TSTP Solution File: RNG005-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG005-1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:49:55 EDT 2024
% Result : Unsatisfiable 1.96s 0.63s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 318
% Syntax : Number of formulae : 1038 ( 30 unt; 0 def)
% Number of atoms : 3575 ( 150 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 4778 (2241 ~;2239 |; 0 &)
% ( 298 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 302 ( 300 usr; 299 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 1859 (1859 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7053,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,f241,f245,f249,f257,f289,f293,f298,f303,f307,f311,f338,f342,f346,f350,f354,f374,f378,f382,f386,f392,f404,f408,f419,f423,f434,f438,f442,f446,f470,f478,f482,f498,f520,f524,f528,f539,f543,f547,f551,f555,f559,f563,f567,f571,f575,f579,f672,f754,f758,f762,f822,f855,f859,f863,f867,f872,f877,f881,f955,f1054,f1058,f1094,f1098,f1102,f1126,f1130,f1134,f1138,f1332,f1363,f1367,f1371,f1375,f1379,f1416,f1420,f1424,f1428,f1432,f1436,f1551,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1742,f1746,f1750,f1754,f1758,f1763,f1767,f1819,f1823,f1827,f1831,f1835,f1901,f1905,f1909,f1950,f1954,f1966,f1970,f1974,f1978,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2108,f2112,f2131,f2141,f2145,f2149,f2153,f2157,f2161,f2165,f2346,f2350,f2359,f2366,f2370,f2374,f2378,f2382,f2386,f2390,f2395,f2400,f2404,f2408,f2412,f2416,f2420,f2816,f2820,f2824,f2829,f2833,f2837,f2841,f2845,f2849,f2853,f2857,f2861,f3055,f3060,f3064,f3068,f3072,f3076,f3080,f3085,f3090,f3094,f3098,f3102,f3107,f3111,f3115,f3119,f3123,f3127,f3131,f3135,f3139,f3143,f3147,f3174,f3178,f3182,f3186,f3190,f3194,f3198,f3202,f3206,f3210,f3215,f3219,f4102,f4669,f4673,f4677,f4681,f4685,f4690,f4694,f4698,f4702,f4736,f4916,f4921,f4925,f4929,f4933,f4937,f4941,f4945,f4949,f4953,f4957,f4962,f4967,f4971,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5008,f5013,f5017,f5021,f5025,f5029,f5033,f5037,f5041,f5045,f5101,f6495,f6499,f6504,f6509,f6513,f6517,f6521,f6525,f6529,f6533,f6537,f6541,f6545,f6550,f6554,f6558,f6562,f6566,f6570,f6946,f7023,f7027,f7031,f7035,f7039,f7043,f7047,f7051,f7052]) ).
fof(f7052,plain,
( spl0_1
| ~ spl0_13
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f6601,f6547,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(f6547,plain,
( spl0_284
<=> additive_identity = add(d,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f6601,plain,
( sum(c,d,additive_identity)
| ~ spl0_13
| ~ spl0_284 ),
inference(superposition,[],[f84,f6549]) ).
fof(f6549,plain,
( additive_identity = add(d,c)
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f6547]) ).
fof(f84,plain,
( ! [X0,X1] : sum(X0,X1,add(X1,X0))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f7051,plain,
( spl0_298
| ~ spl0_41
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f732,f577,f301,f7049]) ).
fof(f7049,plain,
( spl0_298
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X2,X1)
| sum(X3,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f301,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(f577,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(f732,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X2,X1)
| sum(X3,X0,additive_identity) )
| ~ spl0_41
| ~ spl0_79 ),
inference(resolution,[],[f578,f302]) ).
fof(f302,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,[],[f301]) ).
fof(f578,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_inverse(X1),X0)
| ~ sum(X0,X1,X2) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f7047,plain,
( spl0_297
| ~ spl0_42
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f731,f577,f305,f7045]) ).
fof(f7045,plain,
( spl0_297
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,additive_identity,X3)
| sum(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f305,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(f731,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,additive_identity,X3)
| sum(X0,X1,X3) )
| ~ spl0_42
| ~ spl0_79 ),
inference(resolution,[],[f578,f306]) ).
fof(f306,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,[],[f305]) ).
fof(f7043,plain,
( spl0_296
| ~ spl0_11
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f697,f573,f70,f7041]) ).
fof(f7041,plain,
( spl0_296
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| X0 = X1
| ~ sum(additive_inverse(X2),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
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(f573,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(f697,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| X0 = X1
| ~ sum(additive_inverse(X2),X2,X1) )
| ~ spl0_11
| ~ spl0_78 ),
inference(resolution,[],[f574,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(f574,plain,
( ! [X0,X1] :
( sum(additive_inverse(X1),X1,X0)
| ~ sum(additive_identity,additive_identity,X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f7039,plain,
( spl0_295
| ~ spl0_11
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f680,f569,f70,f7037]) ).
fof(f7037,plain,
( spl0_295
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = X2
| ~ sum(X0,additive_inverse(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f569,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(f680,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = X2
| ~ sum(X0,additive_inverse(X1),X2) )
| ~ spl0_11
| ~ spl0_77 ),
inference(resolution,[],[f570,f71]) ).
fof(f570,plain,
( ! [X0,X1] :
( sum(X0,additive_inverse(X1),additive_identity)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f7035,plain,
( spl0_294
| ~ spl0_41
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f678,f569,f301,f7033]) ).
fof(f7033,plain,
( spl0_294
<=> ! [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_294])]) ).
fof(f678,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,[],[f570,f302]) ).
fof(f7031,plain,
( spl0_293
| ~ spl0_42
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f677,f569,f305,f7029]) ).
fof(f7029,plain,
( spl0_293
<=> ! [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_293])]) ).
fof(f677,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,[],[f570,f306]) ).
fof(f7027,plain,
( spl0_292
| ~ spl0_11
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f596,f549,f70,f7025]) ).
fof(f7025,plain,
( spl0_292
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X2
| ~ sum(X0,additive_identity,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f549,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(f596,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X2
| ~ sum(X0,additive_identity,X2) )
| ~ spl0_11
| ~ spl0_72 ),
inference(resolution,[],[f550,f71]) ).
fof(f550,plain,
( ! [X0,X1] :
( sum(X0,additive_identity,additive_inverse(X1))
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f7023,plain,
( spl0_291
| ~ spl0_40
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f593,f549,f296,f7021]) ).
fof(f7021,plain,
( spl0_291
<=> ! [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_291])]) ).
fof(f296,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(f593,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,[],[f550,f297]) ).
fof(f297,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,[],[f296]) ).
fof(f6946,plain,
( spl0_290
| ~ spl0_9
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f6600,f6547,f57,f6943]) ).
fof(f6943,plain,
( spl0_290
<=> sum(d,c,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f57,plain,
( spl0_9
<=> ! [X0,X1] : sum(X0,X1,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f6600,plain,
( sum(d,c,additive_identity)
| ~ spl0_9
| ~ spl0_284 ),
inference(superposition,[],[f58,f6549]) ).
fof(f58,plain,
( ! [X0,X1] : sum(X0,X1,add(X0,X1))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f6570,plain,
( spl0_289
| ~ spl0_2
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2088,f2022,f27,f6568]) ).
fof(f6568,plain,
( spl0_289
<=> ! [X0,X1] :
( ~ sum(a,X0,X1)
| product(X1,b,add(d,multiply(X0,b))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f27,plain,
( spl0_2
<=> product(a,b,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2022,plain,
( spl0_148
<=> ! [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_148])]) ).
fof(f2088,plain,
( ! [X0,X1] :
( ~ sum(a,X0,X1)
| product(X1,b,add(d,multiply(X0,b))) )
| ~ spl0_2
| ~ spl0_148 ),
inference(resolution,[],[f2023,f29]) ).
fof(f29,plain,
( product(a,b,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f2023,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| product(X4,X1,add(X2,multiply(X3,X1))) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f6566,plain,
( spl0_288
| ~ spl0_2
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f2077,f2018,f27,f6564]) ).
fof(f6564,plain,
( spl0_288
<=> ! [X0,X1] :
( ~ sum(a,X0,X1)
| sum(d,multiply(X0,b),multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2018,plain,
( spl0_147
<=> ! [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_147])]) ).
fof(f2077,plain,
( ! [X0,X1] :
( ~ sum(a,X0,X1)
| sum(d,multiply(X0,b),multiply(X1,b)) )
| ~ spl0_2
| ~ spl0_147 ),
inference(resolution,[],[f2019,f29]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X3,X4)
| sum(X2,multiply(X3,X1),multiply(X4,X1)) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f2018]) ).
fof(f6562,plain,
( spl0_287
| ~ spl0_2
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f2052,f2010,f27,f6560]) ).
fof(f6560,plain,
( spl0_287
<=> ! [X0,X1] :
( ~ sum(b,X0,X1)
| product(a,X1,add(d,multiply(a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2010,plain,
( spl0_145
<=> ! [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_145])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( ~ sum(b,X0,X1)
| product(a,X1,add(d,multiply(a,X0))) )
| ~ spl0_2
| ~ spl0_145 ),
inference(resolution,[],[f2011,f29]) ).
fof(f2011,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| product(X0,X4,add(X2,multiply(X0,X3))) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f6558,plain,
( spl0_286
| ~ spl0_2
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f2041,f2006,f27,f6556]) ).
fof(f6556,plain,
( spl0_286
<=> ! [X0,X1] :
( ~ sum(b,X0,X1)
| sum(d,multiply(a,X0),multiply(a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2006,plain,
( spl0_144
<=> ! [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_144])]) ).
fof(f2041,plain,
( ! [X0,X1] :
( ~ sum(b,X0,X1)
| sum(d,multiply(a,X0),multiply(a,X1)) )
| ~ spl0_2
| ~ spl0_144 ),
inference(resolution,[],[f2007,f29]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| sum(X2,multiply(X0,X3),multiply(X0,X4)) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f2006]) ).
fof(f6554,plain,
( spl0_285
| ~ spl0_5
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1912,f1899,f40,f6552]) ).
fof(f6552,plain,
( spl0_285
<=> ! [X0] :
( ~ sum(c,c,X0)
| product(add(additive_inverse(a),additive_inverse(a)),b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f40,plain,
( spl0_5
<=> product(additive_inverse(a),b,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1899,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(X2,b,X0)
| product(add(X2,additive_inverse(a)),b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1912,plain,
( ! [X0] :
( ~ sum(c,c,X0)
| product(add(additive_inverse(a),additive_inverse(a)),b,X0) )
| ~ spl0_5
| ~ spl0_135 ),
inference(resolution,[],[f1900,f42]) ).
fof(f42,plain,
( product(additive_inverse(a),b,c)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f1900,plain,
( ! [X2,X0,X1] :
( ~ product(X2,b,X0)
| ~ sum(X0,c,X1)
| product(add(X2,additive_inverse(a)),b,X1) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1899]) ).
fof(f6550,plain,
( spl0_284
| ~ spl0_224
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f6505,f6501,f3212,f6547]) ).
fof(f3212,plain,
( spl0_224
<=> additive_identity = multiply(additive_identity,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f6501,plain,
( spl0_273
<=> multiply(additive_identity,b) = add(d,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f6505,plain,
( additive_identity = add(d,c)
| ~ spl0_224
| ~ spl0_273 ),
inference(forward_demodulation,[],[f6503,f3214]) ).
fof(f3214,plain,
( additive_identity = multiply(additive_identity,b)
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f3212]) ).
fof(f6503,plain,
( multiply(additive_identity,b) = add(d,c)
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f6501]) ).
fof(f6545,plain,
( spl0_283
| ~ spl0_8
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1813,f1765,f53,f6543]) ).
fof(f6543,plain,
( spl0_283
<=> ! [X0,X1] :
( ~ sum(X0,a,X1)
| sum(multiply(X0,b),d,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
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_129
<=> ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,X2)
| sum(X1,d,multiply(X2,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1813,plain,
( ! [X0,X1] :
( ~ sum(X0,a,X1)
| sum(multiply(X0,b),d,multiply(X1,b)) )
| ~ spl0_8
| ~ spl0_129 ),
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_129 ),
inference(avatar_component_clause,[],[f1765]) ).
fof(f6541,plain,
( spl0_282
| ~ spl0_8
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1800,f1761,f53,f6539]) ).
fof(f6539,plain,
( spl0_282
<=> ! [X0,X1] :
( ~ sum(X0,b,X1)
| sum(multiply(a,X0),d,multiply(a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f1761,plain,
( spl0_128
<=> ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,d,multiply(a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ sum(X0,b,X1)
| sum(multiply(a,X0),d,multiply(a,X1)) )
| ~ spl0_8
| ~ spl0_128 ),
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_128 ),
inference(avatar_component_clause,[],[f1761]) ).
fof(f6537,plain,
( spl0_281
| ~ spl0_9
| ~ spl0_65
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1799,f1752,f496,f57,f6535]) ).
fof(f6535,plain,
( spl0_281
<=> ! [X0,X1] :
( product(X1,b,add(d,multiply(X0,b)))
| ~ sum(X0,a,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f496,plain,
( spl0_65
<=> ! [X0,X1] : add(X0,X1) = add(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1752,plain,
( spl0_126
<=> ! [X2,X0,X1] :
( ~ sum(multiply(X0,b),d,X1)
| ~ sum(X0,a,X2)
| product(X2,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1799,plain,
( ! [X0,X1] :
( product(X1,b,add(d,multiply(X0,b)))
| ~ sum(X0,a,X1) )
| ~ spl0_9
| ~ spl0_65
| ~ spl0_126 ),
inference(forward_demodulation,[],[f1791,f497]) ).
fof(f497,plain,
( ! [X0,X1] : add(X0,X1) = add(X1,X0)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f1791,plain,
( ! [X0,X1] :
( ~ sum(X0,a,X1)
| product(X1,b,add(multiply(X0,b),d)) )
| ~ spl0_9
| ~ spl0_126 ),
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_126 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f6533,plain,
( spl0_280
| ~ spl0_8
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1789,f1748,f53,f6531]) ).
fof(f6531,plain,
( spl0_280
<=> ! [X0,X1] :
( ~ sum(X0,X1,a)
| sum(multiply(X0,b),multiply(X1,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f1748,plain,
( spl0_125
<=> ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1789,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,a)
| sum(multiply(X0,b),multiply(X1,b),d) )
| ~ spl0_8
| ~ spl0_125 ),
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_125 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f6529,plain,
( spl0_279
| ~ spl0_9
| ~ spl0_65
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1783,f1744,f496,f57,f6527]) ).
fof(f6527,plain,
( spl0_279
<=> ! [X0,X1] :
( product(a,X1,add(d,multiply(a,X0)))
| ~ sum(X0,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f1744,plain,
( spl0_124
<=> ! [X2,X0,X1] :
( ~ sum(multiply(a,X0),d,X1)
| ~ sum(X0,b,X2)
| product(a,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1783,plain,
( ! [X0,X1] :
( product(a,X1,add(d,multiply(a,X0)))
| ~ sum(X0,b,X1) )
| ~ spl0_9
| ~ spl0_65
| ~ spl0_124 ),
inference(forward_demodulation,[],[f1776,f497]) ).
fof(f1776,plain,
( ! [X0,X1] :
( ~ sum(X0,b,X1)
| product(a,X1,add(multiply(a,X0),d)) )
| ~ spl0_9
| ~ spl0_124 ),
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_124 ),
inference(avatar_component_clause,[],[f1744]) ).
fof(f6525,plain,
( spl0_278
| ~ spl0_8
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1768,f1740,f53,f6523]) ).
fof(f6523,plain,
( spl0_278
<=> ! [X0,X1] :
( ~ sum(X0,X1,b)
| sum(multiply(a,X0),multiply(a,X1),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f1740,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(a,X2),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1768,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,b)
| sum(multiply(a,X0),multiply(a,X1),d) )
| ~ spl0_8
| ~ spl0_123 ),
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_123 ),
inference(avatar_component_clause,[],[f1740]) ).
fof(f6521,plain,
( spl0_277
| ~ spl0_78
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1680,f1650,f573,f6519]) ).
fof(f6519,plain,
( spl0_277
<=> ! [X0,X1] :
( ~ sum(c,d,X0)
| product(X1,b,X0)
| ~ sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1650,plain,
( spl0_117
<=> ! [X0,X1] :
( ~ sum(c,d,X0)
| ~ sum(additive_inverse(a),a,X1)
| product(X1,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1680,plain,
( ! [X0,X1] :
( ~ sum(c,d,X0)
| product(X1,b,X0)
| ~ sum(additive_identity,additive_identity,X1) )
| ~ spl0_78
| ~ spl0_117 ),
inference(resolution,[],[f1651,f574]) ).
fof(f1651,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(a),a,X1)
| ~ sum(c,d,X0)
| product(X1,b,X0) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1650]) ).
fof(f6517,plain,
( spl0_276
| ~ spl0_79
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1674,f1646,f577,f6515]) ).
fof(f6515,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ product(X0,b,X1)
| sum(X1,c,d)
| ~ sum(a,a,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1646,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),a)
| sum(X1,c,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1674,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| sum(X1,c,d)
| ~ sum(a,a,X0) )
| ~ spl0_79
| ~ spl0_116 ),
inference(resolution,[],[f1647,f578]) ).
fof(f1647,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(a),a)
| ~ product(X0,b,X1)
| sum(X1,c,d) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f6513,plain,
( spl0_275
| ~ spl0_26
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1640,f1434,f183,f6511]) ).
fof(f6511,plain,
( spl0_275
<=> ! [X0,X1] :
( ~ product(X0,X1,additive_inverse(a))
| c = multiply(X0,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f183,plain,
( spl0_26
<=> ! [X0] :
( c = X0
| ~ product(additive_inverse(a),b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1434,plain,
( spl0_113
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| product(X2,X3,multiply(X0,multiply(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1640,plain,
( ! [X0,X1] :
( ~ product(X0,X1,additive_inverse(a))
| c = multiply(X0,multiply(X1,b)) )
| ~ spl0_26
| ~ spl0_113 ),
inference(resolution,[],[f1435,f184]) ).
fof(f184,plain,
( ! [X0] :
( ~ product(additive_inverse(a),b,X0)
| c = X0 )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f1435,plain,
( ! [X2,X3,X0,X1] :
( product(X2,X3,multiply(X0,multiply(X1,X3)))
| ~ product(X0,X1,X2) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f6509,plain,
( spl0_274
| ~ spl0_31
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1081,f1056,f214,f6507]) ).
fof(f6507,plain,
( spl0_274
<=> ! [X0,X1] :
( ~ product(X0,additive_inverse(a),X1)
| multiply(X1,b) = multiply(X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
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(f1056,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ product(X0,additive_inverse(a),X1)
| product(X0,c,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1081,plain,
( ! [X0,X1] :
( ~ product(X0,additive_inverse(a),X1)
| multiply(X1,b) = multiply(X0,c) )
| ~ spl0_31
| ~ spl0_94 ),
inference(resolution,[],[f1057,f215]) ).
fof(f215,plain,
( ! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f1057,plain,
( ! [X0,X1] :
( product(X0,c,multiply(X1,b))
| ~ product(X0,additive_inverse(a),X1) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f6504,plain,
( spl0_273
| ~ spl0_31
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2207,f2128,f214,f6501]) ).
fof(f2128,plain,
( spl0_153
<=> product(additive_identity,b,add(d,c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2207,plain,
( multiply(additive_identity,b) = add(d,c)
| ~ spl0_31
| ~ spl0_153 ),
inference(resolution,[],[f2130,f215]) ).
fof(f2130,plain,
( product(additive_identity,b,add(d,c))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2128]) ).
fof(f6499,plain,
( spl0_272
| ~ spl0_31
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1069,f1052,f214,f6497]) ).
fof(f6497,plain,
( spl0_272
<=> ! [X0,X1] :
( ~ product(X0,c,X1)
| multiply(multiply(X0,additive_inverse(a)),b) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1052,plain,
( spl0_93
<=> ! [X0,X1] :
( ~ product(X0,c,X1)
| product(multiply(X0,additive_inverse(a)),b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1069,plain,
( ! [X0,X1] :
( ~ product(X0,c,X1)
| multiply(multiply(X0,additive_inverse(a)),b) = X1 )
| ~ spl0_31
| ~ spl0_93 ),
inference(resolution,[],[f1053,f215]) ).
fof(f1053,plain,
( ! [X0,X1] :
( product(multiply(X0,additive_inverse(a)),b,X1)
| ~ product(X0,c,X1) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f6495,plain,
( spl0_271
| ~ spl0_48
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f763,f752,f352,f6493]) ).
fof(f6493,plain,
( spl0_271
<=> ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,X2)
| product(X2,b,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f352,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(f752,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| product(X0,multiply(X1,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f763,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,X2)
| product(X2,b,d) )
| ~ spl0_48
| ~ spl0_81 ),
inference(resolution,[],[f753,f353]) ).
fof(f353,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,[],[f352]) ).
fof(f753,plain,
( ! [X0,X1] :
( product(X0,multiply(X1,b),d)
| ~ product(X0,X1,a) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f5101,plain,
( ~ spl0_269
| spl0_270
| ~ spl0_30
| ~ spl0_53
| ~ spl0_190
| ~ spl0_213
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f4090,f3212,f3145,f2859,f390,f209,f5098,f5094]) ).
fof(f5094,plain,
( spl0_269
<=> product(a,b,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f5098,plain,
( spl0_270
<=> additive_identity = c ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f209,plain,
( spl0_30
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f390,plain,
( spl0_53
<=> ! [X0] : add(X0,additive_identity) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f2859,plain,
( spl0_190
<=> ! [X0] :
( ~ product(a,b,X0)
| sum(X0,c,multiply(additive_identity,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f3145,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f4090,plain,
( additive_identity = c
| ~ product(a,b,additive_identity)
| ~ spl0_30
| ~ spl0_53
| ~ spl0_190
| ~ spl0_213
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4089,f391]) ).
fof(f391,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f4089,plain,
( additive_identity = add(c,additive_identity)
| ~ product(a,b,additive_identity)
| ~ spl0_30
| ~ spl0_190
| ~ spl0_213
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4088,f211]) ).
fof(f211,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f4088,plain,
( additive_identity = add(c,additive_inverse(additive_identity))
| ~ product(a,b,additive_identity)
| ~ spl0_190
| ~ spl0_213
| ~ spl0_224 ),
inference(forward_demodulation,[],[f4062,f3214]) ).
fof(f4062,plain,
( additive_identity = add(c,additive_inverse(multiply(additive_identity,b)))
| ~ product(a,b,additive_identity)
| ~ spl0_190
| ~ spl0_213 ),
inference(resolution,[],[f3146,f2860]) ).
fof(f2860,plain,
( ! [X0] :
( sum(X0,c,multiply(additive_identity,b))
| ~ product(a,b,X0) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2859]) ).
fof(f3146,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f3145]) ).
fof(f5045,plain,
( spl0_268
| ~ spl0_23
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1480,f1418,f160,f5043]) ).
fof(f5043,plain,
( spl0_268
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f160,plain,
( spl0_23
<=> ! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1418,plain,
( spl0_109
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X3,X1),add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1480,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X2,X0) )
| ~ spl0_23
| ~ spl0_109 ),
inference(resolution,[],[f1419,f161]) ).
fof(f161,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X1,X0)
| X0 = X1 )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f1419,plain,
( ! [X2,X3,X0,X1] :
( sum(X0,add(X3,X1),add(X2,X3))
| ~ sum(X0,X1,X2) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f5041,plain,
( spl0_267
| ~ spl0_65
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1350,f1136,f496,f5039]) ).
fof(f5039,plain,
( spl0_267
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X1,X0)),X0,X2)
| sum(X2,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1136,plain,
( spl0_101
<=> ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X1,X0)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_65
| ~ spl0_101 ),
inference(superposition,[],[f1137,f497]) ).
fof(f1137,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f5037,plain,
( spl0_266
| ~ spl0_30
| ~ spl0_75
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1325,f1132,f561,f209,f5035]) ).
fof(f5035,plain,
( spl0_266
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f561,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(f1132,plain,
( spl0_100
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,additive_identity,add(X2,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1325,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) )
| ~ spl0_30
| ~ spl0_75
| ~ spl0_100 ),
inference(forward_demodulation,[],[f1312,f211]) ).
fof(f1312,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_identity),X0,X1)
| sum(additive_identity,add(X1,additive_inverse(X0)),additive_identity) )
| ~ spl0_75
| ~ spl0_100 ),
inference(resolution,[],[f1133,f562]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,X1,additive_identity) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f1133,plain,
( ! [X2,X0,X1] :
( sum(X0,additive_identity,add(X2,additive_inverse(X1)))
| ~ sum(X0,X1,X2) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f5033,plain,
( spl0_265
| ~ spl0_65
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1319,f1132,f496,f5031]) ).
fof(f5031,plain,
( spl0_265
<=> ! [X2,X0,X1] :
( sum(X2,additive_identity,add(additive_inverse(X1),X0))
| ~ sum(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1319,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_identity,add(additive_inverse(X1),X0))
| ~ sum(X2,X1,X0) )
| ~ spl0_65
| ~ spl0_100 ),
inference(superposition,[],[f1133,f497]) ).
fof(f5029,plain,
( spl0_264
| ~ spl0_10
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1302,f1132,f61,f5027]) ).
fof(f5027,plain,
( spl0_264
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,X0,add(X2,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
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(f1302,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,X0,add(X2,additive_inverse(X1))) )
| ~ spl0_10
| ~ spl0_100 ),
inference(resolution,[],[f1133,f62]) ).
fof(f62,plain,
( ! [X3,X0,X1] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f5025,plain,
( spl0_263
| ~ spl0_30
| ~ spl0_75
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1293,f1128,f561,f209,f5023]) ).
fof(f5023,plain,
( spl0_263
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1128,plain,
( spl0_99
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(X0,additive_identity,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1293,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_30
| ~ spl0_75
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1281,f211]) ).
fof(f1281,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_identity),additive_inverse(X0),X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_75
| ~ spl0_99 ),
inference(resolution,[],[f1129,f562]) ).
fof(f1129,plain,
( ! [X2,X0,X1] :
( sum(X0,additive_identity,add(X2,X1))
| ~ sum(X0,additive_inverse(X1),X2) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f5021,plain,
( spl0_262
| ~ spl0_65
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1287,f1128,f496,f5019]) ).
fof(f5019,plain,
( spl0_262
<=> ! [X2,X0,X1] :
( sum(X2,additive_identity,add(X1,X0))
| ~ sum(X2,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1287,plain,
( ! [X2,X0,X1] :
( sum(X2,additive_identity,add(X1,X0))
| ~ sum(X2,additive_inverse(X1),X0) )
| ~ spl0_65
| ~ spl0_99 ),
inference(superposition,[],[f1129,f497]) ).
fof(f5017,plain,
( spl0_261
| ~ spl0_10
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1271,f1128,f61,f5015]) ).
fof(f5015,plain,
( spl0_261
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(additive_identity,X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1271,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(additive_identity,X0,add(X2,X1)) )
| ~ spl0_10
| ~ spl0_99 ),
inference(resolution,[],[f1129,f62]) ).
fof(f5013,plain,
( spl0_260
| ~ spl0_68
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1236,f1124,f526,f5011]) ).
fof(f5011,plain,
( spl0_260
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X1),X0),additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f526,plain,
( spl0_68
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1124,plain,
( spl0_98
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X2),X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1236,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X1),X0),additive_identity,additive_identity) )
| ~ spl0_68
| ~ spl0_98 ),
inference(resolution,[],[f1125,f527]) ).
fof(f527,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f1125,plain,
( ! [X2,X0,X1] :
( sum(add(additive_inverse(X2),X0),X2,X1)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f5008,plain,
( spl0_259
| ~ spl0_157
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f3148,f3057,f2151,f5005]) ).
fof(f5005,plain,
( spl0_259
<=> sum(additive_identity,additive_identity,multiply(additive_identity,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2151,plain,
( spl0_157
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f3057,plain,
( spl0_192
<=> sum(multiply(additive_identity,b),c,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f3148,plain,
( sum(additive_identity,additive_identity,multiply(additive_identity,b))
| ~ spl0_157
| ~ spl0_192 ),
inference(resolution,[],[f3059,f2152]) ).
fof(f2152,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2151]) ).
fof(f3059,plain,
( sum(multiply(additive_identity,b),c,c)
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f3057]) ).
fof(f5003,plain,
( spl0_258
| ~ spl0_10
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1225,f1124,f61,f5001]) ).
fof(f5001,plain,
( spl0_258
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(additive_inverse(X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1225,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(additive_inverse(X2),X0),X1) )
| ~ spl0_10
| ~ spl0_98 ),
inference(resolution,[],[f1125,f62]) ).
fof(f4999,plain,
( spl0_257
| ~ spl0_68
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1194,f1100,f526,f4997]) ).
fof(f4997,plain,
( spl0_257
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X1)),additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1100,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X2)),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1194,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X1)),additive_identity,additive_identity) )
| ~ spl0_68
| ~ spl0_97 ),
inference(resolution,[],[f1101,f527]) ).
fof(f1101,plain,
( ! [X2,X0,X1] :
( sum(add(X0,additive_inverse(X2)),X2,X1)
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f4995,plain,
( spl0_256
| ~ spl0_10
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1183,f1100,f61,f4993]) ).
fof(f4993,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(X0,additive_inverse(X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1183,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,add(X0,additive_inverse(X2)),X1) )
| ~ spl0_10
| ~ spl0_97 ),
inference(resolution,[],[f1101,f62]) ).
fof(f4991,plain,
( spl0_255
| ~ spl0_10
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1162,f1096,f61,f4989]) ).
fof(f4989,plain,
( spl0_255
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(additive_inverse(X2),X1),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1096,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(additive_inverse(X2),X1),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(additive_inverse(X2),X1),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_96 ),
inference(resolution,[],[f1097,f62]) ).
fof(f1097,plain,
( ! [X2,X0,X1] :
( sum(X0,add(additive_inverse(X2),X1),additive_identity)
| ~ sum(X0,X1,X2) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f4987,plain,
( spl0_254
| ~ spl0_10
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1140,f1092,f61,f4985]) ).
fof(f4985,plain,
( spl0_254
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,additive_inverse(X2)),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1092,plain,
( spl0_95
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,additive_inverse(X2)),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1140,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,additive_inverse(X2)),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_95 ),
inference(resolution,[],[f1093,f62]) ).
fof(f1093,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X1,additive_inverse(X2)),additive_identity)
| ~ sum(X0,X1,X2) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f4983,plain,
( spl0_253
| ~ spl0_73
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1040,f879,f553,f4981]) ).
fof(f4981,plain,
( spl0_253
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_identity,additive_identity,add(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f553,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(f879,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(f1040,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_identity,additive_identity,add(X0,X1)) )
| ~ spl0_73
| ~ spl0_91 ),
inference(resolution,[],[f880,f554]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f880,plain,
( ! [X2,X0,X1] :
( sum(X1,X2,add(X0,X2))
| ~ sum(additive_identity,X0,X1) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f879]) ).
fof(f4979,plain,
( spl0_252
| ~ spl0_74
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1033,f879,f557,f4977]) ).
fof(f4977,plain,
( spl0_252
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,additive_identity,add(X0,additive_inverse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f557,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(f1033,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,additive_identity,add(X0,additive_inverse(X1))) )
| ~ spl0_74
| ~ spl0_91 ),
inference(resolution,[],[f880,f558]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f4975,plain,
( spl0_251
| ~ spl0_70
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1025,f879,f541,f4973]) ).
fof(f4973,plain,
( spl0_251
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X2,X1) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f541,plain,
( spl0_70
<=> ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1025,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X2,X1) = add(X0,X2) )
| ~ spl0_70
| ~ spl0_91 ),
inference(resolution,[],[f880,f542]) ).
fof(f542,plain,
( ! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f4971,plain,
( spl0_250
| ~ spl0_29
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1021,f879,f205,f4969]) ).
fof(f4969,plain,
( spl0_250
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
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(f1021,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| add(X1,X2) = add(X0,X2) )
| ~ spl0_29
| ~ spl0_91 ),
inference(resolution,[],[f880,f206]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| add(X1,X2) = X0 )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f4967,plain,
( spl0_249
| ~ spl0_73
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1005,f875,f553,f4965]) ).
fof(f4965,plain,
( spl0_249
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f875,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(f1005,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,X0)) )
| ~ spl0_73
| ~ spl0_90 ),
inference(resolution,[],[f876,f554]) ).
fof(f876,plain,
( ! [X2,X0,X1] :
( sum(X0,X2,add(X1,X2))
| ~ sum(X0,additive_identity,X1) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f875]) ).
fof(f4962,plain,
( spl0_248
| ~ spl0_151
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2190,f2128,f2106,f4959]) ).
fof(f4959,plain,
( spl0_248
<=> sum(add(d,c),c,c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2106,plain,
( spl0_151
<=> ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(X0,c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2190,plain,
( sum(add(d,c),c,c)
| ~ spl0_151
| ~ spl0_153 ),
inference(resolution,[],[f2130,f2107]) ).
fof(f2107,plain,
( ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(X0,c,c) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f4957,plain,
( spl0_247
| ~ spl0_75
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1004,f875,f561,f4955]) ).
fof(f4955,plain,
( spl0_247
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,add(X1,X0),additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1004,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(additive_identity,add(X1,X0),additive_identity) )
| ~ spl0_75
| ~ spl0_90 ),
inference(resolution,[],[f876,f562]) ).
fof(f4953,plain,
( spl0_246
| ~ spl0_74
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f998,f875,f557,f4951]) ).
fof(f4951,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,additive_inverse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f998,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_identity,additive_identity,add(X1,additive_inverse(X0))) )
| ~ spl0_74
| ~ spl0_90 ),
inference(resolution,[],[f876,f558]) ).
fof(f4949,plain,
( spl0_245
| ~ spl0_70
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f990,f875,f541,f4947]) ).
fof(f4947,plain,
( spl0_245
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f990,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X2,X0) )
| ~ spl0_70
| ~ spl0_90 ),
inference(resolution,[],[f876,f542]) ).
fof(f4945,plain,
( spl0_244
| ~ spl0_29
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f986,f875,f205,f4943]) ).
fof(f4943,plain,
( spl0_244
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f986,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| add(X1,X2) = add(X0,X2) )
| ~ spl0_29
| ~ spl0_90 ),
inference(resolution,[],[f876,f206]) ).
fof(f4941,plain,
( spl0_243
| ~ spl0_73
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f918,f853,f553,f4939]) ).
fof(f4939,plain,
( spl0_243
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f853,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(f918,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_73
| ~ spl0_85 ),
inference(resolution,[],[f854,f554]) ).
fof(f854,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X2,X1),X2)
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f4937,plain,
( spl0_242
| ~ spl0_70
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f913,f853,f541,f4935]) ).
fof(f4935,plain,
( spl0_242
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X2,X1),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f913,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X2,X1),X0) = X2 )
| ~ spl0_70
| ~ spl0_85 ),
inference(resolution,[],[f854,f542]) ).
fof(f4933,plain,
( spl0_241
| ~ spl0_29
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f909,f853,f205,f4931]) ).
fof(f4931,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X2,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f909,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X2,X1)) = X2 )
| ~ spl0_29
| ~ spl0_85 ),
inference(resolution,[],[f854,f206]) ).
fof(f4929,plain,
( spl0_240
| ~ spl0_73
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f896,f820,f553,f4927]) ).
fof(f4927,plain,
( spl0_240
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f820,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(f896,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_73
| ~ spl0_84 ),
inference(resolution,[],[f821,f554]) ).
fof(f821,plain,
( ! [X2,X0,X1] :
( sum(X0,add(X1,X2),X2)
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f4925,plain,
( spl0_239
| ~ spl0_70
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f891,f820,f541,f4923]) ).
fof(f4923,plain,
( spl0_239
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X1,X2),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f891,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(add(X1,X2),X0) = X2 )
| ~ spl0_70
| ~ spl0_84 ),
inference(resolution,[],[f821,f542]) ).
fof(f4921,plain,
( spl0_238
| ~ spl0_29
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f887,f820,f205,f4919]) ).
fof(f4919,plain,
( spl0_238
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| add(X0,add(X1,X2)) = X2 )
| ~ spl0_29
| ~ spl0_84 ),
inference(resolution,[],[f821,f206]) ).
fof(f4916,plain,
( spl0_237
| ~ spl0_152
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2189,f2128,f2110,f4913]) ).
fof(f4913,plain,
( spl0_237
<=> sum(c,add(d,c),c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2110,plain,
( spl0_152
<=> ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(c,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2189,plain,
( sum(c,add(d,c),c)
| ~ spl0_152
| ~ spl0_153 ),
inference(resolution,[],[f2130,f2111]) ).
fof(f2111,plain,
( ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(c,X0,c) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f4736,plain,
( spl0_236
| ~ spl0_5
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f2001,f1976,f40,f4734]) ).
fof(f4734,plain,
( spl0_236
<=> ! [X0] :
( ~ sum(b,b,X0)
| sum(c,c,multiply(additive_inverse(a),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1976,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,c,multiply(additive_inverse(a),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2001,plain,
( ! [X0] :
( ~ sum(b,b,X0)
| sum(c,c,multiply(additive_inverse(a),X0)) )
| ~ spl0_5
| ~ spl0_143 ),
inference(resolution,[],[f1977,f42]) ).
fof(f1977,plain,
( ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,c,multiply(additive_inverse(a),X2)) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1976]) ).
fof(f4702,plain,
( spl0_235
| ~ spl0_5
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1984,f1964,f40,f4700]) ).
fof(f4700,plain,
( spl0_235
<=> ! [X0] :
( ~ sum(b,X0,b)
| sum(c,multiply(additive_inverse(a),X0),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1964,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(additive_inverse(a),X2),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1984,plain,
( ! [X0] :
( ~ sum(b,X0,b)
| sum(c,multiply(additive_inverse(a),X0),c) )
| ~ spl0_5
| ~ spl0_140 ),
inference(resolution,[],[f1965,f42]) ).
fof(f1965,plain,
( ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(additive_inverse(a),X2),c) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f4698,plain,
( spl0_234
| ~ spl0_5
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1810,f1765,f40,f4696]) ).
fof(f4696,plain,
( spl0_234
<=> ! [X0] :
( ~ sum(additive_inverse(a),a,X0)
| sum(c,d,multiply(X0,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1810,plain,
( ! [X0] :
( ~ sum(additive_inverse(a),a,X0)
| sum(c,d,multiply(X0,b)) )
| ~ spl0_5
| ~ spl0_129 ),
inference(resolution,[],[f1766,f42]) ).
fof(f4694,plain,
( spl0_233
| ~ spl0_5
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1786,f1748,f40,f4692]) ).
fof(f4692,plain,
( spl0_233
<=> ! [X0] :
( ~ sum(additive_inverse(a),X0,a)
| sum(c,multiply(X0,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1786,plain,
( ! [X0] :
( ~ sum(additive_inverse(a),X0,a)
| sum(c,multiply(X0,b),d) )
| ~ spl0_5
| ~ spl0_125 ),
inference(resolution,[],[f1749,f42]) ).
fof(f4690,plain,
( spl0_232
| ~ spl0_8
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1704,f1666,f53,f4688]) ).
fof(f4688,plain,
( spl0_232
<=> ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(additive_inverse(a),X0),c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1666,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,b)
| sum(X1,c,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1704,plain,
( ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(additive_inverse(a),X0),c,c) )
| ~ spl0_8
| ~ spl0_121 ),
inference(resolution,[],[f1667,f54]) ).
fof(f1667,plain,
( ! [X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,b)
| sum(X1,c,c) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f4685,plain,
( spl0_231
| ~ spl0_8
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1702,f1662,f53,f4683]) ).
fof(f4683,plain,
( spl0_231
<=> ! [X0] :
( ~ sum(multiply(additive_identity,b),c,X0)
| product(additive_inverse(a),b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1662,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(additive_identity,b,X0)
| product(additive_inverse(a),b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1702,plain,
( ! [X0] :
( ~ sum(multiply(additive_identity,b),c,X0)
| product(additive_inverse(a),b,X0) )
| ~ spl0_8
| ~ spl0_120 ),
inference(resolution,[],[f1663,f54]) ).
fof(f1663,plain,
( ! [X0,X1] :
( ~ product(additive_identity,b,X0)
| ~ sum(X0,c,X1)
| product(additive_inverse(a),b,X1) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1662]) ).
fof(f4681,plain,
( spl0_230
| ~ spl0_62
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1644,f1434,f467,f4679]) ).
fof(f4679,plain,
( spl0_230
<=> ! [X0,X1] :
( product(X0,b,multiply(X1,c))
| ~ product(X1,additive_inverse(a),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f467,plain,
( spl0_62
<=> c = multiply(additive_inverse(a),b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1644,plain,
( ! [X0,X1] :
( product(X0,b,multiply(X1,c))
| ~ product(X1,additive_inverse(a),X0) )
| ~ spl0_62
| ~ spl0_113 ),
inference(superposition,[],[f1435,f469]) ).
fof(f469,plain,
( c = multiply(additive_inverse(a),b)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f4677,plain,
( spl0_229
| ~ spl0_62
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1616,f1430,f467,f4675]) ).
fof(f4675,plain,
( spl0_229
<=> ! [X0,X1] :
( product(X0,multiply(X1,b),c)
| ~ product(X0,X1,additive_inverse(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1430,plain,
( spl0_112
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,X1,X2)
| product(X0,multiply(X1,X3),multiply(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1616,plain,
( ! [X0,X1] :
( product(X0,multiply(X1,b),c)
| ~ product(X0,X1,additive_inverse(a)) )
| ~ spl0_62
| ~ spl0_112 ),
inference(superposition,[],[f1431,f469]) ).
fof(f1431,plain,
( ! [X2,X3,X0,X1] :
( product(X0,multiply(X1,X3),multiply(X2,X3))
| ~ product(X0,X1,X2) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f4673,plain,
( spl0_228
| ~ spl0_31
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f791,f756,f214,f4671]) ).
fof(f4671,plain,
( spl0_228
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,b) = multiply(X0,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f756,plain,
( spl0_82
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,b,multiply(X0,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f791,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| multiply(X1,b) = multiply(X0,d) )
| ~ spl0_31
| ~ spl0_82 ),
inference(resolution,[],[f757,f215]) ).
fof(f757,plain,
( ! [X0,X1] :
( product(X1,b,multiply(X0,d))
| ~ product(X0,a,X1) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f4669,plain,
( spl0_227
| ~ spl0_31
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f771,f752,f214,f4667]) ).
fof(f4667,plain,
( spl0_227
<=> ! [X0,X1] :
( ~ product(X0,X1,a)
| d = multiply(X0,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f771,plain,
( ! [X0,X1] :
( ~ product(X0,X1,a)
| d = multiply(X0,multiply(X1,b)) )
| ~ spl0_31
| ~ spl0_81 ),
inference(resolution,[],[f753,f215]) ).
fof(f4102,plain,
( spl0_226
| ~ spl0_8
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f3612,f3212,f53,f4099]) ).
fof(f4099,plain,
( spl0_226
<=> product(additive_identity,b,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3612,plain,
( product(additive_identity,b,additive_identity)
| ~ spl0_8
| ~ spl0_224 ),
inference(superposition,[],[f54,f3214]) ).
fof(f3219,plain,
( spl0_225
| ~ spl0_53
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1581,f1426,f390,f3217]) ).
fof(f3217,plain,
( spl0_225
<=> ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X0,X2))
| ~ sum(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1426,plain,
( spl0_111
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(add(X1,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1581,plain,
( ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X0,X2))
| ~ sum(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_111 ),
inference(superposition,[],[f1427,f391]) ).
fof(f1427,plain,
( ! [X2,X3,X0,X1] :
( sum(X2,X3,add(add(X1,X3),X0))
| ~ sum(X0,X1,X2) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f3215,plain,
( spl0_224
| ~ spl0_102
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f3149,f3057,f1330,f3212]) ).
fof(f1330,plain,
( spl0_102
<=> ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f3149,plain,
( additive_identity = multiply(additive_identity,b)
| ~ spl0_102
| ~ spl0_192 ),
inference(resolution,[],[f3059,f1331]) ).
fof(f1331,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f3210,plain,
( spl0_223
| ~ spl0_47
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1580,f1426,f348,f3208]) ).
fof(f3208,plain,
( spl0_223
<=> ! [X2,X0,X1] :
( sum(X1,X0,add(X0,X2))
| ~ sum(X2,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f348,plain,
( spl0_47
<=> ! [X0] : add(additive_identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1580,plain,
( ! [X2,X0,X1] :
( sum(X1,X0,add(X0,X2))
| ~ sum(X2,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_111 ),
inference(superposition,[],[f1427,f349]) ).
fof(f349,plain,
( ! [X0] : add(additive_identity,X0) = X0
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f3206,plain,
( spl0_222
| ~ spl0_53
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1528,f1422,f390,f3204]) ).
fof(f3204,plain,
( spl0_222
<=> ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X2,X0))
| ~ sum(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1422,plain,
( spl0_110
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(X0,add(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1528,plain,
( ! [X2,X0,X1] :
( sum(X1,additive_identity,add(X2,X0))
| ~ sum(X2,X0,X1) )
| ~ spl0_53
| ~ spl0_110 ),
inference(superposition,[],[f1423,f391]) ).
fof(f1423,plain,
( ! [X2,X3,X0,X1] :
( sum(X2,X3,add(X0,add(X1,X3)))
| ~ sum(X0,X1,X2) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1422]) ).
fof(f3202,plain,
( spl0_221
| ~ spl0_47
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1527,f1422,f348,f3200]) ).
fof(f3200,plain,
( spl0_221
<=> ! [X2,X0,X1] :
( sum(X1,X0,add(X2,X0))
| ~ sum(X2,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1527,plain,
( ! [X2,X0,X1] :
( sum(X1,X0,add(X2,X0))
| ~ sum(X2,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_110 ),
inference(superposition,[],[f1423,f349]) ).
fof(f3198,plain,
( spl0_220
| ~ spl0_47
| ~ spl0_72
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1357,f1136,f549,f348,f3196]) ).
fof(f3196,plain,
( spl0_220
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X1),X0,additive_identity)
| sum(additive_inverse(X0),X1,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1357,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X1),X0,additive_identity)
| sum(additive_inverse(X0),X1,additive_identity) )
| ~ spl0_47
| ~ spl0_72
| ~ spl0_101 ),
inference(forward_demodulation,[],[f1346,f349]) ).
fof(f1346,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,additive_identity)
| ~ sum(additive_inverse(add(additive_identity,X1)),X0,additive_identity) )
| ~ spl0_72
| ~ spl0_101 ),
inference(resolution,[],[f1137,f550]) ).
fof(f3194,plain,
( spl0_219
| ~ spl0_25
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1270,f1128,f169,f3192]) ).
fof(f3192,plain,
( spl0_219
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| add(X2,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f169,plain,
( spl0_25
<=> ! [X0,X1] :
( X0 = X1
| ~ sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1270,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| add(X2,X1) = X0 )
| ~ spl0_25
| ~ spl0_99 ),
inference(resolution,[],[f1129,f170]) ).
fof(f170,plain,
( ! [X0,X1] :
( ~ sum(X1,additive_identity,X0)
| X0 = X1 )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f3190,plain,
( spl0_218
| ~ spl0_71
| ~ spl0_92
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1265,f1124,f953,f545,f3188]) ).
fof(f3188,plain,
( spl0_218
<=> ! [X0,X1] :
( sum(add(X1,X0),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f545,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(f953,plain,
( spl0_92
<=> ! [X0] : additive_inverse(additive_inverse(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1265,plain,
( ! [X0,X1] :
( sum(add(X1,X0),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) )
| ~ spl0_71
| ~ spl0_92
| ~ spl0_98 ),
inference(forward_demodulation,[],[f1248,f954]) ).
fof(f954,plain,
( ! [X0] : additive_inverse(additive_inverse(X0)) = X0
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f1248,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(add(additive_inverse(additive_inverse(X1)),X0),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_98 ),
inference(resolution,[],[f1125,f546]) ).
fof(f546,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f3186,plain,
( spl0_217
| ~ spl0_71
| ~ spl0_92
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1223,f1100,f953,f545,f3184]) ).
fof(f3184,plain,
( spl0_217
<=> ! [X0,X1] :
( sum(add(X0,X1),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1223,plain,
( ! [X0,X1] :
( sum(add(X0,X1),additive_identity,X1)
| ~ sum(X0,additive_identity,additive_identity) )
| ~ spl0_71
| ~ spl0_92
| ~ spl0_97 ),
inference(forward_demodulation,[],[f1206,f954]) ).
fof(f1206,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(add(X0,additive_inverse(additive_inverse(X1))),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_97 ),
inference(resolution,[],[f1101,f546]) ).
fof(f3182,plain,
( spl0_216
| ~ spl0_23
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1171,f1096,f160,f3180]) ).
fof(f3180,plain,
( spl0_216
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(additive_inverse(X1),X0) )
| ~ spl0_23
| ~ spl0_96 ),
inference(resolution,[],[f1097,f161]) ).
fof(f3178,plain,
( spl0_215
| ~ spl0_65
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1045,f879,f496,f3176]) ).
fof(f3176,plain,
( spl0_215
<=> ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(additive_identity,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1045,plain,
( ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(additive_identity,X0,X2) )
| ~ spl0_65
| ~ spl0_91 ),
inference(superposition,[],[f880,f497]) ).
fof(f3174,plain,
( spl0_214
| ~ spl0_27
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1041,f879,f189,f3172]) ).
fof(f3172,plain,
( spl0_214
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| additive_identity = add(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
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(f1041,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| additive_identity = add(X0,X1) )
| ~ spl0_27
| ~ spl0_91 ),
inference(resolution,[],[f880,f190]) ).
fof(f190,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X1),X1,X0)
| additive_identity = X0 )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f3147,plain,
( spl0_213
| ~ spl0_28
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1034,f879,f193,f3145]) ).
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(f1034,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_28
| ~ spl0_91 ),
inference(resolution,[],[f880,f194]) ).
fof(f194,plain,
( ! [X0,X1] :
( ~ sum(X1,additive_inverse(X1),X0)
| additive_identity = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f3143,plain,
( spl0_212
| ~ spl0_10
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1017,f879,f61,f3141]) ).
fof(f3141,plain,
( spl0_212
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X2,X1,add(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1017,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X2,X1,add(X0,X2)) )
| ~ spl0_10
| ~ spl0_91 ),
inference(resolution,[],[f880,f62]) ).
fof(f3139,plain,
( spl0_211
| ~ spl0_65
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1010,f875,f496,f3137]) ).
fof(f3137,plain,
( spl0_211
<=> ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(X2,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1010,plain,
( ! [X2,X0,X1] :
( sum(X2,X1,add(X1,X0))
| ~ sum(X2,additive_identity,X0) )
| ~ spl0_65
| ~ spl0_90 ),
inference(superposition,[],[f876,f497]) ).
fof(f3135,plain,
( spl0_210
| ~ spl0_27
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1006,f875,f189,f3133]) ).
fof(f3133,plain,
( spl0_210
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| additive_identity = add(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1006,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| additive_identity = add(X1,X0) )
| ~ spl0_27
| ~ spl0_90 ),
inference(resolution,[],[f876,f190]) ).
fof(f3131,plain,
( spl0_209
| ~ spl0_28
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f999,f875,f193,f3129]) ).
fof(f3129,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X1,additive_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f999,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X1,additive_inverse(X0)) )
| ~ spl0_28
| ~ spl0_90 ),
inference(resolution,[],[f876,f194]) ).
fof(f3127,plain,
( spl0_208
| ~ spl0_10
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f982,f875,f61,f3125]) ).
fof(f3125,plain,
( spl0_208
<=> ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,X0,add(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f982,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X2,X0,add(X1,X2)) )
| ~ spl0_10
| ~ spl0_90 ),
inference(resolution,[],[f876,f62]) ).
fof(f3123,plain,
( spl0_207
| ~ spl0_10
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f961,f861,f61,f3121]) ).
fof(f3121,plain,
( spl0_207
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f861,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(f961,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X1,X0),X2) )
| ~ spl0_10
| ~ spl0_87 ),
inference(resolution,[],[f862,f62]) ).
fof(f862,plain,
( ! [X2,X0,X1] :
( sum(add(X1,X0),additive_identity,X2)
| ~ sum(X0,X1,X2) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f3119,plain,
( spl0_206
| ~ spl0_67
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f960,f861,f522,f3117]) ).
fof(f3117,plain,
( spl0_206
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X0),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f522,plain,
( spl0_67
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f960,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X0),X2,X2) )
| ~ spl0_67
| ~ spl0_87 ),
inference(resolution,[],[f862,f523]) ).
fof(f523,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f3115,plain,
( spl0_205
| ~ spl0_10
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f931,f857,f61,f3113]) ).
fof(f3113,plain,
( spl0_205
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f857,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(f931,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X0,X1),X2) )
| ~ spl0_10
| ~ spl0_86 ),
inference(resolution,[],[f858,f62]) ).
fof(f858,plain,
( ! [X2,X0,X1] :
( sum(add(X0,X1),additive_identity,X2)
| ~ sum(X0,X1,X2) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f3111,plain,
( spl0_204
| ~ spl0_67
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f930,f857,f522,f3109]) ).
fof(f3109,plain,
( spl0_204
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X0,X1),X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X0,X1),X2,X2) )
| ~ spl0_67
| ~ spl0_86 ),
inference(resolution,[],[f858,f523]) ).
fof(f3107,plain,
( spl0_203
| ~ spl0_8
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2136,f2110,f53,f3104]) ).
fof(f3104,plain,
( spl0_203
<=> sum(c,multiply(additive_identity,b),c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2136,plain,
( sum(c,multiply(additive_identity,b),c)
| ~ spl0_8
| ~ spl0_152 ),
inference(resolution,[],[f2111,f54]) ).
fof(f3102,plain,
( spl0_202
| ~ spl0_27
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f919,f853,f189,f3100]) ).
fof(f3100,plain,
( spl0_202
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f919,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X1,additive_identity)
| additive_identity = X0 )
| ~ spl0_27
| ~ spl0_85 ),
inference(resolution,[],[f854,f190]) ).
fof(f3098,plain,
( spl0_201
| ~ spl0_10
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f905,f853,f61,f3096]) ).
fof(f3096,plain,
( spl0_201
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X2,X1),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f905,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X2,X1),X0,X2) )
| ~ spl0_10
| ~ spl0_85 ),
inference(resolution,[],[f854,f62]) ).
fof(f3094,plain,
( spl0_200
| ~ spl0_27
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f897,f820,f189,f3092]) ).
fof(f3092,plain,
( spl0_200
<=> ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| additive_identity = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f897,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,additive_identity)
| additive_identity = X1 )
| ~ spl0_27
| ~ spl0_84 ),
inference(resolution,[],[f821,f190]) ).
fof(f3090,plain,
( spl0_199
| ~ spl0_10
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f883,f820,f61,f3088]) ).
fof(f3088,plain,
( spl0_199
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(add(X1,X2),X0,X2) )
| ~ spl0_10
| ~ spl0_84 ),
inference(resolution,[],[f821,f62]) ).
fof(f3085,plain,
( spl0_198
| ~ spl0_73
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f748,f577,f553,f3083]) ).
fof(f3083,plain,
( spl0_198
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f748,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_73
| ~ spl0_79 ),
inference(resolution,[],[f578,f554]) ).
fof(f3080,plain,
( spl0_197
| ~ spl0_75
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f747,f577,f561,f3078]) ).
fof(f3078,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f747,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| sum(additive_identity,X0,additive_identity) )
| ~ spl0_75
| ~ spl0_79 ),
inference(resolution,[],[f578,f562]) ).
fof(f3076,plain,
( spl0_196
| ~ spl0_70
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f742,f577,f541,f3074]) ).
fof(f3074,plain,
( spl0_196
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(additive_inverse(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(additive_inverse(X1),X2) = X0 )
| ~ spl0_70
| ~ spl0_79 ),
inference(resolution,[],[f578,f542]) ).
fof(f3072,plain,
( spl0_195
| ~ spl0_29
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f738,f577,f205,f3070]) ).
fof(f3070,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(X2,additive_inverse(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f738,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| add(X2,additive_inverse(X1)) = X0 )
| ~ spl0_29
| ~ spl0_79 ),
inference(resolution,[],[f578,f206]) ).
fof(f3068,plain,
( spl0_194
| ~ spl0_70
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f687,f569,f541,f3066]) ).
fof(f3066,plain,
( spl0_194
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f687,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(additive_inverse(X1),X0) )
| ~ spl0_70
| ~ spl0_77 ),
inference(resolution,[],[f570,f542]) ).
fof(f3064,plain,
( spl0_193
| ~ spl0_29
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f683,f569,f205,f3062]) ).
fof(f3062,plain,
( spl0_193
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f683,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| additive_identity = add(X0,additive_inverse(X1)) )
| ~ spl0_29
| ~ spl0_77 ),
inference(resolution,[],[f570,f206]) ).
fof(f3060,plain,
( spl0_192
| ~ spl0_8
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2133,f2106,f53,f3057]) ).
fof(f2133,plain,
( sum(multiply(additive_identity,b),c,c)
| ~ spl0_8
| ~ spl0_151 ),
inference(resolution,[],[f2107,f54]) ).
fof(f3055,plain,
( spl0_191
| ~ spl0_71
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f662,f565,f545,f3053]) ).
fof(f3053,plain,
( spl0_191
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_inverse(X0),additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f565,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(f662,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_inverse(X1))
| sum(additive_inverse(X0),additive_identity,X1) )
| ~ spl0_71
| ~ spl0_76 ),
inference(resolution,[],[f566,f546]) ).
fof(f566,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,additive_identity)
| ~ sum(additive_identity,X0,X1) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f2861,plain,
( spl0_190
| ~ spl0_6
| ~ spl0_92
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1946,f1907,f953,f45,f2859]) ).
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_137
<=> ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),X2)
| sum(X1,c,multiply(X2,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1946,plain,
( ! [X0] :
( ~ product(a,b,X0)
| sum(X0,c,multiply(additive_identity,b)) )
| ~ spl0_6
| ~ spl0_92
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1933,f954]) ).
fof(f1933,plain,
( ! [X0] :
( ~ product(additive_inverse(additive_inverse(a)),b,X0)
| sum(X0,c,multiply(additive_identity,b)) )
| ~ spl0_6
| ~ spl0_137 ),
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(a),X2)
| ~ product(X0,b,X1)
| sum(X1,c,multiply(X2,b)) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1907]) ).
fof(f2857,plain,
( spl0_189
| ~ spl0_2
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1811,f1765,f27,f2855]) ).
fof(f2855,plain,
( spl0_189
<=> ! [X0] :
( ~ sum(a,a,X0)
| sum(d,d,multiply(X0,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1811,plain,
( ! [X0] :
( ~ sum(a,a,X0)
| sum(d,d,multiply(X0,b)) )
| ~ spl0_2
| ~ spl0_129 ),
inference(resolution,[],[f1766,f29]) ).
fof(f2853,plain,
( spl0_188
| ~ spl0_2
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1804,f1761,f27,f2851]) ).
fof(f2851,plain,
( spl0_188
<=> ! [X0] :
( ~ sum(b,b,X0)
| sum(d,d,multiply(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1804,plain,
( ! [X0] :
( ~ sum(b,b,X0)
| sum(d,d,multiply(a,X0)) )
| ~ spl0_2
| ~ spl0_128 ),
inference(resolution,[],[f1762,f29]) ).
fof(f2849,plain,
( spl0_187
| ~ spl0_2
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1787,f1748,f27,f2847]) ).
fof(f2847,plain,
( spl0_187
<=> ! [X0] :
( ~ sum(a,X0,a)
| sum(d,multiply(X0,b),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1787,plain,
( ! [X0] :
( ~ sum(a,X0,a)
| sum(d,multiply(X0,b),d) )
| ~ spl0_2
| ~ spl0_125 ),
inference(resolution,[],[f1749,f29]) ).
fof(f2845,plain,
( spl0_186
| ~ spl0_2
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1772,f1740,f27,f2843]) ).
fof(f2843,plain,
( spl0_186
<=> ! [X0] :
( ~ sum(b,X0,b)
| sum(d,multiply(a,X0),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1772,plain,
( ! [X0] :
( ~ sum(b,X0,b)
| sum(d,multiply(a,X0),d) )
| ~ spl0_2
| ~ spl0_123 ),
inference(resolution,[],[f1741,f29]) ).
fof(f2841,plain,
( spl0_185
| ~ spl0_9
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1395,f1373,f57,f2839]) ).
fof(f2839,plain,
( spl0_185
<=> ! [X0] :
( ~ sum(a,a,X0)
| product(X0,b,add(d,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1373,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1395,plain,
( ! [X0] :
( ~ sum(a,a,X0)
| product(X0,b,add(d,d)) )
| ~ spl0_9
| ~ spl0_106 ),
inference(resolution,[],[f1374,f58]) ).
fof(f1374,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f2837,plain,
( spl0_184
| ~ spl0_8
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1394,f1369,f53,f2835]) ).
fof(f2835,plain,
( spl0_184
<=> ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,b),d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1369,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1394,plain,
( ! [X0] :
( ~ sum(X0,a,a)
| sum(multiply(X0,b),d,d) )
| ~ spl0_8
| ~ spl0_105 ),
inference(resolution,[],[f1370,f54]) ).
fof(f1370,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1369]) ).
fof(f2833,plain,
( spl0_183
| ~ spl0_9
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1386,f1365,f57,f2831]) ).
fof(f2831,plain,
( spl0_183
<=> ! [X0] :
( ~ sum(b,b,X0)
| product(a,X0,add(d,d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1365,plain,
( spl0_104
<=> ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1386,plain,
( ! [X0] :
( ~ sum(b,b,X0)
| product(a,X0,add(d,d)) )
| ~ spl0_9
| ~ spl0_104 ),
inference(resolution,[],[f1366,f58]) ).
fof(f1366,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f2829,plain,
( ~ spl0_182
| spl0_164
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2467,f2368,f2356,f2826]) ).
fof(f2826,plain,
( spl0_182
<=> sum(additive_identity,a,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2356,plain,
( spl0_164
<=> sum(additive_inverse(a),a,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2368,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| sum(additive_inverse(X0),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2467,plain,
( ~ sum(additive_identity,a,additive_identity)
| spl0_164
| ~ spl0_166 ),
inference(resolution,[],[f2369,f2358]) ).
fof(f2358,plain,
( ~ sum(additive_inverse(a),a,a)
| spl0_164 ),
inference(avatar_component_clause,[],[f2356]) ).
fof(f2369,plain,
( ! [X0,X1] :
( sum(additive_inverse(X0),X1,X1)
| ~ sum(additive_identity,X0,additive_identity) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2368]) ).
fof(f2824,plain,
( spl0_181
| ~ spl0_8
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1380,f1361,f53,f2822]) ).
fof(f2822,plain,
( spl0_181
<=> ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(a,X0),d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1361,plain,
( spl0_103
<=> ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1380,plain,
( ! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(a,X0),d,d) )
| ~ spl0_8
| ~ spl0_103 ),
inference(resolution,[],[f1362,f54]) ).
fof(f1362,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f2820,plain,
( spl0_180
| ~ spl0_62
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1090,f1056,f467,f2818]) ).
fof(f2818,plain,
( spl0_180
<=> ! [X0] :
( product(X0,c,c)
| ~ product(X0,additive_inverse(a),additive_inverse(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1090,plain,
( ! [X0] :
( product(X0,c,c)
| ~ product(X0,additive_inverse(a),additive_inverse(a)) )
| ~ spl0_62
| ~ spl0_94 ),
inference(superposition,[],[f1057,f469]) ).
fof(f2816,plain,
( spl0_179
| ~ spl0_26
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f798,f756,f183,f2814]) ).
fof(f2814,plain,
( spl0_179
<=> ! [X0] :
( ~ product(X0,a,additive_inverse(a))
| c = multiply(X0,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f798,plain,
( ! [X0] :
( ~ product(X0,a,additive_inverse(a))
| c = multiply(X0,d) )
| ~ spl0_26
| ~ spl0_82 ),
inference(resolution,[],[f757,f184]) ).
fof(f2420,plain,
( spl0_178
| ~ spl0_9
| ~ spl0_65
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1354,f1136,f496,f57,f2418]) ).
fof(f2418,plain,
( spl0_178
<=> ! [X0,X1] : sum(add(X0,additive_inverse(add(X0,X1))),X1,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1354,plain,
( ! [X0,X1] : sum(add(X0,additive_inverse(add(X0,X1))),X1,additive_identity)
| ~ spl0_9
| ~ spl0_65
| ~ spl0_101 ),
inference(forward_demodulation,[],[f1340,f497]) ).
fof(f1340,plain,
( ! [X0,X1] : sum(add(additive_inverse(add(X0,X1)),X0),X1,additive_identity)
| ~ spl0_9
| ~ spl0_101 ),
inference(resolution,[],[f1137,f58]) ).
fof(f2416,plain,
( spl0_177
| ~ spl0_47
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1347,f1136,f348,f2414]) ).
fof(f2414,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(X1,X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1347,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),additive_identity,X1)
| sum(X1,X0,additive_identity) )
| ~ spl0_47
| ~ spl0_101 ),
inference(superposition,[],[f1137,f349]) ).
fof(f2412,plain,
( spl0_176
| ~ spl0_63
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1012,f875,f476,f2410]) ).
fof(f2410,plain,
( spl0_176
<=> ! [X0,X1] :
( sum(X1,X0,additive_identity)
| ~ sum(X1,additive_identity,additive_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f476,plain,
( spl0_63
<=> ! [X0] : additive_identity = add(additive_inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1012,plain,
( ! [X0,X1] :
( sum(X1,X0,additive_identity)
| ~ sum(X1,additive_identity,additive_inverse(X0)) )
| ~ spl0_63
| ~ spl0_90 ),
inference(superposition,[],[f876,f477]) ).
fof(f477,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f2408,plain,
( spl0_175
| ~ spl0_23
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1003,f875,f160,f2406]) ).
fof(f2406,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| add(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1003,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| add(X0,X1) = X1 )
| ~ spl0_23
| ~ spl0_90 ),
inference(resolution,[],[f876,f161]) ).
fof(f2404,plain,
( spl0_174
| ~ spl0_23
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f916,f853,f160,f2402]) ).
fof(f2402,plain,
( spl0_174
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X1,X0) = X1 )
| ~ spl0_23
| ~ spl0_85 ),
inference(resolution,[],[f854,f161]) ).
fof(f2400,plain,
( ~ spl0_173
| ~ spl0_78
| spl0_164 ),
inference(avatar_split_clause,[],[f2360,f2356,f573,f2397]) ).
fof(f2397,plain,
( spl0_173
<=> sum(additive_identity,additive_identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2360,plain,
( ~ sum(additive_identity,additive_identity,a)
| ~ spl0_78
| spl0_164 ),
inference(resolution,[],[f2358,f574]) ).
fof(f2395,plain,
( spl0_172
| ~ spl0_23
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f894,f820,f160,f2393]) ).
fof(f2393,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f894,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| add(X0,X1) = X1 )
| ~ spl0_23
| ~ spl0_84 ),
inference(resolution,[],[f821,f161]) ).
fof(f2390,plain,
( spl0_171
| ~ spl0_27
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f749,f577,f189,f2388]) ).
fof(f2388,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| additive_identity = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f749,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(additive_inverse(X1)))
| additive_identity = X0 )
| ~ spl0_27
| ~ spl0_79 ),
inference(resolution,[],[f578,f190]) ).
fof(f2386,plain,
( spl0_170
| ~ spl0_68
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f745,f577,f526,f2384]) ).
fof(f2384,plain,
( spl0_170
<=> ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(X1,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f745,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(X1,additive_identity,additive_identity) )
| ~ spl0_68
| ~ spl0_79 ),
inference(resolution,[],[f578,f527]) ).
fof(f2382,plain,
( spl0_169
| ~ spl0_10
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f734,f577,f61,f2380]) ).
fof(f2380,plain,
( spl0_169
<=> ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X1),X2,X0) )
| ~ spl0_10
| ~ spl0_79 ),
inference(resolution,[],[f578,f62]) ).
fof(f2378,plain,
( spl0_168
| ~ spl0_10
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f696,f573,f61,f2376]) ).
fof(f2376,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X1,additive_inverse(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X1,additive_inverse(X1),X0) )
| ~ spl0_10
| ~ spl0_78 ),
inference(resolution,[],[f574,f62]) ).
fof(f2374,plain,
( spl0_167
| ~ spl0_10
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f679,f569,f61,f2372]) ).
fof(f2372,plain,
( spl0_167
<=> ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_inverse(X1),X0,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f679,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(additive_inverse(X1),X0,additive_identity) )
| ~ spl0_10
| ~ spl0_77 ),
inference(resolution,[],[f570,f62]) ).
fof(f2370,plain,
( spl0_166
| ~ spl0_67
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f654,f565,f522,f2368]) ).
fof(f654,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| sum(additive_inverse(X0),X1,X1) )
| ~ spl0_67
| ~ spl0_76 ),
inference(resolution,[],[f566,f523]) ).
fof(f2366,plain,
( spl0_165
| ~ spl0_10
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f595,f549,f61,f2364]) ).
fof(f2364,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X0,additive_inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f595,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X0,additive_inverse(X1)) )
| ~ spl0_10
| ~ spl0_72 ),
inference(resolution,[],[f550,f62]) ).
fof(f2359,plain,
( spl0_163
| ~ spl0_164
| ~ spl0_5
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1392,f1369,f40,f2356,f2352]) ).
fof(f2352,plain,
( spl0_163
<=> sum(c,d,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1392,plain,
( ~ sum(additive_inverse(a),a,a)
| sum(c,d,d)
| ~ spl0_5
| ~ spl0_105 ),
inference(resolution,[],[f1370,f42]) ).
fof(f2350,plain,
( spl0_162
| ~ spl0_62
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f818,f760,f467,f2348]) ).
fof(f2348,plain,
( spl0_162
<=> ! [X0] :
( product(X0,d,c)
| ~ product(X0,a,additive_inverse(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f760,plain,
( spl0_83
<=> ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,d,multiply(X1,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f818,plain,
( ! [X0] :
( product(X0,d,c)
| ~ product(X0,a,additive_inverse(a)) )
| ~ spl0_62
| ~ spl0_83 ),
inference(superposition,[],[f761,f469]) ).
fof(f761,plain,
( ! [X0,X1] :
( product(X0,d,multiply(X1,b))
| ~ product(X0,a,X1) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f2346,plain,
( spl0_161
| ~ spl0_22
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f795,f756,f154,f2344]) ).
fof(f2344,plain,
( spl0_161
<=> ! [X0] :
( ~ product(X0,a,a)
| d = multiply(X0,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f154,plain,
( spl0_22
<=> ! [X0] :
( d = X0
| ~ product(a,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f795,plain,
( ! [X0] :
( ~ product(X0,a,a)
| d = multiply(X0,d) )
| ~ spl0_22
| ~ spl0_82 ),
inference(resolution,[],[f757,f155]) ).
fof(f155,plain,
( ! [X0] :
( ~ product(a,b,X0)
| d = X0 )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f2165,plain,
( spl0_160
| ~ spl0_47
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1042,f879,f348,f2163]) ).
fof(f2163,plain,
( spl0_160
<=> ! [X0,X1] :
( sum(X1,X0,X0)
| ~ sum(additive_identity,additive_identity,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1042,plain,
( ! [X0,X1] :
( sum(X1,X0,X0)
| ~ sum(additive_identity,additive_identity,X1) )
| ~ spl0_47
| ~ spl0_91 ),
inference(superposition,[],[f880,f349]) ).
fof(f2161,plain,
( spl0_159
| ~ spl0_30
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f750,f577,f209,f2159]) ).
fof(f2159,plain,
( spl0_159
<=> ! [X0,X1] :
( sum(X0,additive_identity,X1)
| ~ sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f750,plain,
( ! [X0,X1] :
( sum(X0,additive_identity,X1)
| ~ sum(X1,additive_identity,X0) )
| ~ spl0_30
| ~ spl0_79 ),
inference(superposition,[],[f578,f211]) ).
fof(f2157,plain,
( spl0_158
| ~ spl0_71
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f733,f577,f545,f2155]) ).
fof(f2155,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,additive_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,additive_identity,X0) )
| ~ spl0_71
| ~ spl0_79 ),
inference(resolution,[],[f578,f546]) ).
fof(f2153,plain,
( spl0_157
| ~ spl0_74
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f728,f577,f557,f2151]) ).
fof(f728,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_74
| ~ spl0_79 ),
inference(resolution,[],[f578,f558]) ).
fof(f2149,plain,
( spl0_156
| ~ spl0_23
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f688,f569,f160,f2147]) ).
fof(f2147,plain,
( spl0_156
<=> ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| additive_identity = additive_inverse(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f688,plain,
( ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| additive_identity = additive_inverse(X0) )
| ~ spl0_23
| ~ spl0_77 ),
inference(resolution,[],[f570,f161]) ).
fof(f2145,plain,
( spl0_155
| ~ spl0_30
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f636,f561,f209,f2143]) ).
fof(f2143,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(f636,plain,
( ! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_identity,X0,additive_identity) )
| ~ spl0_30
| ~ spl0_75 ),
inference(superposition,[],[f562,f211]) ).
fof(f2141,plain,
( spl0_154
| ~ spl0_25
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f592,f549,f169,f2139]) ).
fof(f2139,plain,
( spl0_154
<=> ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f592,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X1) = X0 )
| ~ spl0_25
| ~ spl0_72 ),
inference(resolution,[],[f550,f170]) ).
fof(f2131,plain,
( spl0_153
| ~ spl0_9
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f2113,f1972,f57,f2128]) ).
fof(f1972,plain,
( spl0_142
<=> ! [X0] :
( ~ sum(d,c,X0)
| product(additive_identity,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f2113,plain,
( product(additive_identity,b,add(d,c))
| ~ spl0_9
| ~ spl0_142 ),
inference(resolution,[],[f1973,f58]) ).
fof(f1973,plain,
( ! [X0] :
( ~ sum(d,c,X0)
| product(additive_identity,b,X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1972]) ).
fof(f2112,plain,
( spl0_152
| ~ spl0_5
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1696,f1658,f40,f2110]) ).
fof(f1658,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ product(additive_identity,b,X0)
| ~ product(additive_inverse(a),b,X1)
| sum(X1,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1696,plain,
( ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(c,X0,c) )
| ~ spl0_5
| ~ spl0_119 ),
inference(resolution,[],[f1659,f42]) ).
fof(f1659,plain,
( ! [X0,X1] :
( ~ product(additive_inverse(a),b,X1)
| ~ product(additive_identity,b,X0)
| sum(X1,X0,c) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1658]) ).
fof(f2108,plain,
( spl0_151
| ~ spl0_5
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1691,f1654,f40,f2106]) ).
fof(f1654,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ product(additive_inverse(a),b,X0)
| ~ product(additive_identity,b,X1)
| sum(X1,X0,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1691,plain,
( ! [X0] :
( ~ product(additive_identity,b,X0)
| sum(X0,c,c) )
| ~ spl0_5
| ~ spl0_118 ),
inference(resolution,[],[f1655,f42]) ).
fof(f1655,plain,
( ! [X0,X1] :
( ~ product(additive_inverse(a),b,X0)
| ~ product(additive_identity,b,X1)
| sum(X1,X0,c) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f2032,plain,
( spl0_150
| ~ spl0_6
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1681,f1650,f45,f2030]) ).
fof(f2030,plain,
( spl0_150
<=> ! [X0] :
( ~ sum(c,d,X0)
| product(additive_identity,b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1681,plain,
( ! [X0] :
( ~ sum(c,d,X0)
| product(additive_identity,b,X0) )
| ~ spl0_6
| ~ spl0_117 ),
inference(resolution,[],[f1651,f46]) ).
fof(f2028,plain,
( spl0_149
| ~ spl0_13
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f461,f444,f83,f2026]) ).
fof(f2026,plain,
( spl0_149
<=> ! [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_149])]) ).
fof(f444,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(f461,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,[],[f445,f84]) ).
fof(f445,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,[],[f444]) ).
fof(f2024,plain,
( spl0_148
| ~ spl0_9
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f460,f444,f57,f2022]) ).
fof(f460,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,[],[f445,f58]) ).
fof(f2020,plain,
( spl0_147
| ~ spl0_8
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f457,f440,f53,f2018]) ).
fof(f440,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(f457,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,[],[f441,f54]) ).
fof(f441,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,[],[f440]) ).
fof(f2016,plain,
( spl0_146
| ~ spl0_13
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f453,f436,f83,f2014]) ).
fof(f2014,plain,
( spl0_146
<=> ! [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_146])]) ).
fof(f436,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(f453,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,[],[f437,f84]) ).
fof(f437,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,[],[f436]) ).
fof(f2012,plain,
( spl0_145
| ~ spl0_9
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f452,f436,f57,f2010]) ).
fof(f452,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,[],[f437,f58]) ).
fof(f2008,plain,
( spl0_144
| ~ spl0_8
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f449,f432,f53,f2006]) ).
fof(f432,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(f449,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,[],[f433,f54]) ).
fof(f433,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,[],[f432]) ).
fof(f1978,plain,
( spl0_143
| ~ spl0_5
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f448,f432,f40,f1976]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,c,multiply(additive_inverse(a),X2)) )
| ~ spl0_5
| ~ spl0_58 ),
inference(resolution,[],[f433,f42]) ).
fof(f1974,plain,
( spl0_142
| ~ spl0_2
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1409,f1377,f27,f1972]) ).
fof(f1377,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,b,X0)
| product(additive_identity,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1409,plain,
( ! [X0] :
( ~ sum(d,c,X0)
| product(additive_identity,b,X0) )
| ~ spl0_2
| ~ spl0_107 ),
inference(resolution,[],[f1378,f29]) ).
fof(f1378,plain,
( ! [X0,X1] :
( ~ product(a,b,X0)
| ~ sum(X0,c,X1)
| product(additive_identity,b,X1) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f1970,plain,
( spl0_141
| ~ spl0_8
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f430,f421,f53,f1968]) ).
fof(f1968,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ sum(multiply(additive_inverse(a),X0),c,X1)
| ~ sum(X0,b,X2)
| product(additive_inverse(a),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f421,plain,
( spl0_57
<=> ! [X0,X3,X2,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,b,X3)
| product(additive_inverse(a),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f430,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(additive_inverse(a),X0),c,X1)
| ~ sum(X0,b,X2)
| product(additive_inverse(a),X2,X1) )
| ~ spl0_8
| ~ spl0_57 ),
inference(resolution,[],[f422,f54]) ).
fof(f422,plain,
( ! [X2,X3,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,b,X3)
| product(additive_inverse(a),X3,X2) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f1966,plain,
( spl0_140
| ~ spl0_8
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f425,f417,f53,f1964]) ).
fof(f417,plain,
( spl0_56
<=> ! [X0,X3,X2,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ product(additive_inverse(a),X2,X3)
| ~ sum(X0,X2,b)
| sum(X1,X3,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f425,plain,
( ! [X2,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(additive_inverse(a),X2),c) )
| ~ spl0_8
| ~ spl0_56 ),
inference(resolution,[],[f418,f54]) ).
fof(f418,plain,
( ! [X2,X3,X0,X1] :
( ~ product(additive_inverse(a),X2,X3)
| ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,X3,c) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f1954,plain,
( spl0_139
| ~ spl0_6
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f459,f444,f45,f1952]) ).
fof(f1952,plain,
( spl0_139
<=> ! [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_139])]) ).
fof(f459,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,[],[f445,f46]) ).
fof(f1950,plain,
( spl0_138
| ~ spl0_6
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f451,f436,f45,f1948]) ).
fof(f1948,plain,
( spl0_138
<=> ! [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_138])]) ).
fof(f451,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,[],[f437,f46]) ).
fof(f1909,plain,
( spl0_137
| ~ spl0_5
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f456,f440,f40,f1907]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),X2)
| sum(X1,c,multiply(X2,b)) )
| ~ spl0_5
| ~ spl0_60 ),
inference(resolution,[],[f441,f42]) ).
fof(f1905,plain,
( spl0_136
| ~ spl0_13
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f415,f406,f83,f1903]) ).
fof(f1903,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(X2,b,X0)
| product(add(additive_inverse(a),X2),b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f406,plain,
( spl0_55
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,b,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,additive_inverse(a),X3)
| product(X3,b,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(X2,b,X0)
| product(add(additive_inverse(a),X2),b,X1) )
| ~ spl0_13
| ~ spl0_55 ),
inference(resolution,[],[f407,f84]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,additive_inverse(a),X3)
| ~ sum(X1,c,X2)
| ~ product(X0,b,X1)
| product(X3,b,X2) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f1901,plain,
( spl0_135
| ~ spl0_9
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f414,f406,f57,f1899]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(X2,b,X0)
| product(add(X2,additive_inverse(a)),b,X1) )
| ~ spl0_9
| ~ spl0_55 ),
inference(resolution,[],[f407,f58]) ).
fof(f1835,plain,
( spl0_134
| ~ spl0_3
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f458,f444,f32,f1833]) ).
fof(f1833,plain,
( spl0_134
<=> ! [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_134])]) ).
fof(f32,plain,
( spl0_3
<=> ! [X0] : sum(additive_identity,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f458,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,[],[f445,f33]) ).
fof(f33,plain,
( ! [X0] : sum(additive_identity,X0,X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f1831,plain,
( spl0_133
| ~ spl0_3
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f450,f436,f32,f1829]) ).
fof(f1829,plain,
( spl0_133
<=> ! [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_133])]) ).
fof(f450,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,[],[f437,f33]) ).
fof(f1827,plain,
( spl0_132
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f126,f90,f83,f1825]) ).
fof(f1825,plain,
( spl0_132
<=> ! [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_132])]) ).
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(f1823,plain,
( spl0_131
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f125,f94,f83,f1821]) ).
fof(f1821,plain,
( spl0_131
<=> ! [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_131])]) ).
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(f1819,plain,
( spl0_114
| ~ spl0_130
| ~ spl0_2
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1393,f1369,f27,f1816,f1544]) ).
fof(f1544,plain,
( spl0_114
<=> sum(d,d,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1816,plain,
( spl0_130
<=> sum(a,a,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1393,plain,
( ~ sum(a,a,a)
| sum(d,d,d)
| ~ spl0_2
| ~ spl0_105 ),
inference(resolution,[],[f1370,f29]) ).
fof(f1767,plain,
( spl0_129
| ~ spl0_2
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f455,f440,f27,f1765]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,X2)
| sum(X1,d,multiply(X2,b)) )
| ~ spl0_2
| ~ spl0_60 ),
inference(resolution,[],[f441,f29]) ).
fof(f1763,plain,
( spl0_128
| ~ spl0_2
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f447,f432,f27,f1761]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| sum(X1,d,multiply(a,X2)) )
| ~ spl0_2
| ~ spl0_58 ),
inference(resolution,[],[f433,f29]) ).
fof(f1758,plain,
( spl0_127
| ~ spl0_6
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f412,f406,f45,f1756]) ).
fof(f1756,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(additive_inverse(additive_inverse(a)),b,X0)
| product(additive_identity,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(additive_inverse(additive_inverse(a)),b,X0)
| product(additive_identity,b,X1) )
| ~ spl0_6
| ~ spl0_55 ),
inference(resolution,[],[f407,f46]) ).
fof(f1754,plain,
( spl0_126
| ~ spl0_8
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f400,f384,f53,f1752]) ).
fof(f384,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(f400,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(X0,b),d,X1)
| ~ sum(X0,a,X2)
| product(X2,b,X1) )
| ~ spl0_8
| ~ spl0_52 ),
inference(resolution,[],[f385,f54]) ).
fof(f385,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,[],[f384]) ).
fof(f1750,plain,
( spl0_125
| ~ spl0_8
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f397,f380,f53,f1748]) ).
fof(f380,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(f397,plain,
( ! [X2,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,X2,a)
| sum(X1,multiply(X2,b),d) )
| ~ spl0_8
| ~ spl0_51 ),
inference(resolution,[],[f381,f54]) ).
fof(f381,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,[],[f380]) ).
fof(f1746,plain,
( spl0_124
| ~ spl0_8
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f394,f376,f53,f1744]) ).
fof(f376,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(f394,plain,
( ! [X2,X0,X1] :
( ~ sum(multiply(a,X0),d,X1)
| ~ sum(X0,b,X2)
| product(a,X2,X1) )
| ~ spl0_8
| ~ spl0_50 ),
inference(resolution,[],[f377,f54]) ).
fof(f377,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,[],[f376]) ).
fof(f1742,plain,
( spl0_123
| ~ spl0_8
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f388,f372,f53,f1740]) ).
fof(f372,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(f388,plain,
( ! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,X2,b)
| sum(X1,multiply(a,X2),d) )
| ~ spl0_8
| ~ spl0_49 ),
inference(resolution,[],[f373,f54]) ).
fof(f373,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,[],[f372]) ).
fof(f1672,plain,
( spl0_122
| ~ spl0_5
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f429,f421,f40,f1670]) ).
fof(f1670,plain,
( spl0_122
<=> ! [X0,X1] :
( ~ sum(c,c,X0)
| ~ sum(b,b,X1)
| product(additive_inverse(a),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ sum(c,c,X0)
| ~ sum(b,b,X1)
| product(additive_inverse(a),X1,X0) )
| ~ spl0_5
| ~ spl0_57 ),
inference(resolution,[],[f422,f42]) ).
fof(f1668,plain,
( spl0_121
| ~ spl0_5
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f424,f417,f40,f1666]) ).
fof(f424,plain,
( ! [X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X0,b,b)
| sum(X1,c,c) )
| ~ spl0_5
| ~ spl0_56 ),
inference(resolution,[],[f418,f42]) ).
fof(f1664,plain,
( spl0_120
| ~ spl0_3
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f411,f406,f32,f1662]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(additive_identity,b,X0)
| product(additive_inverse(a),b,X1) )
| ~ spl0_3
| ~ spl0_55 ),
inference(resolution,[],[f407,f33]) ).
fof(f1660,plain,
( spl0_119
| ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f410,f402,f36,f1658]) ).
fof(f36,plain,
( spl0_4
<=> ! [X0] : sum(X0,additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f402,plain,
( spl0_54
<=> ! [X0,X3,X2,X1] :
( ~ product(X0,b,X1)
| ~ product(X2,b,X3)
| ~ sum(X0,X2,additive_inverse(a))
| sum(X1,X3,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ product(additive_identity,b,X0)
| ~ product(additive_inverse(a),b,X1)
| sum(X1,X0,c) )
| ~ spl0_4
| ~ spl0_54 ),
inference(resolution,[],[f403,f37]) ).
fof(f37,plain,
( ! [X0] : sum(X0,additive_identity,X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f403,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X2,additive_inverse(a))
| ~ product(X2,b,X3)
| ~ product(X0,b,X1)
| sum(X1,X3,c) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f1656,plain,
( spl0_118
| ~ spl0_3
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f409,f402,f32,f1654]) ).
fof(f409,plain,
( ! [X0,X1] :
( ~ product(additive_inverse(a),b,X0)
| ~ product(additive_identity,b,X1)
| sum(X1,X0,c) )
| ~ spl0_3
| ~ spl0_54 ),
inference(resolution,[],[f403,f33]) ).
fof(f1652,plain,
( spl0_117
| ~ spl0_5
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f399,f384,f40,f1650]) ).
fof(f399,plain,
( ! [X0,X1] :
( ~ sum(c,d,X0)
| ~ sum(additive_inverse(a),a,X1)
| product(X1,b,X0) )
| ~ spl0_5
| ~ spl0_52 ),
inference(resolution,[],[f385,f42]) ).
fof(f1648,plain,
( spl0_116
| ~ spl0_5
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f396,f380,f40,f1646]) ).
fof(f396,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),a)
| sum(X1,c,d) )
| ~ spl0_5
| ~ spl0_51 ),
inference(resolution,[],[f381,f42]) ).
fof(f1551,plain,
( spl0_114
| ~ spl0_115
| ~ spl0_2
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1382,f1361,f27,f1548,f1544]) ).
fof(f1548,plain,
( spl0_115
<=> sum(b,b,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1382,plain,
( ~ sum(b,b,b)
| sum(d,d,d)
| ~ spl0_2
| ~ spl0_103 ),
inference(resolution,[],[f1362,f29]) ).
fof(f1436,plain,
( spl0_113
| ~ spl0_8
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f369,f352,f53,f1434]) ).
fof(f369,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| product(X2,X3,multiply(X0,multiply(X1,X3))) )
| ~ spl0_8
| ~ spl0_48 ),
inference(resolution,[],[f353,f54]) ).
fof(f1432,plain,
( spl0_112
| ~ spl0_8
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f368,f344,f53,f1430]) ).
fof(f344,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(f368,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| product(X0,multiply(X1,X3),multiply(X2,X3)) )
| ~ spl0_8
| ~ spl0_46 ),
inference(resolution,[],[f345,f54]) ).
fof(f345,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,[],[f344]) ).
fof(f1428,plain,
( spl0_111
| ~ spl0_13
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f365,f340,f83,f1426]) ).
fof(f340,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(f365,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(add(X1,X3),X0)) )
| ~ spl0_13
| ~ spl0_45 ),
inference(resolution,[],[f341,f84]) ).
fof(f341,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,[],[f340]) ).
fof(f1424,plain,
( spl0_110
| ~ spl0_9
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f364,f340,f57,f1422]) ).
fof(f364,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,add(X0,add(X1,X3))) )
| ~ spl0_9
| ~ spl0_45 ),
inference(resolution,[],[f341,f58]) ).
fof(f1420,plain,
( spl0_109
| ~ spl0_13
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f360,f336,f83,f1418]) ).
fof(f336,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(f360,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X3,X1),add(X2,X3)) )
| ~ spl0_13
| ~ spl0_44 ),
inference(resolution,[],[f337,f84]) ).
fof(f337,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,[],[f336]) ).
fof(f1416,plain,
( spl0_108
| ~ spl0_9
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f359,f336,f57,f1414]) ).
fof(f1414,plain,
( spl0_108
<=> ! [X0,X3,X2,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,X3),add(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f359,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,X3),add(X2,X3)) )
| ~ spl0_9
| ~ spl0_44 ),
inference(resolution,[],[f337,f58]) ).
fof(f1379,plain,
( spl0_107
| ~ spl0_7
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f413,f406,f49,f1377]) ).
fof(f49,plain,
( spl0_7
<=> ! [X0] : sum(X0,additive_inverse(X0),additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f413,plain,
( ! [X0,X1] :
( ~ sum(X0,c,X1)
| ~ product(a,b,X0)
| product(additive_identity,b,X1) )
| ~ spl0_7
| ~ spl0_55 ),
inference(resolution,[],[f407,f50]) ).
fof(f50,plain,
( ! [X0] : sum(X0,additive_inverse(X0),additive_identity)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f1375,plain,
( spl0_106
| ~ spl0_2
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f398,f384,f27,f1373]) ).
fof(f398,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(a,a,X1)
| product(X1,b,X0) )
| ~ spl0_2
| ~ spl0_52 ),
inference(resolution,[],[f385,f29]) ).
fof(f1371,plain,
( spl0_105
| ~ spl0_2
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f395,f380,f27,f1369]) ).
fof(f395,plain,
( ! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,a,a)
| sum(X1,d,d) )
| ~ spl0_2
| ~ spl0_51 ),
inference(resolution,[],[f381,f29]) ).
fof(f1367,plain,
( spl0_104
| ~ spl0_2
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f393,f376,f27,f1365]) ).
fof(f393,plain,
( ! [X0,X1] :
( ~ sum(d,d,X0)
| ~ sum(b,b,X1)
| product(a,X1,X0) )
| ~ spl0_2
| ~ spl0_50 ),
inference(resolution,[],[f377,f29]) ).
fof(f1363,plain,
( spl0_103
| ~ spl0_2
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f387,f372,f27,f1361]) ).
fof(f387,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,d,d) )
| ~ spl0_2
| ~ spl0_49 ),
inference(resolution,[],[f373,f29]) ).
fof(f1332,plain,
( spl0_102
| ~ spl0_28
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f729,f577,f193,f1330]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 )
| ~ spl0_28
| ~ spl0_79 ),
inference(resolution,[],[f578,f194]) ).
fof(f1138,plain,
( spl0_101
| ~ spl0_6
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f363,f340,f45,f1136]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_inverse(add(X0,X1)),X0,X2)
| sum(X2,X1,additive_identity) )
| ~ spl0_6
| ~ spl0_45 ),
inference(resolution,[],[f341,f46]) ).
fof(f1134,plain,
( spl0_100
| ~ spl0_7
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f358,f336,f49,f1132]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,additive_identity,add(X2,additive_inverse(X1))) )
| ~ spl0_7
| ~ spl0_44 ),
inference(resolution,[],[f337,f50]) ).
fof(f1130,plain,
( spl0_99
| ~ spl0_6
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f357,f336,f45,f1128]) ).
fof(f357,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| sum(X0,additive_identity,add(X2,X1)) )
| ~ spl0_6
| ~ spl0_44 ),
inference(resolution,[],[f337,f46]) ).
fof(f1126,plain,
( spl0_98
| ~ spl0_13
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f325,f305,f83,f1124]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(additive_inverse(X2),X0),X2,X1) )
| ~ spl0_13
| ~ spl0_42 ),
inference(resolution,[],[f306,f84]) ).
fof(f1102,plain,
( spl0_97
| ~ spl0_9
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f324,f305,f57,f1100]) ).
fof(f324,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(add(X0,additive_inverse(X2)),X2,X1) )
| ~ spl0_9
| ~ spl0_42 ),
inference(resolution,[],[f306,f58]) ).
fof(f1098,plain,
( spl0_96
| ~ spl0_13
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f319,f301,f83,f1096]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(additive_inverse(X2),X1),additive_identity) )
| ~ spl0_13
| ~ spl0_41 ),
inference(resolution,[],[f302,f84]) ).
fof(f1094,plain,
( spl0_95
| ~ spl0_9
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f318,f301,f57,f1092]) ).
fof(f318,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X0,add(X1,additive_inverse(X2)),additive_identity) )
| ~ spl0_9
| ~ spl0_41 ),
inference(resolution,[],[f302,f58]) ).
fof(f1058,plain,
( spl0_94
| ~ spl0_5
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f367,f344,f40,f1056]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ product(X0,additive_inverse(a),X1)
| product(X0,c,multiply(X1,b)) )
| ~ spl0_5
| ~ spl0_46 ),
inference(resolution,[],[f345,f42]) ).
fof(f1054,plain,
( spl0_93
| ~ spl0_8
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f294,f291,f53,f1052]) ).
fof(f291,plain,
( spl0_39
<=> ! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,additive_inverse(a),X2)
| product(X2,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f294,plain,
( ! [X0,X1] :
( ~ product(X0,c,X1)
| product(multiply(X0,additive_inverse(a)),b,X1) )
| ~ spl0_8
| ~ spl0_39 ),
inference(resolution,[],[f292,f54]) ).
fof(f292,plain,
( ! [X2,X0,X1] :
( ~ product(X0,additive_inverse(a),X2)
| ~ product(X0,c,X1)
| product(X2,b,X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f955,plain,
( spl0_92
| ~ spl0_25
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f826,f670,f169,f953]) ).
fof(f670,plain,
( spl0_80
<=> ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f826,plain,
( ! [X0] : additive_inverse(additive_inverse(X0)) = X0
| ~ spl0_25
| ~ spl0_80 ),
inference(resolution,[],[f671,f170]) ).
fof(f671,plain,
( ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f881,plain,
( spl0_91
| ~ spl0_3
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f362,f340,f32,f879]) ).
fof(f362,plain,
( ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(X1,X2,add(X0,X2)) )
| ~ spl0_3
| ~ spl0_45 ),
inference(resolution,[],[f341,f33]) ).
fof(f877,plain,
( spl0_90
| ~ spl0_3
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f355,f336,f32,f875]) ).
fof(f355,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,X2,add(X1,X2)) )
| ~ spl0_3
| ~ spl0_44 ),
inference(resolution,[],[f337,f33]) ).
fof(f872,plain,
( spl0_89
| ~ spl0_6
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f322,f305,f45,f870]) ).
fof(f870,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(f322,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| sum(additive_identity,X0,X1) )
| ~ spl0_6
| ~ spl0_42 ),
inference(resolution,[],[f306,f46]) ).
fof(f867,plain,
( spl0_88
| ~ spl0_6
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f316,f301,f45,f865]) ).
fof(f865,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(f316,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(additive_inverse(X1)),X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_6
| ~ spl0_41 ),
inference(resolution,[],[f302,f46]) ).
fof(f863,plain,
( spl0_87
| ~ spl0_13
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f285,f255,f83,f861]) ).
fof(f255,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(f285,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X1,X0),additive_identity,X2) )
| ~ spl0_13
| ~ spl0_37 ),
inference(resolution,[],[f256,f84]) ).
fof(f256,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| sum(X3,additive_identity,X2) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f859,plain,
( spl0_86
| ~ spl0_9
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f284,f255,f57,f857]) ).
fof(f284,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(add(X0,X1),additive_identity,X2) )
| ~ spl0_9
| ~ spl0_37 ),
inference(resolution,[],[f256,f58]) ).
fof(f855,plain,
( spl0_85
| ~ spl0_13
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f263,f239,f83,f853]) ).
fof(f239,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(f263,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X2,X1),X2) )
| ~ spl0_13
| ~ spl0_34 ),
inference(resolution,[],[f240,f84]) ).
fof(f240,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X1,additive_identity)
| sum(X0,X3,X2) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f822,plain,
( spl0_84
| ~ spl0_9
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f262,f239,f57,f820]) ).
fof(f262,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,add(X1,X2),X2) )
| ~ spl0_9
| ~ spl0_34 ),
inference(resolution,[],[f240,f58]) ).
fof(f762,plain,
( spl0_83
| ~ spl0_2
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f366,f344,f27,f760]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ product(X0,a,X1)
| product(X0,d,multiply(X1,b)) )
| ~ spl0_2
| ~ spl0_46 ),
inference(resolution,[],[f345,f29]) ).
fof(f758,plain,
( spl0_82
| ~ spl0_8
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f237,f231,f53,f756]) ).
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(f237,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(f754,plain,
( spl0_81
| ~ spl0_8
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f236,f227,f53,f752]) ).
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(f236,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(f672,plain,
( spl0_80
| ~ spl0_6
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f586,f545,f45,f670]) ).
fof(f586,plain,
( ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0)
| ~ spl0_6
| ~ spl0_71 ),
inference(resolution,[],[f546,f46]) ).
fof(f579,plain,
( spl0_79
| ~ spl0_4
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f328,f309,f36,f577]) ).
fof(f309,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(f328,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X2,additive_inverse(X1),X0) )
| ~ spl0_4
| ~ spl0_43 ),
inference(resolution,[],[f310,f37]) ).
fof(f310,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,[],[f309]) ).
fof(f575,plain,
( spl0_78
| ~ spl0_3
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f321,f305,f32,f573]) ).
fof(f321,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_inverse(X1),X1,X0) )
| ~ spl0_3
| ~ spl0_42 ),
inference(resolution,[],[f306,f33]) ).
fof(f571,plain,
( spl0_77
| ~ spl0_3
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f315,f301,f32,f569]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X0,additive_inverse(X1),additive_identity) )
| ~ spl0_3
| ~ spl0_41 ),
inference(resolution,[],[f302,f33]) ).
fof(f567,plain,
( spl0_76
| ~ spl0_4
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f313,f296,f36,f565]) ).
fof(f313,plain,
( ! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X0),X1,additive_identity) )
| ~ spl0_4
| ~ spl0_40 ),
inference(resolution,[],[f297,f37]) ).
fof(f563,plain,
( spl0_75
| ~ spl0_3
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f312,f296,f32,f561]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,X1,additive_identity) )
| ~ spl0_3
| ~ spl0_40 ),
inference(resolution,[],[f297,f33]) ).
fof(f559,plain,
( spl0_74
| ~ spl0_7
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f283,f255,f49,f557]) ).
fof(f283,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_7
| ~ spl0_37 ),
inference(resolution,[],[f256,f50]) ).
fof(f555,plain,
( spl0_73
| ~ spl0_6
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f282,f255,f45,f553]) ).
fof(f282,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| sum(additive_identity,additive_identity,X1) )
| ~ spl0_6
| ~ spl0_37 ),
inference(resolution,[],[f256,f46]) ).
fof(f551,plain,
( spl0_72
| ~ spl0_7
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f261,f239,f49,f549]) ).
fof(f261,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,additive_identity,additive_inverse(X1)) )
| ~ spl0_7
| ~ spl0_34 ),
inference(resolution,[],[f240,f50]) ).
fof(f547,plain,
( spl0_71
| ~ spl0_6
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f260,f239,f45,f545]) ).
fof(f260,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1) )
| ~ spl0_6
| ~ spl0_34 ),
inference(resolution,[],[f240,f46]) ).
fof(f543,plain,
( spl0_70
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f127,f83,f70,f541]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( add(X1,X2) = X0
| ~ sum(X2,X1,X0) )
| ~ spl0_11
| ~ spl0_13 ),
inference(resolution,[],[f84,f71]) ).
fof(f539,plain,
( spl0_69
| ~ spl0_5
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f235,f227,f40,f537]) ).
fof(f537,plain,
( spl0_69
<=> ! [X0] :
( ~ product(X0,additive_inverse(a),a)
| product(X0,c,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f235,plain,
( ! [X0] :
( ~ product(X0,additive_inverse(a),a)
| product(X0,c,d) )
| ~ spl0_5
| ~ spl0_32 ),
inference(resolution,[],[f228,f42]) ).
fof(f528,plain,
( spl0_68
| ~ spl0_7
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f317,f301,f49,f526]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) )
| ~ spl0_7
| ~ spl0_41 ),
inference(resolution,[],[f302,f50]) ).
fof(f524,plain,
( spl0_67
| ~ spl0_3
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f258,f239,f32,f522]) ).
fof(f258,plain,
( ! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) )
| ~ spl0_3
| ~ spl0_34 ),
inference(resolution,[],[f240,f33]) ).
fof(f520,plain,
( spl0_66
| ~ spl0_2
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f234,f227,f27,f518]) ).
fof(f518,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(f498,plain,
( spl0_65
| ~ spl0_13
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f222,f205,f83,f496]) ).
fof(f222,plain,
( ! [X0,X1] : add(X0,X1) = add(X1,X0)
| ~ spl0_13
| ~ spl0_29 ),
inference(resolution,[],[f206,f84]) ).
fof(f482,plain,
( spl0_64
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f199,f189,f83,f480]) ).
fof(f480,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(f478,plain,
( spl0_63
| ~ spl0_9
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f198,f189,f57,f476]) ).
fof(f198,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_9
| ~ spl0_27 ),
inference(resolution,[],[f190,f58]) ).
fof(f470,plain,
( spl0_62
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f187,f183,f53,f467]) ).
fof(f187,plain,
( c = multiply(additive_inverse(a),b)
| ~ spl0_8
| ~ spl0_26 ),
inference(resolution,[],[f184,f54]) ).
fof(f446,plain,
( spl0_61
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f152,f138,f53,f444]) ).
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(f442,plain,
( spl0_60
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f149,f134,f53,f440]) ).
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(f438,plain,
( spl0_59
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f146,f130,f53,f436]) ).
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(f434,plain,
( spl0_58
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f143,f122,f53,f432]) ).
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(f423,plain,
( spl0_57
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f145,f130,f40,f421]) ).
fof(f145,plain,
( ! [X2,X3,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,b,X3)
| product(additive_inverse(a),X3,X2) )
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[],[f131,f42]) ).
fof(f419,plain,
( spl0_56
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f142,f122,f40,f417]) ).
fof(f142,plain,
( ! [X2,X3,X0,X1] :
( ~ product(additive_inverse(a),X0,X1)
| ~ product(additive_inverse(a),X2,X3)
| ~ sum(X0,X2,b)
| sum(X1,X3,c) )
| ~ spl0_5
| ~ spl0_18 ),
inference(resolution,[],[f123,f42]) ).
fof(f408,plain,
( spl0_55
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f151,f138,f40,f406]) ).
fof(f151,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X1,c,X2)
| ~ sum(X0,additive_inverse(a),X3)
| product(X3,b,X2) )
| ~ spl0_5
| ~ spl0_21 ),
inference(resolution,[],[f139,f42]) ).
fof(f404,plain,
( spl0_54
| ~ spl0_5
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f148,f134,f40,f402]) ).
fof(f148,plain,
( ! [X2,X3,X0,X1] :
( ~ product(X0,b,X1)
| ~ product(X2,b,X3)
| ~ sum(X0,X2,additive_inverse(a))
| sum(X1,X3,c) )
| ~ spl0_5
| ~ spl0_20 ),
inference(resolution,[],[f135,f42]) ).
fof(f392,plain,
( spl0_53
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f176,f160,f83,f390]) ).
fof(f176,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_13
| ~ spl0_23 ),
inference(resolution,[],[f161,f84]) ).
fof(f386,plain,
( spl0_52
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f150,f138,f27,f384]) ).
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(f382,plain,
( spl0_51
| ~ spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f147,f134,f27,f380]) ).
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(f378,plain,
( spl0_50
| ~ spl0_2
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f144,f130,f27,f376]) ).
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(f374,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f141,f122,f27,f372]) ).
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(f354,plain,
( spl0_48
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f120,f102,f53,f352]) ).
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(f350,plain,
( spl0_47
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f175,f160,f57,f348]) ).
fof(f175,plain,
( ! [X0] : add(additive_identity,X0) = X0
| ~ spl0_9
| ~ spl0_23 ),
inference(resolution,[],[f161,f58]) ).
fof(f346,plain,
( spl0_46
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f117,f98,f53,f344]) ).
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(f342,plain,
( spl0_45
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f114,f94,f57,f340]) ).
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(f338,plain,
( spl0_44
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f109,f90,f57,f336]) ).
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(f311,plain,
( spl0_43
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f113,f94,f49,f309]) ).
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(f307,plain,
( spl0_42
| ~ spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f112,f94,f45,f305]) ).
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(f303,plain,
( spl0_41
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f108,f90,f49,f301]) ).
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(f298,plain,
( spl0_40
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f107,f90,f45,f296]) ).
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(f293,plain,
( spl0_39
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f119,f102,f40,f291]) ).
fof(f119,plain,
( ! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,additive_inverse(a),X2)
| product(X2,b,X1) )
| ~ spl0_5
| ~ spl0_17 ),
inference(resolution,[],[f103,f42]) ).
fof(f289,plain,
( spl0_38
| ~ spl0_5
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f116,f98,f40,f287]) ).
fof(f287,plain,
( spl0_38
<=> ! [X2,X0,X1] :
( ~ product(X0,X1,additive_inverse(a))
| ~ product(X1,b,X2)
| product(X0,X2,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f116,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,additive_inverse(a))
| ~ product(X1,b,X2)
| product(X0,X2,c) )
| ~ spl0_5
| ~ spl0_16 ),
inference(resolution,[],[f99,f42]) ).
fof(f257,plain,
( spl0_37
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f111,f94,f36,f255]) ).
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(f249,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f110,f94,f32,f247]) ).
fof(f247,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(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(f245,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f106,f90,f36,f243]) ).
fof(f243,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(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(f241,plain,
( spl0_34
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f105,f90,f32,f239]) ).
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(additive_inverse(a),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(additive_inverse(a),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_id) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 02:13:03 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (29505)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (29508)WARNING: value z3 for option sas not known
% 0.15/0.38 % (29508)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (29509)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (29507)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (29506)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (29510)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (29511)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (29512)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.40 TRYING [3]
% 0.22/0.40 TRYING [4]
% 0.22/0.46 TRYING [5]
% 0.22/0.46 TRYING [4]
% 0.22/0.49 TRYING [1]
% 0.22/0.49 TRYING [2]
% 0.22/0.49 TRYING [3]
% 0.22/0.50 TRYING [4]
% 1.32/0.55 TRYING [5]
% 1.32/0.56 TRYING [6]
% 1.32/0.60 TRYING [5]
% 1.32/0.62 % (29510)First to succeed.
% 1.96/0.63 % (29510)Refutation found. Thanks to Tanya!
% 1.96/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.96/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.96/0.64 % (29510)------------------------------
% 1.96/0.64 % (29510)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.96/0.64 % (29510)Termination reason: Refutation
% 1.96/0.64
% 1.96/0.64 % (29510)Memory used [KB]: 3834
% 1.96/0.64 % (29510)Time elapsed: 0.250 s
% 1.96/0.64 % (29510)Instructions burned: 595 (million)
% 1.96/0.64 % (29510)------------------------------
% 1.96/0.64 % (29510)------------------------------
% 1.96/0.64 % (29505)Success in time 0.259 s
%------------------------------------------------------------------------------