,f2741]) ).
fof(f2741,plain,
( spl1_338
<=> ! [X0] :
( inv(inv(inv(inv(X0)))) = product(inv(inv(inv(inv(X0)))),eh)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_338])]) ).
fof(f1231,plain,
( ! [X0] :
( inv(inv(inv(inv(X0)))) = product(inv(inv(inv(inv(X0)))),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_101 ),
inference(resolution,[],[f808,f101]) ).
fof(f2739,plain,
( spl1_337
| ~ spl1_5
| ~ spl1_133 ),
inference(avatar_split_clause,[],[f1095,f1077,f96,f2737]) ).
fof(f2737,plain,
( spl1_337
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),sum(X1,f(X2))),X3) = sum(opp(X0),sum(sum(X1,f(X2)),X3))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_337])]) ).
fof(f1095,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),sum(X1,f(X2))),X3) = sum(opp(X0),sum(sum(X1,f(X2)),X3))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_133 ),
inference(resolution,[],[f1078,f97]) ).
fof(f2735,plain,
( spl1_336
| ~ spl1_18
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f968,f938,f160,f2733]) ).
fof(f2733,plain,
( spl1_336
<=> ! [X0,X3,X2,X1] :
( sum(sum(f(X0),opp(X1)),sum(X2,X3)) = sum(f(X0),sum(opp(X1),sum(X2,X3)))
| ~ g(X0)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_336])]) ).
fof(f968,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(f(X0),opp(X1)),sum(X2,X3)) = sum(f(X0),sum(opp(X1),sum(X2,X3)))
| ~ g(X0)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_117 ),
inference(resolution,[],[f939,f161]) ).
fof(f2731,plain,
( spl1_335
| ~ spl1_18
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f961,f934,f160,f2729]) ).
fof(f2729,plain,
( spl1_335
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),f(X1)),sum(X2,X3)) = sum(opp(X0),sum(f(X1),sum(X2,X3)))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_335])]) ).
fof(f961,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),f(X1)),sum(X2,X3)) = sum(opp(X0),sum(f(X1),sum(X2,X3)))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_116 ),
inference(resolution,[],[f935,f161]) ).
fof(f2727,plain,
( spl1_334
| ~ spl1_19
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f960,f930,f164,f2725]) ).
fof(f2725,plain,
( spl1_334
<=> ! [X0,X3,X2,X1] :
( product(product(X0,product(X1,X2)),X3) = product(product(product(X0,product(X1,X2)),X3),eh)
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_334])]) ).
fof(f960,plain,
( ! [X2,X3,X0,X1] :
( product(product(X0,product(X1,X2)),X3) = product(product(product(X0,product(X1,X2)),X3),eh)
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_115 ),
inference(resolution,[],[f931,f165]) ).
fof(f2723,plain,
( spl1_333
| ~ spl1_19
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f957,f926,f164,f2721]) ).
fof(f2721,plain,
( spl1_333
<=> ! [X0,X3,X2,X1] :
( product(product(X0,product(X1,X2)),X3) = product(eh,product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_333])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( product(product(X0,product(X1,X2)),X3) = product(eh,product(product(X0,product(X1,X2)),X3))
| ~ g(X3)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_114 ),
inference(resolution,[],[f927,f165]) ).
fof(f2719,plain,
( spl1_332
| ~ spl1_18
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f950,f922,f160,f2717]) ).
fof(f2717,plain,
( spl1_332
<=> ! [X0,X3,X2,X1] :
( sum(sum(X0,sum(X1,X2)),X3) = sum(sum(sum(X0,sum(X1,X2)),X3),eg)
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_332])]) ).
fof(f950,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(X0,sum(X1,X2)),X3) = sum(sum(sum(X0,sum(X1,X2)),X3),eg)
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_113 ),
inference(resolution,[],[f923,f161]) ).
fof(f2715,plain,
( spl1_331
| ~ spl1_18
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f945,f918,f160,f2713]) ).
fof(f2713,plain,
( spl1_331
<=> ! [X0,X3,X2,X1] :
( sum(sum(X0,sum(X1,X2)),X3) = sum(eg,sum(sum(X0,sum(X1,X2)),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_331])]) ).
fof(f945,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(X0,sum(X1,X2)),X3) = sum(eg,sum(sum(X0,sum(X1,X2)),X3))
| ~ h(X3)
| ~ h(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_112 ),
inference(resolution,[],[f919,f161]) ).
fof(f2711,plain,
( spl1_330
| ~ spl1_42
| ~ spl1_111 ),
inference(avatar_split_clause,[],[f916,f910,f340,f2709]) ).
fof(f2709,plain,
( spl1_330
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(X1,X2),X0)),opp(f(product(product(X1,X2),X0))))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_330])]) ).
fof(f916,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(product(X1,X2),X0)),opp(f(product(product(X1,X2),X0))))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_111 ),
inference(resolution,[],[f911,f341]) ).
fof(f2707,plain,
( spl1_329
| ~ spl1_42
| ~ spl1_110 ),
inference(avatar_split_clause,[],[f914,f906,f340,f2705]) ).
fof(f2705,plain,
( spl1_329
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(X1,X2),X0))),f(product(product(X1,X2),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_329])]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(product(X1,X2),X0))),f(product(product(X1,X2),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_110 ),
inference(resolution,[],[f907,f341]) ).
fof(f2701,plain,
( spl1_328
| ~ spl1_6
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1226,f763,f100,f2699]) ).
fof(f2699,plain,
( spl1_328
<=> ! [X0] :
( f(inv(inv(inv(X0)))) = sum(eg,f(inv(inv(inv(X0)))))
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_328])]) ).
fof(f1226,plain,
( ! [X0] :
( f(inv(inv(inv(X0)))) = sum(eg,f(inv(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_92 ),
inference(resolution,[],[f764,f101]) ).
fof(f2685,plain,
( spl1_327
| ~ spl1_5
| ~ spl1_138 ),
inference(avatar_split_clause,[],[f1138,f1115,f96,f2683]) ).
fof(f2683,plain,
( spl1_327
<=> ! [X2,X0,X1] :
( sum(eg,sum(f(product(X0,X1)),X2)) = sum(sum(eg,f(product(X0,X1))),X2)
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_327])]) ).
fof(f1138,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(f(product(X0,X1)),X2)) = sum(sum(eg,f(product(X0,X1))),X2)
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_138 ),
inference(resolution,[],[f1116,f97]) ).
fof(f2681,plain,
( spl1_326
| ~ spl1_42
| ~ spl1_103 ),
inference(avatar_split_clause,[],[f875,f849,f340,f2679]) ).
fof(f2679,plain,
( spl1_326
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| f(product(product(X1,X2),X0)) = sum(f(product(product(X1,X2),X0)),eg)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_326])]) ).
fof(f875,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| f(product(product(X1,X2),X0)) = sum(f(product(product(X1,X2),X0)),eg)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_103 ),
inference(resolution,[],[f850,f341]) ).
fof(f2677,plain,
( spl1_325
| ~ spl1_42
| ~ spl1_102 ),
inference(avatar_split_clause,[],[f873,f845,f340,f2675]) ).
fof(f2675,plain,
( spl1_325
<=> ! [X2,X0,X1] :
( ~ h(f(X0))
| f(product(product(X1,X2),X0)) = sum(eg,f(product(product(X1,X2),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_325])]) ).
fof(f873,plain,
( ! [X2,X0,X1] :
( ~ h(f(X0))
| f(product(product(X1,X2),X0)) = sum(eg,f(product(product(X1,X2),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_102 ),
inference(resolution,[],[f846,f341]) ).
fof(f2673,plain,
( spl1_324
| ~ spl1_21
| ~ spl1_42
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f835,f795,f340,f191,f2671]) ).
fof(f2671,plain,
( spl1_324
<=> ! [X2,X0,X1] :
( eg = sum(f(product(X0,product(X1,X2))),opp(f(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_324])]) ).
fof(f795,plain,
( spl1_98
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(X1),X0),opp(sum(f(X1),X0)))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
fof(f835,plain,
( ! [X2,X0,X1] :
( eg = sum(f(product(X0,product(X1,X2))),opp(f(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_98 ),
inference(forward_demodulation,[],[f833,f192]) ).
fof(f833,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(f(X0),f(product(X1,X2))),opp(sum(f(X0),f(product(X1,X2)))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_98 ),
inference(resolution,[],[f796,f341]) ).
fof(f796,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(X1),X0),opp(sum(f(X1),X0)))
| ~ g(X1) )
| ~ spl1_98 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f2669,plain,
( spl1_323
| ~ spl1_6
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f1165,f717,f100,f2667]) ).
fof(f2667,plain,
( spl1_323
<=> ! [X0] :
( f(inv(inv(inv(X0)))) = sum(f(inv(inv(inv(X0)))),eg)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_323])]) ).
fof(f1165,plain,
( ! [X0] :
( f(inv(inv(inv(X0)))) = sum(f(inv(inv(inv(X0)))),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_87 ),
inference(resolution,[],[f718,f101]) ).
fof(f2665,plain,
( spl1_322
| ~ spl1_21
| ~ spl1_42
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f828,f791,f340,f191,f2663]) ).
fof(f2663,plain,
( spl1_322
<=> ! [X2,X0,X1] :
( eg = sum(opp(f(product(X0,product(X1,X2)))),f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_322])]) ).
fof(f791,plain,
( spl1_97
<=> ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(X1),X0)),sum(f(X1),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
fof(f828,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(f(product(X0,product(X1,X2)))),f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_97 ),
inference(forward_demodulation,[],[f826,f192]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(f(X0),f(product(X1,X2)))),sum(f(X0),f(product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_97 ),
inference(resolution,[],[f792,f341]) ).
fof(f792,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(X1),X0)),sum(f(X1),X0))
| ~ g(X1) )
| ~ spl1_97 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f2661,plain,
( spl1_321
| ~ spl1_42
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f698,f685,f340,f2659]) ).
fof(f2659,plain,
( spl1_321
<=> ! [X2,X0,X1] :
( eg = sum(sum(opp(X0),f(product(X1,X2))),opp(sum(opp(X0),f(product(X1,X2)))))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_321])]) ).
fof(f698,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(opp(X0),f(product(X1,X2))),opp(sum(opp(X0),f(product(X1,X2)))))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_82 ),
inference(resolution,[],[f686,f341]) ).
fof(f2657,plain,
( spl1_320
| ~ spl1_42
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f692,f681,f340,f2655]) ).
fof(f2655,plain,
( spl1_320
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(X1,X2)))),sum(opp(X0),f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_320])]) ).
fof(f692,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(opp(X0),f(product(X1,X2)))),sum(opp(X0),f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_81 ),
inference(resolution,[],[f682,f341]) ).
fof(f2540,plain,
( spl1_319
| ~ spl1_4
| ~ spl1_143 ),
inference(avatar_split_clause,[],[f1153,f1135,f91,f2538]) ).
fof(f2538,plain,
( spl1_319
<=> ! [X2,X0,X1] :
( product(product(product(X0,inv(X1)),X2),eh) = product(product(X0,inv(X1)),product(X2,eh))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_319])]) ).
fof(f1153,plain,
( ! [X2,X0,X1] :
( product(product(product(X0,inv(X1)),X2),eh) = product(product(X0,inv(X1)),product(X2,eh))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_143 ),
inference(resolution,[],[f1136,f93]) ).
fof(f2536,plain,
( spl1_318
| ~ spl1_3
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1150,f1131,f86,f2534]) ).
fof(f2534,plain,
( spl1_318
<=> ! [X2,X0,X1] :
( sum(sum(sum(X0,f(X1)),X2),eg) = sum(sum(X0,f(X1)),sum(X2,eg))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_318])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( sum(sum(sum(X0,f(X1)),X2),eg) = sum(sum(X0,f(X1)),sum(X2,eg))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_142 ),
inference(resolution,[],[f1132,f88]) ).
fof(f2532,plain,
( spl1_317
| ~ spl1_4
| ~ spl1_141 ),
inference(avatar_split_clause,[],[f1145,f1127,f91,f2530]) ).
fof(f2530,plain,
( spl1_317
<=> ! [X2,X0,X1] :
( product(product(inv(product(X0,X1)),X2),eh) = product(inv(product(X0,X1)),product(X2,eh))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_317])]) ).
fof(f1145,plain,
( ! [X2,X0,X1] :
( product(product(inv(product(X0,X1)),X2),eh) = product(inv(product(X0,X1)),product(X2,eh))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_141 ),
inference(resolution,[],[f1128,f93]) ).
fof(f2528,plain,
( spl1_316
| ~ spl1_3
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1142,f1119,f86,f2526]) ).
fof(f2526,plain,
( spl1_316
<=> ! [X2,X0,X1] :
( sum(sum(f(X0),sum(X1,eg)),X2) = sum(f(X0),sum(sum(X1,eg),X2))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_316])]) ).
fof(f1142,plain,
( ! [X2,X0,X1] :
( sum(sum(f(X0),sum(X1,eg)),X2) = sum(f(X0),sum(sum(X1,eg),X2))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_139 ),
inference(resolution,[],[f1120,f88]) ).
fof(f2524,plain,
( spl1_315
| ~ spl1_5
| ~ spl1_137 ),
inference(avatar_split_clause,[],[f1112,f1107,f96,f2522]) ).
fof(f2522,plain,
( spl1_315
<=> ! [X2,X0,X1] :
( eg = sum(sum(f(product(X0,X1)),X2),opp(sum(f(product(X0,X1)),X2)))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_315])]) ).
fof(f1112,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(f(product(X0,X1)),X2),opp(sum(f(product(X0,X1)),X2)))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_137 ),
inference(resolution,[],[f1108,f97]) ).
fof(f2515,plain,
( spl1_314
| ~ spl1_5
| ~ spl1_136 ),
inference(avatar_split_clause,[],[f1110,f1103,f96,f2513]) ).
fof(f2513,plain,
( spl1_314
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(f(product(X0,X1)),X2)),sum(f(product(X0,X1)),X2))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_314])]) ).
fof(f1110,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(f(product(X0,X1)),X2)),sum(f(product(X0,X1)),X2))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_136 ),
inference(resolution,[],[f1104,f97]) ).
fof(f2511,plain,
( spl1_313
| ~ spl1_8
| ~ spl1_134 ),
inference(avatar_split_clause,[],[f1098,f1081,f107,f2509]) ).
fof(f1098,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(sum(X0,opp(X1)),X2),opp(X3)) = sum(sum(X0,opp(X1)),sum(X2,opp(X3)))
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_134 ),
inference(resolution,[],[f1082,f108]) ).
fof(f2507,plain,
( spl1_312
| ~ spl1_8
| ~ spl1_133 ),
inference(avatar_split_clause,[],[f1093,f1077,f107,f2505]) ).
fof(f2505,plain,
( spl1_312
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),sum(X1,opp(X2))),X3) = sum(opp(X0),sum(sum(X1,opp(X2)),X3))
| ~ h(X3)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_312])]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),sum(X1,opp(X2))),X3) = sum(opp(X0),sum(sum(X1,opp(X2)),X3))
| ~ h(X3)
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_133 ),
inference(resolution,[],[f1078,f108]) ).
fof(f2503,plain,
( spl1_311
| ~ spl1_6
| ~ spl1_130 ),
inference(avatar_split_clause,[],[f1066,f1046,f100,f2501]) ).
fof(f1066,plain,
( ! [X2,X0,X1] :
( product(product(product(X0,eh),X1),inv(X2)) = product(product(X0,eh),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) )
| ~ spl1_6
| ~ spl1_130 ),
inference(resolution,[],[f1047,f101]) ).
fof(f2499,plain,
( spl1_310
| ~ spl1_5
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1063,f1038,f96,f2497]) ).
fof(f2497,plain,
( spl1_310
<=> ! [X2,X0,X1] :
( sum(sum(sum(X0,eg),X1),f(X2)) = sum(sum(X0,eg),sum(X1,f(X2)))
| ~ h(X1)
| ~ h(X0)
| ~ g(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_310])]) ).
fof(f1063,plain,
( ! [X2,X0,X1] :
( sum(sum(sum(X0,eg),X1),f(X2)) = sum(sum(X0,eg),sum(X1,f(X2)))
| ~ h(X1)
| ~ h(X0)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_128 ),
inference(resolution,[],[f1039,f97]) ).
fof(f2495,plain,
( spl1_309
| ~ spl1_6
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1058,f1034,f100,f2493]) ).
fof(f1058,plain,
( ! [X2,X0,X1] :
( product(product(inv(inv(X0)),X1),inv(X2)) = product(inv(inv(X0)),product(X1,inv(X2)))
| ~ g(X1)
| ~ g(X0)
| ~ g(X2) )
| ~ spl1_6
| ~ spl1_127 ),
inference(resolution,[],[f1035,f101]) ).
fof(f2491,plain,
( spl1_308
| ~ spl1_6
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f1055,f1030,f100,f2489]) ).
fof(f1055,plain,
( ! [X2,X0,X1] :
( product(eh,product(product(X0,inv(X1)),X2)) = product(product(eh,product(X0,inv(X1))),X2)
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_126 ),
inference(resolution,[],[f1031,f101]) ).
fof(f2487,plain,
( spl1_307
| ~ spl1_5
| ~ spl1_125 ),
inference(avatar_split_clause,[],[f1052,f1026,f96,f2485]) ).
fof(f2485,plain,
( spl1_307
<=> ! [X2,X0,X1] :
( sum(eg,sum(sum(X0,f(X1)),X2)) = sum(sum(eg,sum(X0,f(X1))),X2)
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_307])]) ).
fof(f1052,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(sum(X0,f(X1)),X2)) = sum(sum(eg,sum(X0,f(X1))),X2)
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_125 ),
inference(resolution,[],[f1027,f97]) ).
fof(f2483,plain,
( spl1_306
| ~ spl1_18
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f894,f869,f160,f2481]) ).
fof(f2481,plain,
( spl1_306
<=> ! [X2,X0,X1] :
( sum(sum(f(X0),eg),sum(X1,X2)) = sum(f(X0),sum(eg,sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_306])]) ).
fof(f894,plain,
( ! [X2,X0,X1] :
( sum(sum(f(X0),eg),sum(X1,X2)) = sum(f(X0),sum(eg,sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_108 ),
inference(resolution,[],[f870,f161]) ).
fof(f2479,plain,
( spl1_305
| ~ spl1_18
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f888,f865,f160,f2477]) ).
fof(f2477,plain,
( spl1_305
<=> ! [X0,X3,X2,X1] :
( sum(sum(opp(X0),opp(X1)),sum(X2,X3)) = sum(opp(X0),sum(opp(X1),sum(X2,X3)))
| ~ h(X3)
| ~ h(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_305])]) ).
fof(f888,plain,
( ! [X2,X3,X0,X1] :
( sum(sum(opp(X0),opp(X1)),sum(X2,X3)) = sum(opp(X0),sum(opp(X1),sum(X2,X3)))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_107 ),
inference(resolution,[],[f866,f161]) ).
fof(f2470,plain,
( spl1_304
| ~ spl1_19
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f885,f861,f164,f2468]) ).
fof(f861,plain,
( spl1_106
<=> ! [X0,X1] :
( ~ g(X0)
| product(eh,product(inv(X1),X0)) = product(product(eh,inv(X1)),X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( product(eh,product(inv(product(X0,X1)),X2)) = product(product(eh,inv(product(X0,X1))),X2)
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_106 ),
inference(resolution,[],[f862,f165]) ).
fof(f862,plain,
( ! [X0,X1] :
( ~ g(X1)
| product(eh,product(inv(X1),X0)) = product(product(eh,inv(X1)),X0)
| ~ g(X0) )
| ~ spl1_106 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f2466,plain,
( spl1_303
| ~ spl1_18
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f876,f857,f160,f2464]) ).
fof(f2464,plain,
( spl1_303
<=> ! [X2,X0,X1] :
( sum(eg,sum(f(X0),sum(X1,X2))) = sum(sum(eg,f(X0)),sum(X1,X2))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_303])]) ).
fof(f876,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(f(X0),sum(X1,X2))) = sum(sum(eg,f(X0)),sum(X1,X2))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_105 ),
inference(resolution,[],[f858,f161]) ).
fof(f2462,plain,
( spl1_302
| ~ spl1_21
| ~ spl1_42
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f761,f725,f340,f191,f2460]) ).
fof(f2460,plain,
( spl1_302
<=> ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(f(product(X0,product(X1,X2))),eg)
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_302])]) ).
fof(f725,plain,
( spl1_89
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(sum(f(X1),X0),eg)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
fof(f761,plain,
( ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(f(product(X0,product(X1,X2))),eg)
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_89 ),
inference(forward_demodulation,[],[f759,f192]) ).
fof(f759,plain,
( ! [X2,X0,X1] :
( sum(f(X0),f(product(X1,X2))) = sum(sum(f(X0),f(product(X1,X2))),eg)
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_89 ),
inference(resolution,[],[f726,f341]) ).
fof(f726,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(sum(f(X1),X0),eg)
| ~ g(X1) )
| ~ spl1_89 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f2458,plain,
( spl1_301
| ~ spl1_21
| ~ spl1_42
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f754,f721,f340,f191,f2456]) ).
fof(f2456,plain,
( spl1_301
<=> ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(eg,f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_301])]) ).
fof(f721,plain,
( spl1_88
<=> ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(eg,sum(f(X1),X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
fof(f754,plain,
( ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(eg,f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_88 ),
inference(forward_demodulation,[],[f752,f192]) ).
fof(f752,plain,
( ! [X2,X0,X1] :
( sum(f(X0),f(product(X1,X2))) = sum(eg,sum(f(X0),f(product(X1,X2))))
| ~ g(X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_88 ),
inference(resolution,[],[f722,f341]) ).
fof(f722,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(eg,sum(f(X1),X0))
| ~ g(X1) )
| ~ spl1_88 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f2454,plain,
( spl1_300
| ~ spl1_42
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f679,f660,f340,f2452]) ).
fof(f2452,plain,
( spl1_300
<=> ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(opp(X0),sum(eg,f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_300])]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(opp(X0),sum(eg,f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_80 ),
inference(resolution,[],[f661,f341]) ).
fof(f2450,plain,
( spl1_299
| ~ spl1_42
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f673,f656,f340,f2448]) ).
fof(f2448,plain,
( spl1_299
<=> ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(sum(opp(X0),f(product(X1,X2))),eg)
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_299])]) ).
fof(f673,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(sum(opp(X0),f(product(X1,X2))),eg)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_79 ),
inference(resolution,[],[f657,f341]) ).
fof(f2446,plain,
( spl1_298
| ~ spl1_42
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f667,f652,f340,f2444]) ).
fof(f2444,plain,
( spl1_298
<=> ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(eg,sum(opp(X0),f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_298])]) ).
fof(f667,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(eg,sum(opp(X0),f(product(X1,X2))))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_78 ),
inference(resolution,[],[f653,f341]) ).
fof(f2380,plain,
( spl1_297
| ~ spl1_5
| ~ spl1_132 ),
inference(avatar_split_clause,[],[f1090,f1073,f96,f2378]) ).
fof(f2378,plain,
( spl1_297
<=> ! [X2,X0,X1] :
( sum(f(product(X0,X1)),X2) = sum(sum(f(product(X0,X1)),X2),eg)
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_297])]) ).
fof(f1090,plain,
( ! [X2,X0,X1] :
( sum(f(product(X0,X1)),X2) = sum(sum(f(product(X0,X1)),X2),eg)
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_132 ),
inference(resolution,[],[f1074,f97]) ).
fof(f2376,plain,
( spl1_296
| ~ spl1_5
| ~ spl1_131 ),
inference(avatar_split_clause,[],[f1088,f1069,f96,f2374]) ).
fof(f2374,plain,
( spl1_296
<=> ! [X2,X0,X1] :
( sum(f(product(X0,X1)),X2) = sum(eg,sum(f(product(X0,X1)),X2))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_296])]) ).
fof(f1088,plain,
( ! [X2,X0,X1] :
( sum(f(product(X0,X1)),X2) = sum(eg,sum(f(product(X0,X1)),X2))
| ~ h(X2)
| ~ h(f(X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_131 ),
inference(resolution,[],[f1070,f97]) ).
fof(f2372,plain,
( spl1_295
| ~ spl1_6
| ~ spl1_122 ),
inference(avatar_split_clause,[],[f1012,f987,f100,f2370]) ).
fof(f1012,plain,
( ! [X2,X0,X1] :
( eh = product(product(product(X0,inv(X1)),X2),inv(product(product(X0,inv(X1)),X2)))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_122 ),
inference(resolution,[],[f988,f101]) ).
fof(f2368,plain,
( spl1_294
| ~ spl1_6
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f1009,f983,f100,f2366]) ).
fof(f1009,plain,
( ! [X2,X0,X1] :
( eh = product(inv(product(product(X0,inv(X1)),X2)),product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_121 ),
inference(resolution,[],[f984,f101]) ).
fof(f2364,plain,
( spl1_293
| ~ spl1_5
| ~ spl1_120 ),
inference(avatar_split_clause,[],[f1006,f979,f96,f2362]) ).
fof(f2362,plain,
( spl1_293
<=> ! [X2,X0,X1] :
( eg = sum(sum(sum(X0,f(X1)),X2),opp(sum(sum(X0,f(X1)),X2)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_293])]) ).
fof(f1006,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(sum(X0,f(X1)),X2),opp(sum(sum(X0,f(X1)),X2)))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_120 ),
inference(resolution,[],[f980,f97]) ).
fof(f2360,plain,
( spl1_292
| ~ spl1_5
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f1001,f975,f96,f2358]) ).
fof(f2358,plain,
( spl1_292
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(sum(X0,f(X1)),X2)),sum(sum(X0,f(X1)),X2))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_292])]) ).
fof(f1001,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(sum(X0,f(X1)),X2)),sum(sum(X0,f(X1)),X2))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_119 ),
inference(resolution,[],[f976,f97]) ).
fof(f2356,plain,
( spl1_291
| ~ spl1_19
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f842,f803,f164,f2354]) ).
fof(f842,plain,
( ! [X2,X0,X1] :
( eh = product(product(inv(product(X0,X1)),X2),inv(product(inv(product(X0,X1)),X2)))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_100 ),
inference(resolution,[],[f804,f165]) ).
fof(f2352,plain,
( spl1_290
| ~ spl1_4
| ~ spl1_21
| ~ spl1_59
| ~ spl1_240 ),
inference(avatar_split_clause,[],[f2045,f1960,f481,f191,f91,f2350]) ).
fof(f2045,plain,
( ! [X0] :
( f(product(X0,eh)) = sum(sum(f(X0),eg),f(eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_21
| ~ spl1_59
| ~ spl1_240 ),
inference(forward_demodulation,[],[f2044,f192]) ).
fof(f2044,plain,
( ! [X0] :
( sum(f(X0),f(eh)) = sum(sum(f(X0),eg),f(eh))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_59
| ~ spl1_240 ),
inference(forward_demodulation,[],[f2041,f483]) ).
fof(f2041,plain,
( ! [X0] :
( ~ g(X0)
| sum(sum(f(X0),eg),f(eh)) = sum(f(X0),sum(eg,f(eh))) )
| ~ spl1_4
| ~ spl1_240 ),
inference(resolution,[],[f1961,f93]) ).
fof(f2348,plain,
( spl1_289
| ~ spl1_19
| ~ spl1_99 ),
inference(avatar_split_clause,[],[f838,f799,f164,f2346]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( eh = product(inv(product(inv(product(X0,X1)),X2)),product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_99 ),
inference(resolution,[],[f800,f165]) ).
fof(f2344,plain,
( spl1_288
| ~ spl1_18
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f829,f795,f160,f2342]) ).
fof(f2342,plain,
( spl1_288
<=> ! [X2,X0,X1] :
( eg = sum(sum(f(X0),sum(X1,X2)),opp(sum(f(X0),sum(X1,X2))))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_288])]) ).
fof(f829,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(f(X0),sum(X1,X2)),opp(sum(f(X0),sum(X1,X2))))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_98 ),
inference(resolution,[],[f796,f161]) ).
fof(f2340,plain,
( spl1_287
| ~ spl1_18
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f822,f791,f160,f2338]) ).
fof(f2338,plain,
( spl1_287
<=> ! [X2,X0,X1] :
( eg = sum(opp(sum(f(X0),sum(X1,X2))),sum(f(X0),sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_287])]) ).
fof(f822,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(f(X0),sum(X1,X2))),sum(f(X0),sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_97 ),
inference(resolution,[],[f792,f161]) ).
fof(f2336,plain,
( spl1_286
| ~ spl1_19
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f821,f787,f164,f2334]) ).
fof(f821,plain,
( ! [X2,X0,X1] :
( eh = product(inv(inv(product(X0,product(X1,X2)))),inv(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_96 ),
inference(resolution,[],[f788,f165]) ).
fof(f2332,plain,
( spl1_285
| ~ spl1_19
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f818,f783,f164,f2330]) ).
fof(f818,plain,
( ! [X2,X0,X1] :
( eh = product(inv(product(X0,product(X1,X2))),inv(inv(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_95 ),
inference(resolution,[],[f784,f165]) ).
fof(f2328,plain,
( spl1_284
| ~ spl1_19
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f815,f779,f164,f2326]) ).
fof(f815,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(f(product(X0,product(X1,X2)))),f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_94 ),
inference(resolution,[],[f780,f165]) ).
fof(f2324,plain,
( spl1_283
| ~ spl1_19
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f812,f775,f164,f2322]) ).
fof(f812,plain,
( ! [X2,X0,X1] :
( eg = sum(f(product(X0,product(X1,X2))),opp(f(product(X0,product(X1,X2)))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_93 ),
inference(resolution,[],[f776,f165]) ).
fof(f2320,plain,
( spl1_282
| ~ spl1_42
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f640,f600,f340,f2318]) ).
fof(f2318,plain,
( spl1_282
<=> ! [X0,X1] :
( eg = sum(sum(eg,f(product(X0,X1))),opp(sum(eg,f(product(X0,X1)))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_282])]) ).
fof(f640,plain,
( ! [X0,X1] :
( eg = sum(sum(eg,f(product(X0,X1))),opp(sum(eg,f(product(X0,X1)))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_75 ),
inference(resolution,[],[f601,f341]) ).
fof(f2316,plain,
( spl1_281
| ~ spl1_42
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f633,f596,f340,f2314]) ).
fof(f2314,plain,
( spl1_281
<=> ! [X0,X1] :
( eg = sum(opp(sum(eg,f(product(X0,X1)))),sum(eg,f(product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_281])]) ).
fof(f633,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(eg,f(product(X0,X1)))),sum(eg,f(product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_74 ),
inference(resolution,[],[f597,f341]) ).
fof(f2305,plain,
( spl1_280
| ~ spl1_165
| ~ spl1_203 ),
inference(avatar_split_clause,[],[f1706,f1604,f1335,f2303]) ).
fof(f2303,plain,
( spl1_280
<=> ! [X0,X1] : eg = sum(opp(X0),sum(opp(X1),opp(sum(opp(X0),opp(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_280])]) ).
fof(f1335,plain,
( spl1_165
<=> ! [X0,X1] : eg = sum(sum(opp(X0),opp(X1)),opp(sum(opp(X0),opp(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
fof(f1706,plain,
( ! [X0,X1] : eg = sum(opp(X0),sum(opp(X1),opp(sum(opp(X0),opp(X1)))))
| ~ spl1_165
| ~ spl1_203 ),
inference(superposition,[],[f1605,f1336]) ).
fof(f1336,plain,
( ! [X0,X1] : eg = sum(sum(opp(X0),opp(X1)),opp(sum(opp(X0),opp(X1))))
| ~ spl1_165 ),
inference(avatar_component_clause,[],[f1335]) ).
fof(f2260,plain,
( spl1_279
| ~ spl1_4
| ~ spl1_183 ),
inference(avatar_split_clause,[],[f1532,f1508,f91,f2258]) ).
fof(f2258,plain,
( spl1_279
<=> ! [X0] : eg = sum(sum(f(eh),opp(X0)),opp(sum(f(eh),opp(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_279])]) ).
fof(f1532,plain,
( ! [X0] : eg = sum(sum(f(eh),opp(X0)),opp(sum(f(eh),opp(X0))))
| ~ spl1_4
| ~ spl1_183 ),
inference(resolution,[],[f1509,f93]) ).
fof(f2230,plain,
( spl1_278
| ~ spl1_3
| ~ spl1_134 ),
inference(avatar_split_clause,[],[f1099,f1081,f86,f2228]) ).
fof(f2228,plain,
( spl1_278
<=> ! [X2,X0,X1] :
( sum(sum(sum(X0,opp(X1)),X2),eg) = sum(sum(X0,opp(X1)),sum(X2,eg))
| ~ h(X2)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_278])]) ).
fof(f1099,plain,
( ! [X2,X0,X1] :
( sum(sum(sum(X0,opp(X1)),X2),eg) = sum(sum(X0,opp(X1)),sum(X2,eg))
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_134 ),
inference(resolution,[],[f1082,f88]) ).
fof(f2226,plain,
( spl1_277
| ~ spl1_3
| ~ spl1_133 ),
inference(avatar_split_clause,[],[f1094,f1077,f86,f2224]) ).
fof(f1094,plain,
( ! [X2,X0,X1] :
( sum(sum(opp(X0),sum(X1,eg)),X2) = sum(opp(X0),sum(sum(X1,eg),X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_133 ),
inference(resolution,[],[f1078,f88]) ).
fof(f2222,plain,
( spl1_276
| ~ spl1_4
| ~ spl1_182 ),
inference(avatar_split_clause,[],[f1525,f1504,f91,f2220]) ).
fof(f2220,plain,
( spl1_276
<=> ! [X0] : eg = sum(opp(sum(f(eh),opp(X0))),sum(f(eh),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_276])]) ).
fof(f1525,plain,
( ! [X0] : eg = sum(opp(sum(f(eh),opp(X0))),sum(f(eh),opp(X0)))
| ~ spl1_4
| ~ spl1_182 ),
inference(resolution,[],[f1505,f93]) ).
fof(f2218,plain,
( spl1_275
| ~ spl1_8
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1061,f1038,f107,f2216]) ).
fof(f1061,plain,
( ! [X2,X0,X1] :
( sum(sum(sum(X0,eg),X1),opp(X2)) = sum(sum(X0,eg),sum(X1,opp(X2)))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_128 ),
inference(resolution,[],[f1039,f108]) ).
fof(f2214,plain,
( spl1_274
| ~ spl1_8
| ~ spl1_125 ),
inference(avatar_split_clause,[],[f1050,f1026,f107,f2212]) ).
fof(f1050,plain,
( ! [X2,X0,X1] :
( sum(eg,sum(sum(X0,opp(X1)),X2)) = sum(sum(eg,sum(X0,opp(X1))),X2)
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_125 ),
inference(resolution,[],[f1027,f108]) ).
fof(f2210,plain,
( spl1_273
| ~ spl1_5
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f971,f938,f96,f2208]) ).
fof(f971,plain,
( ! [X2,X0,X1] :
( sum(sum(f(X0),opp(X1)),f(X2)) = sum(f(X0),sum(opp(X1),f(X2)))
| ~ g(X0)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_117 ),
inference(resolution,[],[f939,f97]) ).
fof(f2206,plain,
( spl1_272
| ~ spl1_6
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f959,f930,f100,f2204]) ).
fof(f959,plain,
( ! [X2,X0,X1] :
( product(product(X0,inv(X1)),X2) = product(product(product(X0,inv(X1)),X2),eh)
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_115 ),
inference(resolution,[],[f931,f101]) ).
fof(f2202,plain,
( spl1_271
| ~ spl1_6
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f956,f926,f100,f2200]) ).
fof(f956,plain,
( ! [X2,X0,X1] :
( product(product(X0,inv(X1)),X2) = product(eh,product(product(X0,inv(X1)),X2))
| ~ g(X2)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_114 ),
inference(resolution,[],[f927,f101]) ).
fof(f2198,plain,
( spl1_270
| ~ spl1_5
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f953,f922,f96,f2196]) ).
fof(f953,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,f(X1)),X2) = sum(sum(sum(X0,f(X1)),X2),eg)
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_113 ),
inference(resolution,[],[f923,f97]) ).
fof(f2194,plain,
( spl1_269
| ~ spl1_5
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f948,f918,f96,f2192]) ).
fof(f948,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,f(X1)),X2) = sum(eg,sum(sum(X0,f(X1)),X2))
| ~ h(X2)
| ~ h(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_112 ),
inference(resolution,[],[f919,f97]) ).
fof(f2190,plain,
( spl1_268
| ~ spl1_19
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f772,f733,f164,f2188]) ).
fof(f772,plain,
( ! [X2,X0,X1] :
( product(inv(product(X0,X1)),X2) = product(product(inv(product(X0,X1)),X2),eh)
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_91 ),
inference(resolution,[],[f734,f165]) ).
fof(f2186,plain,
( spl1_267
| ~ spl1_19
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f768,f729,f164,f2184]) ).
fof(f768,plain,
( ! [X2,X0,X1] :
( product(inv(product(X0,X1)),X2) = product(eh,product(inv(product(X0,X1)),X2))
| ~ g(X2)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_90 ),
inference(resolution,[],[f730,f165]) ).
fof(f2182,plain,
( spl1_266
| ~ spl1_18
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f755,f725,f160,f2180]) ).
fof(f755,plain,
( ! [X2,X0,X1] :
( sum(f(X0),sum(X1,X2)) = sum(sum(f(X0),sum(X1,X2)),eg)
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_89 ),
inference(resolution,[],[f726,f161]) ).
fof(f2178,plain,
( spl1_265
| ~ spl1_4
| ~ spl1_181 ),
inference(avatar_split_clause,[],[f1522,f1500,f91,f2176]) ).
fof(f2176,plain,
( spl1_265
<=> ! [X0] : eg = sum(sum(opp(X0),f(eh)),opp(sum(opp(X0),f(eh)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_265])]) ).
fof(f1522,plain,
( ! [X0] : eg = sum(sum(opp(X0),f(eh)),opp(sum(opp(X0),f(eh))))
| ~ spl1_4
| ~ spl1_181 ),
inference(resolution,[],[f1501,f93]) ).
fof(f2174,plain,
( spl1_264
| ~ spl1_18
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f748,f721,f160,f2172]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( sum(f(X0),sum(X1,X2)) = sum(eg,sum(f(X0),sum(X1,X2)))
| ~ g(X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_88 ),
inference(resolution,[],[f722,f161]) ).
fof(f2170,plain,
( spl1_263
| ~ spl1_19
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f747,f713,f164,f2168]) ).
fof(f747,plain,
( ! [X2,X0,X1] :
( inv(product(X0,product(X1,X2))) = product(eh,inv(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_86 ),
inference(resolution,[],[f714,f165]) ).
fof(f2166,plain,
( spl1_262
| ~ spl1_19
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f744,f709,f164,f2164]) ).
fof(f744,plain,
( ! [X2,X0,X1] :
( inv(product(X0,product(X1,X2))) = product(inv(product(X0,product(X1,X2))),eh)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_85 ),
inference(resolution,[],[f710,f165]) ).
fof(f2162,plain,
( spl1_261
| ~ spl1_19
| ~ spl1_84 ),
inference(avatar_split_clause,[],[f741,f705,f164,f2160]) ).
fof(f741,plain,
( ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(eg,f(product(X0,product(X1,X2))))
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_84 ),
inference(resolution,[],[f706,f165]) ).
fof(f2158,plain,
( spl1_260
| ~ spl1_19
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f738,f701,f164,f2156]) ).
fof(f738,plain,
( ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = sum(f(product(X0,product(X1,X2))),eg)
| ~ g(X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_83 ),
inference(resolution,[],[f702,f165]) ).
fof(f2154,plain,
( spl1_259
| ~ spl1_42
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f568,f528,f340,f2152]) ).
fof(f2152,plain,
( spl1_259
<=> ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(product(X0,X1))),eg)
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_259])]) ).
fof(f568,plain,
( ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(product(X0,X1))),eg)
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_67 ),
inference(resolution,[],[f529,f341]) ).
fof(f2150,plain,
( spl1_258
| ~ spl1_42
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f561,f524,f340,f2148]) ).
fof(f2148,plain,
( spl1_258
<=> ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(eg,sum(eg,f(product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_258])]) ).
fof(f561,plain,
( ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(eg,sum(eg,f(product(X0,X1))))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_42
| ~ spl1_66 ),
inference(resolution,[],[f525,f341]) ).
fof(f2133,plain,
( spl1_257
| ~ spl1_4
| ~ spl1_180 ),
inference(avatar_split_clause,[],[f1519,f1496,f91,f2131]) ).
fof(f2131,plain,
( spl1_257
<=> ! [X0] : eg = sum(opp(sum(opp(X0),f(eh))),sum(opp(X0),f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_257])]) ).
fof(f1519,plain,
( ! [X0] : eg = sum(opp(sum(opp(X0),f(eh))),sum(opp(X0),f(eh)))
| ~ spl1_4
| ~ spl1_180 ),
inference(resolution,[],[f1497,f93]) ).
fof(f2116,plain,
( spl1_256
| ~ spl1_8
| ~ spl1_124 ),
inference(avatar_split_clause,[],[f1015,f995,f107,f2114]) ).
fof(f1015,plain,
( ! [X2,X0,X1] :
( sum(f(product(X0,X1)),opp(X2)) = sum(f(X0),sum(f(X1),opp(X2)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_8
| ~ spl1_124 ),
inference(resolution,[],[f996,f108]) ).
fof(f2112,plain,
( spl1_255
| ~ spl1_8
| ~ spl1_120 ),
inference(avatar_split_clause,[],[f1004,f979,f107,f2110]) ).
fof(f1004,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(sum(X0,opp(X1)),X2),opp(sum(sum(X0,opp(X1)),X2)))
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_120 ),
inference(resolution,[],[f980,f108]) ).
fof(f2108,plain,
( spl1_254
| ~ spl1_8
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f999,f975,f107,f2106]) ).
fof(f999,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(sum(X0,opp(X1)),X2)),sum(sum(X0,opp(X1)),X2))
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_119 ),
inference(resolution,[],[f976,f108]) ).
fof(f2104,plain,
( spl1_253
| ~ spl1_5
| ~ spl1_21
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f966,f934,f191,f96,f2102]) ).
fof(f966,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),f(product(X1,X2))) = sum(sum(opp(X0),f(X1)),f(X2))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_116 ),
inference(forward_demodulation,[],[f964,f192]) ).
fof(f964,plain,
( ! [X2,X0,X1] :
( sum(sum(opp(X0),f(X1)),f(X2)) = sum(opp(X0),sum(f(X1),f(X2)))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_116 ),
inference(resolution,[],[f935,f97]) ).
fof(f2100,plain,
( spl1_252
| ~ spl1_18
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f694,f685,f160,f2098]) ).
fof(f694,plain,
( ! [X2,X0,X1] :
( eg = sum(sum(opp(X0),sum(X1,X2)),opp(sum(opp(X0),sum(X1,X2))))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_82 ),
inference(resolution,[],[f686,f161]) ).
fof(f2096,plain,
( spl1_251
| ~ spl1_18
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f688,f681,f160,f2094]) ).
fof(f688,plain,
( ! [X2,X0,X1] :
( eg = sum(opp(sum(opp(X0),sum(X1,X2))),sum(opp(X0),sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_81 ),
inference(resolution,[],[f682,f161]) ).
fof(f2014,plain,
( spl1_250
| ~ spl1_4
| ~ spl1_130 ),
inference(avatar_split_clause,[],[f1065,f1046,f91,f2012]) ).
fof(f2012,plain,
( spl1_250
<=> ! [X0,X1] :
( product(product(product(X0,eh),X1),eh) = product(product(X0,eh),product(X1,eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_250])]) ).
fof(f1065,plain,
( ! [X0,X1] :
( product(product(product(X0,eh),X1),eh) = product(product(X0,eh),product(X1,eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_130 ),
inference(resolution,[],[f1047,f93]) ).
fof(f2010,plain,
( spl1_249
| ~ spl1_3
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1062,f1038,f86,f2008]) ).
fof(f2008,plain,
( spl1_249
<=> ! [X0,X1] :
( sum(sum(sum(X0,eg),X1),eg) = sum(sum(X0,eg),sum(X1,eg))
| ~ h(X1)
| ~ h(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_249])]) ).
fof(f1062,plain,
( ! [X0,X1] :
( sum(sum(sum(X0,eg),X1),eg) = sum(sum(X0,eg),sum(X1,eg))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_128 ),
inference(resolution,[],[f1039,f88]) ).
fof(f2006,plain,
( spl1_248
| ~ spl1_4
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1057,f1034,f91,f2004]) ).
fof(f2004,plain,
( spl1_248
<=> ! [X0,X1] :
( product(product(inv(inv(X0)),X1),eh) = product(inv(inv(X0)),product(X1,eh))
| ~ g(X1)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_248])]) ).
fof(f1057,plain,
( ! [X0,X1] :
( product(product(inv(inv(X0)),X1),eh) = product(inv(inv(X0)),product(X1,eh))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_127 ),
inference(resolution,[],[f1035,f93]) ).
fof(f2002,plain,
( spl1_247
| ~ spl1_4
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f1054,f1030,f91,f2000]) ).
fof(f1054,plain,
( ! [X0,X1] :
( product(eh,product(product(X0,eh),X1)) = product(product(eh,product(X0,eh)),X1)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_126 ),
inference(resolution,[],[f1031,f93]) ).
fof(f1998,plain,
( spl1_246
| ~ spl1_3
| ~ spl1_125 ),
inference(avatar_split_clause,[],[f1051,f1026,f86,f1996]) ).
fof(f1051,plain,
( ! [X0,X1] :
( sum(eg,sum(sum(X0,eg),X1)) = sum(sum(eg,sum(X0,eg)),X1)
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_125 ),
inference(resolution,[],[f1027,f88]) ).
fof(f1982,plain,
( spl1_245
| ~ spl1_5
| ~ spl1_21
| ~ spl1_124 ),
inference(avatar_split_clause,[],[f1021,f995,f191,f96,f1980]) ).
fof(f1021,plain,
( ! [X2,X0,X1] :
( f(product(X0,product(X1,X2))) = f(product(product(X0,X1),X2))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1020,f192]) ).
fof(f1020,plain,
( ! [X2,X0,X1] :
( sum(f(X0),f(product(X1,X2))) = f(product(product(X0,X1),X2))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1019,f192]) ).
fof(f1019,plain,
( ! [X2,X0,X1] :
( sum(f(X0),f(product(X1,X2))) = sum(f(product(X0,X1)),f(X2))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_124 ),
inference(forward_demodulation,[],[f1017,f192]) ).
fof(f1017,plain,
( ! [X2,X0,X1] :
( sum(f(product(X0,X1)),f(X2)) = sum(f(X0),sum(f(X1),f(X2)))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_124 ),
inference(resolution,[],[f996,f97]) ).
fof(f1978,plain,
( spl1_244
| ~ spl1_8
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f969,f938,f107,f1976]) ).
fof(f969,plain,
( ! [X2,X0,X1] :
( sum(sum(f(X0),opp(X1)),opp(X2)) = sum(f(X0),sum(opp(X1),opp(X2)))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_117 ),
inference(resolution,[],[f939,f108]) ).
fof(f1974,plain,
( spl1_243
| ~ spl1_8
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f962,f934,f107,f1972]) ).
fof(f962,plain,
( ! [X2,X0,X1] :
( sum(sum(opp(X0),f(X1)),opp(X2)) = sum(opp(X0),sum(f(X1),opp(X2)))
| ~ g(X1) )
| ~ spl1_8
| ~ spl1_116 ),
inference(resolution,[],[f935,f108]) ).
fof(f1970,plain,
( spl1_242
| ~ spl1_8
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f951,f922,f107,f1968]) ).
fof(f951,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),X2) = sum(sum(sum(X0,opp(X1)),X2),eg)
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_113 ),
inference(resolution,[],[f923,f108]) ).
fof(f1966,plain,
( spl1_241
| ~ spl1_8
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f946,f918,f107,f1964]) ).
fof(f946,plain,
( ! [X2,X0,X1] :
( sum(sum(X0,opp(X1)),X2) = sum(eg,sum(sum(X0,opp(X1)),X2))
| ~ h(X2)
| ~ h(X0) )
| ~ spl1_8
| ~ spl1_112 ),
inference(resolution,[],[f919,f108]) ).
fof(f1962,plain,
( spl1_240
| ~ spl1_5
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f897,f869,f96,f1960]) ).
fof(f897,plain,
( ! [X0,X1] :
( sum(sum(f(X0),eg),f(X1)) = sum(f(X0),sum(eg,f(X1)))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_108 ),
inference(resolution,[],[f870,f97]) ).
fof(f1958,plain,
( spl1_239
| ~ spl1_5
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f891,f865,f96,f1956]) ).
fof(f891,plain,
( ! [X2,X0,X1] :
( sum(sum(opp(X0),opp(X1)),f(X2)) = sum(opp(X0),sum(opp(X1),f(X2)))
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_107 ),
inference(resolution,[],[f866,f97]) ).
fof(f1954,plain,
( spl1_238
| ~ spl1_6
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f884,f861,f100,f1952]) ).
fof(f884,plain,
( ! [X0,X1] :
( product(eh,product(inv(inv(X0)),X1)) = product(product(eh,inv(inv(X0))),X1)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_106 ),
inference(resolution,[],[f862,f101]) ).
fof(f1950,plain,
( spl1_237
| ~ spl1_18
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f675,f660,f160,f1948]) ).
fof(f675,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(opp(X0),sum(eg,sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_80 ),
inference(resolution,[],[f661,f161]) ).
fof(f1946,plain,
( spl1_236
| ~ spl1_18
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f669,f656,f160,f1944]) ).
fof(f669,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(sum(opp(X0),sum(X1,X2)),eg)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_79 ),
inference(resolution,[],[f657,f161]) ).
fof(f1916,plain,
( spl1_235
| ~ spl1_18
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f663,f652,f160,f1914]) ).
fof(f663,plain,
( ! [X2,X0,X1] :
( sum(opp(X0),sum(X1,X2)) = sum(eg,sum(opp(X0),sum(X1,X2)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_78 ),
inference(resolution,[],[f653,f161]) ).
fof(f1878,plain,
( spl1_234
| ~ spl1_28
| ~ spl1_31
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f1837,f1743,f258,f239,f1876]) ).
fof(f1876,plain,
( spl1_234
<=> ! [X0] : opp(X0) = opp(opp(opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_234])]) ).
fof(f1743,plain,
( spl1_213
<=> ! [X0,X1] : opp(X1) = sum(opp(X0),sum(opp(opp(X0)),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_213])]) ).
fof(f1837,plain,
( ! [X0] : opp(X0) = opp(opp(opp(X0)))
| ~ spl1_28
| ~ spl1_31
| ~ spl1_213 ),
inference(forward_demodulation,[],[f1832,f240]) ).
fof(f1832,plain,
( ! [X0] : sum(opp(X0),eg) = opp(opp(opp(X0)))
| ~ spl1_31
| ~ spl1_213 ),
inference(superposition,[],[f1744,f259]) ).
fof(f1744,plain,
( ! [X0,X1] : opp(X1) = sum(opp(X0),sum(opp(opp(X0)),opp(X1)))
| ~ spl1_213 ),
inference(avatar_component_clause,[],[f1743]) ).
fof(f1825,plain,
( spl1_233
| ~ spl1_3
| ~ spl1_124 ),
inference(avatar_split_clause,[],[f1016,f995,f86,f1823]) ).
fof(f1823,plain,
( spl1_233
<=> ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(f(X0),sum(f(X1),eg))
| ~ g(X0)
| ~ g(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_233])]) ).
fof(f1016,plain,
( ! [X0,X1] :
( sum(f(product(X0,X1)),eg) = sum(f(X0),sum(f(X1),eg))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_124 ),
inference(resolution,[],[f996,f88]) ).
fof(f1821,plain,
( spl1_232
| ~ spl1_4
| ~ spl1_122 ),
inference(avatar_split_clause,[],[f1011,f987,f91,f1819]) ).
fof(f1011,plain,
( ! [X0,X1] :
( eh = product(product(product(X0,eh),X1),inv(product(product(X0,eh),X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_122 ),
inference(resolution,[],[f988,f93]) ).
fof(f1817,plain,
( spl1_231
| ~ spl1_4
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f1008,f983,f91,f1815]) ).
fof(f1008,plain,
( ! [X0,X1] :
( eh = product(inv(product(product(X0,eh),X1)),product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_121 ),
inference(resolution,[],[f984,f93]) ).
fof(f1813,plain,
( spl1_230
| ~ spl1_3
| ~ spl1_120 ),
inference(avatar_split_clause,[],[f1005,f979,f86,f1811]) ).
fof(f1005,plain,
( ! [X0,X1] :
( eg = sum(sum(sum(X0,eg),X1),opp(sum(sum(X0,eg),X1)))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_120 ),
inference(resolution,[],[f980,f88]) ).
fof(f1809,plain,
( spl1_229
| ~ spl1_3
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f1000,f975,f86,f1807]) ).
fof(f1000,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(sum(X0,eg),X1)),sum(sum(X0,eg),X1))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_119 ),
inference(resolution,[],[f976,f88]) ).
fof(f1805,plain,
( spl1_228
| ~ spl1_5
| ~ spl1_21
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f881,f857,f191,f96,f1803]) ).
fof(f881,plain,
( ! [X0,X1] :
( sum(eg,f(product(X0,X1))) = sum(sum(eg,f(X0)),f(X1))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_105 ),
inference(forward_demodulation,[],[f879,f192]) ).
fof(f879,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X0),f(X1))) = sum(sum(eg,f(X0)),f(X1))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_105 ),
inference(resolution,[],[f858,f97]) ).
fof(f1801,plain,
( spl1_227
| ~ spl1_6
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f841,f803,f100,f1799]) ).
fof(f841,plain,
( ! [X0,X1] :
( eh = product(product(inv(inv(X0)),X1),inv(product(inv(inv(X0)),X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_100 ),
inference(resolution,[],[f804,f101]) ).
fof(f1797,plain,
( spl1_226
| ~ spl1_6
| ~ spl1_99 ),
inference(avatar_split_clause,[],[f837,f799,f100,f1795]) ).
fof(f837,plain,
( ! [X0,X1] :
( eh = product(inv(product(inv(inv(X0)),X1)),product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_99 ),
inference(resolution,[],[f800,f101]) ).
fof(f1793,plain,
( spl1_225
| ~ spl1_6
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f820,f787,f100,f1791]) ).
fof(f820,plain,
( ! [X0,X1] :
( eh = product(inv(inv(product(X0,inv(X1)))),inv(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_96 ),
inference(resolution,[],[f788,f101]) ).
fof(f1789,plain,
( spl1_224
| ~ spl1_29
| ~ spl1_32
| ~ spl1_203 ),
inference(avatar_split_clause,[],[f1712,f1604,f262,f243,f1787]) ).
fof(f1787,plain,
( spl1_224
<=> ! [X0,X1] : opp(X1) = sum(opp(opp(X0)),sum(opp(X0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_224])]) ).
fof(f1712,plain,
( ! [X0,X1] : opp(X1) = sum(opp(opp(X0)),sum(opp(X0),opp(X1)))
| ~ spl1_29
| ~ spl1_32
| ~ spl1_203 ),
inference(forward_demodulation,[],[f1704,f244]) ).
fof(f1704,plain,
( ! [X0,X1] : sum(eg,opp(X1)) = sum(opp(opp(X0)),sum(opp(X0),opp(X1)))
| ~ spl1_32
| ~ spl1_203 ),
inference(superposition,[],[f1605,f263]) ).
fof(f1785,plain,
( spl1_223
| ~ spl1_6
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f817,f783,f100,f1783]) ).
fof(f817,plain,
( ! [X0,X1] :
( eh = product(inv(product(X0,inv(X1))),inv(inv(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_95 ),
inference(resolution,[],[f784,f101]) ).
fof(f1781,plain,
( spl1_222
| ~ spl1_6
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f814,f779,f100,f1779]) ).
fof(f814,plain,
( ! [X0,X1] :
( eg = sum(opp(f(product(X0,inv(X1)))),f(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_94 ),
inference(resolution,[],[f780,f101]) ).
fof(f1777,plain,
( spl1_221
| ~ spl1_6
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f811,f775,f100,f1775]) ).
fof(f811,plain,
( ! [X0,X1] :
( eg = sum(f(product(X0,inv(X1))),opp(f(product(X0,inv(X1)))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_93 ),
inference(resolution,[],[f776,f101]) ).
fof(f1773,plain,
( spl1_220
| ~ spl1_19
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f649,f608,f164,f1771]) ).
fof(f608,plain,
( spl1_77
<=> ! [X0] :
( ~ g(X0)
| eh = product(product(eh,X0),inv(product(eh,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
fof(f649,plain,
( ! [X0,X1] :
( eh = product(product(eh,product(X0,X1)),inv(product(eh,product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_77 ),
inference(resolution,[],[f609,f165]) ).
fof(f609,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(eh,X0),inv(product(eh,X0))) )
| ~ spl1_77 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f1769,plain,
( spl1_219
| ~ spl1_19
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f645,f604,f164,f1767]) ).
fof(f604,plain,
( spl1_76
<=> ! [X0] :
( ~ g(X0)
| eh = product(inv(product(eh,X0)),product(eh,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_76])]) ).
fof(f645,plain,
( ! [X0,X1] :
( eh = product(inv(product(eh,product(X0,X1))),product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_76 ),
inference(resolution,[],[f605,f165]) ).
fof(f605,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(eh,X0)),product(eh,X0)) )
| ~ spl1_76 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f1765,plain,
( spl1_218
| ~ spl1_18
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f636,f600,f160,f1763]) ).
fof(f636,plain,
( ! [X0,X1] :
( eg = sum(sum(eg,sum(X0,X1)),opp(sum(eg,sum(X0,X1))))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_18
| ~ spl1_75 ),
inference(resolution,[],[f601,f161]) ).
fof(f1761,plain,
( spl1_217
| ~ spl1_18
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f629,f596,f160,f1759]) ).
fof(f629,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(eg,sum(X0,X1))),sum(eg,sum(X0,X1)))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_18
| ~ spl1_74 ),
inference(resolution,[],[f597,f161]) ).
fof(f1757,plain,
( spl1_216
| ~ spl1_19
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f626,f592,f164,f1755]) ).
fof(f626,plain,
( ! [X0,X1] :
( eh = product(inv(inv(inv(product(X0,X1)))),inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_73 ),
inference(resolution,[],[f593,f165]) ).
fof(f1753,plain,
( spl1_215
| ~ spl1_19
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f621,f588,f164,f1751]) ).
fof(f621,plain,
( ! [X0,X1] :
( eh = product(inv(inv(product(X0,X1))),inv(inv(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_72 ),
inference(resolution,[],[f589,f165]) ).
fof(f1749,plain,
( spl1_214
| ~ spl1_19
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f617,f584,f164,f1747]) ).
fof(f617,plain,
( ! [X0,X1] :
( eg = sum(opp(f(inv(product(X0,X1)))),f(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_71 ),
inference(resolution,[],[f585,f165]) ).
fof(f1745,plain,
( spl1_213
| ~ spl1_29
| ~ spl1_31
| ~ spl1_203 ),
inference(avatar_split_clause,[],[f1711,f1604,f258,f243,f1743]) ).
fof(f1711,plain,
( ! [X0,X1] : opp(X1) = sum(opp(X0),sum(opp(opp(X0)),opp(X1)))
| ~ spl1_29
| ~ spl1_31
| ~ spl1_203 ),
inference(forward_demodulation,[],[f1703,f244]) ).
fof(f1703,plain,
( ! [X0,X1] : sum(eg,opp(X1)) = sum(opp(X0),sum(opp(opp(X0)),opp(X1)))
| ~ spl1_31
| ~ spl1_203 ),
inference(superposition,[],[f1605,f259]) ).
fof(f1741,plain,
( spl1_212
| ~ spl1_19
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f613,f580,f164,f1739]) ).
fof(f613,plain,
( ! [X0,X1] :
( eg = sum(f(inv(product(X0,X1))),opp(f(inv(product(X0,X1)))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_70 ),
inference(resolution,[],[f581,f165]) ).
fof(f1638,plain,
( spl1_211
| ~ spl1_3
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f963,f934,f86,f1636]) ).
fof(f963,plain,
( ! [X0,X1] :
( sum(sum(opp(X0),f(X1)),eg) = sum(opp(X0),sum(f(X1),eg))
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_116 ),
inference(resolution,[],[f935,f88]) ).
fof(f1634,plain,
( spl1_210
| ~ spl1_4
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f958,f930,f91,f1632]) ).
fof(f958,plain,
( ! [X0,X1] :
( product(product(X0,eh),X1) = product(product(product(X0,eh),X1),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_115 ),
inference(resolution,[],[f931,f93]) ).
fof(f1630,plain,
( spl1_209
| ~ spl1_4
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f955,f926,f91,f1628]) ).
fof(f955,plain,
( ! [X0,X1] :
( product(product(X0,eh),X1) = product(eh,product(product(X0,eh),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_114 ),
inference(resolution,[],[f927,f93]) ).
fof(f1626,plain,
( spl1_208
| ~ spl1_3
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f952,f922,f86,f1624]) ).
fof(f952,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),X1) = sum(sum(sum(X0,eg),X1),eg)
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_113 ),
inference(resolution,[],[f923,f88]) ).
fof(f1622,plain,
( spl1_207
| ~ spl1_3
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f947,f918,f86,f1620]) ).
fof(f947,plain,
( ! [X0,X1] :
( sum(sum(X0,eg),X1) = sum(eg,sum(sum(X0,eg),X1))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_112 ),
inference(resolution,[],[f919,f88]) ).
fof(f1618,plain,
( spl1_206
| ~ spl1_5
| ~ spl1_111 ),
inference(avatar_split_clause,[],[f915,f910,f96,f1616]) ).
fof(f915,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_111 ),
inference(resolution,[],[f911,f97]) ).
fof(f1614,plain,
( spl1_205
| ~ spl1_4
| ~ spl1_176 ),
inference(avatar_split_clause,[],[f1480,f1457,f91,f1612]) ).
fof(f1612,plain,
( spl1_205
<=> ! [X0] : sum(f(eh),opp(X0)) = sum(sum(f(eh),opp(X0)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_205])]) ).
fof(f1480,plain,
( ! [X0] : sum(f(eh),opp(X0)) = sum(sum(f(eh),opp(X0)),eg)
| ~ spl1_4
| ~ spl1_176 ),
inference(resolution,[],[f1458,f93]) ).
fof(f1610,plain,
( spl1_204
| ~ spl1_5
| ~ spl1_110 ),
inference(avatar_split_clause,[],[f913,f906,f96,f1608]) ).
fof(f913,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_110 ),
inference(resolution,[],[f907,f97]) ).
fof(f1606,plain,
( spl1_203
| ~ spl1_8
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f889,f865,f107,f1604]) ).
fof(f889,plain,
( ! [X2,X0,X1] : sum(sum(opp(X0),opp(X1)),opp(X2)) = sum(opp(X0),sum(opp(X1),opp(X2)))
| ~ spl1_8
| ~ spl1_107 ),
inference(resolution,[],[f866,f108]) ).
fof(f1602,plain,
( spl1_202
| ~ spl1_8
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f877,f857,f107,f1600]) ).
fof(f877,plain,
( ! [X0,X1] :
( sum(eg,sum(f(X0),opp(X1))) = sum(sum(eg,f(X0)),opp(X1))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_105 ),
inference(resolution,[],[f858,f108]) ).
fof(f1598,plain,
( spl1_201
| ~ spl1_6
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f771,f733,f100,f1596]) ).
fof(f771,plain,
( ! [X0,X1] :
( product(inv(inv(X0)),X1) = product(product(inv(inv(X0)),X1),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_91 ),
inference(resolution,[],[f734,f101]) ).
fof(f1594,plain,
( spl1_200
| ~ spl1_6
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f767,f729,f100,f1592]) ).
fof(f767,plain,
( ! [X0,X1] :
( product(inv(inv(X0)),X1) = product(eh,product(inv(inv(X0)),X1))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_90 ),
inference(resolution,[],[f730,f101]) ).
fof(f1590,plain,
( spl1_199
| ~ spl1_6
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f746,f713,f100,f1588]) ).
fof(f746,plain,
( ! [X0,X1] :
( inv(product(X0,inv(X1))) = product(eh,inv(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_86 ),
inference(resolution,[],[f714,f101]) ).
fof(f1586,plain,
( spl1_198
| ~ spl1_6
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f743,f709,f100,f1584]) ).
fof(f743,plain,
( ! [X0,X1] :
( inv(product(X0,inv(X1))) = product(inv(product(X0,inv(X1))),eh)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_85 ),
inference(resolution,[],[f710,f101]) ).
fof(f1582,plain,
( spl1_197
| ~ spl1_6
| ~ spl1_84 ),
inference(avatar_split_clause,[],[f740,f705,f100,f1580]) ).
fof(f740,plain,
( ! [X0,X1] :
( f(product(X0,inv(X1))) = sum(eg,f(product(X0,inv(X1))))
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_84 ),
inference(resolution,[],[f706,f101]) ).
fof(f1578,plain,
( spl1_196
| ~ spl1_6
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f737,f701,f100,f1576]) ).
fof(f737,plain,
( ! [X0,X1] :
( f(product(X0,inv(X1))) = sum(f(product(X0,inv(X1))),eg)
| ~ g(X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_83 ),
inference(resolution,[],[f702,f101]) ).
fof(f1574,plain,
( spl1_195
| ~ spl1_19
| ~ spl1_69 ),
inference(avatar_split_clause,[],[f577,f536,f164,f1572]) ).
fof(f536,plain,
( spl1_69
<=> ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(product(eh,X0),eh) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
fof(f577,plain,
( ! [X0,X1] :
( product(eh,product(X0,X1)) = product(product(eh,product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_69 ),
inference(resolution,[],[f537,f165]) ).
fof(f537,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(product(eh,X0),eh) )
| ~ spl1_69 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f1570,plain,
( spl1_194
| ~ spl1_4
| ~ spl1_175 ),
inference(avatar_split_clause,[],[f1477,f1453,f91,f1568]) ).
fof(f1568,plain,
( spl1_194
<=> ! [X0] : sum(f(eh),opp(X0)) = sum(eg,sum(f(eh),opp(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_194])]) ).
fof(f1477,plain,
( ! [X0] : sum(f(eh),opp(X0)) = sum(eg,sum(f(eh),opp(X0)))
| ~ spl1_4
| ~ spl1_175 ),
inference(resolution,[],[f1454,f93]) ).
fof(f1566,plain,
( spl1_193
| ~ spl1_19
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f573,f532,f164,f1564]) ).
fof(f532,plain,
( spl1_68
<=> ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(eh,product(eh,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
fof(f573,plain,
( ! [X0,X1] :
( product(eh,product(X0,X1)) = product(eh,product(eh,product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_68 ),
inference(resolution,[],[f533,f165]) ).
fof(f533,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(eh,product(eh,X0)) )
| ~ spl1_68 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f1562,plain,
( spl1_192
| ~ spl1_18
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f564,f528,f160,f1560]) ).
fof(f564,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,X1)) = sum(sum(eg,sum(X0,X1)),eg)
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_18
| ~ spl1_67 ),
inference(resolution,[],[f529,f161]) ).
fof(f1558,plain,
( spl1_191
| ~ spl1_18
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f557,f524,f160,f1556]) ).
fof(f557,plain,
( ! [X0,X1] :
( sum(eg,sum(X0,X1)) = sum(eg,sum(eg,sum(X0,X1)))
| ~ h(X1)
| ~ h(X0) )
| ~ spl1_18
| ~ spl1_66 ),
inference(resolution,[],[f525,f161]) ).
fof(f1554,plain,
( spl1_190
| ~ spl1_19
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f554,f520,f164,f1552]) ).
fof(f554,plain,
( ! [X0,X1] :
( inv(inv(product(X0,X1))) = product(eh,inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_65 ),
inference(resolution,[],[f521,f165]) ).
fof(f1550,plain,
( spl1_189
| ~ spl1_19
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f549,f516,f164,f1548]) ).
fof(f549,plain,
( ! [X0,X1] :
( inv(inv(product(X0,X1))) = product(inv(inv(product(X0,X1))),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_64 ),
inference(resolution,[],[f517,f165]) ).
fof(f1546,plain,
( spl1_188
| ~ spl1_19
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f545,f512,f164,f1544]) ).
fof(f545,plain,
( ! [X0,X1] :
( f(inv(product(X0,X1))) = sum(eg,f(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_63 ),
inference(resolution,[],[f513,f165]) ).
fof(f1542,plain,
( spl1_187
| ~ spl1_19
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f541,f508,f164,f1540]) ).
fof(f541,plain,
( ! [X0,X1] :
( f(inv(product(X0,X1))) = sum(f(inv(product(X0,X1))),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_62 ),
inference(resolution,[],[f509,f165]) ).
fof(f1531,plain,
( spl1_186
| ~ spl1_4
| ~ spl1_173 ),
inference(avatar_split_clause,[],[f1471,f1445,f91,f1529]) ).
fof(f1529,plain,
( spl1_186
<=> ! [X0] : sum(opp(X0),f(eh)) = sum(sum(opp(X0),f(eh)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_186])]) ).
fof(f1471,plain,
( ! [X0] : sum(opp(X0),f(eh)) = sum(sum(opp(X0),f(eh)),eg)
| ~ spl1_4
| ~ spl1_173 ),
inference(resolution,[],[f1446,f93]) ).
fof(f1518,plain,
( spl1_185
| ~ spl1_5
| ~ spl1_103 ),
inference(avatar_split_clause,[],[f874,f849,f96,f1516]) ).
fof(f874,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_103 ),
inference(resolution,[],[f850,f97]) ).
fof(f1514,plain,
( spl1_184
| ~ spl1_5
| ~ spl1_102 ),
inference(avatar_split_clause,[],[f872,f845,f96,f1512]) ).
fof(f872,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_102 ),
inference(resolution,[],[f846,f97]) ).
fof(f1510,plain,
( spl1_183
| ~ spl1_8
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f830,f795,f107,f1508]) ).
fof(f830,plain,
( ! [X0,X1] :
( eg = sum(sum(f(X0),opp(X1)),opp(sum(f(X0),opp(X1))))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_98 ),
inference(resolution,[],[f796,f108]) ).
fof(f1506,plain,
( spl1_182
| ~ spl1_8
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f823,f791,f107,f1504]) ).
fof(f823,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(f(X0),opp(X1))),sum(f(X0),opp(X1)))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_97 ),
inference(resolution,[],[f792,f108]) ).
fof(f1502,plain,
( spl1_181
| ~ spl1_5
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f697,f685,f96,f1500]) ).
fof(f697,plain,
( ! [X0,X1] :
( eg = sum(sum(opp(X0),f(X1)),opp(sum(opp(X0),f(X1))))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_82 ),
inference(resolution,[],[f686,f97]) ).
fof(f1498,plain,
( spl1_180
| ~ spl1_5
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f691,f681,f96,f1496]) ).
fof(f691,plain,
( ! [X0,X1] :
( eg = sum(opp(sum(opp(X0),f(X1))),sum(opp(X0),f(X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_81 ),
inference(resolution,[],[f682,f97]) ).
fof(f1491,plain,
( spl1_179
| ~ spl1_4
| ~ spl1_172 ),
inference(avatar_split_clause,[],[f1468,f1441,f91,f1489]) ).
fof(f1489,plain,
( spl1_179
<=> ! [X0] : sum(opp(X0),f(eh)) = sum(eg,sum(opp(X0),f(eh))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_179])]) ).
fof(f1468,plain,
( ! [X0] : sum(opp(X0),f(eh)) = sum(eg,sum(opp(X0),f(eh)))
| ~ spl1_4
| ~ spl1_172 ),
inference(resolution,[],[f1442,f93]) ).
fof(f1467,plain,
( spl1_178
| ~ spl1_8
| ~ spl1_29
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f899,f869,f243,f107,f1465]) ).
fof(f899,plain,
( ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(sum(f(X0),eg),opp(X1))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_29
| ~ spl1_108 ),
inference(forward_demodulation,[],[f895,f244]) ).
fof(f895,plain,
( ! [X0,X1] :
( sum(sum(f(X0),eg),opp(X1)) = sum(f(X0),sum(eg,opp(X1)))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_108 ),
inference(resolution,[],[f870,f108]) ).
fof(f1463,plain,
( spl1_177
| ~ spl1_3
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f878,f857,f86,f1461]) ).
fof(f878,plain,
( ! [X0] :
( sum(sum(eg,f(X0)),eg) = sum(eg,sum(f(X0),eg))
| ~ g(X0) )
| ~ spl1_3
| ~ spl1_105 ),
inference(resolution,[],[f858,f88]) ).
fof(f1459,plain,
( spl1_176
| ~ spl1_8
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f756,f725,f107,f1457]) ).
fof(f756,plain,
( ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(sum(f(X0),opp(X1)),eg)
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_89 ),
inference(resolution,[],[f726,f108]) ).
fof(f1455,plain,
( spl1_175
| ~ spl1_8
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f749,f721,f107,f1453]) ).
fof(f749,plain,
( ! [X0,X1] :
( sum(f(X0),opp(X1)) = sum(eg,sum(f(X0),opp(X1)))
| ~ g(X0) )
| ~ spl1_8
| ~ spl1_88 ),
inference(resolution,[],[f722,f108]) ).
fof(f1451,plain,
( spl1_174
| ~ spl1_5
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f678,f660,f96,f1449]) ).
fof(f678,plain,
( ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(opp(X0),sum(eg,f(X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_80 ),
inference(resolution,[],[f661,f97]) ).
fof(f1447,plain,
( spl1_173
| ~ spl1_5
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f672,f656,f96,f1445]) ).
fof(f672,plain,
( ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(sum(opp(X0),f(X1)),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_79 ),
inference(resolution,[],[f657,f97]) ).
fof(f1443,plain,
( spl1_172
| ~ spl1_5
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f666,f652,f96,f1441]) ).
fof(f666,plain,
( ! [X0,X1] :
( sum(opp(X0),f(X1)) = sum(eg,sum(opp(X0),f(X1)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_78 ),
inference(resolution,[],[f653,f97]) ).
fof(f1361,plain,
( spl1_171
| ~ spl1_3
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f831,f795,f86,f1359]) ).
fof(f831,plain,
( ! [X0] :
( eg = sum(sum(f(X0),eg),opp(sum(f(X0),eg)))
| ~ g(X0) )
| ~ spl1_3
| ~ spl1_98 ),
inference(resolution,[],[f796,f88]) ).
fof(f1357,plain,
( spl1_170
| ~ spl1_3
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f824,f791,f86,f1355]) ).
fof(f824,plain,
( ! [X0] :
( eg = sum(opp(sum(f(X0),eg)),sum(f(X0),eg))
| ~ g(X0) )
| ~ spl1_3
| ~ spl1_97 ),
inference(resolution,[],[f792,f88]) ).
fof(f1353,plain,
( spl1_169
| ~ spl1_4
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f819,f787,f91,f1351]) ).
fof(f819,plain,
( ! [X0] :
( eh = product(inv(inv(product(X0,eh))),inv(product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_96 ),
inference(resolution,[],[f788,f93]) ).
fof(f1349,plain,
( spl1_168
| ~ spl1_4
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f816,f783,f91,f1347]) ).
fof(f816,plain,
( ! [X0] :
( eh = product(inv(product(X0,eh)),inv(inv(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_95 ),
inference(resolution,[],[f784,f93]) ).
fof(f1345,plain,
( spl1_167
| ~ spl1_4
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f813,f779,f91,f1343]) ).
fof(f813,plain,
( ! [X0] :
( eg = sum(opp(f(product(X0,eh))),f(product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_94 ),
inference(resolution,[],[f780,f93]) ).
fof(f1341,plain,
( spl1_166
| ~ spl1_4
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f810,f775,f91,f1339]) ).
fof(f810,plain,
( ! [X0] :
( eg = sum(f(product(X0,eh)),opp(f(product(X0,eh))))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_93 ),
inference(resolution,[],[f776,f93]) ).
fof(f1337,plain,
( spl1_165
| ~ spl1_8
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f695,f685,f107,f1335]) ).
fof(f695,plain,
( ! [X0,X1] : eg = sum(sum(opp(X0),opp(X1)),opp(sum(opp(X0),opp(X1))))
| ~ spl1_8
| ~ spl1_82 ),
inference(resolution,[],[f686,f108]) ).
fof(f1333,plain,
( spl1_164
| ~ spl1_8
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f689,f681,f107,f1331]) ).
fof(f1331,plain,
( spl1_164
<=> ! [X0,X1] : eg = sum(opp(sum(opp(X0),opp(X1))),sum(opp(X0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_164])]) ).
fof(f689,plain,
( ! [X0,X1] : eg = sum(opp(sum(opp(X0),opp(X1))),sum(opp(X0),opp(X1)))
| ~ spl1_8
| ~ spl1_81 ),
inference(resolution,[],[f682,f108]) ).
fof(f1329,plain,
( spl1_163
| ~ spl1_6
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f648,f608,f100,f1327]) ).
fof(f648,plain,
( ! [X0] :
( eh = product(product(eh,inv(X0)),inv(product(eh,inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_77 ),
inference(resolution,[],[f609,f101]) ).
fof(f1325,plain,
( spl1_162
| ~ spl1_6
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f644,f604,f100,f1323]) ).
fof(f644,plain,
( ! [X0] :
( eh = product(inv(product(eh,inv(X0))),product(eh,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_76 ),
inference(resolution,[],[f605,f101]) ).
fof(f1321,plain,
( spl1_161
| ~ spl1_5
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f639,f600,f96,f1319]) ).
fof(f639,plain,
( ! [X0] :
( eg = sum(sum(eg,f(X0)),opp(sum(eg,f(X0))))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_75 ),
inference(resolution,[],[f601,f97]) ).
fof(f1317,plain,
( spl1_160
| ~ spl1_5
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f632,f596,f96,f1315]) ).
fof(f632,plain,
( ! [X0] :
( eg = sum(opp(sum(eg,f(X0))),sum(eg,f(X0)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_74 ),
inference(resolution,[],[f597,f97]) ).
fof(f1313,plain,
( spl1_159
| ~ spl1_6
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f625,f592,f100,f1311]) ).
fof(f625,plain,
( ! [X0] :
( eh = product(inv(inv(inv(inv(X0)))),inv(inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_73 ),
inference(resolution,[],[f593,f101]) ).
fof(f1309,plain,
( spl1_158
| ~ spl1_6
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f620,f588,f100,f1307]) ).
fof(f620,plain,
( ! [X0] :
( eh = product(inv(inv(inv(X0))),inv(inv(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_72 ),
inference(resolution,[],[f589,f101]) ).
fof(f1305,plain,
( spl1_157
| ~ spl1_6
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f616,f584,f100,f1303]) ).
fof(f616,plain,
( ! [X0] :
( eg = sum(opp(f(inv(inv(X0)))),f(inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_71 ),
inference(resolution,[],[f585,f101]) ).
fof(f1301,plain,
( spl1_156
| ~ spl1_6
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f612,f580,f100,f1299]) ).
fof(f612,plain,
( ! [X0] :
( eg = sum(f(inv(inv(X0))),opp(f(inv(inv(X0)))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_70 ),
inference(resolution,[],[f581,f101]) ).
fof(f1224,plain,
( spl1_155
| ~ spl1_3
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f757,f725,f86,f1222]) ).
fof(f757,plain,
( ! [X0] :
( sum(f(X0),eg) = sum(sum(f(X0),eg),eg)
| ~ g(X0) )
| ~ spl1_3
| ~ spl1_89 ),
inference(resolution,[],[f726,f88]) ).
fof(f1220,plain,
( spl1_154
| ~ spl1_3
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f750,f721,f86,f1218]) ).
fof(f750,plain,
( ! [X0] :
( sum(f(X0),eg) = sum(eg,sum(f(X0),eg))
| ~ g(X0) )
| ~ spl1_3
| ~ spl1_88 ),
inference(resolution,[],[f722,f88]) ).
fof(f1216,plain,
( spl1_153
| ~ spl1_4
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f745,f713,f91,f1214]) ).
fof(f745,plain,
( ! [X0] :
( inv(product(X0,eh)) = product(eh,inv(product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_86 ),
inference(resolution,[],[f714,f93]) ).
fof(f1212,plain,
( spl1_152
| ~ spl1_4
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f742,f709,f91,f1210]) ).
fof(f742,plain,
( ! [X0] :
( inv(product(X0,eh)) = product(inv(product(X0,eh)),eh)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_85 ),
inference(resolution,[],[f710,f93]) ).
fof(f1208,plain,
( spl1_151
| ~ spl1_4
| ~ spl1_84 ),
inference(avatar_split_clause,[],[f739,f705,f91,f1206]) ).
fof(f739,plain,
( ! [X0] :
( f(product(X0,eh)) = sum(eg,f(product(X0,eh)))
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_84 ),
inference(resolution,[],[f706,f93]) ).
fof(f1204,plain,
( spl1_150
| ~ spl1_4
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f736,f701,f91,f1202]) ).
fof(f736,plain,
( ! [X0] :
( f(product(X0,eh)) = sum(f(product(X0,eh)),eg)
| ~ g(X0) )
| ~ spl1_4
| ~ spl1_83 ),
inference(resolution,[],[f702,f93]) ).
fof(f1198,plain,
( spl1_149
| ~ spl1_42
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f489,f473,f340,f1196]) ).
fof(f489,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(X0)
| sum(sum(sum(X1,f(product(X2,X3))),X0),X4) = sum(sum(X1,f(product(X2,X3))),sum(X0,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_57 ),
inference(resolution,[],[f474,f341]) ).
fof(f1186,plain,
( spl1_148
| ~ spl1_19
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f492,f477,f164,f1184]) ).
fof(f492,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ g(X0)
| product(product(product(X1,product(X2,X3)),X0),X4) = product(product(X1,product(X2,X3)),product(X0,X4))
| ~ g(X4)
| ~ g(X1)
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_19
| ~ spl1_58 ),
inference(resolution,[],[f478,f165]) ).
fof(f1182,plain,
( spl1_147
| ~ spl1_18
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f485,f473,f160,f1180]) ).
fof(f485,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ h(X0)
| sum(sum(sum(X1,sum(X2,X3)),X0),X4) = sum(sum(X1,sum(X2,X3)),sum(X0,X4))
| ~ h(X4)
| ~ h(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_57 ),
inference(resolution,[],[f474,f161]) ).
fof(f1176,plain,
( spl1_146
| ~ spl1_21
| ~ spl1_42
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f467,f454,f340,f191,f1174]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1] :
( sum(f(X1),sum(f(product(X2,X3)),X0)) = sum(f(product(X1,product(X2,X3))),X0)
| ~ h(X0)
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_21
| ~ spl1_42
| ~ spl1_55 ),
inference(forward_demodulation,[],[f465,f192]) ).
fof(f465,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),f(product(X2,X3))),X0) = sum(f(X1),sum(f(product(X2,X3)),X0))
| ~ g(X1)
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_55 ),
inference(resolution,[],[f455,f341]) ).
fof(f1163,plain,
( spl1_145
| ~ spl1_42
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f451,f444,f340,f1161]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),f(product(X2,X3))),X0) = sum(opp(X1),sum(f(product(X2,X3)),X0))
| ~ h(f(X3))
| ~ h(f(X2)) )
| ~ spl1_42
| ~ spl1_54 ),
inference(resolution,[],[f445,f341]) ).
fof(f1159,plain,
( spl1_144
| ~ spl1_22
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f343,f340,f196,f1157]) ).
fof(f343,plain,
( ! [X2,X3,X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| ~ h(X2)
| ~ h(X3)
| sum(sum(f(product(X1,X0)),X3),X2) = sum(f(product(X1,X0)),sum(X3,X2)) )
| ~ spl1_22
| ~ spl1_42 ),
inference(resolution,[],[f341,f197]) ).
fof(f1137,plain,
( spl1_143
| ~ spl1_6
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f491,f477,f100,f1135]) ).
fof(f491,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X0)
| product(product(product(X1,inv(X2)),X0),X3) = product(product(X1,inv(X2)),product(X0,X3))
| ~ g(X3)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_6
| ~ spl1_58 ),
inference(resolution,[],[f478,f101]) ).
fof(f1133,plain,
( spl1_142
| ~ spl1_5
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f488,f473,f96,f1131]) ).
fof(f488,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(sum(X1,f(X2)),X0),X3) = sum(sum(X1,f(X2)),sum(X0,X3))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_57 ),
inference(resolution,[],[f474,f97]) ).
fof(f1129,plain,
( spl1_141
| ~ spl1_19
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f470,f458,f164,f1127]) ).
fof(f470,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X0)
| product(product(inv(product(X1,X2)),X0),X3) = product(inv(product(X1,X2)),product(X0,X3))
| ~ g(X3)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_56 ),
inference(resolution,[],[f459,f165]) ).
fof(f1125,plain,
( spl1_140
| ~ spl1_8
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f670,f656,f107,f1123]) ).
fof(f1123,plain,
( spl1_140
<=> ! [X0,X1] : sum(opp(X0),opp(X1)) = sum(sum(opp(X0),opp(X1)),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
fof(f670,plain,
( ! [X0,X1] : sum(opp(X0),opp(X1)) = sum(sum(opp(X0),opp(X1)),eg)
| ~ spl1_8
| ~ spl1_79 ),
inference(resolution,[],[f657,f108]) ).
fof(f1121,plain,
( spl1_139
| ~ spl1_18
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f461,f454,f160,f1119]) ).
fof(f461,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),sum(X2,X3)),X0) = sum(f(X1),sum(sum(X2,X3),X0))
| ~ g(X1)
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_55 ),
inference(resolution,[],[f455,f161]) ).
fof(f1117,plain,
( spl1_138
| ~ spl1_42
| ~ spl1_51 ),
inference(avatar_split_clause,[],[f436,f420,f340,f1115]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(eg,sum(f(product(X1,X2)),X0)) = sum(sum(eg,f(product(X1,X2))),X0)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_51 ),
inference(resolution,[],[f421,f341]) ).
fof(f1109,plain,
( spl1_137
| ~ spl1_42
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f412,f392,f340,f1107]) ).
fof(f412,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(product(X1,X2)),X0),opp(sum(f(product(X1,X2)),X0)))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_48 ),
inference(resolution,[],[f393,f341]) ).
fof(f1105,plain,
( spl1_136
| ~ spl1_42
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f407,f388,f340,f1103]) ).
fof(f407,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(product(X1,X2)),X0)),sum(f(product(X1,X2)),X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_47 ),
inference(resolution,[],[f389,f341]) ).
fof(f1087,plain,
( spl1_135
| ~ spl1_8
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f664,f652,f107,f1085]) ).
fof(f1085,plain,
( spl1_135
<=> ! [X0,X1] : sum(opp(X0),opp(X1)) = sum(eg,sum(opp(X0),opp(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
fof(f664,plain,
( ! [X0,X1] : sum(opp(X0),opp(X1)) = sum(eg,sum(opp(X0),opp(X1)))
| ~ spl1_8
| ~ spl1_78 ),
inference(resolution,[],[f653,f108]) ).
fof(f1083,plain,
( spl1_134
| ~ spl1_8
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f486,f473,f107,f1081]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(sum(X1,opp(X2)),X0),X3) = sum(sum(X1,opp(X2)),sum(X0,X3))
| ~ h(X3)
| ~ h(X1) )
| ~ spl1_8
| ~ spl1_57 ),
inference(resolution,[],[f474,f108]) ).
fof(f1079,plain,
( spl1_133
| ~ spl1_18
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f447,f444,f160,f1077]) ).
fof(f447,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),sum(X2,X3)),X0) = sum(opp(X1),sum(sum(X2,X3),X0))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_54 ),
inference(resolution,[],[f445,f161]) ).
fof(f1075,plain,
( spl1_132
| ~ spl1_42
| ~ spl1_44 ),
inference(avatar_split_clause,[],[f377,f357,f340,f1073]) ).
fof(f377,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(f(product(X1,X2)),X0) = sum(sum(f(product(X1,X2)),X0),eg)
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_44 ),
inference(resolution,[],[f358,f341]) ).
fof(f1071,plain,
( spl1_131
| ~ spl1_42
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f372,f353,f340,f1069]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(f(product(X1,X2)),X0) = sum(eg,sum(f(product(X1,X2)),X0))
| ~ h(f(X2))
| ~ h(f(X1)) )
| ~ spl1_42
| ~ spl1_43 ),
inference(resolution,[],[f354,f341]) ).
fof(f1048,plain,
( spl1_130
| ~ spl1_4
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f490,f477,f91,f1046]) ).
fof(f490,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(product(X1,eh),X0),X2) = product(product(X1,eh),product(X0,X2))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_4
| ~ spl1_58 ),
inference(resolution,[],[f478,f93]) ).
fof(f1044,plain,
( spl1_129
| ~ spl1_6
| ~ spl1_69 ),
inference(avatar_split_clause,[],[f576,f536,f100,f1042]) ).
fof(f576,plain,
( ! [X0] :
( product(eh,inv(X0)) = product(product(eh,inv(X0)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_69 ),
inference(resolution,[],[f537,f101]) ).
fof(f1040,plain,
( spl1_128
| ~ spl1_3
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f487,f473,f86,f1038]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(sum(X1,eg),X0),X2) = sum(sum(X1,eg),sum(X0,X2))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_3
| ~ spl1_57 ),
inference(resolution,[],[f474,f88]) ).
fof(f1036,plain,
( spl1_127
| ~ spl1_6
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f469,f458,f100,f1034]) ).
fof(f469,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(inv(inv(X1)),X0),X2) = product(inv(inv(X1)),product(X0,X2))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_56 ),
inference(resolution,[],[f459,f101]) ).
fof(f1032,plain,
( spl1_126
| ~ spl1_19
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f441,f424,f164,f1030]) ).
fof(f424,plain,
( spl1_52
<=> ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(eh,product(X1,X0)) = product(product(eh,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
fof(f441,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(eh,product(product(X1,X2),X0)) = product(product(eh,product(X1,X2)),X0)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_52 ),
inference(resolution,[],[f425,f165]) ).
fof(f425,plain,
( ! [X0,X1] :
( ~ g(X1)
| ~ g(X0)
| product(eh,product(X1,X0)) = product(product(eh,X1),X0) )
| ~ spl1_52 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f1028,plain,
( spl1_125
| ~ spl1_18
| ~ spl1_51 ),
inference(avatar_split_clause,[],[f432,f420,f160,f1026]) ).
fof(f432,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(eg,sum(sum(X1,X2),X0)) = sum(sum(eg,sum(X1,X2)),X0)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_51 ),
inference(resolution,[],[f421,f161]) ).
fof(f997,plain,
( spl1_124
| ~ spl1_5
| ~ spl1_21
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f466,f454,f191,f96,f995]) ).
fof(f466,plain,
( ! [X2,X0,X1] :
( sum(f(product(X1,X2)),X0) = sum(f(X1),sum(f(X2),X0))
| ~ h(X0)
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_21
| ~ spl1_55 ),
inference(forward_demodulation,[],[f464,f192]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),f(X2)),X0) = sum(f(X1),sum(f(X2),X0))
| ~ g(X1)
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_55 ),
inference(resolution,[],[f455,f97]) ).
fof(f993,plain,
( spl1_123
| ~ spl1_6
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f572,f532,f100,f991]) ).
fof(f572,plain,
( ! [X0] :
( product(eh,inv(X0)) = product(eh,product(eh,inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_68 ),
inference(resolution,[],[f533,f101]) ).
fof(f989,plain,
( spl1_122
| ~ spl1_19
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f418,f400,f164,f987]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| eh = product(product(product(X1,X2),X0),inv(product(product(X1,X2),X0)))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_50 ),
inference(resolution,[],[f401,f165]) ).
fof(f985,plain,
( spl1_121
| ~ spl1_19
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f415,f396,f164,f983]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| eh = product(inv(product(product(X1,X2),X0)),product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_49 ),
inference(resolution,[],[f397,f165]) ).
fof(f981,plain,
( spl1_120
| ~ spl1_18
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f408,f392,f160,f979]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(sum(sum(X1,X2),X0),opp(sum(sum(X1,X2),X0)))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_48 ),
inference(resolution,[],[f393,f161]) ).
fof(f977,plain,
( spl1_119
| ~ spl1_18
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f403,f388,f160,f975]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(sum(X1,X2),X0)),sum(sum(X1,X2),X0))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_47 ),
inference(resolution,[],[f389,f161]) ).
fof(f944,plain,
( spl1_118
| ~ spl1_5
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f567,f528,f96,f942]) ).
fof(f567,plain,
( ! [X0] :
( sum(eg,f(X0)) = sum(sum(eg,f(X0)),eg)
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_67 ),
inference(resolution,[],[f529,f97]) ).
fof(f940,plain,
( spl1_117
| ~ spl1_8
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f462,f454,f107,f938]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),opp(X2)),X0) = sum(f(X1),sum(opp(X2),X0))
| ~ g(X1) )
| ~ spl1_8
| ~ spl1_55 ),
inference(resolution,[],[f455,f108]) ).
fof(f936,plain,
( spl1_116
| ~ spl1_5
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f450,f444,f96,f934]) ).
fof(f450,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),f(X2)),X0) = sum(opp(X1),sum(f(X2),X0))
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_54 ),
inference(resolution,[],[f445,f97]) ).
fof(f932,plain,
( spl1_115
| ~ spl1_19
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f383,f365,f164,f930]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(X1,X2),X0) = product(product(product(X1,X2),X0),eh)
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_46 ),
inference(resolution,[],[f366,f165]) ).
fof(f928,plain,
( spl1_114
| ~ spl1_19
| ~ spl1_45 ),
inference(avatar_split_clause,[],[f380,f361,f164,f926]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| product(product(X1,X2),X0) = product(eh,product(product(X1,X2),X0))
| ~ g(X2)
| ~ g(X1) )
| ~ spl1_19
| ~ spl1_45 ),
inference(resolution,[],[f362,f165]) ).
fof(f924,plain,
( spl1_113
| ~ spl1_18
| ~ spl1_44 ),
inference(avatar_split_clause,[],[f373,f357,f160,f922]) ).
fof(f373,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(X1,X2),X0) = sum(sum(sum(X1,X2),X0),eg)
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_44 ),
inference(resolution,[],[f358,f161]) ).
fof(f920,plain,
( spl1_112
| ~ spl1_18
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f368,f353,f160,f918]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(X1,X2),X0) = sum(eg,sum(sum(X1,X2),X0))
| ~ h(X2)
| ~ h(X1) )
| ~ spl1_18
| ~ spl1_43 ),
inference(resolution,[],[f354,f161]) ).
fof(f912,plain,
( spl1_111
| ~ spl1_13
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f345,f340,f139,f910]) ).
fof(f345,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(f(product(X1,X0)),opp(f(product(X1,X0)))) )
| ~ spl1_13
| ~ spl1_42 ),
inference(resolution,[],[f341,f140]) ).
fof(f908,plain,
( spl1_110
| ~ spl1_15
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f344,f340,f148,f906]) ).
fof(f344,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| eg = sum(opp(f(product(X1,X0))),f(product(X1,X0))) )
| ~ spl1_15
| ~ spl1_42 ),
inference(resolution,[],[f341,f149]) ).
fof(f904,plain,
( spl1_109
| ~ spl1_5
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f560,f524,f96,f902]) ).
fof(f560,plain,
( ! [X0] :
( sum(eg,f(X0)) = sum(eg,sum(eg,f(X0)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_66 ),
inference(resolution,[],[f525,f97]) ).
fof(f871,plain,
( spl1_108
| ~ spl1_3
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f463,f454,f86,f869]) ).
fof(f463,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),eg),X0) = sum(f(X1),sum(eg,X0))
| ~ g(X1) )
| ~ spl1_3
| ~ spl1_55 ),
inference(resolution,[],[f455,f88]) ).
fof(f867,plain,
( spl1_107
| ~ spl1_8
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f448,f444,f107,f865]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),opp(X2)),X0) = sum(opp(X1),sum(opp(X2),X0)) )
| ~ spl1_8
| ~ spl1_54 ),
inference(resolution,[],[f445,f108]) ).
fof(f863,plain,
( spl1_106
| ~ spl1_6
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f440,f424,f100,f861]) ).
fof(f440,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(eh,product(inv(X1),X0)) = product(product(eh,inv(X1)),X0)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_52 ),
inference(resolution,[],[f425,f101]) ).
fof(f859,plain,
( spl1_105
| ~ spl1_5
| ~ spl1_51 ),
inference(avatar_split_clause,[],[f435,f420,f96,f857]) ).
fof(f435,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(eg,sum(f(X1),X0)) = sum(sum(eg,f(X1)),X0)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_51 ),
inference(resolution,[],[f421,f97]) ).
fof(f855,plain,
( spl1_104
| ~ spl1_6
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f553,f520,f100,f853]) ).
fof(f553,plain,
( ! [X0] :
( inv(inv(inv(X0))) = product(eh,inv(inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_65 ),
inference(resolution,[],[f521,f101]) ).
fof(f851,plain,
( spl1_103
| ~ spl1_9
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f347,f340,f113,f849]) ).
fof(f347,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(X1,X0)) = sum(f(product(X1,X0)),eg) )
| ~ spl1_9
| ~ spl1_42 ),
inference(resolution,[],[f341,f114]) ).
fof(f847,plain,
( spl1_102
| ~ spl1_10
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f346,f340,f117,f845]) ).
fof(f346,plain,
( ! [X0,X1] :
( ~ h(f(X0))
| ~ h(f(X1))
| f(product(X1,X0)) = sum(eg,f(product(X1,X0))) )
| ~ spl1_10
| ~ spl1_42 ),
inference(resolution,[],[f341,f118]) ).
fof(f809,plain,
( spl1_101
| ~ spl1_6
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f548,f516,f100,f807]) ).
fof(f548,plain,
( ! [X0] :
( inv(inv(inv(X0))) = product(inv(inv(inv(X0))),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_64 ),
inference(resolution,[],[f517,f101]) ).
fof(f805,plain,
( spl1_100
| ~ spl1_6
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f417,f400,f100,f803]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ g(X0)
| eh = product(product(inv(X1),X0),inv(product(inv(X1),X0)))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_50 ),
inference(resolution,[],[f401,f101]) ).
fof(f801,plain,
( spl1_99
| ~ spl1_6
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f414,f396,f100,f799]) ).
fof(f414,plain,
( ! [X0,X1] :
( ~ g(X0)
| eh = product(inv(product(inv(X1),X0)),product(inv(X1),X0))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_49 ),
inference(resolution,[],[f397,f101]) ).
fof(f797,plain,
( spl1_98
| ~ spl1_5
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f411,f392,f96,f795]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(f(X1),X0),opp(sum(f(X1),X0)))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_48 ),
inference(resolution,[],[f393,f97]) ).
fof(f793,plain,
( spl1_97
| ~ spl1_5
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f406,f388,f96,f791]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(f(X1),X0)),sum(f(X1),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_47 ),
inference(resolution,[],[f389,f97]) ).
fof(f789,plain,
( spl1_96
| ~ spl1_19
| ~ spl1_40 ),
inference(avatar_split_clause,[],[f332,f317,f164,f787]) ).
fof(f332,plain,
( ! [X0,X1] :
( eh = product(inv(inv(product(X0,X1))),inv(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_40 ),
inference(resolution,[],[f318,f165]) ).
fof(f785,plain,
( spl1_95
| ~ spl1_19
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f328,f313,f164,f783]) ).
fof(f328,plain,
( ! [X0,X1] :
( eh = product(inv(product(X0,X1)),inv(inv(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_39 ),
inference(resolution,[],[f314,f165]) ).
fof(f781,plain,
( spl1_94
| ~ spl1_19
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f325,f309,f164,f779]) ).
fof(f325,plain,
( ! [X0,X1] :
( eg = sum(opp(f(product(X0,X1))),f(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_38 ),
inference(resolution,[],[f310,f165]) ).
fof(f777,plain,
( spl1_93
| ~ spl1_19
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f322,f305,f164,f775]) ).
fof(f322,plain,
( ! [X0,X1] :
( eg = sum(f(product(X0,X1)),opp(f(product(X0,X1))))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_37 ),
inference(resolution,[],[f306,f165]) ).
fof(f765,plain,
( spl1_92
| ~ spl1_6
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f544,f512,f100,f763]) ).
fof(f544,plain,
( ! [X0] :
( f(inv(inv(X0))) = sum(eg,f(inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_63 ),
inference(resolution,[],[f513,f101]) ).
fof(f735,plain,
( spl1_91
| ~ spl1_6
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f382,f365,f100,f733]) ).
fof(f382,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(inv(X1),X0) = product(product(inv(X1),X0),eh)
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_46 ),
inference(resolution,[],[f366,f101]) ).
fof(f731,plain,
( spl1_90
| ~ spl1_6
| ~ spl1_45 ),
inference(avatar_split_clause,[],[f379,f361,f100,f729]) ).
fof(f379,plain,
( ! [X0,X1] :
( ~ g(X0)
| product(inv(X1),X0) = product(eh,product(inv(X1),X0))
| ~ g(X1) )
| ~ spl1_6
| ~ spl1_45 ),
inference(resolution,[],[f362,f101]) ).
fof(f727,plain,
( spl1_89
| ~ spl1_5
| ~ spl1_44 ),
inference(avatar_split_clause,[],[f376,f357,f96,f725]) ).
fof(f376,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(sum(f(X1),X0),eg)
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_44 ),
inference(resolution,[],[f358,f97]) ).
fof(f723,plain,
( spl1_88
| ~ spl1_5
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f371,f353,f96,f721]) ).
fof(f371,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(f(X1),X0) = sum(eg,sum(f(X1),X0))
| ~ g(X1) )
| ~ spl1_5
| ~ spl1_43 ),
inference(resolution,[],[f354,f97]) ).
fof(f719,plain,
( spl1_87
| ~ spl1_6
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f540,f508,f100,f717]) ).
fof(f540,plain,
( ! [X0] :
( f(inv(inv(X0))) = sum(f(inv(inv(X0))),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_62 ),
inference(resolution,[],[f509,f101]) ).
fof(f715,plain,
( spl1_86
| ~ spl1_19
| ~ spl1_36 ),
inference(avatar_split_clause,[],[f302,f280,f164,f713]) ).
fof(f302,plain,
( ! [X0,X1] :
( inv(product(X0,X1)) = product(eh,inv(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_36 ),
inference(resolution,[],[f281,f165]) ).
fof(f711,plain,
( spl1_85
| ~ spl1_19
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f298,f276,f164,f709]) ).
fof(f298,plain,
( ! [X0,X1] :
( inv(product(X0,X1)) = product(inv(product(X0,X1)),eh)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_35 ),
inference(resolution,[],[f277,f165]) ).
fof(f707,plain,
( spl1_84
| ~ spl1_19
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f288,f272,f164,f705]) ).
fof(f288,plain,
( ! [X0,X1] :
( f(product(X0,X1)) = sum(eg,f(product(X0,X1)))
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_34 ),
inference(resolution,[],[f273,f165]) ).
fof(f703,plain,
( spl1_83
| ~ spl1_19
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f285,f268,f164,f701]) ).
fof(f285,plain,
( ! [X0,X1] :
( f(product(X0,X1)) = sum(f(product(X0,X1)),eg)
| ~ g(X1)
| ~ g(X0) )
| ~ spl1_19
| ~ spl1_33 ),
inference(resolution,[],[f269,f165]) ).
fof(f687,plain,
( spl1_82
| ~ spl1_8
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f409,f392,f107,f685]) ).
fof(f409,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(sum(opp(X1),X0),opp(sum(opp(X1),X0))) )
| ~ spl1_8
| ~ spl1_48 ),
inference(resolution,[],[f393,f108]) ).
fof(f683,plain,
( spl1_81
| ~ spl1_8
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f404,f388,f107,f681]) ).
fof(f404,plain,
( ! [X0,X1] :
( ~ h(X0)
| eg = sum(opp(sum(opp(X1),X0)),sum(opp(X1),X0)) )
| ~ spl1_8
| ~ spl1_47 ),
inference(resolution,[],[f389,f108]) ).
fof(f662,plain,
( spl1_80
| ~ spl1_3
| ~ spl1_28
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f452,f444,f239,f86,f660]) ).
fof(f452,plain,
( ! [X0,X1] :
( sum(opp(X1),X0) = sum(opp(X1),sum(eg,X0))
| ~ h(X0) )
| ~ spl1_3
| ~ spl1_28
| ~ spl1_54 ),
inference(forward_demodulation,[],[f449,f240]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),eg),X0) = sum(opp(X1),sum(eg,X0)) )
| ~ spl1_3
| ~ spl1_54 ),
inference(resolution,[],[f445,f88]) ).
fof(f658,plain,
( spl1_79
| ~ spl1_8
| ~ spl1_44 ),
inference(avatar_split_clause,[],[f374,f357,f107,f656]) ).
fof(f374,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(sum(opp(X1),X0),eg) )
| ~ spl1_8
| ~ spl1_44 ),
inference(resolution,[],[f358,f108]) ).
fof(f654,plain,
( spl1_78
| ~ spl1_8
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f369,f353,f107,f652]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(opp(X1),X0) = sum(eg,sum(opp(X1),X0)) )
| ~ spl1_8
| ~ spl1_43 ),
inference(resolution,[],[f354,f108]) ).
fof(f610,plain,
( spl1_77
| ~ spl1_4
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f416,f400,f91,f608]) ).
fof(f416,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(product(eh,X0),inv(product(eh,X0))) )
| ~ spl1_4
| ~ spl1_50 ),
inference(resolution,[],[f401,f93]) ).
fof(f606,plain,
( spl1_76
| ~ spl1_4
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f413,f396,f91,f604]) ).
fof(f413,plain,
( ! [X0] :
( ~ g(X0)
| eh = product(inv(product(eh,X0)),product(eh,X0)) )
| ~ spl1_4
| ~ spl1_49 ),
inference(resolution,[],[f397,f93]) ).
fof(f602,plain,
( spl1_75
| ~ spl1_3
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f410,f392,f86,f600]) ).
fof(f410,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(sum(eg,X0),opp(sum(eg,X0))) )
| ~ spl1_3
| ~ spl1_48 ),
inference(resolution,[],[f393,f88]) ).
fof(f598,plain,
( spl1_74
| ~ spl1_3
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f405,f388,f86,f596]) ).
fof(f405,plain,
( ! [X0] :
( ~ h(X0)
| eg = sum(opp(sum(eg,X0)),sum(eg,X0)) )
| ~ spl1_3
| ~ spl1_47 ),
inference(resolution,[],[f389,f88]) ).
fof(f594,plain,
( spl1_73
| ~ spl1_6
| ~ spl1_40 ),
inference(avatar_split_clause,[],[f331,f317,f100,f592]) ).
fof(f331,plain,
( ! [X0] :
( eh = product(inv(inv(inv(X0))),inv(inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_40 ),
inference(resolution,[],[f318,f101]) ).
fof(f590,plain,
( spl1_72
| ~ spl1_6
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f327,f313,f100,f588]) ).
fof(f327,plain,
( ! [X0] :
( eh = product(inv(inv(X0)),inv(inv(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_39 ),
inference(resolution,[],[f314,f101]) ).
fof(f586,plain,
( spl1_71
| ~ spl1_6
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f324,f309,f100,f584]) ).
fof(f324,plain,
( ! [X0] :
( eg = sum(opp(f(inv(X0))),f(inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_38 ),
inference(resolution,[],[f310,f101]) ).
fof(f582,plain,
( spl1_70
| ~ spl1_6
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f321,f305,f100,f580]) ).
fof(f321,plain,
( ! [X0] :
( eg = sum(f(inv(X0)),opp(f(inv(X0))))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_37 ),
inference(resolution,[],[f306,f101]) ).
fof(f538,plain,
( spl1_69
| ~ spl1_4
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f381,f365,f91,f536]) ).
fof(f381,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(product(eh,X0),eh) )
| ~ spl1_4
| ~ spl1_46 ),
inference(resolution,[],[f366,f93]) ).
fof(f534,plain,
( spl1_68
| ~ spl1_4
| ~ spl1_45 ),
inference(avatar_split_clause,[],[f378,f361,f91,f532]) ).
fof(f378,plain,
( ! [X0] :
( ~ g(X0)
| product(eh,X0) = product(eh,product(eh,X0)) )
| ~ spl1_4
| ~ spl1_45 ),
inference(resolution,[],[f362,f93]) ).
fof(f530,plain,
( spl1_67
| ~ spl1_3
| ~ spl1_44 ),
inference(avatar_split_clause,[],[f375,f357,f86,f528]) ).
fof(f375,plain,
( ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(sum(eg,X0),eg) )
| ~ spl1_3
| ~ spl1_44 ),
inference(resolution,[],[f358,f88]) ).
fof(f526,plain,
( spl1_66
| ~ spl1_3
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f370,f353,f86,f524]) ).
fof(f370,plain,
( ! [X0] :
( ~ h(X0)
| sum(eg,X0) = sum(eg,sum(eg,X0)) )
| ~ spl1_3
| ~ spl1_43 ),
inference(resolution,[],[f354,f88]) ).
fof(f522,plain,
( spl1_65
| ~ spl1_6
| ~ spl1_36 ),
inference(avatar_split_clause,[],[f301,f280,f100,f520]) ).
fof(f301,plain,
( ! [X0] :
( inv(inv(X0)) = product(eh,inv(inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_36 ),
inference(resolution,[],[f281,f101]) ).
fof(f518,plain,
( spl1_64
| ~ spl1_6
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f297,f276,f100,f516]) ).
fof(f297,plain,
( ! [X0] :
( inv(inv(X0)) = product(inv(inv(X0)),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_35 ),
inference(resolution,[],[f277,f101]) ).
fof(f514,plain,
( spl1_63
| ~ spl1_6
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f287,f272,f100,f512]) ).
fof(f287,plain,
( ! [X0] :
( f(inv(X0)) = sum(eg,f(inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_34 ),
inference(resolution,[],[f273,f101]) ).
fof(f510,plain,
( spl1_62
| ~ spl1_6
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f284,f268,f100,f508]) ).
fof(f284,plain,
( ! [X0] :
( f(inv(X0)) = sum(f(inv(X0)),eg)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_33 ),
inference(resolution,[],[f269,f101]) ).
fof(f504,plain,
( spl1_61
| ~ spl1_4
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f323,f309,f91,f501]) ).
fof(f323,plain,
( eg = sum(opp(f(eh)),f(eh))
| ~ spl1_4
| ~ spl1_38 ),
inference(resolution,[],[f310,f93]) ).
fof(f499,plain,
( spl1_60
| ~ spl1_4
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f320,f305,f91,f496]) ).
fof(f320,plain,
( eg = sum(f(eh),opp(f(eh)))
| ~ spl1_4
| ~ spl1_37 ),
inference(resolution,[],[f306,f93]) ).
fof(f484,plain,
( spl1_59
| ~ spl1_4
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f286,f272,f91,f481]) ).
fof(f286,plain,
( f(eh) = sum(eg,f(eh))
| ~ spl1_4
| ~ spl1_34 ),
inference(resolution,[],[f273,f93]) ).
fof(f479,plain,
( spl1_58
| ~ spl1_19
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f209,f200,f164,f477]) ).
fof(f209,plain,
( ! [X2,X3,X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(product(X2,X3),X1),X0) = product(product(X2,X3),product(X1,X0))
| ~ g(X3)
| ~ g(X2) )
| ~ spl1_19
| ~ spl1_23 ),
inference(resolution,[],[f201,f165]) ).
fof(f475,plain,
( spl1_57
| ~ spl1_18
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f203,f196,f160,f473]) ).
fof(f203,plain,
( ! [X2,X3,X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(sum(X2,X3),X1),X0) = sum(sum(X2,X3),sum(X1,X0))
| ~ h(X3)
| ~ h(X2) )
| ~ spl1_18
| ~ spl1_22 ),
inference(resolution,[],[f197,f161]) ).
fof(f460,plain,
( spl1_56
| ~ spl1_6
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f208,f200,f100,f458]) ).
fof(f208,plain,
( ! [X2,X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(product(inv(X2),X1),X0) = product(inv(X2),product(X1,X0))
| ~ g(X2) )
| ~ spl1_6
| ~ spl1_23 ),
inference(resolution,[],[f201,f101]) ).
fof(f456,plain,
( spl1_55
| ~ spl1_5
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f206,f196,f96,f454]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(f(X2),X1),X0) = sum(f(X2),sum(X1,X0))
| ~ g(X2) )
| ~ spl1_5
| ~ spl1_22 ),
inference(resolution,[],[f197,f97]) ).
fof(f446,plain,
( spl1_54
| ~ spl1_8
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f204,f196,f107,f444]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(sum(opp(X2),X1),X0) = sum(opp(X2),sum(X1,X0)) )
| ~ spl1_8
| ~ spl1_22 ),
inference(resolution,[],[f197,f108]) ).
fof(f431,plain,
( spl1_53
| ~ spl1_4
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f283,f268,f91,f428]) ).
fof(f428,plain,
( spl1_53
<=> f(eh) = sum(f(eh),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
fof(f283,plain,
( f(eh) = sum(f(eh),eg)
| ~ spl1_4
| ~ spl1_33 ),
inference(resolution,[],[f269,f93]) ).
fof(f426,plain,
( spl1_52
| ~ spl1_4
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f207,f200,f91,f424]) ).
fof(f207,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(eh,product(X1,X0)) = product(product(eh,X1),X0) )
| ~ spl1_4
| ~ spl1_23 ),
inference(resolution,[],[f201,f93]) ).
fof(f422,plain,
( spl1_51
| ~ spl1_3
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f205,f196,f86,f420]) ).
fof(f205,plain,
( ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(eg,sum(X1,X0)) = sum(sum(eg,X1),X0) )
| ~ spl1_3
| ~ spl1_22 ),
inference(resolution,[],[f197,f88]) ).
fof(f402,plain,
( spl1_50
| ~ spl1_16
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f187,f164,f152,f400]) ).
fof(f187,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| eh = product(product(X1,X0),inv(product(X1,X0))) )
| ~ spl1_16
| ~ spl1_19 ),
inference(resolution,[],[f165,f153]) ).
fof(f398,plain,
( spl1_49
| ~ spl1_17
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f186,f164,f156,f396]) ).
fof(f186,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| eh = product(inv(product(X1,X0)),product(X1,X0)) )
| ~ spl1_17
| ~ spl1_19 ),
inference(resolution,[],[f165,f157]) ).
fof(f394,plain,
( spl1_48
| ~ spl1_13
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f178,f160,f139,f392]) ).
fof(f178,plain,
( ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| eg = sum(sum(X1,X0),opp(sum(X1,X0))) )
| ~ spl1_13
| ~ spl1_18 ),
inference(resolution,[],[f161,f140]) ).
fof(f390,plain,
( spl1_47
| ~ spl1_15
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f177,f160,f148,f388]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| eg = sum(opp(sum(X1,X0)),sum(X1,X0)) )
| ~ spl1_15
| ~ spl1_18 ),
inference(resolution,[],[f161,f149]) ).
fof(f367,plain,
( spl1_46
| ~ spl1_11
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f189,f164,f121,f365]) ).
fof(f189,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(X1,X0) = product(product(X1,X0),eh) )
| ~ spl1_11
| ~ spl1_19 ),
inference(resolution,[],[f165,f122]) ).
fof(f363,plain,
( spl1_45
| ~ spl1_12
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f188,f164,f125,f361]) ).
fof(f188,plain,
( ! [X0,X1] :
( ~ g(X0)
| ~ g(X1)
| product(X1,X0) = product(eh,product(X1,X0)) )
| ~ spl1_12
| ~ spl1_19 ),
inference(resolution,[],[f165,f126]) ).
fof(f359,plain,
( spl1_44
| ~ spl1_9
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f180,f160,f113,f357]) ).
fof(f180,plain,
( ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(X1,X0) = sum(sum(X1,X0),eg) )
| ~ spl1_9
| ~ spl1_18 ),
inference(resolution,[],[f161,f114]) ).
fof(f355,plain,
( spl1_43
| ~ spl1_10
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f179,f160,f117,f353]) ).
fof(f179,plain,
( ! [X0,X1] :
( ~ h(X0)
| ~ h(X1)
| sum(X1,X0) = sum(eg,sum(X1,X0)) )
| ~ spl1_10
| ~ spl1_18 ),
inference(resolution,[],[f161,f118]) ).
fof(f342,plain,
( spl1_42
| ~ spl1_18
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f194,f191,f160,f340]) ).
fof(f194,plain,
( ! [X0,X1] :
( h(f(product(X0,X1)))
| ~ h(f(X1))
| ~ h(f(X0)) )
| ~ spl1_18
| ~ spl1_21 ),
inference(superposition,[],[f161,f192]) ).
fof(f338,plain,
( spl1_41
| ~ spl1_4
| ~ spl1_27
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f299,f276,f230,f91,f335]) ).
fof(f335,plain,
( spl1_41
<=> eh = inv(eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
fof(f230,plain,
( spl1_27
<=> eh = product(inv(eh),eh) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f299,plain,
( eh = inv(eh)
| ~ spl1_4
| ~ spl1_27
| ~ spl1_35 ),
inference(forward_demodulation,[],[f296,f232]) ).
fof(f232,plain,
( eh = product(inv(eh),eh)
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f296,plain,
( inv(eh) = product(inv(eh),eh)
| ~ spl1_4
| ~ spl1_35 ),
inference(resolution,[],[f277,f93]) ).
fof(f319,plain,
( spl1_40
| ~ spl1_6
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f176,f156,f100,f317]) ).
fof(f176,plain,
( ! [X0] :
( eh = product(inv(inv(X0)),inv(X0))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_17 ),
inference(resolution,[],[f157,f101]) ).
fof(f315,plain,
( spl1_39
| ~ spl1_6
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f174,f152,f100,f313]) ).
fof(f174,plain,
( ! [X0] :
( eh = product(inv(X0),inv(inv(X0)))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_16 ),
inference(resolution,[],[f153,f101]) ).
fof(f311,plain,
( spl1_38
| ~ spl1_5
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f172,f148,f96,f309]) ).
fof(f172,plain,
( ! [X0] :
( eg = sum(opp(f(X0)),f(X0))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_15 ),
inference(resolution,[],[f149,f97]) ).
fof(f307,plain,
( spl1_37
| ~ spl1_5
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f169,f139,f96,f305]) ).
fof(f169,plain,
( ! [X0] :
( eg = sum(f(X0),opp(f(X0)))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_13 ),
inference(resolution,[],[f140,f97]) ).
fof(f282,plain,
( spl1_36
| ~ spl1_6
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f137,f125,f100,f280]) ).
fof(f137,plain,
( ! [X0] :
( inv(X0) = product(eh,inv(X0))
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_12 ),
inference(resolution,[],[f126,f101]) ).
fof(f278,plain,
( spl1_35
| ~ spl1_6
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f135,f121,f100,f276]) ).
fof(f135,plain,
( ! [X0] :
( inv(X0) = product(inv(X0),eh)
| ~ g(X0) )
| ~ spl1_6
| ~ spl1_11 ),
inference(resolution,[],[f122,f101]) ).
fof(f274,plain,
( spl1_34
| ~ spl1_5
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f133,f117,f96,f272]) ).
fof(f133,plain,
( ! [X0] :
( f(X0) = sum(eg,f(X0))
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_10 ),
inference(resolution,[],[f118,f97]) ).
fof(f270,plain,
( spl1_33
| ~ spl1_5
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f130,f113,f96,f268]) ).
fof(f130,plain,
( ! [X0] :
( f(X0) = sum(f(X0),eg)
| ~ g(X0) )
| ~ spl1_5
| ~ spl1_9 ),
inference(resolution,[],[f114,f97]) ).
fof(f264,plain,
( spl1_32
| ~ spl1_8
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f171,f148,f107,f262]) ).
fof(f171,plain,
( ! [X0] : eg = sum(opp(opp(X0)),opp(X0))
| ~ spl1_8
| ~ spl1_15 ),
inference(resolution,[],[f149,f108]) ).
fof(f260,plain,
( spl1_31
| ~ spl1_8
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f168,f139,f107,f258]) ).
fof(f168,plain,
( ! [X0] : eg = sum(opp(X0),opp(opp(X0)))
| ~ spl1_8
| ~ spl1_13 ),
inference(resolution,[],[f140,f108]) ).
fof(f256,plain,
( spl1_30
| ~ spl1_25
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f246,f239,f220,f253]) ).
fof(f220,plain,
( spl1_25
<=> eg = sum(opp(eg),eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f246,plain,
( eg = opp(eg)
| ~ spl1_25
| ~ spl1_28 ),
inference(superposition,[],[f240,f222]) ).
fof(f222,plain,
( eg = sum(opp(eg),eg)
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f245,plain,
( spl1_29
| ~ spl1_8
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f132,f117,f107,f243]) ).
fof(f132,plain,
( ! [X0] : opp(X0) = sum(eg,opp(X0))
| ~ spl1_8
| ~ spl1_10 ),
inference(resolution,[],[f118,f108]) ).
fof(f241,plain,
( spl1_28
| ~ spl1_8
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f129,f113,f107,f239]) ).
fof(f129,plain,
( ! [X0] : opp(X0) = sum(opp(X0),eg)
| ~ spl1_8
| ~ spl1_9 ),
inference(resolution,[],[f114,f108]) ).
fof(f233,plain,
( spl1_27
| ~ spl1_4
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f175,f156,f91,f230]) ).
fof(f175,plain,
( eh = product(inv(eh),eh)
| ~ spl1_4
| ~ spl1_17 ),
inference(resolution,[],[f157,f93]) ).
fof(f228,plain,
( spl1_26
| ~ spl1_4
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f173,f152,f91,f225]) ).
fof(f225,plain,
( spl1_26
<=> eh = product(eh,inv(eh)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f173,plain,
( eh = product(eh,inv(eh))
| ~ spl1_4
| ~ spl1_16 ),
inference(resolution,[],[f153,f93]) ).
fof(f223,plain,
( spl1_25
| ~ spl1_3
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f170,f148,f86,f220]) ).
fof(f170,plain,
( eg = sum(opp(eg),eg)
| ~ spl1_3
| ~ spl1_15 ),
inference(resolution,[],[f149,f88]) ).
fof(f218,plain,
( spl1_24
| ~ spl1_3
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f167,f139,f86,f215]) ).
fof(f215,plain,
( spl1_24
<=> eg = sum(eg,opp(eg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f167,plain,
( eg = sum(eg,opp(eg))
| ~ spl1_3
| ~ spl1_13 ),
inference(resolution,[],[f140,f88]) ).
fof(f202,plain,
spl1_23,
inference(avatar_split_clause,[],[f75,f200]) ).
fof(f75,plain,
! [X2,X0,X1] :
( product(product(X2,X1),X0) = product(X2,product(X1,X0))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( product(product(X2,X1),X0) = product(X2,product(X1,X0))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( product(product(X2,X1),X0) = product(X2,product(X1,X0))
| ~ g(X0)
| ~ g(X1)
| ~ g(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( g(X0)
& g(X1)
& g(X2) )
=> product(product(X2,X1),X0) = product(X2,product(X1,X0)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ( g(X2)
& g(X0)
& g(X1) )
=> product(product(X1,X0),X2) = product(X1,product(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(f198,plain,
spl1_22,
inference(avatar_split_clause,[],[f74,f196]) ).
fof(f74,plain,
! [X2,X0,X1] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X0)
| ~ h(X1)
| ~ h(X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X0)
| ~ h(X1)
| ~ h(X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X0)
| ~ h(X1)
| ~ h(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( h(X0)
& h(X1)
& h(X2) )
=> sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0)) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ( h(X2)
& h(X0)
& h(X1) )
=> sum(sum(X1,X0),X2) = sum(X1,sum(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(f193,plain,
spl1_21,
inference(avatar_split_clause,[],[f70,f191]) ).
fof(f70,plain,
! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
fof(f185,plain,
( spl1_20
| ~ spl1_4
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f134,f121,f91,f182]) ).
fof(f134,plain,
( eh = product(eh,eh)
| ~ spl1_4
| ~ spl1_11 ),
inference(resolution,[],[f122,f93]) ).
fof(f166,plain,
spl1_19,
inference(avatar_split_clause,[],[f73,f164]) ).
fof(f73,plain,
! [X0,X1] :
( g(product(X1,X0))
| ~ g(X0)
| ~ g(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( g(product(X1,X0))
| ~ g(X0)
| ~ g(X1) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( g(product(X1,X0))
| ~ g(X0)
| ~ g(X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( g(X0)
& g(X1) )
=> g(product(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(f162,plain,
spl1_18,
inference(avatar_split_clause,[],[f72,f160]) ).
fof(f72,plain,
! [X0,X1] :
( h(sum(X1,X0))
| ~ h(X0)
| ~ h(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( h(sum(X1,X0))
| ~ h(X0)
| ~ h(X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( h(sum(X1,X0))
| ~ h(X0)
| ~ h(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( h(X0)
& h(X1) )
=> h(sum(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(f158,plain,
spl1_17,
inference(avatar_split_clause,[],[f69,f156]) ).
fof(f69,plain,
! [X0] :
( eh = product(inv(X0),X0)
| ~ g(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( eh = product(inv(X0),X0)
| ~ g(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] :
( g(X0)
=> eh = product(inv(X0),X0) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1] :
( g(X1)
=> eh = product(inv(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(f154,plain,
spl1_16,
inference(avatar_split_clause,[],[f68,f152]) ).
fof(f68,plain,
! [X0] :
( eh = product(X0,inv(X0))
| ~ g(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( eh = product(X0,inv(X0))
| ~ g(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( g(X0)
=> eh = product(X0,inv(X0)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1] :
( g(X1)
=> eh = product(X1,inv(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(f150,plain,
spl1_15,
inference(avatar_split_clause,[],[f63,f148]) ).
fof(f63,plain,
! [X0] :
( eg = sum(opp(X0),X0)
| ~ h(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( eg = sum(opp(X0),X0)
| ~ h(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( h(X0)
=> eg = sum(opp(X0),X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X1] :
( h(X1)
=> eg = sum(opp(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
fof(f146,plain,
( spl1_14
| ~ spl1_3
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f128,f113,f86,f143]) ).
fof(f143,plain,
( spl1_14
<=> eg = sum(eg,eg) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f128,plain,
( eg = sum(eg,eg)
| ~ spl1_3
| ~ spl1_9 ),
inference(resolution,[],[f114,f88]) ).
fof(f141,plain,
spl1_13,
inference(avatar_split_clause,[],[f62,f139]) ).
fof(f62,plain,
! [X0] :
( eg = sum(X0,opp(X0))
| ~ h(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( eg = sum(X0,opp(X0))
| ~ h(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( h(X0)
=> eg = sum(X0,opp(X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1] :
( h(X1)
=> eg = sum(X1,opp(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
fof(f127,plain,
spl1_12,
inference(avatar_split_clause,[],[f67,f125]) ).
fof(f67,plain,
! [X0] :
( product(eh,X0) = X0
| ~ g(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( product(eh,X0) = X0
| ~ g(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( g(X0)
=> product(eh,X0) = X0 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1] :
( g(X1)
=> product(eh,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(f123,plain,
spl1_11,
inference(avatar_split_clause,[],[f66,f121]) ).
fof(f66,plain,
! [X0] :
( product(X0,eh) = X0
| ~ g(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( product(X0,eh) = X0
| ~ g(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( g(X0)
=> product(X0,eh) = X0 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1] :
( g(X1)
=> product(X1,eh) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(f119,plain,
spl1_10,
inference(avatar_split_clause,[],[f61,f117]) ).
fof(f61,plain,
! [X0] :
( sum(eg,X0) = X0
| ~ h(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( sum(eg,X0) = X0
| ~ h(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( h(X0)
=> sum(eg,X0) = X0 ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X1] :
( h(X1)
=> sum(eg,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
fof(f115,plain,
spl1_9,
inference(avatar_split_clause,[],[f60,f113]) ).
fof(f60,plain,
! [X0] :
( sum(X0,eg) = X0
| ~ h(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( sum(X0,eg) = X0
| ~ h(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( h(X0)
=> sum(X0,eg) = X0 ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X1] :
( h(X1)
=> sum(X1,eg) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
fof(f111,plain,
( ~ spl1_3
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f110,plain,
( $false
| ~ spl1_3
| ~ spl1_7 ),
inference(resolution,[],[f105,f88]) ).
fof(f105,plain,
( ! [X1] : ~ h(X1)
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl1_7
<=> ! [X1] : ~ h(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f109,plain,
( spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f71,f107,f104]) ).
fof(f71,plain,
! [X0,X1] :
( h(opp(X0))
| ~ h(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( h(opp(X0))
| ~ h(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( h(X1)
=> h(opp(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(f102,plain,
spl1_6,
inference(avatar_split_clause,[],[f65,f100]) ).
fof(f65,plain,
! [X0] :
( g(inv(X0))
| ~ g(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( g(inv(X0))
| ~ g(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( g(X0)
=> g(inv(X0)) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1] :
( g(X1)
=> g(inv(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(f98,plain,
spl1_5,
inference(avatar_split_clause,[],[f64,f96]) ).
fof(f64,plain,
! [X0] :
( h(f(X0))
| ~ g(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( h(f(X0))
| ~ g(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( g(X0)
=> h(f(X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X1] :
( g(X1)
=> h(f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
fof(f94,plain,
spl1_4,
inference(avatar_split_clause,[],[f59,f91]) ).
fof(f59,plain,
g(eh),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
g(eh),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f89,plain,
spl1_3,
inference(avatar_split_clause,[],[f58,f86]) ).
fof(f58,plain,
h(eg),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
h(eg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(f84,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f56,f81,f77]) ).
fof(f56,plain,
( g(sK0)
| eg != f(eh) ),
inference(cnf_transformation,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.31 % Computer : n010.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Apr 30 04:08:35 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.17/0.31 % (24561)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33 % (24564)WARNING: value z3 for option sas not known
% 0.17/0.33 % (24562)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.33 % (24567)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)
% 0.17/0.33 % (24568)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)
% 0.17/0.33 % (24563)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.33 % (24565)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.33 % (24564)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)
% 0.17/0.33 % (24566)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)
% 0.17/0.33 TRYING [1]
% 0.17/0.33 TRYING [2]
% 0.17/0.33 TRYING [1]
% 0.17/0.33 TRYING [2]
% 0.17/0.33 TRYING [3]
% 0.17/0.33 TRYING [3]
% 0.17/0.34 TRYING [4]
% 0.17/0.34 TRYING [4]
% 0.17/0.36 TRYING [5]
% 0.17/0.37 TRYING [5]
% 0.17/0.42 TRYING [6]
% 0.17/0.44 TRYING [6]
% 0.17/0.55 TRYING [7]
% 2.21/0.63 TRYING [7]
% 3.34/0.82 TRYING [8]
% 3.95/0.88 % (24566)First to succeed.
% 4.39/0.94 % (24566)Refutation found. Thanks to Tanya!
% 4.39/0.94 % SZS status Theorem for theBenchmark
% 4.39/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 4.39/0.97 % (24566)------------------------------
% 4.39/0.97 % (24566)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.39/0.97 % (24566)Termination reason: Refutation
% 4.39/0.97
% 4.39/0.97 % (24566)Memory used [KB]: 8355
% 4.39/0.97 % (24566)Time elapsed: 0.609 s
% 4.39/0.97 % (24566)Instructions burned: 1110 (million)
% 4.39/0.97 % (24566)------------------------------
% 4.39/0.97 % (24566)------------------------------
% 4.39/0.97 % (24561)Success in time 0.634 s
%------------------------------------------------------------------------------