TSTP Solution File: RNG037-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG037-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:55:17 EDT 2024
% Result : Unsatisfiable 2.28s 0.65s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 332
% Syntax : Number of formulae : 1087 ( 30 unt; 0 def)
% Number of atoms : 3770 ( 165 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 5056 (2373 ~;2371 |; 0 &)
% ( 312 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 316 ( 314 usr; 313 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 1987 (1987 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7071,plain,
$false,
inference(avatar_sat_refutation,[],[f25,f30,f34,f38,f43,f47,f51,f55,f59,f63,f72,f76,f85,f92,f96,f100,f104,f124,f132,f136,f140,f156,f162,f167,f171,f185,f191,f195,f207,f212,f216,f229,f233,f240,f244,f248,f256,f288,f292,f299,f304,f308,f312,f339,f343,f347,f351,f355,f375,f379,f383,f387,f394,f405,f409,f420,f424,f435,f439,f443,f447,f471,f479,f483,f499,f521,f525,f529,f533,f544,f548,f552,f556,f560,f564,f568,f572,f576,f580,f673,f755,f759,f763,f814,f847,f851,f855,f859,f864,f869,f873,f947,f1046,f1050,f1054,f1105,f1129,f1133,f1137,f1141,f1145,f1149,f1281,f1374,f1378,f1382,f1386,f1390,f1428,f1432,f1436,f1440,f1444,f1448,f1488,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1742,f1746,f1750,f1754,f1758,f1763,f1767,f1805,f1825,f1829,f1833,f1837,f1901,f1905,f1909,f1967,f1971,f1981,f1985,f1989,f1993,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2123,f2127,f2149,f2153,f2157,f2161,f2165,f2169,f2173,f2178,f2320,f2324,f2333,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2368,f2372,f2376,f2380,f2384,f2388,f2392,f2788,f2792,f2797,f2801,f2805,f2809,f2813,f2817,f2821,f2825,f3018,f3022,f3026,f3030,f3035,f3039,f3043,f3048,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3082,f3086,f3090,f3094,f3098,f3102,f3106,f3110,f3114,f3118,f3122,f3164,f3168,f3172,f3176,f3180,f3184,f3188,f3192,f3730,f4626,f4630,f4635,f4639,f4644,f4686,f4690,f4694,f4698,f4702,f4839,f4843,f4847,f4851,f4855,f4889,f4893,f4897,f4901,f4905,f4909,f4913,f4917,f4921,f4925,f4930,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4976,f4981,f4985,f4989,f4993,f5226,f5747,f6453,f6457,f6461,f6465,f6469,f6473,f6477,f6481,f6485,f6489,f6493,f6497,f6501,f6505,f6509,f6513,f6520,f6736,f6909,f6913,f6917,f6921,f6925,f6986,f6990,f6994,f6998,f7002,f7006,f7010,f7014,f7018,f7022,f7027,f7031,f7035,f7039,f7044,f7049,f7053,f7057,f7061,f7065,f7069,f7070]) ).
fof(f7070,plain,
( spl0_1
| ~ spl0_13
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f6928,f6733,f83,f22]) ).
fof(f22,plain,
( spl0_1
<=> sum(c,d,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f83,plain,
( spl0_13
<=> ! [X0,X1] : sum(X0,X1,add(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f6733,plain,
( spl0_286
<=> additive_identity = add(d,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f6928,plain,
( sum(c,d,additive_identity)
| ~ spl0_13
| ~ spl0_286 ),
inference(superposition,[],[f84,f6735]) ).
fof(f6735,plain,
( additive_identity = add(d,c)
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f6733]) ).
fof(f84,plain,
( ! [X0,X1] : sum(X0,X1,add(X1,X0))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f7069,plain,
( spl0_312
| ~ spl0_27
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1464,f1426,f189,f7067]) ).
fof(f7067,plain,
( spl0_312
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| additive_identity = add(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f189,plain,
( spl0_27
<=> ! [X0,X1] :
( additive_identity = X0
| ~ sum(additive_inverse(X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1426,plain,
( spl0_109
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,X3),add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1464,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| additive_identity = add(X2,X1) )
| ~ spl0_27
| ~ spl0_109 ),
inference(resolution,[],[f1427,f190]) ).
fof(f190,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X1),X1,X0)
| additive_identity = X0 )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f1427,plain,
( ! [X2,X3,X0,X1] :
( sum(X0,add(X1,X3),add(X2,X3))
| ~ sum(X0,X1,X2) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f7065,plain,
( spl0_311
| ~ spl0_10
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1450,f1426,f61,f7063]) ).
fof(f7063,plain,
( spl0_311
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,X3),X0,add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f61,plain,
( spl0_10
<=> ! [X0,X1,X3] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1450,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,X3),X0,add(X2,X3)) )
| ~ spl0_10
| ~ spl0_109 ),
inference(resolution,[],[f1427,f62]) ).
fof(f62,plain,
( ! [X3,X0,X1] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f7061,plain,
( spl0_310
| ~ spl0_47
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1367,f1147,f1143,f349,f7059]) ).
fof(f7059,plain,
( spl0_310
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(X2),X1,X0)
| sum(add(X0,additive_inverse(X1)),X2,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f349,plain,
( spl0_47
<=> ! [X0] : add(additive_identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1143,plain,
( spl0_101
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,additive_identity,add(X2,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1147,plain,
( spl0_102
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(X2),X1,X0)
| sum(add(X0,additive_inverse(X1)),X2,additive_identity) )
| ~ spl0_47
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1356,f350]) ).
fof(f350,plain,
( ! [X0] : add(additive_identity,X0) = X0
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f1356,plain,
( ! [X2,X0,X1] :
( sum(add(X0,additive_inverse(X1)),X2,additive_identity)
| ~ sum(additive_inverse(add(additive_identity,X2)),X1,X0) )
| ~ spl0_101
| ~ spl0_102 ),
inference(resolution,[],[f1148,f1144]) ).
fof(f1144,plain,
( ! [X2,X0,X1] :
( sum(X0,additive_identity,add(X2,additive_inverse(X1)))
| ~ sum(X0,X1,X2) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f1148,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f7057,plain,
( spl0_309
| ~ spl0_47
| ~ spl0_100
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1366,f1147,f1139,f349,f7055]) ).
fof(f7055,plain,
( spl0_309
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(X2),additive_inverse(X1),X0)
| sum(add(X0,X1),X2,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f1139,plain,
( spl0_100
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(X0,additive_identity,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(X2),additive_inverse(X1),X0)
| sum(add(X0,X1),X2,additive_identity) )
| ~ spl0_47
| ~ spl0_100
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1355,f350]) ).
fof(f1355,plain,
( ! [X2,X0,X1] :
( sum(add(X0,X1),X2,additive_identity)
| ~ sum(additive_inverse(add(additive_identity,X2)),additive_inverse(X1),X0) )
| ~ spl0_100
| ~ spl0_102 ),
inference(resolution,[],[f1148,f1140]) ).
fof(f1140,plain,
( ! [X2,X0,X1] :
( sum(X0,additive_identity,add(X2,X1))
| ~ sum(X0,additive_inverse(X1),X2) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f7053,plain,
( spl0_308
| ~ spl0_77
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1348,f1147,f570,f7051]) ).
fof(f7051,plain,
( spl0_308
<=> ! [X0,X1] :
( sum(additive_identity,X0,additive_identity)
| ~ sum(additive_inverse(add(additive_inverse(X1),X0)),additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f570,plain,
( spl0_77
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,additive_inverse(X1),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1348,plain,
( ! [X0,X1] :
( sum(additive_identity,X0,additive_identity)
| ~ sum(additive_inverse(add(additive_inverse(X1),X0)),additive_identity,X1) )
| ~ spl0_77
| ~ spl0_102 ),
inference(resolution,[],[f1148,f571]) ).
fof(f571,plain,
( ! [X0,X1] :
( sum(X0,additive_inverse(X1),additive_identity)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f7049,plain,
( spl0_307
| ~ spl0_79
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1346,f1147,f578,f7047]) ).
fof(f7047,plain,
( spl0_307
<=> ! [X2,X0,X1] :
( sum(X0,X1,additive_identity)
| ~ sum(X0,X2,additive_inverse(add(additive_inverse(X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f578,plain,
( spl0_79
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1346,plain,
( ! [X2,X0,X1] :
( sum(X0,X1,additive_identity)
| ~ sum(X0,X2,additive_inverse(add(additive_inverse(X2),X1))) )
| ~ spl0_79
| ~ spl0_102 ),
inference(resolution,[],[f1148,f579]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_inverse(X1),X0)
| ~ sum(X0,X1,X2) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f7044,plain,
( spl0_306
| ~ spl0_29
| ~ spl0_65
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1267,f1135,f497,f205,f7042]) ).
fof(f7042,plain,
( spl0_306
<=> ! [X2,X0,X1] :
( add(X2,add(additive_inverse(X2),X0)) = X1
| ~ sum(X0,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f205,plain,
( spl0_29
<=> ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f497,plain,
( spl0_65
<=> ! [X0,X1] : add(X0,X1) = add(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1135,plain,
( spl0_99
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X2),X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1267,plain,
( ! [X2,X0,X1] :
( add(X2,add(additive_inverse(X2),X0)) = X1
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_29
| ~ spl0_65
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1240,f498]) ).
fof(f498,plain,
( ! [X0,X1] : add(X0,X1) = add(X1,X0)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(add(additive_inverse(X2),X0),X2) = X1 )
| ~ spl0_29
| ~ spl0_99 ),
inference(resolution,[],[f1136,f206]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| add(X1,X2) = X0 )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f1136,plain,
( ! [X2,X0,X1] :
( sum(add(additive_inverse(X2),X0),X2,X1)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f7039,plain,
( spl0_305
| ~ spl0_29
| ~ spl0_65
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1225,f1131,f497,f205,f7037]) ).
fof(f7037,plain,
( spl0_305
<=> ! [X2,X0,X1] :
( add(X2,add(X0,additive_inverse(X2))) = X1
| ~ sum(X0,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f1131,plain,
( spl0_98
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X2)),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1225,plain,
( ! [X2,X0,X1] :
( add(X2,add(X0,additive_inverse(X2))) = X1
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_29
| ~ spl0_65
| ~ spl0_98 ),
inference(forward_demodulation,[],[f1198,f498]) ).
fof(f1198,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(add(X0,additive_inverse(X2)),X2) = X1 )
| ~ spl0_29
| ~ spl0_98 ),
inference(resolution,[],[f1132,f206]) ).
fof(f1132,plain,
( ! [X2,X0,X1] :
( sum(add(X0,additive_inverse(X2)),X2,X1)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f7035,plain,
( spl0_304
| ~ spl0_70
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1181,f1127,f542,f7033]) ).
fof(f7033,plain,
( spl0_304
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(add(additive_inverse(X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f542,plain,
( spl0_70
<=> ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1127,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(additive_inverse(X2),X1),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(add(additive_inverse(X2),X1),X0) )
| ~ spl0_70
| ~ spl0_97 ),
inference(resolution,[],[f1128,f543]) ).
fof(f543,plain,
( ! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f1128,plain,
( ! [X2,X0,X1] :
( sum(X0,add(additive_inverse(X2),X1),additive_identity)
| ~ sum(X0,X1,X2) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f7031,plain,
( spl0_303
| ~ spl0_29
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1177,f1127,f205,f7029]) ).
fof(f7029,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(X0,add(additive_inverse(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f1177,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(X0,add(additive_inverse(X2),X1)) )
| ~ spl0_29
| ~ spl0_97 ),
inference(resolution,[],[f1128,f206]) ).
fof(f7027,plain,
( spl0_302
| ~ spl0_9
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f6927,f6733,f57,f7024]) ).
fof(f7024,plain,
( spl0_302
<=> sum(d,c,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f57,plain,
( spl0_9
<=> ! [X0,X1] : sum(X0,X1,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f6927,plain,
( sum(d,c,additive_identity)
| ~ spl0_9
| ~ spl0_286 ),
inference(superposition,[],[f58,f6735]) ).
fof(f58,plain,
( ! [X0,X1] : sum(X0,X1,add(X0,X1))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f7022,plain,
( spl0_301
| ~ spl0_70
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1159,f1103,f542,f7020]) ).
fof(f7020,plain,
( spl0_301
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(add(X1,additive_inverse(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f1103,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,additive_inverse(X2)),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1159,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(add(X1,additive_inverse(X2)),X0) )
| ~ spl0_70
| ~ spl0_96 ),
inference(resolution,[],[f1104,f543]) ).
fof(f1104,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X1,additive_inverse(X2)),additive_identity)
| ~ sum(X0,X1,X2) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f7018,plain,
( spl0_300
| ~ spl0_29
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1155,f1103,f205,f7016]) ).
fof(f7016,plain,
( spl0_300
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(X0,add(X1,additive_inverse(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| additive_identity = add(X0,add(X1,additive_inverse(X2))) )
| ~ spl0_29
| ~ spl0_96 ),
inference(resolution,[],[f1104,f206]) ).
fof(f7014,plain,
( spl0_299
| ~ spl0_35
| ~ spl0_53
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1042,f871,f392,f242,f7012]) ).
fof(f7012,plain,
( spl0_299
<=> ! [X0,X3,X2,X1] :
( sum(X2,X0,X3)
| ~ sum(additive_identity,X0,X1)
| ~ sum(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f242,plain,
( spl0_35
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,additive_identity,X3)
| sum(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f392,plain,
( spl0_53
<=> ! [X0] : add(X0,additive_identity) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f871,plain,
( spl0_91
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,X2,add(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1042,plain,
( ! [X2,X3,X0,X1] :
( sum(X2,X0,X3)
| ~ sum(additive_identity,X0,X1)
| ~ sum(X2,X1,X3) )
| ~ spl0_35
| ~ spl0_53
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1020,f393]) ).
fof(f393,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f1020,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| ~ sum(X2,X1,X3)
| sum(X2,add(X0,additive_identity),X3) )
| ~ spl0_35
| ~ spl0_91 ),
inference(resolution,[],[f872,f243]) ).
fof(f243,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X1,additive_identity,X3)
| ~ sum(X0,X1,X2)
| sum(X0,X3,X2) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f872,plain,
( ! [X2,X0,X1] :
( sum(X1,X2,add(X0,X2))
| ~ sum(additive_identity,X0,X1) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f7010,plain,
( spl0_298
| ~ spl0_36
| ~ spl0_53
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1041,f871,f392,f246,f7008]) ).
fof(f7008,plain,
( spl0_298
<=> ! [X0,X3,X2,X1] :
( sum(X0,X2,X3)
| ~ sum(additive_identity,X0,X1)
| ~ sum(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f246,plain,
( spl0_36
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,additive_identity,X3)
| sum(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1041,plain,
( ! [X2,X3,X0,X1] :
( sum(X0,X2,X3)
| ~ sum(additive_identity,X0,X1)
| ~ sum(X1,X2,X3) )
| ~ spl0_36
| ~ spl0_53
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1019,f393]) ).
fof(f1019,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| ~ sum(X1,X2,X3)
| sum(add(X0,additive_identity),X2,X3) )
| ~ spl0_36
| ~ spl0_91 ),
inference(resolution,[],[f872,f247]) ).
fof(f247,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X3)
| ~ sum(X0,X1,X2)
| sum(X3,X1,X2) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f7006,plain,
( spl0_297
| ~ spl0_45
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f896,f845,f341,f7004]) ).
fof(f7004,plain,
( spl0_297
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X0,X2,X3)
| sum(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f341,plain,
( spl0_45
<=> ! [X4,X0,X3,X2,X1] :
( ~ sum(X0,add(X1,X2),X3)
| ~ sum(X0,X1,X4)
| sum(X4,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f845,plain,
( spl0_85
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X2,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f896,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X0,X2,X3)
| sum(X3,X1,X2) )
| ~ spl0_45
| ~ spl0_85 ),
inference(resolution,[],[f846,f342]) ).
fof(f342,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X0,add(X1,X2),X3)
| ~ sum(X0,X1,X4)
| sum(X4,X2,X3) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f846,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X2,X1),X2)
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f7002,plain,
( spl0_296
| ~ spl0_45
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f874,f812,f341,f7000]) ).
fof(f7000,plain,
( spl0_296
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X0,X1,X2)
| sum(X2,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f812,plain,
( spl0_84
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f874,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X0,X1,X2)
| sum(X2,X3,X3) )
| ~ spl0_45
| ~ spl0_84 ),
inference(resolution,[],[f813,f342]) ).
fof(f813,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X1,X2),X2)
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f6998,plain,
( spl0_295
| ~ spl0_11
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f736,f578,f70,f6996]) ).
fof(f6996,plain,
( spl0_295
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| X0 = X3
| ~ sum(X2,additive_inverse(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f70,plain,
( spl0_11
<=> ! [X4,X0,X2,X1] :
( X2 = X4
| ~ sum(X0,X1,X4)
| ~ sum(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f736,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| X0 = X3
| ~ sum(X2,additive_inverse(X1),X3) )
| ~ spl0_11
| ~ spl0_79 ),
inference(resolution,[],[f579,f71]) ).
fof(f71,plain,
( ! [X2,X0,X1,X4] :
( ~ sum(X0,X1,X4)
| X2 = X4
| ~ sum(X0,X1,X2) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f6994,plain,
( spl0_294
| ~ spl0_41
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f733,f578,f302,f6992]) ).
fof(f6992,plain,
( spl0_294
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X2,X1)
| sum(X3,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f302,plain,
( spl0_41
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,additive_inverse(X2),X3)
| sum(X0,X3,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f733,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X2,X1)
| sum(X3,X0,additive_identity) )
| ~ spl0_41
| ~ spl0_79 ),
inference(resolution,[],[f579,f303]) ).
fof(f303,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X1,additive_inverse(X2),X3)
| ~ sum(X0,X1,X2)
| sum(X0,X3,additive_identity) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f6990,plain,
( spl0_293
| ~ spl0_42
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f732,f578,f306,f6988]) ).
fof(f6988,plain,
( spl0_293
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,additive_identity,X3)
| sum(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f306,plain,
( spl0_42
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,additive_inverse(X2),X3)
| sum(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f732,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,additive_identity,X3)
| sum(X0,X1,X3) )
| ~ spl0_42
| ~ spl0_79 ),
inference(resolution,[],[f579,f307]) ).
fof(f307,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_inverse(X2),X3)
| ~ sum(X0,additive_identity,X1)
| sum(X3,X2,X1) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f6986,plain,
( spl0_292
| ~ spl0_11
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f698,f574,f70,f6984]) ).
fof(f6984,plain,
( spl0_292
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| X0 = X1
| ~ sum(additive_inverse(X2),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f574,plain,
( spl0_78
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_inverse(X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f698,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| X0 = X1
| ~ sum(additive_inverse(X2),X2,X1) )
| ~ spl0_11
| ~ spl0_78 ),
inference(resolution,[],[f575,f71]) ).
fof(f575,plain,
( ! [X0,X1] :
( sum(additive_inverse(X1),X1,X0)
| ~ sum(additive_identity,additive_identity,X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f6925,plain,
( spl0_291
| ~ spl0_11
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f681,f570,f70,f6923]) ).
fof(f6923,plain,
( spl0_291
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = X2
| ~ sum(X0,additive_inverse(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f681,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = X2
| ~ sum(X0,additive_inverse(X1),X2) )
| ~ spl0_11
| ~ spl0_77 ),
inference(resolution,[],[f571,f71]) ).
fof(f6921,plain,
( spl0_290
| ~ spl0_41
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f679,f570,f302,f6919]) ).
fof(f6919,plain,
( spl0_290
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X2,X0,X1)
| sum(X2,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X2,X0,X1)
| sum(X2,additive_identity,additive_identity) )
| ~ spl0_41
| ~ spl0_77 ),
inference(resolution,[],[f571,f303]) ).
fof(f6917,plain,
( spl0_289
| ~ spl0_42
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f678,f570,f306,f6915]) ).
fof(f6915,plain,
( spl0_289
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,additive_identity,X2)
| sum(additive_identity,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,additive_identity,X2)
| sum(additive_identity,X1,X2) )
| ~ spl0_42
| ~ spl0_77 ),
inference(resolution,[],[f571,f307]) ).
fof(f6913,plain,
( spl0_288
| ~ spl0_11
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f597,f550,f70,f6911]) ).
fof(f6911,plain,
( spl0_288
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X2
| ~ sum(X0,additive_identity,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f550,plain,
( spl0_72
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,additive_identity,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f597,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X2
| ~ sum(X0,additive_identity,X2) )
| ~ spl0_11
| ~ spl0_72 ),
inference(resolution,[],[f551,f71]) ).
fof(f551,plain,
( ! [X0,X1] :
( sum(X0,additive_identity,additive_inverse(X1))
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f6909,plain,
( spl0_287
| ~ spl0_40
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f594,f550,f297,f6907]) ).
fof(f6907,plain,
( spl0_287
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(additive_identity,X1,X2)
| sum(X0,X2,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f297,plain,
( spl0_40
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,additive_inverse(X2))
| ~ sum(X1,X2,X3)
| sum(X0,X3,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f594,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(additive_identity,X1,X2)
| sum(X0,X2,additive_identity) )
| ~ spl0_40
| ~ spl0_72 ),
inference(resolution,[],[f551,f298]) ).
fof(f298,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,additive_inverse(X2))
| ~ sum(X1,X2,X3)
| sum(X0,X3,additive_identity) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f6736,plain,
( spl0_286
| ~ spl0_224
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f6521,f6517,f3727,f6733]) ).
fof(f3727,plain,
( spl0_224
<=> additive_identity = multiply(a,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f6517,plain,
( spl0_285
<=> multiply(a,additive_identity) = add(d,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f6521,plain,
( additive_identity = add(d,c)
| ~ spl0_224
| ~ spl0_285 ),
inference(forward_demodulation,[],[f6519,f3729]) ).
fof(f3729,plain,
( additive_identity = multiply(a,additive_identity)
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f3727]) ).
fof(f6519,plain,
( multiply(a,additive_identity) = add(d,c)
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f6517]) ).
fof(f6520,plain,
( spl0_285
| ~ spl0_31
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f3140,f2175,f214,f6517]) ).
fof(f214,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( multiply(X1,X2) = X0
| ~ product(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2175,plain,
( spl0_161
<=> product(a,additive_identity,add(d,c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f3140,plain,
( multiply(a,additive_identity) = add(d,c)
| ~ spl0_31
| ~ spl0_161 ),
inference(resolution,[],[f2177,f215]) ).
fof(f215,plain,
( ! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f2177,plain,
( product(a,additive_identity,add(d,c))
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2175]) ).
fof(f6513,plain,
( spl0_284
| ~ spl0_2
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f2092,f2033,f27,f6511]) ).
fof(f6511,plain,
( spl0_284
<=> ! [X0,X1] :
( ~ sum(a,X0,X1)
| product(X1,b,add(d,multiply(X0,b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f27,plain,
( spl0_2
<=> product(a,b,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2033,plain,
( spl0_150
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(X2,multiply(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2092,plain,
( ! [X0,X1] :
( ~ sum(a,X0,X1)
| product(X1,b,add(d,multiply(X0,b))) )
| ~ spl0_2
| ~ spl0_150 ),
inference(resolution,[],[f2034,f29]) ).
fof(f29,plain,
( product(a,b,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f2034,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(X2,multiply(X3,X1))) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f2033]) ).
fof(f6509,plain,
( spl0_283
| ~ spl0_2
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2080,f2025,f27,f6507]) ).
fof(f6507,plain,
( spl0_283
<=> ! [X0,X1] :
( ~ sum(a,X0,X1)
| sum(d,multiply(X0,b),multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2025,plain,
( spl0_148
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| sum(X2,multiply(X3,X1),multiply(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2080,plain,
( ! [X0,X1] :
( ~ sum(a,X0,X1)
| sum(d,multiply(X0,b),multiply(X1,b)) )
| ~ spl0_2
| ~ spl0_148 ),
inference(resolution,[],[f2026,f29]) ).
fof(f2026,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| sum(X2,multiply(X3,X1),multiply(X4,X1)) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f6505,plain,
( spl0_282
| ~ spl0_2
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f2052,f2017,f27,f6503]) ).
fof(f6503,plain,
( spl0_282
<=> ! [X0,X1] :
( ~ sum(b,X0,X1)
| product(a,X1,add(d,multiply(a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2017,plain,
( spl0_146
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(X2,multiply(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( ~ sum(b,X0,X1)
| product(a,X1,add(d,multiply(a,X0))) )
| ~ spl0_2
| ~ spl0_146 ),
inference(resolution,[],[f2018,f29]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(X2,multiply(X0,X3))) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f2017]) ).
fof(f6501,plain,
( spl0_281
| ~ spl0_2
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f2040,f2013,f27,f6499]) ).
fof(f6499,plain,
( spl0_281
<=> ! [X0,X1] :
( ~ sum(b,X0,X1)
| sum(d,multiply(a,X0),multiply(a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2013,plain,
( spl0_145
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X2,multiply(X0,X3),multiply(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f2040,plain,
( ! [X0,X1] :
( ~ sum(b,X0,X1)
| sum(d,multiply(a,X0),multiply(a,X1)) )
| ~ spl0_2
| ~ spl0_145 ),
inference(resolution,[],[f2014,f29]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X2,multiply(X0,X3),multiply(X0,X4)) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f6497,plain,
( spl0_280
| ~ spl0_5
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1911,f1899,f40,f6495]) ).
fof(f6495,plain,
( spl0_280
<=> ! [X0] :
( ~ sum(c,c,X0)
| product(a,add(additive_inverse(b),additive_inverse(b)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f40,plain,
( spl0_5
<=> product(a,additive_inverse(b),c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1899,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,X2,X0)
| product(a,add(X2,additive_inverse(b)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1911,plain,
( ! [X0] :
( ~ sum(c,c,X0)
| product(a,add(additive_inverse(b),additive_inverse(b)),X0) )
| ~ spl0_5
| ~ spl0_136 ),
inference(resolution,[],[f1900,f42]) ).
fof(f42,plain,
( product(a,additive_inverse(b),c)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f1900,plain,
( ! [X2,X0,X1] :
( ~ product(a,X2,X0)
| ~ sum(X0,c,X1)
| product(a,add(X2,additive_inverse(b)),X1) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1899]) ).
fof(f6493,plain,
( spl0_279
| ~ spl0_8
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1820,f1765,f53,f6491]) ).
fof(f6491,plain,
( spl0_279
<=> ! [X0,X1] :
( ~ sum(X0,a,X1)
| sum(multiply(X0,b),d,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f53,plain,
( spl0_8
<=> ! [X0,X1] : product(X0,X1,multiply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1765,plain,
( spl0_130
<=> ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,X2)
| sum(X1,d,multiply(X2,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1820,plain,
( ! [X0,X1] :
( ~ sum(X0,a,X1)
| sum(multiply(X0,b),d,multiply(X1,b)) )
| ~ spl0_8
| ~ spl0_130 ),
inference(resolution,[],[f1766,f54]) ).
fof(f54,plain,
( ! [X0,X1] : product(X0,X1,multiply(X0,X1))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f1766,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,X2)
| sum(X1,d,multiply(X2,b)) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1765]) ).
fof(f6489,plain,
( spl0_278
| ~ spl0_8
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1808,f1761,f53,f6487]) ).
fof(f6487,plain,
( spl0_278
<=> ! [X0,X1] :
( ~ sum(X0,b,X1)
| sum(multiply(a,X0),d,multiply(a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f1761,plain,
( spl0_129
<=> ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,d,multiply(a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1808,plain,
( ! [X0,X1] :
( ~ sum(X0,b,X1)
| sum(multiply(a,X0),d,multiply(a,X1)) )
| ~ spl0_8
| ~ spl0_129 ),
inference(resolution,[],[f1762,f54]) ).
fof(f1762,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,d,multiply(a,X2)) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1761]) ).
fof(f6485,plain,
( spl0_277
| ~ spl0_9
| ~ spl0_65
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1800,f1752,f497,f57,f6483]) ).
fof(f6483,plain,
( spl0_277
<=> ! [X0,X1] :
( product(X1,b,add(d,multiply(X0,b)))
| ~ sum(X0,a,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1752,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( ~ sum(multiply(X0,b),d,X1)
| ~ sum(X0,a,X2)
| product(X2,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1800,plain,
( ! [X0,X1] :
( product(X1,b,add(d,multiply(X0,b)))
| ~ sum(X0,a,X1) )
| ~ spl0_9
| ~ spl0_65
| ~ spl0_127 ),
inference(forward_demodulation,[],[f1793,f498]) ).
fof(f1793,plain,
( ! [X0,X1] :
( ~ sum(X0,a,X1)
| product(X1,b,add(multiply(X0,b),d)) )
| ~ spl0_9
| ~ spl0_127 ),
inference(resolution,[],[f1753,f58]) ).
fof(f1753,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(X0,b),d,X1)
| ~ sum(X0,a,X2)
| product(X2,b,X1) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f6481,plain,
( spl0_276
| ~ spl0_8
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1791,f1748,f53,f6479]) ).
fof(f6479,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ sum(X0,X1,a)
| sum(multiply(X0,b),multiply(X1,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1748,plain,
( spl0_126
<=> ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1791,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,a)
| sum(multiply(X0,b),multiply(X1,b),d) )
| ~ spl0_8
| ~ spl0_126 ),
inference(resolution,[],[f1749,f54]) ).
fof(f1749,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,b),d) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f6477,plain,
( spl0_275
| ~ spl0_9
| ~ spl0_65
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1788,f1744,f497,f57,f6475]) ).
fof(f6475,plain,
( spl0_275
<=> ! [X0,X1] :
( product(a,X1,add(d,multiply(a,X0)))
| ~ sum(X0,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f1744,plain,
( spl0_125
<=> ! [X2,X0,X1] :
( ~ sum(multiply(a,X0),d,X1)
| ~ sum(X0,b,X2)
| product(a,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1788,plain,
( ! [X0,X1] :
( product(a,X1,add(d,multiply(a,X0)))
| ~ sum(X0,b,X1) )
| ~ spl0_9
| ~ spl0_65
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1780,f498]) ).
fof(f1780,plain,
( ! [X0,X1] :
( ~ sum(X0,b,X1)
| product(a,X1,add(multiply(a,X0),d)) )
| ~ spl0_9
| ~ spl0_125 ),
inference(resolution,[],[f1745,f58]) ).
fof(f1745,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(a,X0),d,X1)
| ~ sum(X0,b,X2)
| product(a,X2,X1) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1744]) ).
fof(f6473,plain,
( spl0_274
| ~ spl0_8
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1770,f1740,f53,f6471]) ).
fof(f6471,plain,
( spl0_274
<=> ! [X0,X1] :
( ~ sum(X0,X1,b)
| sum(multiply(a,X0),multiply(a,X1),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1740,plain,
( spl0_124
<=> ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(a,X2),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1770,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,b)
| sum(multiply(a,X0),multiply(a,X1),d) )
| ~ spl0_8
| ~ spl0_124 ),
inference(resolution,[],[f1741,f54]) ).
fof(f1741,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(a,X2),d) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1740]) ).
fof(f6469,plain,
( spl0_273
| ~ spl0_78
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1691,f1661,f574,f6467]) ).
fof(f6467,plain,
( spl0_273
<=> ! [X0,X1] :
( ~ sum(c,d,X0)
| product(a,X1,X0)
| ~ sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1661,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ sum(c,d,X0)
| ~ sum(additive_inverse(b),b,X1)
| product(a,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1691,plain,
( ! [X0,X1] :
( ~ sum(c,d,X0)
| product(a,X1,X0)
| ~ sum(additive_identity,additive_identity,X1) )
| ~ spl0_78
| ~ spl0_118 ),
inference(resolution,[],[f1662,f575]) ).
fof(f1662,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(b),b,X1)
| ~ sum(c,d,X0)
| product(a,X1,X0) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f6465,plain,
( spl0_272
| ~ spl0_79
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1685,f1657,f578,f6463]) ).
fof(f6463,plain,
( spl0_272
<=> ! [X0,X1] :
( ~ product(a,X0,X1)
| sum(X1,c,d)
| ~ sum(b,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1657,plain,
( spl0_117
<=> ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,additive_inverse(b),b)
| sum(X1,c,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1685,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| sum(X1,c,d)
| ~ sum(b,b,X0) )
| ~ spl0_79
| ~ spl0_117 ),
inference(resolution,[],[f1658,f579]) ).
fof(f1658,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(b),b)
| ~ product(a,X0,X1)
| sum(X1,c,d) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f6461,plain,
( spl0_271
| ~ spl0_31
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1080,f1048,f214,f6459]) ).
fof(f6459,plain,
( spl0_271
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,additive_inverse(b)) = multiply(X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1048,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,additive_inverse(b),multiply(X0,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,additive_inverse(b)) = multiply(X0,c) )
| ~ spl0_31
| ~ spl0_94 ),
inference(resolution,[],[f1049,f215]) ).
fof(f1049,plain,
( ! [X0,X1] :
( product(X1,additive_inverse(b),multiply(X0,c))
| ~ product(X0,a,X1) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f6457,plain,
( spl0_270
| ~ spl0_31
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1063,f1044,f214,f6455]) ).
fof(f6455,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| c = multiply(X0,multiply(X1,additive_inverse(b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1044,plain,
( spl0_93
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| product(X0,multiply(X1,additive_inverse(b)),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1063,plain,
( ! [X0,X1] :
( ~ product(X0,X1,a)
| c = multiply(X0,multiply(X1,additive_inverse(b))) )
| ~ spl0_31
| ~ spl0_93 ),
inference(resolution,[],[f1045,f215]) ).
fof(f1045,plain,
( ! [X0,X1] :
( product(X0,multiply(X1,additive_inverse(b)),c)
| ~ product(X0,X1,a) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f6453,plain,
( spl0_269
| ~ spl0_48
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f764,f753,f353,f6451]) ).
fof(f6451,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,X2)
| product(X2,b,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f353,plain,
( spl0_48
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,multiply(X1,X2),X3)
| ~ product(X0,X1,X4)
| product(X4,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f753,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| product(X0,multiply(X1,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f764,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,X2)
| product(X2,b,d) )
| ~ spl0_48
| ~ spl0_81 ),
inference(resolution,[],[f754,f354]) ).
fof(f354,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,multiply(X1,X2),X3)
| ~ product(X0,X1,X4)
| product(X4,X2,X3) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f754,plain,
( ! [X0,X1] :
( product(X0,multiply(X1,b),d)
| ~ product(X0,X1,a) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f5747,plain,
( ~ spl0_267
| spl0_268
| ~ spl0_30
| ~ spl0_53
| ~ spl0_189
| ~ spl0_212
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f4071,f3727,f3108,f2823,f392,f209,f5744,f5740]) ).
fof(f5740,plain,
( spl0_267
<=> product(a,b,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f5744,plain,
( spl0_268
<=> additive_identity = c ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f209,plain,
( spl0_30
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2823,plain,
( spl0_189
<=> ! [X0] :
( ~ product(a,b,X0)
| sum(X0,c,multiply(a,additive_identity)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f3108,plain,
( spl0_212
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f4071,plain,
( additive_identity = c
| ~ product(a,b,additive_identity)
| ~ spl0_30
| ~ spl0_53
| ~ spl0_189
| ~ spl0_212
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4070,f393]) ).
fof(f4070,plain,
( additive_identity = add(c,additive_identity)
| ~ product(a,b,additive_identity)
| ~ spl0_30
| ~ spl0_189
| ~ spl0_212
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4069,f211]) ).
fof(f211,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f4069,plain,
( additive_identity = add(c,additive_inverse(additive_identity))
| ~ product(a,b,additive_identity)
| ~ spl0_189
| ~ spl0_212
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4043,f3729]) ).
fof(f4043,plain,
( additive_identity = add(c,additive_inverse(multiply(a,additive_identity)))
| ~ product(a,b,additive_identity)
| ~ spl0_189
| ~ spl0_212 ),
inference(resolution,[],[f3109,f2824]) ).
fof(f2824,plain,
( ! [X0] :
( sum(X0,c,multiply(a,additive_identity))
| ~ product(a,b,X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f3109,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f3108]) ).
fof(f5226,plain,
( spl0_266
| ~ spl0_157
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f3244,f3032,f2159,f5223]) ).
fof(f5223,plain,
( spl0_266
<=> sum(additive_identity,additive_identity,multiply(a,additive_identity)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2159,plain,
( spl0_157
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f3032,plain,
( spl0_194
<=> sum(multiply(a,additive_identity),c,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f3244,plain,
( sum(additive_identity,additive_identity,multiply(a,additive_identity))
| ~ spl0_157
| ~ spl0_194 ),
inference(resolution,[],[f3034,f2160]) ).
fof(f2160,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2159]) ).
fof(f3034,plain,
( sum(multiply(a,additive_identity),c,c)
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f3032]) ).
fof(f4993,plain,
( spl0_265
| ~ spl0_23
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1501,f1430,f160,f4991]) ).
fof(f4991,plain,
( spl0_265
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f160,plain,
( spl0_23
<=> ! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1430,plain,
( spl0_110
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X3,X1),add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1501,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X2,X0) )
| ~ spl0_23
| ~ spl0_110 ),
inference(resolution,[],[f1431,f161]) ).
fof(f161,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X1,X0)
| X0 = X1 )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f1431,plain,
( ! [X2,X3,X0,X1] :
( sum(X0,add(X3,X1),add(X2,X3))
| ~ sum(X0,X1,X2) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f4989,plain,
( spl0_264
| ~ spl0_65
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1361,f1147,f497,f4987]) ).
fof(f4987,plain,
( spl0_264
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X1,X0)),X0,X2)
| sum(X2,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1361,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X1,X0)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_65
| ~ spl0_102 ),
inference(superposition,[],[f1148,f498]) ).
fof(f4985,plain,
( spl0_263
| ~ spl0_30
| ~ spl0_75
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1340,f1143,f562,f209,f4983]) ).
fof(f4983,plain,
( spl0_263
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f562,plain,
( spl0_75
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1340,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) )
| ~ spl0_30
| ~ spl0_75
| ~ spl0_101 ),
inference(forward_demodulation,[],[f1327,f211]) ).
fof(f1327,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_identity),X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) )
| ~ spl0_75
| ~ spl0_101 ),
inference(resolution,[],[f1144,f563]) ).
fof(f563,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,X1,additive_identity) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f4981,plain,
( spl0_262
| ~ spl0_65
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1334,f1143,f497,f4979]) ).
fof(f4979,plain,
( spl0_262
<=> ! [X2,X0,X1] :
( sum(X2,additive_identity,add(additive_inverse(X1),X0))
| ~ sum(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1334,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_identity,add(additive_inverse(X1),X0))
| ~ sum(X2,X1,X0) )
| ~ spl0_65
| ~ spl0_101 ),
inference(superposition,[],[f1144,f498]) ).
fof(f4976,plain,
( spl0_261
| ~ spl0_152
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f3124,f2175,f2121,f4973]) ).
fof(f4973,plain,
( spl0_261
<=> sum(add(d,c),c,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2121,plain,
( spl0_152
<=> ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(X0,c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f3124,plain,
( sum(add(d,c),c,c)
| ~ spl0_152
| ~ spl0_161 ),
inference(resolution,[],[f2177,f2122]) ).
fof(f2122,plain,
( ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(X0,c,c) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f4971,plain,
( spl0_260
| ~ spl0_10
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1317,f1143,f61,f4969]) ).
fof(f4969,plain,
( spl0_260
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,X0,add(X2,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1317,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,X0,add(X2,additive_inverse(X1))) )
| ~ spl0_10
| ~ spl0_101 ),
inference(resolution,[],[f1144,f62]) ).
fof(f4967,plain,
( spl0_259
| ~ spl0_30
| ~ spl0_75
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1308,f1139,f562,f209,f4965]) ).
fof(f4965,plain,
( spl0_259
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1308,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_30
| ~ spl0_75
| ~ spl0_100 ),
inference(forward_demodulation,[],[f1296,f211]) ).
fof(f1296,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_identity),additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_75
| ~ spl0_100 ),
inference(resolution,[],[f1140,f563]) ).
fof(f4963,plain,
( spl0_258
| ~ spl0_65
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1302,f1139,f497,f4961]) ).
fof(f4961,plain,
( spl0_258
<=> ! [X2,X0,X1] :
( sum(X2,additive_identity,add(X1,X0))
| ~ sum(X2,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_identity,add(X1,X0))
| ~ sum(X2,additive_inverse(X1),X0) )
| ~ spl0_65
| ~ spl0_100 ),
inference(superposition,[],[f1140,f498]) ).
fof(f4959,plain,
( spl0_257
| ~ spl0_10
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1286,f1139,f61,f4957]) ).
fof(f4957,plain,
( spl0_257
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(additive_identity,X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1286,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(additive_identity,X0,add(X2,X1)) )
| ~ spl0_10
| ~ spl0_100 ),
inference(resolution,[],[f1140,f62]) ).
fof(f4955,plain,
( spl0_256
| ~ spl0_69
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1247,f1135,f531,f4953]) ).
fof(f4953,plain,
( spl0_256
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X1),X0),additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f531,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1247,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X1),X0),additive_identity,additive_identity) )
| ~ spl0_69
| ~ spl0_99 ),
inference(resolution,[],[f1136,f532]) ).
fof(f532,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f4951,plain,
( spl0_255
| ~ spl0_10
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1236,f1135,f61,f4949]) ).
fof(f4949,plain,
( spl0_255
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(additive_inverse(X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1236,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(additive_inverse(X2),X0),X1) )
| ~ spl0_10
| ~ spl0_99 ),
inference(resolution,[],[f1136,f62]) ).
fof(f4947,plain,
( spl0_254
| ~ spl0_69
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1205,f1131,f531,f4945]) ).
fof(f4945,plain,
( spl0_254
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X1)),additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X1)),additive_identity,additive_identity) )
| ~ spl0_69
| ~ spl0_98 ),
inference(resolution,[],[f1132,f532]) ).
fof(f4943,plain,
( spl0_253
| ~ spl0_10
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1194,f1131,f61,f4941]) ).
fof(f4941,plain,
( spl0_253
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(X0,additive_inverse(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1194,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(X0,additive_inverse(X2)),X1) )
| ~ spl0_10
| ~ spl0_98 ),
inference(resolution,[],[f1132,f62]) ).
fof(f4939,plain,
( spl0_252
| ~ spl0_10
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1173,f1127,f61,f4937]) ).
fof(f4937,plain,
( spl0_252
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(additive_inverse(X2),X1),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1173,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(additive_inverse(X2),X1),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_97 ),
inference(resolution,[],[f1128,f62]) ).
fof(f4935,plain,
( spl0_251
| ~ spl0_10
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1151,f1103,f61,f4933]) ).
fof(f4933,plain,
( spl0_251
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,additive_inverse(X2)),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1151,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,additive_inverse(X2)),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_96 ),
inference(resolution,[],[f1104,f62]) ).
fof(f4930,plain,
( spl0_250
| ~ spl0_153
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f3123,f2175,f2125,f4927]) ).
fof(f4927,plain,
( spl0_250
<=> sum(c,add(d,c),c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2125,plain,
( spl0_153
<=> ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(c,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f3123,plain,
( sum(c,add(d,c),c)
| ~ spl0_153
| ~ spl0_161 ),
inference(resolution,[],[f2177,f2126]) ).
fof(f2126,plain,
( ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(c,X0,c) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2125]) ).
fof(f4925,plain,
( spl0_249
| ~ spl0_73
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1032,f871,f554,f4923]) ).
fof(f4923,plain,
( spl0_249
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_identity,additive_identity,add(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f554,plain,
( spl0_73
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1032,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_identity,additive_identity,add(X0,X1)) )
| ~ spl0_73
| ~ spl0_91 ),
inference(resolution,[],[f872,f555]) ).
fof(f555,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f4921,plain,
( spl0_248
| ~ spl0_74
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1025,f871,f558,f4919]) ).
fof(f4919,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,additive_identity,add(X0,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f558,plain,
( spl0_74
<=> ! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1025,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,additive_identity,add(X0,additive_inverse(X1))) )
| ~ spl0_74
| ~ spl0_91 ),
inference(resolution,[],[f872,f559]) ).
fof(f559,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f4917,plain,
( spl0_247
| ~ spl0_70
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1017,f871,f542,f4915]) ).
fof(f4915,plain,
( spl0_247
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X2,X1) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1017,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X2,X1) = add(X0,X2) )
| ~ spl0_70
| ~ spl0_91 ),
inference(resolution,[],[f872,f543]) ).
fof(f4913,plain,
( spl0_246
| ~ spl0_29
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1013,f871,f205,f4911]) ).
fof(f4911,plain,
( spl0_246
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1013,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X0,X2) )
| ~ spl0_29
| ~ spl0_91 ),
inference(resolution,[],[f872,f206]) ).
fof(f4909,plain,
( spl0_245
| ~ spl0_73
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f997,f867,f554,f4907]) ).
fof(f4907,plain,
( spl0_245
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f867,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,X2,add(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f997,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,X0)) )
| ~ spl0_73
| ~ spl0_90 ),
inference(resolution,[],[f868,f555]) ).
fof(f868,plain,
( ! [X2,X0,X1] :
( sum(X0,X2,add(X1,X2))
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f4905,plain,
( spl0_244
| ~ spl0_75
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f996,f867,f562,f4903]) ).
fof(f4903,plain,
( spl0_244
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,add(X1,X0),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f996,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_75
| ~ spl0_90 ),
inference(resolution,[],[f868,f563]) ).
fof(f4901,plain,
( spl0_243
| ~ spl0_74
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f990,f867,f558,f4899]) ).
fof(f4899,plain,
( spl0_243
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,additive_inverse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f990,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,additive_inverse(X0))) )
| ~ spl0_74
| ~ spl0_90 ),
inference(resolution,[],[f868,f559]) ).
fof(f4897,plain,
( spl0_242
| ~ spl0_70
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f982,f867,f542,f4895]) ).
fof(f4895,plain,
( spl0_242
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f982,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X2,X0) )
| ~ spl0_70
| ~ spl0_90 ),
inference(resolution,[],[f868,f543]) ).
fof(f4893,plain,
( spl0_241
| ~ spl0_29
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f978,f867,f205,f4891]) ).
fof(f4891,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f978,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X0,X2) )
| ~ spl0_29
| ~ spl0_90 ),
inference(resolution,[],[f868,f206]) ).
fof(f4889,plain,
( spl0_240
| ~ spl0_73
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f910,f845,f554,f4887]) ).
fof(f4887,plain,
( spl0_240
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f910,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_73
| ~ spl0_85 ),
inference(resolution,[],[f846,f555]) ).
fof(f4855,plain,
( spl0_239
| ~ spl0_70
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f905,f845,f542,f4853]) ).
fof(f4853,plain,
( spl0_239
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X2,X1),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f905,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X2,X1),X0) = X2 )
| ~ spl0_70
| ~ spl0_85 ),
inference(resolution,[],[f846,f543]) ).
fof(f4851,plain,
( spl0_238
| ~ spl0_29
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f901,f845,f205,f4849]) ).
fof(f4849,plain,
( spl0_238
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X2,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f901,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X2,X1)) = X2 )
| ~ spl0_29
| ~ spl0_85 ),
inference(resolution,[],[f846,f206]) ).
fof(f4847,plain,
( spl0_237
| ~ spl0_73
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f888,f812,f554,f4845]) ).
fof(f4845,plain,
( spl0_237
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f888,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_73
| ~ spl0_84 ),
inference(resolution,[],[f813,f555]) ).
fof(f4843,plain,
( spl0_236
| ~ spl0_70
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f883,f812,f542,f4841]) ).
fof(f4841,plain,
( spl0_236
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X1,X2),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X1,X2),X0) = X2 )
| ~ spl0_70
| ~ spl0_84 ),
inference(resolution,[],[f813,f543]) ).
fof(f4839,plain,
( spl0_235
| ~ spl0_29
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f879,f812,f205,f4837]) ).
fof(f4837,plain,
( spl0_235
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f879,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X1,X2)) = X2 )
| ~ spl0_29
| ~ spl0_84 ),
inference(resolution,[],[f813,f206]) ).
fof(f4702,plain,
( spl0_234
| ~ spl0_5
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f2007,f1991,f40,f4700]) ).
fof(f4700,plain,
( spl0_234
<=> ! [X0] :
( ~ sum(a,a,X0)
| sum(c,c,multiply(X0,additive_inverse(b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1991,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,X2)
| sum(X1,c,multiply(X2,additive_inverse(b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2007,plain,
( ! [X0] :
( ~ sum(a,a,X0)
| sum(c,c,multiply(X0,additive_inverse(b))) )
| ~ spl0_5
| ~ spl0_144 ),
inference(resolution,[],[f1992,f42]) ).
fof(f1992,plain,
( ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,X2)
| sum(X1,c,multiply(X2,additive_inverse(b))) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1991]) ).
fof(f4698,plain,
( spl0_233
| ~ spl0_5
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1994,f1983,f40,f4696]) ).
fof(f4696,plain,
( spl0_233
<=> ! [X0] :
( ~ sum(a,X0,a)
| sum(c,multiply(X0,additive_inverse(b)),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1983,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,additive_inverse(b)),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1994,plain,
( ! [X0] :
( ~ sum(a,X0,a)
| sum(c,multiply(X0,additive_inverse(b)),c) )
| ~ spl0_5
| ~ spl0_142 ),
inference(resolution,[],[f1984,f42]) ).
fof(f1984,plain,
( ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,additive_inverse(b)),c) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f4694,plain,
( spl0_232
| ~ spl0_5
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1807,f1761,f40,f4692]) ).
fof(f4692,plain,
( spl0_232
<=> ! [X0] :
( ~ sum(additive_inverse(b),b,X0)
| sum(c,d,multiply(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1807,plain,
( ! [X0] :
( ~ sum(additive_inverse(b),b,X0)
| sum(c,d,multiply(a,X0)) )
| ~ spl0_5
| ~ spl0_129 ),
inference(resolution,[],[f1762,f42]) ).
fof(f4690,plain,
( spl0_231
| ~ spl0_5
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1769,f1740,f40,f4688]) ).
fof(f4688,plain,
( spl0_231
<=> ! [X0] :
( ~ sum(additive_inverse(b),X0,b)
| sum(c,multiply(a,X0),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1769,plain,
( ! [X0] :
( ~ sum(additive_inverse(b),X0,b)
| sum(c,multiply(a,X0),d) )
| ~ spl0_5
| ~ spl0_124 ),
inference(resolution,[],[f1741,f42]) ).
fof(f4686,plain,
( spl0_230
| ~ spl0_8
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1716,f1677,f53,f4684]) ).
fof(f4684,plain,
( spl0_230
<=> ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,additive_inverse(b)),c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1677,plain,
( spl0_122
<=> ! [X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,a)
| sum(X1,c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1716,plain,
( ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,additive_inverse(b)),c,c) )
| ~ spl0_8
| ~ spl0_122 ),
inference(resolution,[],[f1678,f54]) ).
fof(f1678,plain,
( ! [X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,a)
| sum(X1,c,c) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1677]) ).
fof(f4644,plain,
( spl0_229
| ~ spl0_224
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f4640,f4637,f3727,f4642]) ).
fof(f4642,plain,
( spl0_229
<=> ! [X0] :
( ~ sum(additive_identity,c,X0)
| product(a,additive_inverse(b),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f4637,plain,
( spl0_228
<=> ! [X0] :
( ~ sum(multiply(a,additive_identity),c,X0)
| product(a,additive_inverse(b),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f4640,plain,
( ! [X0] :
( ~ sum(additive_identity,c,X0)
| product(a,additive_inverse(b),X0) )
| ~ spl0_224
| ~ spl0_228 ),
inference(forward_demodulation,[],[f4638,f3729]) ).
fof(f4638,plain,
( ! [X0] :
( ~ sum(multiply(a,additive_identity),c,X0)
| product(a,additive_inverse(b),X0) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f4637]) ).
fof(f4639,plain,
( spl0_228
| ~ spl0_8
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1712,f1673,f53,f4637]) ).
fof(f1673,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,additive_identity,X0)
| product(a,additive_inverse(b),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1712,plain,
( ! [X0] :
( ~ sum(multiply(a,additive_identity),c,X0)
| product(a,additive_inverse(b),X0) )
| ~ spl0_8
| ~ spl0_121 ),
inference(resolution,[],[f1674,f54]) ).
fof(f1674,plain,
( ! [X0,X1] :
( ~ product(a,additive_identity,X0)
| ~ sum(X0,c,X1)
| product(a,additive_inverse(b),X1) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1673]) ).
fof(f4635,plain,
( spl0_227
| ~ spl0_8
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f4213,f3727,f53,f4632]) ).
fof(f4632,plain,
( spl0_227
<=> product(a,additive_identity,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f4213,plain,
( product(a,additive_identity,additive_identity)
| ~ spl0_8
| ~ spl0_224 ),
inference(superposition,[],[f54,f3729]) ).
fof(f4630,plain,
( spl0_226
| ~ spl0_31
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f789,f757,f214,f4628]) ).
fof(f4628,plain,
( spl0_226
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,b) = multiply(X0,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f757,plain,
( spl0_82
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,b,multiply(X0,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f789,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,b) = multiply(X0,d) )
| ~ spl0_31
| ~ spl0_82 ),
inference(resolution,[],[f758,f215]) ).
fof(f758,plain,
( ! [X0,X1] :
( product(X1,b,multiply(X0,d))
| ~ product(X0,a,X1) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f4626,plain,
( spl0_225
| ~ spl0_31
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f772,f753,f214,f4624]) ).
fof(f4624,plain,
( spl0_225
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| d = multiply(X0,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f772,plain,
( ! [X0,X1] :
( ~ product(X0,X1,a)
| d = multiply(X0,multiply(X1,b)) )
| ~ spl0_31
| ~ spl0_81 ),
inference(resolution,[],[f754,f215]) ).
fof(f3730,plain,
( spl0_224
| ~ spl0_103
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f3245,f3032,f1279,f3727]) ).
fof(f1279,plain,
( spl0_103
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f3245,plain,
( additive_identity = multiply(a,additive_identity)
| ~ spl0_103
| ~ spl0_194 ),
inference(resolution,[],[f3034,f1280]) ).
fof(f1280,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f3192,plain,
( spl0_223
| ~ spl0_53
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1593,f1438,f392,f3190]) ).
fof(f3190,plain,
( spl0_223
<=> ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X0,X2))
| ~ sum(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1438,plain,
( spl0_112
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(add(X1,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1593,plain,
( ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X0,X2))
| ~ sum(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_112 ),
inference(superposition,[],[f1439,f393]) ).
fof(f1439,plain,
( ! [X2,X3,X0,X1] :
( sum(X2,X3,add(add(X1,X3),X0))
| ~ sum(X0,X1,X2) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f3188,plain,
( spl0_222
| ~ spl0_47
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1592,f1438,f349,f3186]) ).
fof(f3186,plain,
( spl0_222
<=> ! [X2,X0,X1] :
( sum(X1,X0,add(X0,X2))
| ~ sum(X2,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1592,plain,
( ! [X2,X0,X1] :
( sum(X1,X0,add(X0,X2))
| ~ sum(X2,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_112 ),
inference(superposition,[],[f1439,f350]) ).
fof(f3184,plain,
( spl0_221
| ~ spl0_53
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1549,f1434,f392,f3182]) ).
fof(f3182,plain,
( spl0_221
<=> ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X2,X0))
| ~ sum(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1434,plain,
( spl0_111
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(X0,add(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1549,plain,
( ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X2,X0))
| ~ sum(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_111 ),
inference(superposition,[],[f1435,f393]) ).
fof(f1435,plain,
( ! [X2,X3,X0,X1] :
( sum(X2,X3,add(X0,add(X1,X3)))
| ~ sum(X0,X1,X2) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f3180,plain,
( spl0_220
| ~ spl0_47
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1548,f1434,f349,f3178]) ).
fof(f3178,plain,
( spl0_220
<=> ! [X2,X0,X1] :
( sum(X1,X0,add(X2,X0))
| ~ sum(X2,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1548,plain,
( ! [X2,X0,X1] :
( sum(X1,X0,add(X2,X0))
| ~ sum(X2,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_111 ),
inference(superposition,[],[f1435,f350]) ).
fof(f3176,plain,
( spl0_219
| ~ spl0_47
| ~ spl0_72
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1368,f1147,f550,f349,f3174]) ).
fof(f3174,plain,
( spl0_219
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X1),X0,additive_identity)
| sum(additive_inverse(X0),X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1368,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X1),X0,additive_identity)
| sum(additive_inverse(X0),X1,additive_identity) )
| ~ spl0_47
| ~ spl0_72
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1357,f350]) ).
fof(f1357,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,additive_identity)
| ~ sum(additive_inverse(add(additive_identity,X1)),X0,additive_identity) )
| ~ spl0_72
| ~ spl0_102 ),
inference(resolution,[],[f1148,f551]) ).
fof(f3172,plain,
( spl0_218
| ~ spl0_25
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1285,f1139,f169,f3170]) ).
fof(f3170,plain,
( spl0_218
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| add(X2,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f169,plain,
( spl0_25
<=> ! [X0,X1] :
( X0 = X1
| ~ sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1285,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| add(X2,X1) = X0 )
| ~ spl0_25
| ~ spl0_100 ),
inference(resolution,[],[f1140,f170]) ).
fof(f170,plain,
( ! [X0,X1] :
( ~ sum(X1,additive_identity,X0)
| X0 = X1 )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f3168,plain,
( spl0_217
| ~ spl0_71
| ~ spl0_92
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1276,f1135,f945,f546,f3166]) ).
fof(f3166,plain,
( spl0_217
<=> ! [X0,X1] :
( sum(add(X1,X0),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f546,plain,
( spl0_71
<=> ! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f945,plain,
( spl0_92
<=> ! [X0] : additive_inverse(additive_inverse(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1276,plain,
( ! [X0,X1] :
( sum(add(X1,X0),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) )
| ~ spl0_71
| ~ spl0_92
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1259,f946]) ).
fof(f946,plain,
( ! [X0] : additive_inverse(additive_inverse(X0)) = X0
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f1259,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(add(additive_inverse(additive_inverse(X1)),X0),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_99 ),
inference(resolution,[],[f1136,f547]) ).
fof(f547,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f3164,plain,
( spl0_216
| ~ spl0_71
| ~ spl0_92
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1234,f1131,f945,f546,f3162]) ).
fof(f3162,plain,
( spl0_216
<=> ! [X0,X1] :
( sum(add(X0,X1),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1234,plain,
( ! [X0,X1] :
( sum(add(X0,X1),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) )
| ~ spl0_71
| ~ spl0_92
| ~ spl0_98 ),
inference(forward_demodulation,[],[f1217,f946]) ).
fof(f1217,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(add(X0,additive_inverse(additive_inverse(X1))),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_98 ),
inference(resolution,[],[f1132,f547]) ).
fof(f3122,plain,
( spl0_215
| ~ spl0_23
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1182,f1127,f160,f3120]) ).
fof(f3120,plain,
( spl0_215
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1182,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(additive_inverse(X1),X0) )
| ~ spl0_23
| ~ spl0_97 ),
inference(resolution,[],[f1128,f161]) ).
fof(f3118,plain,
( spl0_214
| ~ spl0_65
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1037,f871,f497,f3116]) ).
fof(f3116,plain,
( spl0_214
<=> ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(additive_identity,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1037,plain,
( ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(additive_identity,X0,X2) )
| ~ spl0_65
| ~ spl0_91 ),
inference(superposition,[],[f872,f498]) ).
fof(f3114,plain,
( spl0_213
| ~ spl0_27
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1033,f871,f189,f3112]) ).
fof(f3112,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| additive_identity = add(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1033,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| additive_identity = add(X0,X1) )
| ~ spl0_27
| ~ spl0_91 ),
inference(resolution,[],[f872,f190]) ).
fof(f3110,plain,
( spl0_212
| ~ spl0_28
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1026,f871,f193,f3108]) ).
fof(f193,plain,
( spl0_28
<=> ! [X0,X1] :
( additive_identity = X0
| ~ sum(X1,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1026,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_28
| ~ spl0_91 ),
inference(resolution,[],[f872,f194]) ).
fof(f194,plain,
( ! [X0,X1] :
( ~ sum(X1,additive_inverse(X1),X0)
| additive_identity = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f3106,plain,
( spl0_211
| ~ spl0_10
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1009,f871,f61,f3104]) ).
fof(f3104,plain,
( spl0_211
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X2,X1,add(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1009,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X2,X1,add(X0,X2)) )
| ~ spl0_10
| ~ spl0_91 ),
inference(resolution,[],[f872,f62]) ).
fof(f3102,plain,
( spl0_210
| ~ spl0_65
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1002,f867,f497,f3100]) ).
fof(f3100,plain,
( spl0_210
<=> ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(X2,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1002,plain,
( ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(X2,additive_identity,X0) )
| ~ spl0_65
| ~ spl0_90 ),
inference(superposition,[],[f868,f498]) ).
fof(f3098,plain,
( spl0_209
| ~ spl0_27
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f998,f867,f189,f3096]) ).
fof(f3096,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| additive_identity = add(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f998,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| additive_identity = add(X1,X0) )
| ~ spl0_27
| ~ spl0_90 ),
inference(resolution,[],[f868,f190]) ).
fof(f3094,plain,
( spl0_208
| ~ spl0_28
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f991,f867,f193,f3092]) ).
fof(f3092,plain,
( spl0_208
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X1,additive_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f991,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X1,additive_inverse(X0)) )
| ~ spl0_28
| ~ spl0_90 ),
inference(resolution,[],[f868,f194]) ).
fof(f3090,plain,
( spl0_207
| ~ spl0_10
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f974,f867,f61,f3088]) ).
fof(f3088,plain,
( spl0_207
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,X0,add(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f974,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,X0,add(X1,X2)) )
| ~ spl0_10
| ~ spl0_90 ),
inference(resolution,[],[f868,f62]) ).
fof(f3086,plain,
( spl0_206
| ~ spl0_10
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f953,f853,f61,f3084]) ).
fof(f3084,plain,
( spl0_206
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f853,plain,
( spl0_87
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,X0),additive_identity,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f953,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X1,X0),X2) )
| ~ spl0_10
| ~ spl0_87 ),
inference(resolution,[],[f854,f62]) ).
fof(f854,plain,
( ! [X2,X0,X1] :
( sum(add(X1,X0),additive_identity,X2)
| ~ sum(X0,X1,X2) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f3082,plain,
( spl0_205
| ~ spl0_8
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2144,f2125,f53,f3079]) ).
fof(f3079,plain,
( spl0_205
<=> sum(c,multiply(a,additive_identity),c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2144,plain,
( sum(c,multiply(a,additive_identity),c)
| ~ spl0_8
| ~ spl0_153 ),
inference(resolution,[],[f2126,f54]) ).
fof(f3077,plain,
( spl0_204
| ~ spl0_68
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f952,f853,f527,f3075]) ).
fof(f3075,plain,
( spl0_204
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X0),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f527,plain,
( spl0_68
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f952,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X0),X2,X2) )
| ~ spl0_68
| ~ spl0_87 ),
inference(resolution,[],[f854,f528]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f3073,plain,
( spl0_203
| ~ spl0_10
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f923,f849,f61,f3071]) ).
fof(f3071,plain,
( spl0_203
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f849,plain,
( spl0_86
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X0,X1),additive_identity,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X0,X1),X2) )
| ~ spl0_10
| ~ spl0_86 ),
inference(resolution,[],[f850,f62]) ).
fof(f850,plain,
( ! [X2,X0,X1] :
( sum(add(X0,X1),additive_identity,X2)
| ~ sum(X0,X1,X2) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f3069,plain,
( spl0_202
| ~ spl0_68
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f922,f849,f527,f3067]) ).
fof(f3067,plain,
( spl0_202
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X0,X1),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f922,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X0,X1),X2,X2) )
| ~ spl0_68
| ~ spl0_86 ),
inference(resolution,[],[f850,f528]) ).
fof(f3065,plain,
( spl0_201
| ~ spl0_27
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f911,f845,f189,f3063]) ).
fof(f3063,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f911,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| additive_identity = X0 )
| ~ spl0_27
| ~ spl0_85 ),
inference(resolution,[],[f846,f190]) ).
fof(f3061,plain,
( spl0_200
| ~ spl0_10
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f897,f845,f61,f3059]) ).
fof(f3059,plain,
( spl0_200
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X2,X1),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f897,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X2,X1),X0,X2) )
| ~ spl0_10
| ~ spl0_85 ),
inference(resolution,[],[f846,f62]) ).
fof(f3057,plain,
( spl0_199
| ~ spl0_27
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f889,f812,f189,f3055]) ).
fof(f3055,plain,
( spl0_199
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| additive_identity = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f889,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| additive_identity = X1 )
| ~ spl0_27
| ~ spl0_84 ),
inference(resolution,[],[f813,f190]) ).
fof(f3053,plain,
( spl0_198
| ~ spl0_10
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f875,f812,f61,f3051]) ).
fof(f3051,plain,
( spl0_198
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f875,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X2),X0,X2) )
| ~ spl0_10
| ~ spl0_84 ),
inference(resolution,[],[f813,f62]) ).
fof(f3048,plain,
( spl0_197
| ~ spl0_73
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f749,f578,f554,f3046]) ).
fof(f3046,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f749,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_73
| ~ spl0_79 ),
inference(resolution,[],[f579,f555]) ).
fof(f3043,plain,
( spl0_196
| ~ spl0_75
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f748,f578,f562,f3041]) ).
fof(f3041,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f748,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,X0,additive_identity) )
| ~ spl0_75
| ~ spl0_79 ),
inference(resolution,[],[f579,f563]) ).
fof(f3039,plain,
( spl0_195
| ~ spl0_70
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f743,f578,f542,f3037]) ).
fof(f3037,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(additive_inverse(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(additive_inverse(X1),X2) = X0 )
| ~ spl0_70
| ~ spl0_79 ),
inference(resolution,[],[f579,f543]) ).
fof(f3035,plain,
( spl0_194
| ~ spl0_8
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2142,f2121,f53,f3032]) ).
fof(f2142,plain,
( sum(multiply(a,additive_identity),c,c)
| ~ spl0_8
| ~ spl0_152 ),
inference(resolution,[],[f2122,f54]) ).
fof(f3030,plain,
( spl0_193
| ~ spl0_29
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f739,f578,f205,f3028]) ).
fof(f3028,plain,
( spl0_193
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(X2,additive_inverse(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f739,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(X2,additive_inverse(X1)) = X0 )
| ~ spl0_29
| ~ spl0_79 ),
inference(resolution,[],[f579,f206]) ).
fof(f3026,plain,
( spl0_192
| ~ spl0_70
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f688,f570,f542,f3024]) ).
fof(f3024,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f688,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(additive_inverse(X1),X0) )
| ~ spl0_70
| ~ spl0_77 ),
inference(resolution,[],[f571,f543]) ).
fof(f3022,plain,
( spl0_191
| ~ spl0_29
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f684,f570,f205,f3020]) ).
fof(f3020,plain,
( spl0_191
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f684,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_29
| ~ spl0_77 ),
inference(resolution,[],[f571,f206]) ).
fof(f3018,plain,
( spl0_190
| ~ spl0_71
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f663,f566,f546,f3016]) ).
fof(f3016,plain,
( spl0_190
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_inverse(X0),additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f566,plain,
( spl0_76
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X0),X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f663,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_inverse(X0),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_76 ),
inference(resolution,[],[f567,f547]) ).
fof(f567,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,additive_identity)
| ~ sum(additive_identity,X0,X1) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f2825,plain,
( spl0_189
| ~ spl0_6
| ~ spl0_92
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1963,f1907,f945,f45,f2823]) ).
fof(f45,plain,
( spl0_6
<=> ! [X0] : sum(additive_inverse(X0),X0,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1907,plain,
( spl0_138
<=> ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,additive_inverse(b),X2)
| sum(X1,c,multiply(a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1963,plain,
( ! [X0] :
( ~ product(a,b,X0)
| sum(X0,c,multiply(a,additive_identity)) )
| ~ spl0_6
| ~ spl0_92
| ~ spl0_138 ),
inference(forward_demodulation,[],[f1950,f946]) ).
fof(f1950,plain,
( ! [X0] :
( ~ product(a,additive_inverse(additive_inverse(b)),X0)
| sum(X0,c,multiply(a,additive_identity)) )
| ~ spl0_6
| ~ spl0_138 ),
inference(resolution,[],[f1908,f46]) ).
fof(f46,plain,
( ! [X0] : sum(additive_inverse(X0),X0,additive_identity)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f1908,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(b),X2)
| ~ product(a,X0,X1)
| sum(X1,c,multiply(a,X2)) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1907]) ).
fof(f2821,plain,
( spl0_188
| ~ spl0_2
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1818,f1765,f27,f2819]) ).
fof(f2819,plain,
( spl0_188
<=> ! [X0] :
( ~ sum(a,a,X0)
| sum(d,d,multiply(X0,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1818,plain,
( ! [X0] :
( ~ sum(a,a,X0)
| sum(d,d,multiply(X0,b)) )
| ~ spl0_2
| ~ spl0_130 ),
inference(resolution,[],[f1766,f29]) ).
fof(f2817,plain,
( spl0_187
| ~ spl0_2
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1806,f1761,f27,f2815]) ).
fof(f2815,plain,
( spl0_187
<=> ! [X0] :
( ~ sum(b,b,X0)
| sum(d,d,multiply(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1806,plain,
( ! [X0] :
( ~ sum(b,b,X0)
| sum(d,d,multiply(a,X0)) )
| ~ spl0_2
| ~ spl0_129 ),
inference(resolution,[],[f1762,f29]) ).
fof(f2813,plain,
( spl0_186
| ~ spl0_2
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1789,f1748,f27,f2811]) ).
fof(f2811,plain,
( spl0_186
<=> ! [X0] :
( ~ sum(a,X0,a)
| sum(d,multiply(X0,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1789,plain,
( ! [X0] :
( ~ sum(a,X0,a)
| sum(d,multiply(X0,b),d) )
| ~ spl0_2
| ~ spl0_126 ),
inference(resolution,[],[f1749,f29]) ).
fof(f2809,plain,
( spl0_185
| ~ spl0_2
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1768,f1740,f27,f2807]) ).
fof(f2807,plain,
( spl0_185
<=> ! [X0] :
( ~ sum(b,X0,b)
| sum(d,multiply(a,X0),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1768,plain,
( ! [X0] :
( ~ sum(b,X0,b)
| sum(d,multiply(a,X0),d) )
| ~ spl0_2
| ~ spl0_124 ),
inference(resolution,[],[f1741,f29]) ).
fof(f2805,plain,
( spl0_184
| ~ spl0_9
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1417,f1384,f57,f2803]) ).
fof(f2803,plain,
( spl0_184
<=> ! [X0] :
( ~ sum(a,a,X0)
| product(X0,b,add(d,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1384,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1417,plain,
( ! [X0] :
( ~ sum(a,a,X0)
| product(X0,b,add(d,d)) )
| ~ spl0_9
| ~ spl0_107 ),
inference(resolution,[],[f1385,f58]) ).
fof(f1385,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f2801,plain,
( spl0_183
| ~ spl0_8
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1416,f1380,f53,f2799]) ).
fof(f2799,plain,
( spl0_183
<=> ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,b),d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1380,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1416,plain,
( ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,b),d,d) )
| ~ spl0_8
| ~ spl0_106 ),
inference(resolution,[],[f1381,f54]) ).
fof(f1381,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1380]) ).
fof(f2797,plain,
( ~ spl0_182
| spl0_165
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2439,f2340,f2330,f2794]) ).
fof(f2794,plain,
( spl0_182
<=> sum(additive_identity,b,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2330,plain,
( spl0_165
<=> sum(additive_inverse(b),b,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2340,plain,
( spl0_167
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| sum(additive_inverse(X0),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2439,plain,
( ~ sum(additive_identity,b,additive_identity)
| spl0_165
| ~ spl0_167 ),
inference(resolution,[],[f2341,f2332]) ).
fof(f2332,plain,
( ~ sum(additive_inverse(b),b,b)
| spl0_165 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f2341,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,X1)
| ~ sum(additive_identity,X0,additive_identity) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2340]) ).
fof(f2792,plain,
( spl0_181
| ~ spl0_9
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1400,f1376,f57,f2790]) ).
fof(f2790,plain,
( spl0_181
<=> ! [X0] :
( ~ sum(b,b,X0)
| product(a,X0,add(d,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1376,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1400,plain,
( ! [X0] :
( ~ sum(b,b,X0)
| product(a,X0,add(d,d)) )
| ~ spl0_9
| ~ spl0_105 ),
inference(resolution,[],[f1377,f58]) ).
fof(f1377,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f2788,plain,
( spl0_180
| ~ spl0_8
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1393,f1372,f53,f2786]) ).
fof(f2786,plain,
( spl0_180
<=> ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(a,X0),d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1372,plain,
( spl0_104
<=> ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1393,plain,
( ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(a,X0),d,d) )
| ~ spl0_8
| ~ spl0_104 ),
inference(resolution,[],[f1373,f54]) ).
fof(f1373,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1372]) ).
fof(f2392,plain,
( spl0_179
| ~ spl0_9
| ~ spl0_65
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1365,f1147,f497,f57,f2390]) ).
fof(f2390,plain,
( spl0_179
<=> ! [X0,X1] : sum(add(X0,additive_inverse(add(X0,X1))),X1,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1365,plain,
( ! [X0,X1] : sum(add(X0,additive_inverse(add(X0,X1))),X1,additive_identity)
| ~ spl0_9
| ~ spl0_65
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1351,f498]) ).
fof(f1351,plain,
( ! [X0,X1] : sum(add(additive_inverse(add(X0,X1)),X0),X1,additive_identity)
| ~ spl0_9
| ~ spl0_102 ),
inference(resolution,[],[f1148,f58]) ).
fof(f2388,plain,
( spl0_178
| ~ spl0_47
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1358,f1147,f349,f2386]) ).
fof(f2386,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(X1,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1358,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(X1,X0,additive_identity) )
| ~ spl0_47
| ~ spl0_102 ),
inference(superposition,[],[f1148,f350]) ).
fof(f2384,plain,
( spl0_177
| ~ spl0_63
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1004,f867,f477,f2382]) ).
fof(f2382,plain,
( spl0_177
<=> ! [X0,X1] :
( sum(X1,X0,additive_identity)
| ~ sum(X1,additive_identity,additive_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f477,plain,
( spl0_63
<=> ! [X0] : additive_identity = add(additive_inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1004,plain,
( ! [X0,X1] :
( sum(X1,X0,additive_identity)
| ~ sum(X1,additive_identity,additive_inverse(X0)) )
| ~ spl0_63
| ~ spl0_90 ),
inference(superposition,[],[f868,f478]) ).
fof(f478,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f2380,plain,
( spl0_176
| ~ spl0_23
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f995,f867,f160,f2378]) ).
fof(f2378,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| add(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f995,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| add(X0,X1) = X1 )
| ~ spl0_23
| ~ spl0_90 ),
inference(resolution,[],[f868,f161]) ).
fof(f2376,plain,
( spl0_175
| ~ spl0_23
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f908,f845,f160,f2374]) ).
fof(f2374,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f908,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X1,X0) = X1 )
| ~ spl0_23
| ~ spl0_85 ),
inference(resolution,[],[f846,f161]) ).
fof(f2372,plain,
( spl0_174
| ~ spl0_23
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f886,f812,f160,f2370]) ).
fof(f2370,plain,
( spl0_174
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f886,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X0,X1) = X1 )
| ~ spl0_23
| ~ spl0_84 ),
inference(resolution,[],[f813,f161]) ).
fof(f2368,plain,
( ~ spl0_173
| ~ spl0_78
| spl0_165 ),
inference(avatar_split_clause,[],[f2334,f2330,f574,f2365]) ).
fof(f2365,plain,
( spl0_173
<=> sum(additive_identity,additive_identity,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2334,plain,
( ~ sum(additive_identity,additive_identity,b)
| ~ spl0_78
| spl0_165 ),
inference(resolution,[],[f2332,f575]) ).
fof(f2362,plain,
( spl0_172
| ~ spl0_27
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f750,f578,f189,f2360]) ).
fof(f2360,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f750,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| additive_identity = X0 )
| ~ spl0_27
| ~ spl0_79 ),
inference(resolution,[],[f579,f190]) ).
fof(f2358,plain,
( spl0_171
| ~ spl0_69
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f746,f578,f531,f2356]) ).
fof(f2356,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(X1,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f746,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(X1,additive_identity,additive_identity) )
| ~ spl0_69
| ~ spl0_79 ),
inference(resolution,[],[f579,f532]) ).
fof(f2354,plain,
( spl0_170
| ~ spl0_10
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f735,f578,f61,f2352]) ).
fof(f2352,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X1),X2,X0) )
| ~ spl0_10
| ~ spl0_79 ),
inference(resolution,[],[f579,f62]) ).
fof(f2350,plain,
( spl0_169
| ~ spl0_10
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f697,f574,f61,f2348]) ).
fof(f2348,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X1,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f697,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X1,additive_inverse(X1),X0) )
| ~ spl0_10
| ~ spl0_78 ),
inference(resolution,[],[f575,f62]) ).
fof(f2346,plain,
( spl0_168
| ~ spl0_10
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f680,f570,f61,f2344]) ).
fof(f2344,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_inverse(X1),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f680,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_inverse(X1),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_77 ),
inference(resolution,[],[f571,f62]) ).
fof(f2342,plain,
( spl0_167
| ~ spl0_68
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f655,f566,f527,f2340]) ).
fof(f655,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| sum(additive_inverse(X0),X1,X1) )
| ~ spl0_68
| ~ spl0_76 ),
inference(resolution,[],[f567,f528]) ).
fof(f2338,plain,
( spl0_166
| ~ spl0_10
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f596,f550,f61,f2336]) ).
fof(f2336,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f596,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X0,additive_inverse(X1)) )
| ~ spl0_10
| ~ spl0_72 ),
inference(resolution,[],[f551,f62]) ).
fof(f2333,plain,
( spl0_164
| ~ spl0_165
| ~ spl0_5
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1392,f1372,f40,f2330,f2326]) ).
fof(f2326,plain,
( spl0_164
<=> sum(c,d,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1392,plain,
( ~ sum(additive_inverse(b),b,b)
| sum(c,d,d)
| ~ spl0_5
| ~ spl0_104 ),
inference(resolution,[],[f1373,f42]) ).
fof(f2324,plain,
( spl0_163
| ~ spl0_26
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1084,f1048,f183,f2322]) ).
fof(f2322,plain,
( spl0_163
<=> ! [X0] :
( ~ product(X0,a,a)
| c = multiply(X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f183,plain,
( spl0_26
<=> ! [X0] :
( c = X0
| ~ product(a,additive_inverse(b),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1084,plain,
( ! [X0] :
( ~ product(X0,a,a)
| c = multiply(X0,c) )
| ~ spl0_26
| ~ spl0_94 ),
inference(resolution,[],[f1049,f184]) ).
fof(f184,plain,
( ! [X0] :
( ~ product(a,additive_inverse(b),X0)
| c = X0 )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f2320,plain,
( spl0_162
| ~ spl0_22
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f793,f757,f154,f2318]) ).
fof(f2318,plain,
( spl0_162
<=> ! [X0] :
( ~ product(X0,a,a)
| d = multiply(X0,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f154,plain,
( spl0_22
<=> ! [X0] :
( d = X0
| ~ product(a,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f793,plain,
( ! [X0] :
( ~ product(X0,a,a)
| d = multiply(X0,d) )
| ~ spl0_22
| ~ spl0_82 ),
inference(resolution,[],[f758,f155]) ).
fof(f155,plain,
( ! [X0] :
( ~ product(a,b,X0)
| d = X0 )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f2178,plain,
( spl0_161
| ~ spl0_9
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2128,f1979,f57,f2175]) ).
fof(f1979,plain,
( spl0_141
<=> ! [X0] :
( ~ sum(d,c,X0)
| product(a,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f2128,plain,
( product(a,additive_identity,add(d,c))
| ~ spl0_9
| ~ spl0_141 ),
inference(resolution,[],[f1980,f58]) ).
fof(f1980,plain,
( ! [X0] :
( ~ sum(d,c,X0)
| product(a,additive_identity,X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1979]) ).
fof(f2173,plain,
( spl0_160
| ~ spl0_47
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1034,f871,f349,f2171]) ).
fof(f2171,plain,
( spl0_160
<=> ! [X0,X1] :
( sum(X1,X0,X0)
| ~ sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1034,plain,
( ! [X0,X1] :
( sum(X1,X0,X0)
| ~ sum(additive_identity,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_91 ),
inference(superposition,[],[f872,f350]) ).
fof(f2169,plain,
( spl0_159
| ~ spl0_30
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f751,f578,f209,f2167]) ).
fof(f2167,plain,
( spl0_159
<=> ! [X0,X1] :
( sum(X0,additive_identity,X1)
| ~ sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f751,plain,
( ! [X0,X1] :
( sum(X0,additive_identity,X1)
| ~ sum(X1,additive_identity,X0) )
| ~ spl0_30
| ~ spl0_79 ),
inference(superposition,[],[f579,f211]) ).
fof(f2165,plain,
( spl0_158
| ~ spl0_71
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f734,f578,f546,f2163]) ).
fof(f2163,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f734,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,additive_identity,X0) )
| ~ spl0_71
| ~ spl0_79 ),
inference(resolution,[],[f579,f547]) ).
fof(f2161,plain,
( spl0_157
| ~ spl0_74
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f729,f578,f558,f2159]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_74
| ~ spl0_79 ),
inference(resolution,[],[f579,f559]) ).
fof(f2157,plain,
( spl0_156
| ~ spl0_23
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f689,f570,f160,f2155]) ).
fof(f2155,plain,
( spl0_156
<=> ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| additive_identity = additive_inverse(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f689,plain,
( ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| additive_identity = additive_inverse(X0) )
| ~ spl0_23
| ~ spl0_77 ),
inference(resolution,[],[f571,f161]) ).
fof(f2153,plain,
( spl0_155
| ~ spl0_30
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f637,f562,f209,f2151]) ).
fof(f2151,plain,
( spl0_155
<=> ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_identity,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f637,plain,
( ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_identity,X0,additive_identity) )
| ~ spl0_30
| ~ spl0_75 ),
inference(superposition,[],[f563,f211]) ).
fof(f2149,plain,
( spl0_154
| ~ spl0_25
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f593,f550,f169,f2147]) ).
fof(f2147,plain,
( spl0_154
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f593,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X0 )
| ~ spl0_25
| ~ spl0_72 ),
inference(resolution,[],[f551,f170]) ).
fof(f2127,plain,
( spl0_153
| ~ spl0_5
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1707,f1669,f40,f2125]) ).
fof(f1669,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ product(a,additive_identity,X0)
| ~ product(a,additive_inverse(b),X1)
| sum(X1,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1707,plain,
( ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(c,X0,c) )
| ~ spl0_5
| ~ spl0_120 ),
inference(resolution,[],[f1670,f42]) ).
fof(f1670,plain,
( ! [X0,X1] :
( ~ product(a,additive_inverse(b),X1)
| ~ product(a,additive_identity,X0)
| sum(X1,X0,c) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f2123,plain,
( spl0_152
| ~ spl0_5
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1702,f1665,f40,f2121]) ).
fof(f1665,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ product(a,additive_inverse(b),X0)
| ~ product(a,additive_identity,X1)
| sum(X1,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1702,plain,
( ! [X0] :
( ~ product(a,additive_identity,X0)
| sum(X0,c,c) )
| ~ spl0_5
| ~ spl0_119 ),
inference(resolution,[],[f1666,f42]) ).
fof(f1666,plain,
( ! [X0,X1] :
( ~ product(a,additive_inverse(b),X0)
| ~ product(a,additive_identity,X1)
| sum(X1,X0,c) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f2039,plain,
( spl0_151
| ~ spl0_13
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f462,f445,f83,f2037]) ).
fof(f2037,plain,
( spl0_151
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(multiply(X3,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f445,plain,
( spl0_61
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X2,multiply(X3,X1),X4)
| ~ sum(X0,X3,X5)
| product(X5,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f462,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(multiply(X3,X1),X2)) )
| ~ spl0_13
| ~ spl0_61 ),
inference(resolution,[],[f446,f84]) ).
fof(f446,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X2,multiply(X3,X1),X4)
| ~ product(X0,X1,X2)
| ~ sum(X0,X3,X5)
| product(X5,X1,X4) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f2035,plain,
( spl0_150
| ~ spl0_9
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f461,f445,f57,f2033]) ).
fof(f461,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(X2,multiply(X3,X1))) )
| ~ spl0_9
| ~ spl0_61 ),
inference(resolution,[],[f446,f58]) ).
fof(f2031,plain,
( spl0_149
| ~ spl0_6
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1692,f1661,f45,f2029]) ).
fof(f2029,plain,
( spl0_149
<=> ! [X0] :
( ~ sum(c,d,X0)
| product(a,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1692,plain,
( ! [X0] :
( ~ sum(c,d,X0)
| product(a,additive_identity,X0) )
| ~ spl0_6
| ~ spl0_118 ),
inference(resolution,[],[f1662,f46]) ).
fof(f2027,plain,
( spl0_148
| ~ spl0_8
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f458,f441,f53,f2025]) ).
fof(f441,plain,
( spl0_60
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| sum(X2,X4,multiply(X5,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| sum(X2,multiply(X3,X1),multiply(X4,X1)) )
| ~ spl0_8
| ~ spl0_60 ),
inference(resolution,[],[f442,f54]) ).
fof(f442,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X1,X4)
| ~ product(X0,X1,X2)
| ~ sum(X0,X3,X5)
| sum(X2,X4,multiply(X5,X1)) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f2023,plain,
( spl0_147
| ~ spl0_13
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f454,f437,f83,f2021]) ).
fof(f2021,plain,
( spl0_147
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(multiply(X0,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f437,plain,
( spl0_59
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X2,multiply(X0,X3),X4)
| ~ sum(X1,X3,X5)
| product(X0,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f454,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(multiply(X0,X3),X2)) )
| ~ spl0_13
| ~ spl0_59 ),
inference(resolution,[],[f438,f84]) ).
fof(f438,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X2,multiply(X0,X3),X4)
| ~ product(X0,X1,X2)
| ~ sum(X1,X3,X5)
| product(X0,X5,X4) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f2019,plain,
( spl0_146
| ~ spl0_9
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f453,f437,f57,f2017]) ).
fof(f453,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(X2,multiply(X0,X3))) )
| ~ spl0_9
| ~ spl0_59 ),
inference(resolution,[],[f438,f58]) ).
fof(f2015,plain,
( spl0_145
| ~ spl0_8
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f450,f433,f53,f2013]) ).
fof(f433,plain,
( spl0_58
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| sum(X2,X4,multiply(X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f450,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X2,multiply(X0,X3),multiply(X0,X4)) )
| ~ spl0_8
| ~ spl0_58 ),
inference(resolution,[],[f434,f54]) ).
fof(f434,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X3,X4)
| ~ product(X0,X1,X2)
| ~ sum(X1,X3,X5)
| sum(X2,X4,multiply(X0,X5)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f1993,plain,
( spl0_144
| ~ spl0_5
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f457,f441,f40,f1991]) ).
fof(f457,plain,
( ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,X2)
| sum(X1,c,multiply(X2,additive_inverse(b))) )
| ~ spl0_5
| ~ spl0_60 ),
inference(resolution,[],[f442,f42]) ).
fof(f1989,plain,
( spl0_143
| ~ spl0_8
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f431,f422,f53,f1987]) ).
fof(f1987,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ sum(multiply(X0,additive_inverse(b)),c,X1)
| ~ sum(X0,a,X2)
| product(X2,additive_inverse(b),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f422,plain,
( spl0_57
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,a,X3)
| product(X3,additive_inverse(b),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f431,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(X0,additive_inverse(b)),c,X1)
| ~ sum(X0,a,X2)
| product(X2,additive_inverse(b),X1) )
| ~ spl0_8
| ~ spl0_57 ),
inference(resolution,[],[f423,f54]) ).
fof(f423,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,a,X3)
| product(X3,additive_inverse(b),X2) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f1985,plain,
( spl0_142
| ~ spl0_8
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f426,f418,f53,f1983]) ).
fof(f418,plain,
( spl0_56
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ product(X2,additive_inverse(b),X3)
| ~ sum(X0,X2,a)
| sum(X1,X3,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f426,plain,
( ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,additive_inverse(b)),c) )
| ~ spl0_8
| ~ spl0_56 ),
inference(resolution,[],[f419,f54]) ).
fof(f419,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X2,additive_inverse(b),X3)
| ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,X2,a)
| sum(X1,X3,c) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f1981,plain,
( spl0_141
| ~ spl0_2
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1421,f1388,f27,f1979]) ).
fof(f1388,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,b,X0)
| product(a,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1421,plain,
( ! [X0] :
( ~ sum(d,c,X0)
| product(a,additive_identity,X0) )
| ~ spl0_2
| ~ spl0_108 ),
inference(resolution,[],[f1389,f29]) ).
fof(f1389,plain,
( ! [X0,X1] :
( ~ product(a,b,X0)
| ~ sum(X0,c,X1)
| product(a,additive_identity,X1) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f1971,plain,
( spl0_140
| ~ spl0_6
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f460,f445,f45,f1969]) ).
fof(f1969,plain,
( spl0_140
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,additive_inverse(multiply(X2,X1)))
| ~ sum(X0,X2,X3)
| product(X3,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f460,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,additive_inverse(multiply(X2,X1)))
| ~ sum(X0,X2,X3)
| product(X3,X1,additive_identity) )
| ~ spl0_6
| ~ spl0_61 ),
inference(resolution,[],[f446,f46]) ).
fof(f1967,plain,
( spl0_139
| ~ spl0_6
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f452,f437,f45,f1965]) ).
fof(f1965,plain,
( spl0_139
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,additive_inverse(multiply(X0,X2)))
| ~ sum(X1,X2,X3)
| product(X0,X3,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f452,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,additive_inverse(multiply(X0,X2)))
| ~ sum(X1,X2,X3)
| product(X0,X3,additive_identity) )
| ~ spl0_6
| ~ spl0_59 ),
inference(resolution,[],[f438,f46]) ).
fof(f1909,plain,
( spl0_138
| ~ spl0_5
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f449,f433,f40,f1907]) ).
fof(f449,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,additive_inverse(b),X2)
| sum(X1,c,multiply(a,X2)) )
| ~ spl0_5
| ~ spl0_58 ),
inference(resolution,[],[f434,f42]) ).
fof(f1905,plain,
( spl0_137
| ~ spl0_13
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f416,f407,f83,f1903]) ).
fof(f1903,plain,
( spl0_137
<=> ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,X2,X0)
| product(a,add(additive_inverse(b),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f407,plain,
( spl0_55
<=> ! [X0,X3,X2,X1] :
( ~ product(a,X0,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,additive_inverse(b),X3)
| product(a,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f416,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,X2,X0)
| product(a,add(additive_inverse(b),X2),X1) )
| ~ spl0_13
| ~ spl0_55 ),
inference(resolution,[],[f408,f84]) ).
fof(f408,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_inverse(b),X3)
| ~ sum(X1,c,X2)
| ~ product(a,X0,X1)
| product(a,X3,X2) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f1901,plain,
( spl0_136
| ~ spl0_9
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f415,f407,f57,f1899]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,X2,X0)
| product(a,add(X2,additive_inverse(b)),X1) )
| ~ spl0_9
| ~ spl0_55 ),
inference(resolution,[],[f408,f58]) ).
fof(f1837,plain,
( spl0_135
| ~ spl0_3
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f459,f445,f32,f1835]) ).
fof(f1835,plain,
( spl0_135
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,additive_identity)
| ~ sum(X0,X2,X3)
| product(X3,X1,multiply(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f32,plain,
( spl0_3
<=> ! [X0] : sum(additive_identity,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f459,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,additive_identity)
| ~ sum(X0,X2,X3)
| product(X3,X1,multiply(X2,X1)) )
| ~ spl0_3
| ~ spl0_61 ),
inference(resolution,[],[f446,f33]) ).
fof(f33,plain,
( ! [X0] : sum(additive_identity,X0,X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f1833,plain,
( spl0_134
| ~ spl0_3
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f451,f437,f32,f1831]) ).
fof(f1831,plain,
( spl0_134
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| product(X0,X3,multiply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| product(X0,X3,multiply(X0,X2)) )
| ~ spl0_3
| ~ spl0_59 ),
inference(resolution,[],[f438,f33]) ).
fof(f1829,plain,
( spl0_133
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f126,f90,f83,f1827]) ).
fof(f1827,plain,
( spl0_133
<=> ! [X4,X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X0,X4,add(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f90,plain,
( spl0_14
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| sum(X0,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f126,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X0,X4,add(X3,X2)) )
| ~ spl0_13
| ~ spl0_14 ),
inference(resolution,[],[f84,f91]) ).
fof(f91,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X2,X3,X5)
| ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X0,X4,X5) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f1825,plain,
( spl0_132
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f125,f94,f83,f1823]) ).
fof(f1823,plain,
( spl0_132
<=> ! [X4,X0,X3,X2,X1] :
( ~ sum(X0,add(X1,X2),X3)
| ~ sum(X0,X2,X4)
| sum(X4,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f94,plain,
( spl0_15
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| sum(X2,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f125,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X0,add(X1,X2),X3)
| ~ sum(X0,X2,X4)
| sum(X4,X1,X3) )
| ~ spl0_13
| ~ spl0_15 ),
inference(resolution,[],[f84,f95]) ).
fof(f95,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5)
| ~ sum(X0,X1,X2)
| sum(X2,X3,X5) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f1805,plain,
( spl0_115
| ~ spl0_131
| ~ spl0_2
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1414,f1380,f27,f1802,f1481]) ).
fof(f1481,plain,
( spl0_115
<=> sum(d,d,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1802,plain,
( spl0_131
<=> sum(a,a,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1414,plain,
( ~ sum(a,a,a)
| sum(d,d,d)
| ~ spl0_2
| ~ spl0_106 ),
inference(resolution,[],[f1381,f29]) ).
fof(f1767,plain,
( spl0_130
| ~ spl0_2
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f456,f441,f27,f1765]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,X2)
| sum(X1,d,multiply(X2,b)) )
| ~ spl0_2
| ~ spl0_60 ),
inference(resolution,[],[f442,f29]) ).
fof(f1763,plain,
( spl0_129
| ~ spl0_2
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f448,f433,f27,f1761]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,d,multiply(a,X2)) )
| ~ spl0_2
| ~ spl0_58 ),
inference(resolution,[],[f434,f29]) ).
fof(f1758,plain,
( spl0_128
| ~ spl0_6
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f413,f407,f45,f1756]) ).
fof(f1756,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,additive_inverse(additive_inverse(b)),X0)
| product(a,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f413,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,additive_inverse(additive_inverse(b)),X0)
| product(a,additive_identity,X1) )
| ~ spl0_6
| ~ spl0_55 ),
inference(resolution,[],[f408,f46]) ).
fof(f1754,plain,
( spl0_127
| ~ spl0_8
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f401,f385,f53,f1752]) ).
fof(f385,plain,
( spl0_52
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,b,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,a,X3)
| product(X3,b,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(X0,b),d,X1)
| ~ sum(X0,a,X2)
| product(X2,b,X1) )
| ~ spl0_8
| ~ spl0_52 ),
inference(resolution,[],[f386,f54]) ).
fof(f386,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,a,X3)
| product(X3,b,X2) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f1750,plain,
( spl0_126
| ~ spl0_8
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f399,f381,f53,f1748]) ).
fof(f381,plain,
( spl0_51
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,b,X1)
| ~ product(X2,b,X3)
| ~ sum(X0,X2,a)
| sum(X1,X3,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f399,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,b),d) )
| ~ spl0_8
| ~ spl0_51 ),
inference(resolution,[],[f382,f54]) ).
fof(f382,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X2,b,X3)
| ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,X3,d) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f1746,plain,
( spl0_125
| ~ spl0_8
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f397,f377,f53,f1744]) ).
fof(f377,plain,
( spl0_50
<=> ! [X0,X3,X2,X1] :
( ~ product(a,X0,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,b,X3)
| product(a,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f397,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(a,X0),d,X1)
| ~ sum(X0,b,X2)
| product(a,X2,X1) )
| ~ spl0_8
| ~ spl0_50 ),
inference(resolution,[],[f378,f54]) ).
fof(f378,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,b,X3)
| product(a,X3,X2) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f1742,plain,
( spl0_124
| ~ spl0_8
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f390,f373,f53,f1740]) ).
fof(f373,plain,
( spl0_49
<=> ! [X0,X3,X2,X1] :
( ~ product(a,X0,X1)
| ~ product(a,X2,X3)
| ~ sum(X0,X2,b)
| sum(X1,X3,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f390,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(a,X2),d) )
| ~ spl0_8
| ~ spl0_49 ),
inference(resolution,[],[f374,f54]) ).
fof(f374,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X2,X3)
| ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,X3,d) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f1683,plain,
( spl0_123
| ~ spl0_5
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f430,f422,f40,f1681]) ).
fof(f1681,plain,
( spl0_123
<=> ! [X0,X1] :
( ~ sum(c,c,X0)
| ~ sum(a,a,X1)
| product(X1,additive_inverse(b),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f430,plain,
( ! [X0,X1] :
( ~ sum(c,c,X0)
| ~ sum(a,a,X1)
| product(X1,additive_inverse(b),X0) )
| ~ spl0_5
| ~ spl0_57 ),
inference(resolution,[],[f423,f42]) ).
fof(f1679,plain,
( spl0_122
| ~ spl0_5
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f425,f418,f40,f1677]) ).
fof(f425,plain,
( ! [X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,a,a)
| sum(X1,c,c) )
| ~ spl0_5
| ~ spl0_56 ),
inference(resolution,[],[f419,f42]) ).
fof(f1675,plain,
( spl0_121
| ~ spl0_3
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f412,f407,f32,f1673]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,additive_identity,X0)
| product(a,additive_inverse(b),X1) )
| ~ spl0_3
| ~ spl0_55 ),
inference(resolution,[],[f408,f33]) ).
fof(f1671,plain,
( spl0_120
| ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f411,f403,f36,f1669]) ).
fof(f36,plain,
( spl0_4
<=> ! [X0] : sum(X0,additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f403,plain,
( spl0_54
<=> ! [X0,X3,X2,X1] :
( ~ product(a,X0,X1)
| ~ product(a,X2,X3)
| ~ sum(X0,X2,additive_inverse(b))
| sum(X1,X3,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ product(a,additive_identity,X0)
| ~ product(a,additive_inverse(b),X1)
| sum(X1,X0,c) )
| ~ spl0_4
| ~ spl0_54 ),
inference(resolution,[],[f404,f37]) ).
fof(f37,plain,
( ! [X0] : sum(X0,additive_identity,X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f404,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X2,additive_inverse(b))
| ~ product(a,X2,X3)
| ~ product(a,X0,X1)
| sum(X1,X3,c) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f1667,plain,
( spl0_119
| ~ spl0_3
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f410,f403,f32,f1665]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ product(a,additive_inverse(b),X0)
| ~ product(a,additive_identity,X1)
| sum(X1,X0,c) )
| ~ spl0_3
| ~ spl0_54 ),
inference(resolution,[],[f404,f33]) ).
fof(f1663,plain,
( spl0_118
| ~ spl0_5
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f396,f377,f40,f1661]) ).
fof(f396,plain,
( ! [X0,X1] :
( ~ sum(c,d,X0)
| ~ sum(additive_inverse(b),b,X1)
| product(a,X1,X0) )
| ~ spl0_5
| ~ spl0_50 ),
inference(resolution,[],[f378,f42]) ).
fof(f1659,plain,
( spl0_117
| ~ spl0_5
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f389,f373,f40,f1657]) ).
fof(f389,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,additive_inverse(b),b)
| sum(X1,c,d) )
| ~ spl0_5
| ~ spl0_49 ),
inference(resolution,[],[f374,f42]) ).
fof(f1488,plain,
( spl0_115
| ~ spl0_116
| ~ spl0_2
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1391,f1372,f27,f1485,f1481]) ).
fof(f1485,plain,
( spl0_116
<=> sum(b,b,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1391,plain,
( ~ sum(b,b,b)
| sum(d,d,d)
| ~ spl0_2
| ~ spl0_104 ),
inference(resolution,[],[f1373,f29]) ).
fof(f1448,plain,
( spl0_114
| ~ spl0_8
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f370,f353,f53,f1446]) ).
fof(f1446,plain,
( spl0_114
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| product(X2,X3,multiply(X0,multiply(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f370,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| product(X2,X3,multiply(X0,multiply(X1,X3))) )
| ~ spl0_8
| ~ spl0_48 ),
inference(resolution,[],[f354,f54]) ).
fof(f1444,plain,
( spl0_113
| ~ spl0_8
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f369,f345,f53,f1442]) ).
fof(f1442,plain,
( spl0_113
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| product(X0,multiply(X1,X3),multiply(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f345,plain,
( spl0_46
<=> ! [X4,X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| product(X0,X4,multiply(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f369,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| product(X0,multiply(X1,X3),multiply(X2,X3)) )
| ~ spl0_8
| ~ spl0_46 ),
inference(resolution,[],[f346,f54]) ).
fof(f346,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,multiply(X2,X3)) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f1440,plain,
( spl0_112
| ~ spl0_13
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f366,f341,f83,f1438]) ).
fof(f366,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(add(X1,X3),X0)) )
| ~ spl0_13
| ~ spl0_45 ),
inference(resolution,[],[f342,f84]) ).
fof(f1436,plain,
( spl0_111
| ~ spl0_9
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f365,f341,f57,f1434]) ).
fof(f365,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(X0,add(X1,X3))) )
| ~ spl0_9
| ~ spl0_45 ),
inference(resolution,[],[f342,f58]) ).
fof(f1432,plain,
( spl0_110
| ~ spl0_13
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f361,f337,f83,f1430]) ).
fof(f337,plain,
( spl0_44
<=> ! [X4,X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X0,X4,add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f361,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X3,X1),add(X2,X3)) )
| ~ spl0_13
| ~ spl0_44 ),
inference(resolution,[],[f338,f84]) ).
fof(f338,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2)
| sum(X0,X4,add(X2,X3)) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f1428,plain,
( spl0_109
| ~ spl0_9
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f360,f337,f57,f1426]) ).
fof(f360,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,X3),add(X2,X3)) )
| ~ spl0_9
| ~ spl0_44 ),
inference(resolution,[],[f338,f58]) ).
fof(f1390,plain,
( spl0_108
| ~ spl0_7
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f414,f407,f49,f1388]) ).
fof(f49,plain,
( spl0_7
<=> ! [X0] : sum(X0,additive_inverse(X0),additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f414,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,b,X0)
| product(a,additive_identity,X1) )
| ~ spl0_7
| ~ spl0_55 ),
inference(resolution,[],[f408,f50]) ).
fof(f50,plain,
( ! [X0] : sum(X0,additive_inverse(X0),additive_identity)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f1386,plain,
( spl0_107
| ~ spl0_2
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f400,f385,f27,f1384]) ).
fof(f400,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) )
| ~ spl0_2
| ~ spl0_52 ),
inference(resolution,[],[f386,f29]) ).
fof(f1382,plain,
( spl0_106
| ~ spl0_2
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f398,f381,f27,f1380]) ).
fof(f398,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) )
| ~ spl0_2
| ~ spl0_51 ),
inference(resolution,[],[f382,f29]) ).
fof(f1378,plain,
( spl0_105
| ~ spl0_2
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f395,f377,f27,f1376]) ).
fof(f395,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) )
| ~ spl0_2
| ~ spl0_50 ),
inference(resolution,[],[f378,f29]) ).
fof(f1374,plain,
( spl0_104
| ~ spl0_2
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f388,f373,f27,f1372]) ).
fof(f388,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) )
| ~ spl0_2
| ~ spl0_49 ),
inference(resolution,[],[f374,f29]) ).
fof(f1281,plain,
( spl0_103
| ~ spl0_28
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f730,f578,f193,f1279]) ).
fof(f730,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 )
| ~ spl0_28
| ~ spl0_79 ),
inference(resolution,[],[f579,f194]) ).
fof(f1149,plain,
( spl0_102
| ~ spl0_6
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f364,f341,f45,f1147]) ).
fof(f364,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_6
| ~ spl0_45 ),
inference(resolution,[],[f342,f46]) ).
fof(f1145,plain,
( spl0_101
| ~ spl0_7
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f359,f337,f49,f1143]) ).
fof(f359,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,additive_identity,add(X2,additive_inverse(X1))) )
| ~ spl0_7
| ~ spl0_44 ),
inference(resolution,[],[f338,f50]) ).
fof(f1141,plain,
( spl0_100
| ~ spl0_6
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f358,f337,f45,f1139]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(X0,additive_identity,add(X2,X1)) )
| ~ spl0_6
| ~ spl0_44 ),
inference(resolution,[],[f338,f46]) ).
fof(f1137,plain,
( spl0_99
| ~ spl0_13
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f326,f306,f83,f1135]) ).
fof(f326,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X2),X0),X2,X1) )
| ~ spl0_13
| ~ spl0_42 ),
inference(resolution,[],[f307,f84]) ).
fof(f1133,plain,
( spl0_98
| ~ spl0_9
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f325,f306,f57,f1131]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X2)),X2,X1) )
| ~ spl0_9
| ~ spl0_42 ),
inference(resolution,[],[f307,f58]) ).
fof(f1129,plain,
( spl0_97
| ~ spl0_13
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f320,f302,f83,f1127]) ).
fof(f320,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(additive_inverse(X2),X1),additive_identity) )
| ~ spl0_13
| ~ spl0_41 ),
inference(resolution,[],[f303,f84]) ).
fof(f1105,plain,
( spl0_96
| ~ spl0_9
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f319,f302,f57,f1103]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,additive_inverse(X2)),additive_identity) )
| ~ spl0_9
| ~ spl0_41 ),
inference(resolution,[],[f303,f58]) ).
fof(f1054,plain,
( spl0_95
| ~ spl0_5
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f368,f345,f40,f1052]) ).
fof(f1052,plain,
( spl0_95
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,c,multiply(X1,additive_inverse(b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f368,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,c,multiply(X1,additive_inverse(b))) )
| ~ spl0_5
| ~ spl0_46 ),
inference(resolution,[],[f346,f42]) ).
fof(f1050,plain,
( spl0_94
| ~ spl0_8
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f295,f290,f53,f1048]) ).
fof(f290,plain,
( spl0_39
<=> ! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,a,X2)
| product(X2,additive_inverse(b),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f295,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,additive_inverse(b),multiply(X0,c)) )
| ~ spl0_8
| ~ spl0_39 ),
inference(resolution,[],[f291,f54]) ).
fof(f291,plain,
( ! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,a,X2)
| product(X2,additive_inverse(b),X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f1046,plain,
( spl0_93
| ~ spl0_8
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f294,f286,f53,f1044]) ).
fof(f286,plain,
( spl0_38
<=> ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X1,additive_inverse(b),X2)
| product(X0,X2,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f294,plain,
( ! [X0,X1] :
( ~ product(X0,X1,a)
| product(X0,multiply(X1,additive_inverse(b)),c) )
| ~ spl0_8
| ~ spl0_38 ),
inference(resolution,[],[f287,f54]) ).
fof(f287,plain,
( ! [X2,X0,X1] :
( ~ product(X1,additive_inverse(b),X2)
| ~ product(X0,X1,a)
| product(X0,X2,c) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f947,plain,
( spl0_92
| ~ spl0_25
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f818,f671,f169,f945]) ).
fof(f671,plain,
( spl0_80
<=> ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f818,plain,
( ! [X0] : additive_inverse(additive_inverse(X0)) = X0
| ~ spl0_25
| ~ spl0_80 ),
inference(resolution,[],[f672,f170]) ).
fof(f672,plain,
( ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f873,plain,
( spl0_91
| ~ spl0_3
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f363,f341,f32,f871]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,X2,add(X0,X2)) )
| ~ spl0_3
| ~ spl0_45 ),
inference(resolution,[],[f342,f33]) ).
fof(f869,plain,
( spl0_90
| ~ spl0_3
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f356,f337,f32,f867]) ).
fof(f356,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,X2,add(X1,X2)) )
| ~ spl0_3
| ~ spl0_44 ),
inference(resolution,[],[f338,f33]) ).
fof(f864,plain,
( spl0_89
| ~ spl0_6
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f323,f306,f45,f862]) ).
fof(f862,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| sum(additive_identity,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| sum(additive_identity,X0,X1) )
| ~ spl0_6
| ~ spl0_42 ),
inference(resolution,[],[f307,f46]) ).
fof(f859,plain,
( spl0_88
| ~ spl0_6
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f317,f302,f45,f857]) ).
fof(f857,plain,
( spl0_88
<=> ! [X0,X1] :
( ~ sum(X0,additive_inverse(additive_inverse(X1)),X1)
| sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(additive_inverse(X1)),X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_6
| ~ spl0_41 ),
inference(resolution,[],[f303,f46]) ).
fof(f855,plain,
( spl0_87
| ~ spl0_13
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f284,f254,f83,f853]) ).
fof(f254,plain,
( spl0_37
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| sum(X3,additive_identity,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f284,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,X0),additive_identity,X2) )
| ~ spl0_13
| ~ spl0_37 ),
inference(resolution,[],[f255,f84]) ).
fof(f255,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| sum(X3,additive_identity,X2) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f851,plain,
( spl0_86
| ~ spl0_9
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f283,f254,f57,f849]) ).
fof(f283,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X0,X1),additive_identity,X2) )
| ~ spl0_9
| ~ spl0_37 ),
inference(resolution,[],[f255,f58]) ).
fof(f847,plain,
( spl0_85
| ~ spl0_13
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f262,f238,f83,f845]) ).
fof(f238,plain,
( spl0_34
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| sum(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f262,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X2,X1),X2) )
| ~ spl0_13
| ~ spl0_34 ),
inference(resolution,[],[f239,f84]) ).
fof(f239,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X1,additive_identity)
| sum(X0,X3,X2) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f814,plain,
( spl0_84
| ~ spl0_9
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f261,f238,f57,f812]) ).
fof(f261,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X1,X2),X2) )
| ~ spl0_9
| ~ spl0_34 ),
inference(resolution,[],[f239,f58]) ).
fof(f763,plain,
( spl0_83
| ~ spl0_2
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f367,f345,f27,f761]) ).
fof(f761,plain,
( spl0_83
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,d,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,d,multiply(X1,b)) )
| ~ spl0_2
| ~ spl0_46 ),
inference(resolution,[],[f346,f29]) ).
fof(f759,plain,
( spl0_82
| ~ spl0_8
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f236,f231,f53,f757]) ).
fof(f231,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,a,X2)
| product(X2,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f236,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,b,multiply(X0,d)) )
| ~ spl0_8
| ~ spl0_33 ),
inference(resolution,[],[f232,f54]) ).
fof(f232,plain,
( ! [X2,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,a,X2)
| product(X2,b,X1) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f755,plain,
( spl0_81
| ~ spl0_8
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f235,f227,f53,f753]) ).
fof(f227,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X1,b,X2)
| product(X0,X2,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f235,plain,
( ! [X0,X1] :
( ~ product(X0,X1,a)
| product(X0,multiply(X1,b),d) )
| ~ spl0_8
| ~ spl0_32 ),
inference(resolution,[],[f228,f54]) ).
fof(f228,plain,
( ! [X2,X0,X1] :
( ~ product(X1,b,X2)
| ~ product(X0,X1,a)
| product(X0,X2,d) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f673,plain,
( spl0_80
| ~ spl0_6
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f587,f546,f45,f671]) ).
fof(f587,plain,
( ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0)
| ~ spl0_6
| ~ spl0_71 ),
inference(resolution,[],[f547,f46]) ).
fof(f580,plain,
( spl0_79
| ~ spl0_4
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f329,f310,f36,f578]) ).
fof(f310,plain,
( spl0_43
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,X2,X3)
| sum(X3,additive_inverse(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f329,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,additive_inverse(X1),X0) )
| ~ spl0_4
| ~ spl0_43 ),
inference(resolution,[],[f311,f37]) ).
fof(f311,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,X2,X3)
| sum(X3,additive_inverse(X2),X1) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f576,plain,
( spl0_78
| ~ spl0_3
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f322,f306,f32,f574]) ).
fof(f322,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_inverse(X1),X1,X0) )
| ~ spl0_3
| ~ spl0_42 ),
inference(resolution,[],[f307,f33]) ).
fof(f572,plain,
( spl0_77
| ~ spl0_3
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f316,f302,f32,f570]) ).
fof(f316,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,additive_inverse(X1),additive_identity) )
| ~ spl0_3
| ~ spl0_41 ),
inference(resolution,[],[f303,f33]) ).
fof(f568,plain,
( spl0_76
| ~ spl0_4
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f314,f297,f36,f566]) ).
fof(f314,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X0),X1,additive_identity) )
| ~ spl0_4
| ~ spl0_40 ),
inference(resolution,[],[f298,f37]) ).
fof(f564,plain,
( spl0_75
| ~ spl0_3
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f313,f297,f32,f562]) ).
fof(f313,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,X1,additive_identity) )
| ~ spl0_3
| ~ spl0_40 ),
inference(resolution,[],[f298,f33]) ).
fof(f560,plain,
( spl0_74
| ~ spl0_7
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f282,f254,f49,f558]) ).
fof(f282,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_7
| ~ spl0_37 ),
inference(resolution,[],[f255,f50]) ).
fof(f556,plain,
( spl0_73
| ~ spl0_6
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f281,f254,f45,f554]) ).
fof(f281,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_6
| ~ spl0_37 ),
inference(resolution,[],[f255,f46]) ).
fof(f552,plain,
( spl0_72
| ~ spl0_7
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f260,f238,f49,f550]) ).
fof(f260,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,additive_identity,additive_inverse(X1)) )
| ~ spl0_7
| ~ spl0_34 ),
inference(resolution,[],[f239,f50]) ).
fof(f548,plain,
( spl0_71
| ~ spl0_6
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f259,f238,f45,f546]) ).
fof(f259,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1) )
| ~ spl0_6
| ~ spl0_34 ),
inference(resolution,[],[f239,f46]) ).
fof(f544,plain,
( spl0_70
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f127,f83,f70,f542]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X2,X1,X0) )
| ~ spl0_11
| ~ spl0_13 ),
inference(resolution,[],[f84,f71]) ).
fof(f533,plain,
( spl0_69
| ~ spl0_7
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f318,f302,f49,f531]) ).
fof(f318,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_7
| ~ spl0_41 ),
inference(resolution,[],[f303,f50]) ).
fof(f529,plain,
( spl0_68
| ~ spl0_3
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f257,f238,f32,f527]) ).
fof(f257,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) )
| ~ spl0_3
| ~ spl0_34 ),
inference(resolution,[],[f239,f33]) ).
fof(f525,plain,
( spl0_67
| ~ spl0_5
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f293,f286,f40,f523]) ).
fof(f523,plain,
( spl0_67
<=> ! [X0] :
( ~ product(X0,a,a)
| product(X0,c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f293,plain,
( ! [X0] :
( ~ product(X0,a,a)
| product(X0,c,c) )
| ~ spl0_5
| ~ spl0_38 ),
inference(resolution,[],[f287,f42]) ).
fof(f521,plain,
( spl0_66
| ~ spl0_2
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f234,f227,f27,f519]) ).
fof(f519,plain,
( spl0_66
<=> ! [X0] :
( ~ product(X0,a,a)
| product(X0,d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f234,plain,
( ! [X0] :
( ~ product(X0,a,a)
| product(X0,d,d) )
| ~ spl0_2
| ~ spl0_32 ),
inference(resolution,[],[f228,f29]) ).
fof(f499,plain,
( spl0_65
| ~ spl0_13
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f222,f205,f83,f497]) ).
fof(f222,plain,
( ! [X0,X1] : add(X0,X1) = add(X1,X0)
| ~ spl0_13
| ~ spl0_29 ),
inference(resolution,[],[f206,f84]) ).
fof(f483,plain,
( spl0_64
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f199,f189,f83,f481]) ).
fof(f481,plain,
( spl0_64
<=> ! [X0] : additive_identity = add(X0,additive_inverse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f199,plain,
( ! [X0] : additive_identity = add(X0,additive_inverse(X0))
| ~ spl0_13
| ~ spl0_27 ),
inference(resolution,[],[f190,f84]) ).
fof(f479,plain,
( spl0_63
| ~ spl0_9
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f198,f189,f57,f477]) ).
fof(f198,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_9
| ~ spl0_27 ),
inference(resolution,[],[f190,f58]) ).
fof(f471,plain,
( spl0_62
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f187,f183,f53,f468]) ).
fof(f468,plain,
( spl0_62
<=> c = multiply(a,additive_inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f187,plain,
( c = multiply(a,additive_inverse(b))
| ~ spl0_8
| ~ spl0_26 ),
inference(resolution,[],[f184,f54]) ).
fof(f447,plain,
( spl0_61
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f152,f138,f53,f445]) ).
fof(f138,plain,
( spl0_21
<=> ! [X3,X9,X0,X8,X6,X1,X7] :
( ~ product(X1,X0,X6)
| ~ product(X3,X0,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X8,X0,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f152,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X2,multiply(X3,X1),X4)
| ~ sum(X0,X3,X5)
| product(X5,X1,X4) )
| ~ spl0_8
| ~ spl0_21 ),
inference(resolution,[],[f139,f54]) ).
fof(f139,plain,
( ! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X3,X0,X7)
| ~ product(X1,X0,X6)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X8,X0,X9) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f443,plain,
( spl0_60
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f149,f134,f53,f441]) ).
fof(f134,plain,
( spl0_20
<=> ! [X3,X9,X0,X8,X6,X1,X7] :
( ~ product(X1,X0,X6)
| ~ product(X8,X0,X9)
| ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f149,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| sum(X2,X4,multiply(X5,X1)) )
| ~ spl0_8
| ~ spl0_20 ),
inference(resolution,[],[f135,f54]) ).
fof(f135,plain,
( ! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X8,X0,X9)
| ~ product(X1,X0,X6)
| ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f439,plain,
( spl0_59
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f146,f130,f53,f437]) ).
fof(f130,plain,
( spl0_19
<=> ! [X3,X9,X0,X8,X6,X1,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X3,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X0,X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f146,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X2,multiply(X0,X3),X4)
| ~ sum(X1,X3,X5)
| product(X0,X5,X4) )
| ~ spl0_8
| ~ spl0_19 ),
inference(resolution,[],[f131,f54]) ).
fof(f131,plain,
( ! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X3,X7)
| ~ product(X0,X1,X6)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X0,X8,X9) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f435,plain,
( spl0_58
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f143,f122,f53,f433]) ).
fof(f122,plain,
( spl0_18
<=> ! [X3,X9,X0,X8,X6,X1,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f143,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| sum(X2,X4,multiply(X0,X5)) )
| ~ spl0_8
| ~ spl0_18 ),
inference(resolution,[],[f123,f54]) ).
fof(f123,plain,
( ! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X8,X9)
| ~ product(X0,X1,X6)
| ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f424,plain,
( spl0_57
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f151,f138,f40,f422]) ).
fof(f151,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,a,X3)
| product(X3,additive_inverse(b),X2) )
| ~ spl0_5
| ~ spl0_21 ),
inference(resolution,[],[f139,f42]) ).
fof(f420,plain,
( spl0_56
| ~ spl0_5
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f148,f134,f40,f418]) ).
fof(f148,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ product(X2,additive_inverse(b),X3)
| ~ sum(X0,X2,a)
| sum(X1,X3,c) )
| ~ spl0_5
| ~ spl0_20 ),
inference(resolution,[],[f135,f42]) ).
fof(f409,plain,
( spl0_55
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f145,f130,f40,f407]) ).
fof(f145,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,additive_inverse(b),X3)
| product(a,X3,X2) )
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[],[f131,f42]) ).
fof(f405,plain,
( spl0_54
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f142,f122,f40,f403]) ).
fof(f142,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ product(a,X2,X3)
| ~ sum(X0,X2,additive_inverse(b))
| sum(X1,X3,c) )
| ~ spl0_5
| ~ spl0_18 ),
inference(resolution,[],[f123,f42]) ).
fof(f394,plain,
( spl0_53
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f176,f160,f83,f392]) ).
fof(f176,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_13
| ~ spl0_23 ),
inference(resolution,[],[f161,f84]) ).
fof(f387,plain,
( spl0_52
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f150,f138,f27,f385]) ).
fof(f150,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,a,X3)
| product(X3,b,X2) )
| ~ spl0_2
| ~ spl0_21 ),
inference(resolution,[],[f139,f29]) ).
fof(f383,plain,
( spl0_51
| ~ spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f147,f134,f27,f381]) ).
fof(f147,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,b,X1)
| ~ product(X2,b,X3)
| ~ sum(X0,X2,a)
| sum(X1,X3,d) )
| ~ spl0_2
| ~ spl0_20 ),
inference(resolution,[],[f135,f29]) ).
fof(f379,plain,
( spl0_50
| ~ spl0_2
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f144,f130,f27,f377]) ).
fof(f144,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X1,d,X2)
| ~ sum(X0,b,X3)
| product(a,X3,X2) )
| ~ spl0_2
| ~ spl0_19 ),
inference(resolution,[],[f131,f29]) ).
fof(f375,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f141,f122,f27,f373]) ).
fof(f141,plain,
( ! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ product(a,X2,X3)
| ~ sum(X0,X2,b)
| sum(X1,X3,d) )
| ~ spl0_2
| ~ spl0_18 ),
inference(resolution,[],[f123,f29]) ).
fof(f355,plain,
( spl0_48
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f120,f102,f53,f353]) ).
fof(f102,plain,
( spl0_17
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| product(X2,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f120,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,multiply(X1,X2),X3)
| ~ product(X0,X1,X4)
| product(X4,X2,X3) )
| ~ spl0_8
| ~ spl0_17 ),
inference(resolution,[],[f103,f54]) ).
fof(f103,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| ~ product(X0,X1,X2)
| product(X2,X3,X5) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f351,plain,
( spl0_47
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f175,f160,f57,f349]) ).
fof(f175,plain,
( ! [X0] : add(additive_identity,X0) = X0
| ~ spl0_9
| ~ spl0_23 ),
inference(resolution,[],[f161,f58]) ).
fof(f347,plain,
( spl0_46
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f117,f98,f53,f345]) ).
fof(f98,plain,
( spl0_16
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| product(X0,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f117,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| product(X0,X4,multiply(X2,X3)) )
| ~ spl0_8
| ~ spl0_16 ),
inference(resolution,[],[f99,f54]) ).
fof(f99,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| product(X0,X4,X5) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f343,plain,
( spl0_45
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f114,f94,f57,f341]) ).
fof(f114,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X0,add(X1,X2),X3)
| ~ sum(X0,X1,X4)
| sum(X4,X2,X3) )
| ~ spl0_9
| ~ spl0_15 ),
inference(resolution,[],[f95,f58]) ).
fof(f339,plain,
( spl0_44
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f109,f90,f57,f337]) ).
fof(f109,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X0,X4,add(X2,X3)) )
| ~ spl0_9
| ~ spl0_14 ),
inference(resolution,[],[f91,f58]) ).
fof(f312,plain,
( spl0_43
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f113,f94,f49,f310]) ).
fof(f113,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,X2,X3)
| sum(X3,additive_inverse(X2),X1) )
| ~ spl0_7
| ~ spl0_15 ),
inference(resolution,[],[f95,f50]) ).
fof(f308,plain,
( spl0_42
| ~ spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f112,f94,f45,f306]) ).
fof(f112,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(X0,additive_inverse(X2),X3)
| sum(X3,X2,X1) )
| ~ spl0_6
| ~ spl0_15 ),
inference(resolution,[],[f95,f46]) ).
fof(f304,plain,
( spl0_41
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f108,f90,f49,f302]) ).
fof(f108,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,additive_inverse(X2),X3)
| sum(X0,X3,additive_identity) )
| ~ spl0_7
| ~ spl0_14 ),
inference(resolution,[],[f91,f50]) ).
fof(f299,plain,
( spl0_40
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f107,f90,f45,f297]) ).
fof(f107,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,additive_inverse(X2))
| ~ sum(X1,X2,X3)
| sum(X0,X3,additive_identity) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f91,f46]) ).
fof(f292,plain,
( spl0_39
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f119,f102,f40,f290]) ).
fof(f119,plain,
( ! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,a,X2)
| product(X2,additive_inverse(b),X1) )
| ~ spl0_5
| ~ spl0_17 ),
inference(resolution,[],[f103,f42]) ).
fof(f288,plain,
( spl0_38
| ~ spl0_5
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f116,f98,f40,f286]) ).
fof(f116,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X1,additive_inverse(b),X2)
| product(X0,X2,c) )
| ~ spl0_5
| ~ spl0_16 ),
inference(resolution,[],[f99,f42]) ).
fof(f256,plain,
( spl0_37
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f111,f94,f36,f254]) ).
fof(f111,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| sum(X3,additive_identity,X2) )
| ~ spl0_4
| ~ spl0_15 ),
inference(resolution,[],[f95,f37]) ).
fof(f248,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f110,f94,f32,f246]) ).
fof(f110,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,additive_identity,X3)
| sum(X3,X1,X2) )
| ~ spl0_3
| ~ spl0_15 ),
inference(resolution,[],[f95,f33]) ).
fof(f244,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f106,f90,f36,f242]) ).
fof(f106,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,additive_identity,X3)
| sum(X0,X3,X2) )
| ~ spl0_4
| ~ spl0_14 ),
inference(resolution,[],[f91,f37]) ).
fof(f240,plain,
( spl0_34
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f105,f90,f32,f238]) ).
fof(f105,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| sum(X0,X3,X2) )
| ~ spl0_3
| ~ spl0_14 ),
inference(resolution,[],[f91,f33]) ).
fof(f233,plain,
( spl0_33
| ~ spl0_2
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f118,f102,f27,f231]) ).
fof(f118,plain,
( ! [X2,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,a,X2)
| product(X2,b,X1) )
| ~ spl0_2
| ~ spl0_17 ),
inference(resolution,[],[f103,f29]) ).
fof(f229,plain,
( spl0_32
| ~ spl0_2
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f115,f98,f27,f227]) ).
fof(f115,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X1,b,X2)
| product(X0,X2,d) )
| ~ spl0_2
| ~ spl0_16 ),
inference(resolution,[],[f99,f29]) ).
fof(f216,plain,
( spl0_31
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f88,f74,f53,f214]) ).
fof(f74,plain,
( spl0_12
<=> ! [X4,X0,X2,X1] :
( X2 = X4
| ~ product(X0,X1,X4)
| ~ product(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f88,plain,
( ! [X2,X0,X1] :
( multiply(X1,X2) = X0
| ~ product(X1,X2,X0) )
| ~ spl0_8
| ~ spl0_12 ),
inference(resolution,[],[f75,f54]) ).
fof(f75,plain,
( ! [X2,X0,X1,X4] :
( ~ product(X0,X1,X4)
| X2 = X4
| ~ product(X0,X1,X2) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f212,plain,
( spl0_30
| ~ spl0_7
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f174,f160,f49,f209]) ).
fof(f174,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_7
| ~ spl0_23 ),
inference(resolution,[],[f161,f50]) ).
fof(f207,plain,
( spl0_29
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f81,f70,f57,f205]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X1,X2,X0) )
| ~ spl0_9
| ~ spl0_11 ),
inference(resolution,[],[f71,f58]) ).
fof(f195,plain,
( spl0_28
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f80,f70,f49,f193]) ).
fof(f80,plain,
( ! [X0,X1] :
( additive_identity = X0
| ~ sum(X1,additive_inverse(X1),X0) )
| ~ spl0_7
| ~ spl0_11 ),
inference(resolution,[],[f71,f50]) ).
fof(f191,plain,
( spl0_27
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f79,f70,f45,f189]) ).
fof(f79,plain,
( ! [X0,X1] :
( additive_identity = X0
| ~ sum(additive_inverse(X1),X1,X0) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f71,f46]) ).
fof(f185,plain,
( spl0_26
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f87,f74,f40,f183]) ).
fof(f87,plain,
( ! [X0] :
( c = X0
| ~ product(a,additive_inverse(b),X0) )
| ~ spl0_5
| ~ spl0_12 ),
inference(resolution,[],[f75,f42]) ).
fof(f171,plain,
( spl0_25
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f78,f70,f36,f169]) ).
fof(f78,plain,
( ! [X0,X1] :
( X0 = X1
| ~ sum(X1,additive_identity,X0) )
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[],[f71,f37]) ).
fof(f167,plain,
( spl0_24
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f158,f154,f53,f164]) ).
fof(f164,plain,
( spl0_24
<=> d = multiply(a,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f158,plain,
( d = multiply(a,b)
| ~ spl0_8
| ~ spl0_22 ),
inference(resolution,[],[f155,f54]) ).
fof(f162,plain,
( spl0_23
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f77,f70,f32,f160]) ).
fof(f77,plain,
( ! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X1,X0) )
| ~ spl0_3
| ~ spl0_11 ),
inference(resolution,[],[f71,f33]) ).
fof(f156,plain,
( spl0_22
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f86,f74,f27,f154]) ).
fof(f86,plain,
( ! [X0] :
( d = X0
| ~ product(a,b,X0) )
| ~ spl0_2
| ~ spl0_12 ),
inference(resolution,[],[f75,f29]) ).
fof(f140,plain,
spl0_21,
inference(avatar_split_clause,[],[f15,f138]) ).
fof(f15,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X3,X0,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X8,X0,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f136,plain,
spl0_20,
inference(avatar_split_clause,[],[f14,f134]) ).
fof(f14,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X8,X0,X9)
| ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f132,plain,
spl0_19,
inference(avatar_split_clause,[],[f13,f130]) ).
fof(f13,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X3,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X0,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f124,plain,
spl0_18,
inference(avatar_split_clause,[],[f12,f122]) ).
fof(f12,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f104,plain,
spl0_17,
inference(avatar_split_clause,[],[f11,f102]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f100,plain,
spl0_16,
inference(avatar_split_clause,[],[f10,f98]) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f96,plain,
spl0_15,
inference(avatar_split_clause,[],[f8,f94]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| sum(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f92,plain,
spl0_14,
inference(avatar_split_clause,[],[f7,f90]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| sum(X0,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f85,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f68,f61,f57,f83]) ).
fof(f68,plain,
( ! [X0,X1] : sum(X0,X1,add(X1,X0))
| ~ spl0_9
| ~ spl0_10 ),
inference(resolution,[],[f62,f58]) ).
fof(f76,plain,
spl0_12,
inference(avatar_split_clause,[],[f17,f74]) ).
fof(f17,axiom,
! [X2,X0,X1,X4] :
( X2 = X4
| ~ product(X0,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f72,plain,
spl0_11,
inference(avatar_split_clause,[],[f16,f70]) ).
fof(f16,axiom,
! [X2,X0,X1,X4] :
( X2 = X4
| ~ sum(X0,X1,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f63,plain,
spl0_10,
inference(avatar_split_clause,[],[f9,f61]) ).
fof(f9,axiom,
! [X3,X0,X1] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f59,plain,
spl0_9,
inference(avatar_split_clause,[],[f4,f57]) ).
fof(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f55,plain,
spl0_8,
inference(avatar_split_clause,[],[f3,f53]) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f51,plain,
spl0_7,
inference(avatar_split_clause,[],[f6,f49]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f47,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f45]) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f43,plain,
spl0_5,
inference(avatar_split_clause,[],[f19,f40]) ).
fof(f19,axiom,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f38,plain,
spl0_4,
inference(avatar_split_clause,[],[f2,f36]) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f34,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f32]) ).
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f30,plain,
spl0_2,
inference(avatar_split_clause,[],[f18,f27]) ).
fof(f18,axiom,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f25,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f20,f22]) ).
fof(f20,axiom,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG037-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 18:24:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % (18787)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (18790)WARNING: value z3 for option sas not known
% 0.16/0.33 % (18789)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (18788)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (18791)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (18794)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)
% 0.16/0.33 % (18792)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)
% 0.16/0.33 % (18793)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)
% 0.16/0.33 % (18790)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.40 TRYING [5]
% 0.16/0.43 TRYING [1]
% 0.16/0.43 TRYING [2]
% 0.16/0.43 TRYING [3]
% 0.16/0.45 TRYING [4]
% 0.16/0.51 TRYING [5]
% 0.16/0.54 TRYING [6]
% 0.16/0.56 TRYING [5]
% 2.28/0.63 % (18792)First to succeed.
% 2.28/0.64 % (18792)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18787"
% 2.28/0.65 % (18792)Refutation found. Thanks to Tanya!
% 2.28/0.65 % SZS status Unsatisfiable for theBenchmark
% 2.28/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.28/0.66 % (18792)------------------------------
% 2.28/0.66 % (18792)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.28/0.66 % (18792)Termination reason: Refutation
% 2.28/0.66
% 2.28/0.66 % (18792)Memory used [KB]: 3810
% 2.28/0.66 % (18792)Time elapsed: 0.316 s
% 2.28/0.66 % (18792)Instructions burned: 600 (million)
% 2.28/0.66 % (18787)Success in time 0.325 s
%------------------------------------------------------------------------------