TSTP Solution File: LCL558+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:24:50 EDT 2023
% Result : Theorem 34.84s 5.35s
% Output : Refutation 34.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1238
% Syntax : Number of formulae : 5377 ( 80 unt; 0 def)
% Number of atoms : 17153 ( 698 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 22613 (10837 ~;10532 |; 4 &)
% (1215 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 1224 (1222 usr;1222 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 8998 (;8994 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f126840,plain,
$false,
inference(avatar_sat_refutation,[],[f183,f188,f193,f198,f203,f208,f213,f218,f223,f228,f233,f238,f243,f248,f253,f258,f263,f267,f271,f275,f279,f283,f288,f292,f296,f300,f304,f313,f317,f321,f332,f338,f342,f346,f361,f365,f375,f379,f404,f408,f412,f434,f438,f442,f446,f452,f459,f463,f472,f476,f480,f491,f497,f507,f512,f531,f542,f546,f556,f560,f570,f584,f596,f600,f604,f625,f629,f633,f646,f683,f740,f750,f782,f804,f808,f812,f816,f820,f824,f858,f913,f917,f1026,f1048,f1052,f1056,f1060,f1076,f1086,f1090,f1094,f1108,f1112,f1116,f1120,f1124,f1235,f1275,f1288,f1308,f1312,f1382,f1386,f1390,f1460,f1464,f1468,f1472,f1476,f1483,f1501,f1560,f1564,f1642,f1686,f1698,f1702,f1706,f1710,f1714,f1718,f1833,f1846,f1850,f1854,f1858,f1862,f2064,f2140,f2153,f2226,f2295,f2299,f2303,f2307,f2346,f2371,f2464,f2468,f2472,f2476,f2530,f2534,f2538,f2542,f2560,f2596,f2600,f2618,f2622,f2645,f2667,f2671,f2675,f2728,f2732,f2736,f2740,f2744,f2748,f2752,f2756,f2760,f2764,f2768,f2772,f2776,f2780,f2784,f2788,f2792,f3344,f3348,f3352,f3356,f3396,f3400,f3404,f3440,f3444,f3448,f3452,f3505,f3509,f3513,f3569,f3573,f3577,f3774,f4076,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4831,f4849,f4853,f4857,f4861,f4865,f4887,f4929,f4933,f4937,f4970,f5423,f5464,f5468,f5532,f5536,f5540,f5597,f5601,f5605,f6115,f6119,f6123,f6127,f6131,f6135,f6139,f6143,f6147,f6151,f6155,f6159,f6163,f6167,f6171,f6175,f6953,f6957,f6961,f6965,f6969,f6973,f6977,f6981,f7158,f7162,f7166,f7199,f7375,f7491,f7540,f7544,f7548,f7552,f7556,f7560,f7964,f8070,f8074,f8078,f8162,f8166,f8170,f8174,f8178,f8182,f8186,f8190,f8194,f8382,f8409,f8433,f8437,f8553,f8727,f8731,f8824,f9062,f9066,f9265,f9309,f9328,f9332,f9351,f9370,f9374,f9378,f9382,f9397,f9401,f9405,f9409,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9824,f9828,f9932,f9936,f10074,f10112,f10116,f10242,f10417,f10545,f10549,f10568,f10589,f10593,f10622,f10704,f10708,f11030,f11034,f11088,f11208,f11236,f11374,f11378,f11382,f11545,f11549,f11553,f11738,f11774,f11778,f11899,f11927,f11931,f11935,f11986,f11990,f12074,f12078,f12082,f12086,f12090,f12159,f12225,f12229,f12233,f12237,f12241,f12245,f12249,f12253,f12257,f12261,f12375,f12446,f12450,f12454,f12458,f12462,f12482,f12486,f12657,f12661,f13443,f13499,f13558,f13620,f13661,f13749,f13772,f14077,f14081,f14085,f14104,f14155,f14159,f14163,f14167,f14218,f14290,f14310,f14314,f14318,f14322,f14326,f14327,f14354,f14374,f14441,f14445,f14449,f14474,f14492,f14496,f14500,f14555,f14607,f14611,f14615,f14619,f14623,f14627,f14631,f14635,f14802,f14872,f14876,f14890,f14894,f14898,f14902,f14906,f14910,f14914,f14918,f14919,f15002,f15006,f15069,f15093,f15125,f15129,f15130,f15134,f15138,f15139,f15219,f15223,f15231,f15693,f15710,f16096,f16309,f16313,f16317,f16321,f16333,f16397,f16524,f16619,f16782,f16871,f16875,f16879,f17089,f17192,f17196,f17443,f17447,f17553,f17557,f17561,f17565,f17965,f17969,f17973,f18065,f18069,f18073,f18077,f18138,f18142,f18146,f18221,f18225,f18229,f18233,f18299,f18303,f18307,f18711,f18715,f18719,f19278,f19364,f22733,f22737,f22741,f22903,f22907,f22911,f22991,f22995,f22999,f23003,f23094,f23140,f23219,f23236,f23250,f23254,f23258,f23262,f23266,f24813,f24817,f24821,f25493,f25497,f25501,f25505,f25509,f25557,f25561,f26847,f26957,f26961,f26993,f27683,f27808,f27812,f27816,f27820,f27868,f27885,f28067,f28130,f28206,f28265,f28307,f28311,f28315,f28411,f28567,f28571,f28605,f28609,f28613,f28617,f28621,f28625,f28629,f28633,f28637,f28953,f29011,f29162,f29222,f29226,f29230,f29234,f29238,f29242,f29246,f29250,f29254,f29258,f29335,f29339,f29354,f29358,f29362,f29411,f29415,f29419,f29453,f29457,f29461,f29559,f29563,f29567,f29690,f29946,f29950,f30017,f30021,f30267,f30399,f30495,f30499,f30503,f30507,f30511,f30515,f30519,f30523,f30527,f30593,f30693,f30697,f30798,f30802,f30806,f30810,f30872,f30876,f30880,f30884,f30888,f30889,f30893,f30897,f31726,f31730,f31947,f31951,f31955,f32219,f32223,f32977,f32981,f32985,f33158,f33162,f33166,f33170,f33174,f33178,f33182,f33186,f33190,f33194,f34355,f34593,f34597,f34601,f34605,f34609,f34613,f34617,f34621,f34625,f34629,f34633,f34637,f34641,f34645,f34649,f35813,f36001,f36219,f36245,f36249,f36253,f36257,f36261,f36265,f36269,f36273,f36277,f36281,f36436,f37033,f37075,f37079,f37083,f37087,f37091,f37095,f37099,f37103,f37107,f37229,f37544,f37548,f38352,f38356,f38602,f38810,f38814,f38978,f39164,f39226,f39383,f39387,f39391,f39526,f39530,f39534,f39538,f40240,f40364,f40980,f41050,f41206,f41210,f41421,f41425,f41519,f41676,f41680,f42109,f42390,f42459,f42463,f42467,f42471,f42475,f42479,f42483,f42487,f42491,f42495,f42499,f42503,f42507,f42511,f42515,f42519,f42523,f42527,f42531,f42578,f42936,f43095,f43268,f44353,f44637,f44641,f44645,f45039,f45043,f45047,f45051,f45376,f45380,f45384,f45665,f45669,f45670,f45674,f45809,f45813,f45817,f45821,f45825,f45829,f45833,f45837,f45841,f45845,f45922,f46196,f46485,f46750,f48033,f48845,f48849,f48853,f48857,f49060,f49064,f49068,f49123,f49127,f49131,f49135,f49190,f49194,f49198,f49202,f49206,f49210,f49214,f49218,f49222,f49226,f49230,f49234,f49238,f49242,f49246,f49250,f49254,f49258,f49262,f49323,f49591,f49813,f50038,f50095,f50124,f51471,f51891,f51895,f51899,f51903,f52375,f52379,f52383,f52766,f52770,f52774,f52778,f53112,f53116,f53120,f53228,f53232,f53236,f53240,f53443,f53534,f53657,f53728,f53732,f53943,f54027,f54187,f54206,f54210,f55123,f55124,f55128,f55132,f55267,f55271,f55275,f55720,f56477,f56481,f56485,f56555,f57258,f57320,f57324,f57328,f57332,f57336,f57340,f57344,f57348,f57493,f57680,f57684,f58049,f58053,f58057,f58601,f59393,f60064,f60068,f60072,f60076,f60080,f60554,f60558,f60562,f60566,f60570,f60574,f60805,f61554,f61558,f61562,f62020,f62024,f62028,f62032,f62036,f62040,f62044,f62048,f62052,f62056,f62060,f62064,f62068,f62072,f62076,f62080,f62084,f62088,f62092,f62096,f62100,f62104,f62108,f62112,f62116,f62120,f62344,f62348,f62352,f62356,f62608,f62612,f62616,f62808,f62812,f62816,f62820,f62824,f62828,f62832,f62836,f63348,f63352,f63356,f63360,f63364,f63368,f63372,f64150,f64332,f64386,f64411,f64632,f64889,f65184,f65188,f65192,f65292,f65383,f65387,f65449,f65502,f65538,f66457,f66725,f66729,f66733,f66812,f66816,f66820,f66824,f66903,f66907,f66911,f66961,f66965,f66969,f66973,f67023,f67027,f67031,f67044,f67048,f67052,f67056,f67065,f67069,f67073,f67158,f67162,f67166,f67170,f67174,f67178,f67424,f67752,f68174,f68470,f68527,f68550,f68785,f69868,f70386,f70390,f70875,f71038,f71128,f72014,f72988,f73029,f73053,f73057,f73100,f73104,f73135,f73204,f73208,f73486,f73487,f73488,f73489,f73490,f73491,f73492,f73493,f73494,f73495,f73496,f73497,f73498,f73499,f73500,f73501,f73502,f73503,f73504,f73505,f73506,f73507,f73508,f73509,f73510,f73511,f73512,f73513,f73514,f73515,f73516,f73517,f73518,f73519,f73520,f73521,f73522,f73523,f73524,f73525,f73526,f73527,f73528,f73529,f73530,f73531,f73532,f73533,f73534,f73535,f73536,f73537,f73538,f73539,f73540,f73541,f73542,f73543,f73544,f73545,f73546,f73547,f73548,f73549,f73550,f73551,f73552,f73553,f73554,f73555,f73556,f73557,f73558,f73559,f73560,f73561,f73562,f73563,f73564,f73565,f73566,f73567,f73568,f73569,f73570,f73571,f73572,f73573,f73574,f73575,f73576,f73577,f73578,f73579,f73580,f73581,f73582,f73583,f73584,f73585,f73586,f73587,f73588,f73589,f73590,f73591,f73592,f73593,f73594,f73595,f73596,f73597,f73598,f73599,f73600,f73601,f73602,f73603,f73604,f73605,f73606,f73607,f73608,f73609,f73610,f73611,f73612,f73613,f73614,f73615,f73616,f73617,f73618,f73619,f73620,f73621,f73622,f73623,f73624,f73625,f73626,f73627,f73628,f73629,f73630,f73631,f73632,f73633,f73634,f73635,f73636,f73637,f73638,f73639,f73640,f73641,f73642,f73643,f73644,f73645,f73646,f73647,f73648,f73649,f73650,f73651,f73652,f73653,f73654,f73655,f73656,f73657,f73658,f73659,f73660,f73661,f73662,f73663,f73664,f73665,f73666,f73667,f73668,f73669,f73670,f73671,f73672,f73673,f73674,f73675,f73676,f73677,f73678,f73679,f73680,f73681,f73682,f73683,f73684,f73685,f73686,f73687,f73688,f73689,f73690,f73691,f73692,f73693,f73694,f73695,f73696,f73697,f73698,f73699,f73700,f73701,f73702,f73703,f73704,f73705,f73706,f73707,f73708,f73709,f73710,f73711,f73712,f73713,f73714,f73715,f73716,f73717,f73718,f73719,f73720,f73721,f73722,f73723,f73724,f73725,f73726,f73727,f73728,f73729,f73730,f73731,f73732,f73733,f73734,f73735,f73736,f73737,f73738,f73739,f73740,f73741,f73742,f73743,f73744,f73790,f73794,f73956,f73960,f73964,f73998,f74002,f74006,f74010,f74181,f74185,f74266,f74270,f74345,f74420,f74424,f74491,f74495,f74499,f74503,f74507,f74511,f74515,f74519,f74523,f74527,f74546,f75033,f75272,f75276,f75280,f75284,f75288,f75292,f75296,f75300,f75304,f75308,f75513,f75668,f75672,f75676,f75787,f75791,f75795,f75924,f75928,f75971,f75975,f75979,f75983,f75987,f75991,f75995,f75999,f76197,f76201,f76276,f76363,f76842,f76846,f76850,f76854,f76858,f76862,f76866,f76870,f76874,f76878,f77126,f77441,f77445,f77449,f77453,f77457,f77461,f77465,f77469,f77473,f78360,f78364,f78368,f78466,f78470,f79124,f79234,f79238,f79527,f79531,f80221,f80452,f80456,f80460,f80901,f81030,f81128,f82416,f82420,f82424,f82556,f82560,f82564,f82906,f83127,f83131,f83206,f83210,f83214,f83328,f83675,f83822,f83850,f83935,f83965,f84176,f84180,f84615,f84619,f84735,f84899,f84913,f85326,f85414,f85415,f85430,f85546,f85600,f85604,f85605,f85609,f85636,f85640,f85644,f85648,f85702,f85703,f85842,f85846,f86626,f86630,f86720,f86724,f86812,f86865,f86949,f86953,f87035,f87084,f87088,f87092,f87142,f87191,f87241,f87245,f87249,f88380,f88384,f89443,f89680,f89684,f89754,f89758,f89788,f89818,f89822,f89852,f89932,f89936,f89969,f89973,f89977,f90030,f90086,f90090,f90501,f90502,f90503,f90504,f90505,f90506,f90581,f90585,f90589,f90638,f90665,f90669,f90673,f90677,f90681,f90913,f90917,f90975,f90979,f91019,f91023,f91027,f91186,f91235,f91239,f91285,f91289,f91293,f91297,f91301,f92496,f93198,f93202,f93206,f93370,f93374,f93457,f93461,f93557,f93872,f93876,f93880,f94119,f94204,f94421,f94473,f97729,f97733,f124502,f124506,f125644,f125669,f125727,f125731,f125735,f125768,f126044,f126094,f126098,f126116,f126123,f126127,f126132,f126136,f126140,f126144,f126148,f126477,f126774,f126811,f126815,f126819,f126837]) ).
fof(f126837,plain,
( spl2_2
| ~ spl2_1203 ),
inference(avatar_contradiction_clause,[],[f126824]) ).
fof(f126824,plain,
( $false
| spl2_2
| ~ spl2_1203 ),
inference(resolution,[],[f126810,f187]) ).
fof(f187,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| spl2_2 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f185,plain,
( spl2_2
<=> is_a_theorem(implies(sK0,or(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f126810,plain,
( ! [X16,X17] : is_a_theorem(implies(X16,or(X16,X17)))
| ~ spl2_1203 ),
inference(avatar_component_clause,[],[f126809]) ).
fof(f126809,plain,
( spl2_1203
<=> ! [X16,X17] : is_a_theorem(implies(X16,or(X16,X17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1203])]) ).
fof(f126819,plain,
( spl2_1205
| ~ spl2_24
| ~ spl2_1202 ),
inference(avatar_split_clause,[],[f126802,f126772,f290,f126817]) ).
fof(f126817,plain,
( spl2_1205
<=> ! [X6,X7] : is_a_theorem(or(X6,strict_implies(X7,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1205])]) ).
fof(f290,plain,
( spl2_24
<=> ! [X0,X1] : or(X0,X1) = implies(not(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f126772,plain,
( spl2_1202
<=> ! [X8,X7] : is_a_theorem(implies(X7,strict_implies(X8,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1202])]) ).
fof(f126802,plain,
( ! [X6,X7] : is_a_theorem(or(X6,strict_implies(X7,X7)))
| ~ spl2_24
| ~ spl2_1202 ),
inference(superposition,[],[f126773,f291]) ).
fof(f291,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_24 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f126773,plain,
( ! [X8,X7] : is_a_theorem(implies(X7,strict_implies(X8,X8)))
| ~ spl2_1202 ),
inference(avatar_component_clause,[],[f126772]) ).
fof(f126815,plain,
( spl2_1204
| ~ spl2_72
| ~ spl2_77
| ~ spl2_125
| ~ spl2_157
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f98006,f97731,f2734,f1852,f814,f748,f126813]) ).
fof(f126813,plain,
( spl2_1204
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X0,not(implies(X1,X2))),not(and(X0,implies(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1204])]) ).
fof(f748,plain,
( spl2_72
<=> ! [X0] : and(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_72])]) ).
fof(f814,plain,
( spl2_77
<=> ! [X2,X4,X3] : implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_77])]) ).
fof(f1852,plain,
( spl2_125
<=> ! [X2,X0,X1] : or(X0,and(X1,not(X2))) = implies(implies(X1,X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_125])]) ).
fof(f2734,plain,
( spl2_157
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X0,and(X1,not(X2))),not(and(X0,implies(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_157])]) ).
fof(f97731,plain,
( spl2_1181
<=> ! [X15] : or(X15,X15) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1181])]) ).
fof(f98006,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X0,not(implies(X1,X2))),not(and(X0,implies(X1,X2)))))
| ~ spl2_72
| ~ spl2_77
| ~ spl2_125
| ~ spl2_157
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f2735,f97971]) ).
fof(f97971,plain,
( ! [X3,X4] : and(X3,not(X4)) = not(implies(X3,X4))
| ~ spl2_72
| ~ spl2_77
| ~ spl2_125
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f97970,f749]) ).
fof(f749,plain,
( ! [X0] : and(X0,X0) = X0
| ~ spl2_72 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f97970,plain,
( ! [X3,X4] : and(X3,not(X4)) = not(and(implies(X3,X4),implies(X3,X4)))
| ~ spl2_77
| ~ spl2_125
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f97734,f815]) ).
fof(f815,plain,
( ! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3)))
| ~ spl2_77 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f97734,plain,
( ! [X3,X4] : and(X3,not(X4)) = implies(implies(X3,X4),and(X3,not(X4)))
| ~ spl2_125
| ~ spl2_1181 ),
inference(superposition,[],[f97732,f1853]) ).
fof(f1853,plain,
( ! [X2,X0,X1] : or(X0,and(X1,not(X2))) = implies(implies(X1,X2),X0)
| ~ spl2_125 ),
inference(avatar_component_clause,[],[f1852]) ).
fof(f97732,plain,
( ! [X15] : or(X15,X15) = X15
| ~ spl2_1181 ),
inference(avatar_component_clause,[],[f97731]) ).
fof(f2735,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X0,and(X1,not(X2))),not(and(X0,implies(X1,X2)))))
| ~ spl2_157 ),
inference(avatar_component_clause,[],[f2734]) ).
fof(f126811,plain,
( spl2_1203
| ~ spl2_24
| ~ spl2_981
| ~ spl2_1182 ),
inference(avatar_split_clause,[],[f124752,f124500,f74264,f290,f126809]) ).
fof(f74264,plain,
( spl2_981
<=> ! [X16,X17] : is_a_theorem(or(not(X16),or(X16,X17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_981])]) ).
fof(f124500,plain,
( spl2_1182
<=> ! [X4] : not(not(X4)) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1182])]) ).
fof(f124752,plain,
( ! [X16,X17] : is_a_theorem(implies(X16,or(X16,X17)))
| ~ spl2_24
| ~ spl2_981
| ~ spl2_1182 ),
inference(backward_demodulation,[],[f74265,f124515]) ).
fof(f124515,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ spl2_24
| ~ spl2_1182 ),
inference(superposition,[],[f291,f124501]) ).
fof(f124501,plain,
( ! [X4] : not(not(X4)) = X4
| ~ spl2_1182 ),
inference(avatar_component_clause,[],[f124500]) ).
fof(f74265,plain,
( ! [X16,X17] : is_a_theorem(or(not(X16),or(X16,X17)))
| ~ spl2_981 ),
inference(avatar_component_clause,[],[f74264]) ).
fof(f126774,plain,
( spl2_1202
| ~ spl2_1134
| ~ spl2_1199 ),
inference(avatar_split_clause,[],[f126440,f126142,f89971,f126772]) ).
fof(f89971,plain,
( spl2_1134
<=> ! [X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(implies(strict_implies(X7,X7),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1134])]) ).
fof(f126142,plain,
( spl2_1199
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1199])]) ).
fof(f126440,plain,
( ! [X8,X7] : is_a_theorem(implies(X7,strict_implies(X8,X8)))
| ~ spl2_1134
| ~ spl2_1199 ),
inference(resolution,[],[f126143,f89972]) ).
fof(f89972,plain,
( ! [X6,X7] :
( ~ is_a_theorem(implies(strict_implies(X7,X7),X6))
| is_a_theorem(X6) )
| ~ spl2_1134 ),
inference(avatar_component_clause,[],[f89971]) ).
fof(f126143,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl2_1199 ),
inference(avatar_component_clause,[],[f126142]) ).
fof(f126477,plain,
( spl2_1201
| ~ spl2_322
| ~ spl2_1198 ),
inference(avatar_split_clause,[],[f126149,f126138,f10110,f126475]) ).
fof(f126475,plain,
( spl2_1201
<=> ! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1201])]) ).
fof(f10110,plain,
( spl2_322
<=> ! [X9,X10] :
( is_a_theorem(or(X9,X10))
| ~ is_a_theorem(or(X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_322])]) ).
fof(f126138,plain,
( spl2_1198
<=> ! [X6,X7] : is_a_theorem(or(implies(X6,X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1198])]) ).
fof(f126149,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1)))
| ~ spl2_322
| ~ spl2_1198 ),
inference(resolution,[],[f126139,f10111]) ).
fof(f10111,plain,
( ! [X10,X9] :
( ~ is_a_theorem(or(X10,X9))
| is_a_theorem(or(X9,X10)) )
| ~ spl2_322 ),
inference(avatar_component_clause,[],[f10110]) ).
fof(f126139,plain,
( ! [X6,X7] : is_a_theorem(or(implies(X6,X6),X7))
| ~ spl2_1198 ),
inference(avatar_component_clause,[],[f126138]) ).
fof(f126148,plain,
( spl2_1200
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_524
| ~ spl2_954
| ~ spl2_970
| ~ spl2_1163
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f104329,f97731,f91299,f73788,f69866,f27818,f26955,f1852,f1122,f814,f748,f738,f681,f286,f126146]) ).
fof(f126146,plain,
( spl2_1200
<=> ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1200])]) ).
fof(f286,plain,
( spl2_23
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f681,plain,
( spl2_70
<=> ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X6,X7))
| ~ is_a_theorem(strict_implies(X7,X6))
| X6 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
fof(f738,plain,
( spl2_71
<=> ! [X0] : is_a_theorem(strict_implies(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_71])]) ).
fof(f1122,plain,
( spl2_96
<=> ! [X27,X28] : implies(X27,X28) = not(and(not(X28),X27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
fof(f26955,plain,
( spl2_517
<=> ! [X20,X21,X19] : and(X19,and(X20,X21)) = and(X21,and(X19,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_517])]) ).
fof(f27818,plain,
( spl2_524
<=> ! [X0,X1] : is_a_theorem(strict_implies(implies(implies(X0,X1),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_524])]) ).
fof(f69866,plain,
( spl2_954
<=> ! [X2,X3] : not(X2) = and(not(X2),implies(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_954])]) ).
fof(f73788,plain,
( spl2_970
<=> ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_970])]) ).
fof(f91299,plain,
( spl2_1163
<=> ! [X114,X115] : implies(X115,not(not(X114))) = implies(X115,X114) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1163])]) ).
fof(f104329,plain,
( ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,X3)))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_524
| ~ spl2_954
| ~ spl2_970
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f73789,f104311]) ).
fof(f104311,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = implies(X419,implies(X420,X418))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f104310,f94970]) ).
fof(f94970,plain,
( ! [X4] : not(not(X4)) = X4
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(subsumption_resolution,[],[f94872,f739]) ).
fof(f739,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,X0))
| ~ spl2_71 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f94872,plain,
( ! [X4] :
( ~ is_a_theorem(strict_implies(X4,X4))
| not(not(X4)) = X4 )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f70168,f94870]) ).
fof(f94870,plain,
( ! [X29,X30] : strict_implies(X29,X30) = strict_implies(X29,not(not(X30)))
| ~ spl2_23
| ~ spl2_1163 ),
inference(forward_demodulation,[],[f94525,f287]) ).
fof(f287,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f94525,plain,
( ! [X29,X30] : necessarily(implies(X29,X30)) = strict_implies(X29,not(not(X30)))
| ~ spl2_23
| ~ spl2_1163 ),
inference(superposition,[],[f287,f91300]) ).
fof(f91300,plain,
( ! [X114,X115] : implies(X115,not(not(X114))) = implies(X115,X114)
| ~ spl2_1163 ),
inference(avatar_component_clause,[],[f91299]) ).
fof(f70168,plain,
( ! [X4] :
( not(not(X4)) = X4
| ~ is_a_theorem(strict_implies(X4,not(not(X4)))) )
| ~ spl2_70
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70137,f69904]) ).
fof(f69904,plain,
( ! [X4,X5] : not(not(X4)) = implies(implies(X4,X5),X4)
| ~ spl2_96
| ~ spl2_954 ),
inference(superposition,[],[f1123,f69867]) ).
fof(f69867,plain,
( ! [X2,X3] : not(X2) = and(not(X2),implies(X2,X3))
| ~ spl2_954 ),
inference(avatar_component_clause,[],[f69866]) ).
fof(f1123,plain,
( ! [X28,X27] : implies(X27,X28) = not(and(not(X28),X27))
| ~ spl2_96 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f70137,plain,
( ! [X4,X5] :
( ~ is_a_theorem(strict_implies(X4,not(not(X4))))
| implies(implies(X4,X5),X4) = X4 )
| ~ spl2_70
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954 ),
inference(backward_demodulation,[],[f27990,f69904]) ).
fof(f27990,plain,
( ! [X4,X5] :
( ~ is_a_theorem(strict_implies(X4,implies(implies(X4,X5),X4)))
| implies(implies(X4,X5),X4) = X4 )
| ~ spl2_70
| ~ spl2_524 ),
inference(resolution,[],[f27819,f682]) ).
fof(f682,plain,
( ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X7,X6))
| ~ is_a_theorem(strict_implies(X6,X7))
| X6 = X7 )
| ~ spl2_70 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f27819,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(implies(implies(X0,X1),X0),X0))
| ~ spl2_524 ),
inference(avatar_component_clause,[],[f27818]) ).
fof(f104310,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = not(not(implies(X419,implies(X420,X418))))
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f98404,f97971]) ).
fof(f98404,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = not(and(X419,not(implies(X420,X418))))
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f27370,f97971]) ).
fof(f27370,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = not(and(X419,and(X420,not(X418))))
| ~ spl2_96
| ~ spl2_517 ),
inference(superposition,[],[f1123,f26956]) ).
fof(f26956,plain,
( ! [X21,X19,X20] : and(X19,and(X20,X21)) = and(X21,and(X19,X20))
| ~ spl2_517 ),
inference(avatar_component_clause,[],[f26955]) ).
fof(f73789,plain,
( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3))
| ~ spl2_970 ),
inference(avatar_component_clause,[],[f73788]) ).
fof(f126144,plain,
( spl2_1199
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_524
| ~ spl2_954
| ~ spl2_968
| ~ spl2_1163
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f104312,f97731,f91299,f73202,f69866,f27818,f26955,f1852,f1122,f814,f748,f738,f681,f286,f126142]) ).
fof(f73202,plain,
( spl2_968
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_968])]) ).
fof(f104312,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_77
| ~ spl2_96
| ~ spl2_125
| ~ spl2_517
| ~ spl2_524
| ~ spl2_954
| ~ spl2_968
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f73203,f104311]) ).
fof(f73203,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_968 ),
inference(avatar_component_clause,[],[f73202]) ).
fof(f126140,plain,
( spl2_1198
| ~ spl2_23
| ~ spl2_24
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_980
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f103352,f97731,f91299,f91295,f88382,f87247,f80899,f74183,f69866,f27818,f27681,f9479,f9463,f3772,f1852,f1122,f1024,f814,f810,f806,f748,f738,f681,f290,f286,f126138]) ).
fof(f806,plain,
( spl2_75
<=> ! [X4,X5] : equiv(X4,X5) = equiv(X5,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
fof(f810,plain,
( spl2_76
<=> ! [X11,X10] : and(X10,X11) = and(X11,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
fof(f1024,plain,
( spl2_83
<=> ! [X15] : not(not(X15)) = or(X15,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_83])]) ).
fof(f3772,plain,
( spl2_189
<=> ! [X0,X1] : equiv(not(X1),not(X0)) = and(or(X1,not(X0)),or(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_189])]) ).
fof(f9463,plain,
( spl2_307
<=> ! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_implies(X1,not(X0)))
| not(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_307])]) ).
fof(f9479,plain,
( spl2_311
<=> ! [X2,X4,X3] : implies(implies(X2,X3),X4) = or(X4,and(not(X3),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_311])]) ).
fof(f27681,plain,
( spl2_520
<=> ! [X0,X1] : is_a_theorem(strict_implies(or(X0,and(X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_520])]) ).
fof(f74183,plain,
( spl2_980
<=> ! [X6,X7] : is_a_theorem(implies(and(X6,not(X6)),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_980])]) ).
fof(f80899,plain,
( spl2_1063
<=> ! [X0] : is_a_theorem(necessarily(or(X0,not(not(not(X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1063])]) ).
fof(f87247,plain,
( spl2_1119
<=> ! [X9,X10] : not(not(X9)) = or(X9,and(X9,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1119])]) ).
fof(f88382,plain,
( spl2_1121
<=> ! [X35] : not(X35) = not(not(not(X35))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1121])]) ).
fof(f91295,plain,
( spl2_1162
<=> ! [X112,X113] : or(X112,X113) = or(not(not(X112)),X113) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1162])]) ).
fof(f103352,plain,
( ! [X6,X7] : is_a_theorem(or(implies(X6,X6),X7))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_980
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f102734,f291]) ).
fof(f102734,plain,
( ! [X6,X7] : is_a_theorem(implies(not(implies(X6,X6)),X7))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_980
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f97141,f97972]) ).
fof(f97972,plain,
( ! [X5] : equiv(X5,not(X5)) = not(implies(X5,X5))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f97140,f97971]) ).
fof(f97140,plain,
( ! [X5] : equiv(X5,not(X5)) = and(X5,not(X5))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_75
| ~ spl2_76
| ~ spl2_83
| ~ spl2_96
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163 ),
inference(forward_demodulation,[],[f97139,f807]) ).
fof(f807,plain,
( ! [X4,X5] : equiv(X4,X5) = equiv(X5,X4)
| ~ spl2_75 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f97139,plain,
( ! [X5] : equiv(not(X5),X5) = and(X5,not(X5))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_75
| ~ spl2_76
| ~ spl2_83
| ~ spl2_96
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163 ),
inference(forward_demodulation,[],[f95626,f811]) ).
fof(f811,plain,
( ! [X10,X11] : and(X10,X11) = and(X11,X10)
| ~ spl2_76 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f95626,plain,
( ! [X5] : equiv(not(X5),X5) = and(not(X5),X5)
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_75
| ~ spl2_83
| ~ spl2_96
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f92868,f94970]) ).
fof(f92868,plain,
( ! [X5] : equiv(not(X5),not(not(X5))) = and(not(X5),not(not(X5)))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162 ),
inference(backward_demodulation,[],[f87906,f92865]) ).
fof(f92865,plain,
( ! [X2] : not(not(X2)) = or(X2,not(not(X2)))
| ~ spl2_83
| ~ spl2_1121
| ~ spl2_1162 ),
inference(forward_demodulation,[],[f92562,f88383]) ).
fof(f88383,plain,
( ! [X35] : not(X35) = not(not(not(X35)))
| ~ spl2_1121 ),
inference(avatar_component_clause,[],[f88382]) ).
fof(f92562,plain,
( ! [X2] : not(not(not(not(X2)))) = or(X2,not(not(X2)))
| ~ spl2_83
| ~ spl2_1162 ),
inference(superposition,[],[f91296,f1025]) ).
fof(f1025,plain,
( ! [X15] : not(not(X15)) = or(X15,X15)
| ~ spl2_83 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f91296,plain,
( ! [X113,X112] : or(X112,X113) = or(not(not(X112)),X113)
| ~ spl2_1162 ),
inference(avatar_component_clause,[],[f91295]) ).
fof(f87906,plain,
( ! [X5] : equiv(not(X5),not(not(X5))) = and(not(X5),or(X5,not(not(X5))))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119 ),
inference(backward_demodulation,[],[f3911,f87905]) ).
fof(f87905,plain,
( ! [X35] : not(X35) = not(not(not(X35)))
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119 ),
inference(forward_demodulation,[],[f87904,f87344]) ).
fof(f87344,plain,
( ! [X11,X12] : not(not(not(X11))) = implies(implies(X12,X11),not(X11))
| ~ spl2_311
| ~ spl2_1119 ),
inference(superposition,[],[f87248,f9480]) ).
fof(f9480,plain,
( ! [X2,X3,X4] : implies(implies(X2,X3),X4) = or(X4,and(not(X3),X2))
| ~ spl2_311 ),
inference(avatar_component_clause,[],[f9479]) ).
fof(f87248,plain,
( ! [X10,X9] : not(not(X9)) = or(X9,and(X9,X10))
| ~ spl2_1119 ),
inference(avatar_component_clause,[],[f87247]) ).
fof(f87904,plain,
( ! [X36,X35] : not(X35) = implies(implies(X36,X35),not(X35))
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119 ),
inference(subsumption_resolution,[],[f87895,f80900]) ).
fof(f80900,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(not(not(X0))))))
| ~ spl2_1063 ),
inference(avatar_component_clause,[],[f80899]) ).
fof(f87895,plain,
( ! [X36,X35] :
( ~ is_a_theorem(necessarily(or(X35,not(not(not(X35))))))
| not(X35) = implies(implies(X36,X35),not(X35)) )
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1119 ),
inference(backward_demodulation,[],[f27782,f87344]) ).
fof(f27782,plain,
( ! [X36,X35] :
( not(X35) = implies(implies(X36,X35),not(X35))
| ~ is_a_theorem(necessarily(or(X35,implies(implies(X36,X35),not(X35))))) )
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520 ),
inference(forward_demodulation,[],[f27781,f9480]) ).
fof(f27781,plain,
( ! [X36,X35] :
( ~ is_a_theorem(necessarily(or(X35,implies(implies(X36,X35),not(X35)))))
| not(X35) = or(not(X35),and(not(X35),X36)) )
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520 ),
inference(forward_demodulation,[],[f27727,f9480]) ).
fof(f27727,plain,
( ! [X36,X35] :
( ~ is_a_theorem(necessarily(or(X35,or(not(X35),and(not(X35),X36)))))
| not(X35) = or(not(X35),and(not(X35),X36)) )
| ~ spl2_307
| ~ spl2_520 ),
inference(resolution,[],[f27682,f9464]) ).
fof(f9464,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,not(X0)))
| ~ is_a_theorem(necessarily(or(X0,X1)))
| not(X0) = X1 )
| ~ spl2_307 ),
inference(avatar_component_clause,[],[f9463]) ).
fof(f27682,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(or(X0,and(X0,X1)),X0))
| ~ spl2_520 ),
inference(avatar_component_clause,[],[f27681]) ).
fof(f3911,plain,
( ! [X5] : and(not(not(not(X5))),or(X5,not(not(X5)))) = equiv(not(X5),not(not(X5)))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_189 ),
inference(forward_demodulation,[],[f3842,f807]) ).
fof(f3842,plain,
( ! [X5] : equiv(not(not(X5)),not(X5)) = and(not(not(not(X5))),or(X5,not(not(X5))))
| ~ spl2_83
| ~ spl2_189 ),
inference(superposition,[],[f3773,f1025]) ).
fof(f3773,plain,
( ! [X0,X1] : equiv(not(X1),not(X0)) = and(or(X1,not(X0)),or(X0,not(X1)))
| ~ spl2_189 ),
inference(avatar_component_clause,[],[f3772]) ).
fof(f97141,plain,
( ! [X6,X7] : is_a_theorem(implies(equiv(X6,not(X6)),X7))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_75
| ~ spl2_76
| ~ spl2_83
| ~ spl2_96
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_954
| ~ spl2_980
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f74184,f97140]) ).
fof(f74184,plain,
( ! [X6,X7] : is_a_theorem(implies(and(X6,not(X6)),X7))
| ~ spl2_980 ),
inference(avatar_component_clause,[],[f74183]) ).
fof(f126136,plain,
( spl2_1197
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_116
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f121383,f97731,f1696,f1388,f748,f505,f126134]) ).
fof(f126134,plain,
( spl2_1197
<=> ! [X6,X7] : strict_implies(X6,not(possibly(X7))) = not(possibly(and(X6,possibly(X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1197])]) ).
fof(f505,plain,
( spl2_54
<=> ! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
fof(f1388,plain,
( spl2_104
<=> ! [X0,X1] : or(X0,necessarily(not(X1))) = implies(possibly(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_104])]) ).
fof(f1696,plain,
( spl2_116
<=> ! [X6,X7] : strict_implies(X6,necessarily(not(X7))) = necessarily(not(and(X6,possibly(X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_116])]) ).
fof(f121383,plain,
( ! [X6,X7] : strict_implies(X6,not(possibly(X7))) = not(possibly(and(X6,possibly(X7))))
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_116
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f118075,f118064]) ).
fof(f118064,plain,
( ! [X14] : necessarily(not(X14)) = not(possibly(X14))
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f118063,f749]) ).
fof(f118063,plain,
( ! [X14] : necessarily(not(X14)) = not(and(possibly(X14),possibly(X14)))
| ~ spl2_54
| ~ spl2_104
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f97738,f506]) ).
fof(f506,plain,
( ! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0)))
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f97738,plain,
( ! [X14] : necessarily(not(X14)) = implies(possibly(X14),necessarily(not(X14)))
| ~ spl2_104
| ~ spl2_1181 ),
inference(superposition,[],[f97732,f1389]) ).
fof(f1389,plain,
( ! [X0,X1] : or(X0,necessarily(not(X1))) = implies(possibly(X1),X0)
| ~ spl2_104 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f118075,plain,
( ! [X6,X7] : necessarily(not(and(X6,possibly(X7)))) = strict_implies(X6,not(possibly(X7)))
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_116
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f1697,f118064]) ).
fof(f1697,plain,
( ! [X6,X7] : strict_implies(X6,necessarily(not(X7))) = necessarily(not(and(X6,possibly(X7))))
| ~ spl2_116 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f126132,plain,
( ~ spl2_1196
| ~ spl2_1186
| spl2_1193 ),
inference(avatar_split_clause,[],[f126118,f126113,f125725,f126129]) ).
fof(f126129,plain,
( spl2_1196
<=> is_a_theorem(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1196])]) ).
fof(f125725,plain,
( spl2_1186
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1186])]) ).
fof(f126113,plain,
( spl2_1193
<=> is_a_theorem(or(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1193])]) ).
fof(f126118,plain,
( ~ is_a_theorem(sK0)
| ~ spl2_1186
| spl2_1193 ),
inference(resolution,[],[f126115,f125726]) ).
fof(f125726,plain,
( ! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) )
| ~ spl2_1186 ),
inference(avatar_component_clause,[],[f125725]) ).
fof(f126115,plain,
( ~ is_a_theorem(or(sK0,sK1))
| spl2_1193 ),
inference(avatar_component_clause,[],[f126113]) ).
fof(f126127,plain,
( spl2_1195
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_114
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f118073,f97731,f1640,f1388,f748,f505,f126125]) ).
fof(f126125,plain,
( spl2_1195
<=> ! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,not(possibly(X1))),not(and(X0,possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1195])]) ).
fof(f1640,plain,
( spl2_114
<=> ! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,necessarily(not(X1))),not(and(X0,possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_114])]) ).
fof(f118073,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,not(possibly(X1))),not(and(X0,possibly(X1)))))
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_114
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f1641,f118064]) ).
fof(f1641,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,necessarily(not(X1))),not(and(X0,possibly(X1)))))
| ~ spl2_114 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f126123,plain,
( ~ spl2_1194
| ~ spl2_1189
| spl2_1193 ),
inference(avatar_split_clause,[],[f126117,f126113,f125766,f126120]) ).
fof(f126120,plain,
( spl2_1194
<=> is_a_theorem(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1194])]) ).
fof(f125766,plain,
( spl2_1189
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1189])]) ).
fof(f126117,plain,
( ~ is_a_theorem(sK1)
| ~ spl2_1189
| spl2_1193 ),
inference(resolution,[],[f126115,f125767]) ).
fof(f125767,plain,
( ! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(X0) )
| ~ spl2_1189 ),
inference(avatar_component_clause,[],[f125766]) ).
fof(f126116,plain,
( ~ spl2_1193
| spl2_2
| ~ spl2_1191 ),
inference(avatar_split_clause,[],[f126104,f126092,f185,f126113]) ).
fof(f126092,plain,
( spl2_1191
<=> ! [X13,X14] :
( ~ is_a_theorem(X14)
| is_a_theorem(implies(X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1191])]) ).
fof(f126104,plain,
( ~ is_a_theorem(or(sK0,sK1))
| spl2_2
| ~ spl2_1191 ),
inference(resolution,[],[f126093,f187]) ).
fof(f126093,plain,
( ! [X14,X13] :
( is_a_theorem(implies(X13,X14))
| ~ is_a_theorem(X14) )
| ~ spl2_1191 ),
inference(avatar_component_clause,[],[f126092]) ).
fof(f126098,plain,
( spl2_1192
| ~ spl2_72
| ~ spl2_77
| ~ spl2_125
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f97987,f97731,f1852,f814,f748,f126096]) ).
fof(f126096,plain,
( spl2_1192
<=> ! [X2,X0,X1] : implies(implies(X1,X2),X0) = or(X0,not(implies(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1192])]) ).
fof(f97987,plain,
( ! [X2,X0,X1] : implies(implies(X1,X2),X0) = or(X0,not(implies(X1,X2)))
| ~ spl2_72
| ~ spl2_77
| ~ spl2_125
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f1853,f97971]) ).
fof(f126094,plain,
( spl2_1191
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_591
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f95154,f91299,f69866,f30695,f27818,f1122,f738,f681,f286,f126092]) ).
fof(f30695,plain,
( spl2_591
<=> ! [X13,X14] :
( is_a_theorem(implies(X13,X14))
| ~ is_a_theorem(not(not(X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_591])]) ).
fof(f95154,plain,
( ! [X14,X13] :
( ~ is_a_theorem(X14)
| is_a_theorem(implies(X13,X14)) )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_591
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f30696,f94970]) ).
fof(f30696,plain,
( ! [X14,X13] :
( ~ is_a_theorem(not(not(X14)))
| is_a_theorem(implies(X13,X14)) )
| ~ spl2_591 ),
inference(avatar_component_clause,[],[f30695]) ).
fof(f126044,plain,
( spl2_1190
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1077
| ~ spl2_1140
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f97014,f91299,f90579,f83212,f69866,f27818,f1122,f738,f681,f286,f126042]) ).
fof(f126042,plain,
( spl2_1190
<=> ! [X76] :
( ~ is_a_theorem(necessarily(X76))
| ~ is_a_theorem(not(X76)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1190])]) ).
fof(f83212,plain,
( spl2_1077
<=> ! [X76] :
( ~ is_a_theorem(not(X76))
| ~ is_a_theorem(necessarily(not(not(X76))))
| is_a_theorem(X76) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1077])]) ).
fof(f90579,plain,
( spl2_1140
<=> ! [X1] :
( ~ is_a_theorem(not(X1))
| ~ is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1140])]) ).
fof(f97014,plain,
( ! [X76] :
( ~ is_a_theorem(necessarily(X76))
| ~ is_a_theorem(not(X76)) )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1077
| ~ spl2_1140
| ~ spl2_1163 ),
inference(subsumption_resolution,[],[f95455,f90580]) ).
fof(f90580,plain,
( ! [X1] :
( ~ is_a_theorem(not(X1))
| ~ is_a_theorem(X1) )
| ~ spl2_1140 ),
inference(avatar_component_clause,[],[f90579]) ).
fof(f95455,plain,
( ! [X76] :
( ~ is_a_theorem(necessarily(X76))
| ~ is_a_theorem(not(X76))
| is_a_theorem(X76) )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1077
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f83213,f94970]) ).
fof(f83213,plain,
( ! [X76] :
( ~ is_a_theorem(not(X76))
| ~ is_a_theorem(necessarily(not(not(X76))))
| is_a_theorem(X76) )
| ~ spl2_1077 ),
inference(avatar_component_clause,[],[f83212]) ).
fof(f125768,plain,
( spl2_1189
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_402
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f95028,f91299,f69866,f27818,f14352,f1122,f738,f681,f286,f125766]) ).
fof(f14352,plain,
( spl2_402
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_402])]) ).
fof(f95028,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,X0)) )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_402
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f14353,f94970]) ).
fof(f14353,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) )
| ~ spl2_402 ),
inference(avatar_component_clause,[],[f14352]) ).
fof(f125735,plain,
( spl2_1188
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f118071,f97731,f1388,f748,f505,f125733]) ).
fof(f125733,plain,
( spl2_1188
<=> ! [X0,X1] : implies(possibly(X1),X0) = or(X0,not(possibly(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1188])]) ).
fof(f118071,plain,
( ! [X0,X1] : implies(possibly(X1),X0) = or(X0,not(possibly(X1)))
| ~ spl2_54
| ~ spl2_72
| ~ spl2_104
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f1389,f118064]) ).
fof(f125731,plain,
( spl2_1187
| ~ spl2_23
| ~ spl2_24
| ~ spl2_535
| ~ spl2_1182 ),
inference(avatar_split_clause,[],[f125107,f124500,f28565,f290,f286,f125729]) ).
fof(f125729,plain,
( spl2_1187
<=> ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1187])]) ).
fof(f28565,plain,
( spl2_535
<=> ! [X0,X1] : is_a_theorem(necessarily(or(not(X0),implies(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_535])]) ).
fof(f125107,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0)))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_535
| ~ spl2_1182 ),
inference(forward_demodulation,[],[f124719,f287]) ).
fof(f124719,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(X0,implies(X1,X0))))
| ~ spl2_24
| ~ spl2_535
| ~ spl2_1182 ),
inference(backward_demodulation,[],[f28566,f124515]) ).
fof(f28566,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(not(X0),implies(X1,X0))))
| ~ spl2_535 ),
inference(avatar_component_clause,[],[f28565]) ).
fof(f125727,plain,
( spl2_1186
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_396
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f95024,f91299,f69866,f27818,f14288,f1122,f738,f681,f286,f125725]) ).
fof(f14288,plain,
( spl2_396
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_396])]) ).
fof(f95024,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) )
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_396
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f14289,f94970]) ).
fof(f14289,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) )
| ~ spl2_396 ),
inference(avatar_component_clause,[],[f14288]) ).
fof(f125669,plain,
( spl2_1185
| ~ spl2_23
| ~ spl2_24
| ~ spl2_331
| ~ spl2_1182 ),
inference(avatar_split_clause,[],[f125259,f124500,f10620,f290,f286,f125667]) ).
fof(f125667,plain,
( spl2_1185
<=> ! [X9,X10] : is_a_theorem(strict_implies(X9,or(X10,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1185])]) ).
fof(f10620,plain,
( spl2_331
<=> ! [X9,X10] : is_a_theorem(necessarily(or(not(X9),or(X10,X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_331])]) ).
fof(f125259,plain,
( ! [X10,X9] : is_a_theorem(strict_implies(X9,or(X10,X9)))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_331
| ~ spl2_1182 ),
inference(forward_demodulation,[],[f124755,f287]) ).
fof(f124755,plain,
( ! [X10,X9] : is_a_theorem(necessarily(implies(X9,or(X10,X9))))
| ~ spl2_24
| ~ spl2_331
| ~ spl2_1182 ),
inference(backward_demodulation,[],[f10621,f124515]) ).
fof(f10621,plain,
( ! [X10,X9] : is_a_theorem(necessarily(or(not(X9),or(X10,X9))))
| ~ spl2_331 ),
inference(avatar_component_clause,[],[f10620]) ).
fof(f125644,plain,
( spl2_1184
| ~ spl2_23
| ~ spl2_24
| ~ spl2_330
| ~ spl2_1182 ),
inference(avatar_split_clause,[],[f125258,f124500,f10591,f290,f286,f125642]) ).
fof(f125642,plain,
( spl2_1184
<=> ! [X6,X5] : is_a_theorem(strict_implies(X5,or(X5,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1184])]) ).
fof(f10591,plain,
( spl2_330
<=> ! [X6,X5] : is_a_theorem(necessarily(or(not(X5),or(X5,X6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_330])]) ).
fof(f125258,plain,
( ! [X6,X5] : is_a_theorem(strict_implies(X5,or(X5,X6)))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_330
| ~ spl2_1182 ),
inference(forward_demodulation,[],[f124753,f287]) ).
fof(f124753,plain,
( ! [X6,X5] : is_a_theorem(necessarily(implies(X5,or(X5,X6))))
| ~ spl2_24
| ~ spl2_330
| ~ spl2_1182 ),
inference(backward_demodulation,[],[f10592,f124515]) ).
fof(f10592,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(not(X5),or(X5,X6))))
| ~ spl2_330 ),
inference(avatar_component_clause,[],[f10591]) ).
fof(f124506,plain,
( spl2_1183
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_65
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(avatar_split_clause,[],[f103213,f97731,f91299,f91295,f88382,f87247,f80899,f75977,f69866,f68172,f27818,f27681,f9479,f9463,f3772,f1852,f1122,f1024,f814,f810,f806,f748,f738,f681,f602,f340,f290,f286,f124504]) ).
fof(f124504,plain,
( spl2_1183
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),strict_implies(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1183])]) ).
fof(f340,plain,
( spl2_33
<=> ! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f602,plain,
( spl2_65
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).
fof(f68172,plain,
( spl2_949
<=> ! [X4,X3] : necessarily(not(equiv(X3,not(X4)))) = necessarily(not(equiv(not(X4),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_949])]) ).
fof(f75977,plain,
( spl2_1019
<=> ! [X0] : necessarily(not(equiv(X0,not(X0)))) = strict_implies(implies(X0,not(X0)),not(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1019])]) ).
fof(f103213,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),strict_implies(X0,X0)))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_65
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f603,f103212]) ).
fof(f103212,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = strict_implies(X1131,X1131)
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f103211,f287]) ).
fof(f103211,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = necessarily(implies(X1131,X1131))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(forward_demodulation,[],[f102733,f94970]) ).
fof(f102733,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = necessarily(not(not(implies(X1131,X1131))))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_70
| ~ spl2_71
| ~ spl2_72
| ~ spl2_75
| ~ spl2_76
| ~ spl2_77
| ~ spl2_83
| ~ spl2_96
| ~ spl2_125
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162
| ~ spl2_1163
| ~ spl2_1181 ),
inference(backward_demodulation,[],[f97084,f97972]) ).
fof(f97084,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = necessarily(not(equiv(X1131,not(X1131))))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_70
| ~ spl2_71
| ~ spl2_83
| ~ spl2_96
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1121
| ~ spl2_1163 ),
inference(forward_demodulation,[],[f95593,f68173]) ).
fof(f68173,plain,
( ! [X3,X4] : necessarily(not(equiv(X3,not(X4)))) = necessarily(not(equiv(not(X4),X3)))
| ~ spl2_949 ),
inference(avatar_component_clause,[],[f68172]) ).
fof(f95593,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = necessarily(not(equiv(not(X1131),X1131)))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_33
| ~ spl2_70
| ~ spl2_71
| ~ spl2_83
| ~ spl2_96
| ~ spl2_524
| ~ spl2_949
| ~ spl2_954
| ~ spl2_1019
| ~ spl2_1121
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f89416,f94970]) ).
fof(f89416,plain,
( ! [X1131] : necessarily(or(X1131,not(X1131))) = necessarily(not(equiv(not(X1131),not(not(X1131)))))
| ~ spl2_24
| ~ spl2_33
| ~ spl2_83
| ~ spl2_949
| ~ spl2_1019
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f89415,f68173]) ).
fof(f89415,plain,
( ! [X1131] : necessarily(not(equiv(not(not(X1131)),not(X1131)))) = necessarily(or(X1131,not(X1131)))
| ~ spl2_24
| ~ spl2_33
| ~ spl2_83
| ~ spl2_1019
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f89414,f88939]) ).
fof(f88939,plain,
( ! [X113,X112] : or(X112,X113) = or(not(not(X112)),X113)
| ~ spl2_24
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f88459,f291]) ).
fof(f88459,plain,
( ! [X113,X112] : or(not(not(X112)),X113) = implies(not(X112),X113)
| ~ spl2_24
| ~ spl2_1121 ),
inference(superposition,[],[f291,f88383]) ).
fof(f89414,plain,
( ! [X1131] : necessarily(not(equiv(not(not(X1131)),not(X1131)))) = necessarily(or(not(not(X1131)),not(X1131)))
| ~ spl2_24
| ~ spl2_33
| ~ spl2_83
| ~ spl2_1019
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f89413,f341]) ).
fof(f341,plain,
( ! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1))
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f89413,plain,
( ! [X1131] : necessarily(not(equiv(not(not(X1131)),not(X1131)))) = strict_implies(not(not(not(X1131))),not(X1131))
| ~ spl2_24
| ~ spl2_83
| ~ spl2_1019
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f89412,f1025]) ).
fof(f89412,plain,
( ! [X1131] : necessarily(not(equiv(not(not(X1131)),not(X1131)))) = strict_implies(or(not(X1131),not(X1131)),not(X1131))
| ~ spl2_24
| ~ spl2_1019
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f88868,f291]) ).
fof(f88868,plain,
( ! [X1131] : necessarily(not(equiv(not(not(X1131)),not(X1131)))) = strict_implies(implies(not(not(X1131)),not(X1131)),not(X1131))
| ~ spl2_1019
| ~ spl2_1121 ),
inference(superposition,[],[f75978,f88383]) ).
fof(f75978,plain,
( ! [X0] : necessarily(not(equiv(X0,not(X0)))) = strict_implies(implies(X0,not(X0)),not(X0))
| ~ spl2_1019 ),
inference(avatar_component_clause,[],[f75977]) ).
fof(f603,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,not(X0)))))
| ~ spl2_65 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f124502,plain,
( spl2_1182
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f94970,f91299,f69866,f27818,f1122,f738,f681,f286,f124500]) ).
fof(f97733,plain,
( spl2_1181
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_83
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f94971,f91299,f69866,f27818,f1122,f1024,f738,f681,f286,f97731]) ).
fof(f94971,plain,
( ! [X15] : or(X15,X15) = X15
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_83
| ~ spl2_96
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f1025,f94970]) ).
fof(f97729,plain,
( spl2_1180
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_432
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(avatar_split_clause,[],[f95040,f91299,f69866,f27818,f15067,f1122,f738,f681,f286,f97727]) ).
fof(f97727,plain,
( spl2_1180
<=> ! [X11,X10] : necessarily(not(equiv(not(X10),X11))) = strict_implies(or(X10,X11),and(X11,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1180])]) ).
fof(f15067,plain,
( spl2_432
<=> ! [X11,X10] : strict_implies(or(X10,X11),and(X11,not(not(X10)))) = necessarily(not(equiv(not(X10),X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_432])]) ).
fof(f95040,plain,
( ! [X10,X11] : necessarily(not(equiv(not(X10),X11))) = strict_implies(or(X10,X11),and(X11,X10))
| ~ spl2_23
| ~ spl2_70
| ~ spl2_71
| ~ spl2_96
| ~ spl2_432
| ~ spl2_524
| ~ spl2_954
| ~ spl2_1163 ),
inference(backward_demodulation,[],[f15068,f94970]) ).
fof(f15068,plain,
( ! [X10,X11] : strict_implies(or(X10,X11),and(X11,not(not(X10)))) = necessarily(not(equiv(not(X10),X11)))
| ~ spl2_432 ),
inference(avatar_component_clause,[],[f15067]) ).
fof(f94473,plain,
( spl2_1179
| ~ spl2_75
| ~ spl2_83
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_495
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92872,f91295,f88382,f87247,f80899,f27681,f22997,f9479,f9463,f3772,f1024,f806,f94471]) ).
fof(f94471,plain,
( spl2_1179
<=> ! [X0] :
( ~ is_a_theorem(equiv(not(X0),not(not(X0))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1179])]) ).
fof(f22997,plain,
( spl2_495
<=> ! [X0] :
( ~ is_a_theorem(and(not(X0),not(not(X0))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_495])]) ).
fof(f92872,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(not(X0),not(not(X0))))
| is_a_theorem(X0) )
| ~ spl2_75
| ~ spl2_83
| ~ spl2_189
| ~ spl2_307
| ~ spl2_311
| ~ spl2_495
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119
| ~ spl2_1121
| ~ spl2_1162 ),
inference(backward_demodulation,[],[f22998,f92868]) ).
fof(f22998,plain,
( ! [X0] :
( ~ is_a_theorem(and(not(X0),not(not(X0))))
| is_a_theorem(X0) )
| ~ spl2_495 ),
inference(avatar_component_clause,[],[f22997]) ).
fof(f94421,plain,
( spl2_1178
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1168 ),
inference(avatar_split_clause,[],[f93435,f93368,f373,f273,f94419]) ).
fof(f94419,plain,
( spl2_1178
<=> ! [X48,X49] : is_a_theorem(implies(possibly(X48),or(X49,possibly(X48)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1178])]) ).
fof(f273,plain,
( spl2_20
<=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f373,plain,
( spl2_37
<=> ! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f93368,plain,
( spl2_1168
<=> ! [X4,X5] : is_a_theorem(or(X4,or(X5,not(X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1168])]) ).
fof(f93435,plain,
( ! [X48,X49] : is_a_theorem(implies(possibly(X48),or(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1168 ),
inference(forward_demodulation,[],[f93390,f374]) ).
fof(f374,plain,
( ! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1)
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f93390,plain,
( ! [X48,X49] : is_a_theorem(or(necessarily(not(X48)),or(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_1168 ),
inference(superposition,[],[f93369,f274]) ).
fof(f274,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f93369,plain,
( ! [X4,X5] : is_a_theorem(or(X4,or(X5,not(X4))))
| ~ spl2_1168 ),
inference(avatar_component_clause,[],[f93368]) ).
fof(f94204,plain,
( spl2_1177
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1167 ),
inference(avatar_split_clause,[],[f93348,f93204,f373,f273,f94202]) ).
fof(f94202,plain,
( spl2_1177
<=> ! [X48,X49] : is_a_theorem(implies(possibly(X48),implies(X49,possibly(X48)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1177])]) ).
fof(f93204,plain,
( spl2_1167
<=> ! [X9,X8] : is_a_theorem(or(X8,implies(X9,not(X8)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1167])]) ).
fof(f93348,plain,
( ! [X48,X49] : is_a_theorem(implies(possibly(X48),implies(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1167 ),
inference(forward_demodulation,[],[f93304,f374]) ).
fof(f93304,plain,
( ! [X48,X49] : is_a_theorem(or(necessarily(not(X48)),implies(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_1167 ),
inference(superposition,[],[f93205,f274]) ).
fof(f93205,plain,
( ! [X8,X9] : is_a_theorem(or(X8,implies(X9,not(X8))))
| ~ spl2_1167 ),
inference(avatar_component_clause,[],[f93204]) ).
fof(f94119,plain,
( spl2_1176
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1165 ),
inference(avatar_split_clause,[],[f93268,f93196,f373,f273,f94117]) ).
fof(f94117,plain,
( spl2_1176
<=> ! [X48,X49] : is_a_theorem(implies(possibly(X48),or(possibly(X48),X49))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1176])]) ).
fof(f93196,plain,
( spl2_1165
<=> ! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1165])]) ).
fof(f93268,plain,
( ! [X48,X49] : is_a_theorem(implies(possibly(X48),or(possibly(X48),X49)))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1165 ),
inference(forward_demodulation,[],[f93222,f374]) ).
fof(f93222,plain,
( ! [X48,X49] : is_a_theorem(or(necessarily(not(X48)),or(possibly(X48),X49)))
| ~ spl2_20
| ~ spl2_1165 ),
inference(superposition,[],[f93197,f274]) ).
fof(f93197,plain,
( ! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1)))
| ~ spl2_1165 ),
inference(avatar_component_clause,[],[f93196]) ).
fof(f93880,plain,
( spl2_1175
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1172 ),
inference(avatar_split_clause,[],[f93829,f93555,f373,f286,f273,f93878]) ).
fof(f93878,plain,
( spl2_1175
<=> ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),implies(X49,possibly(X48)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1175])]) ).
fof(f93555,plain,
( spl2_1172
<=> ! [X11,X10] : is_a_theorem(necessarily(or(X10,implies(X11,not(X10))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1172])]) ).
fof(f93829,plain,
( ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),implies(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1172 ),
inference(forward_demodulation,[],[f93828,f287]) ).
fof(f93828,plain,
( ! [X48,X49] : is_a_theorem(necessarily(implies(possibly(X48),implies(X49,possibly(X48)))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1172 ),
inference(forward_demodulation,[],[f93777,f374]) ).
fof(f93777,plain,
( ! [X48,X49] : is_a_theorem(necessarily(or(necessarily(not(X48)),implies(X49,possibly(X48)))))
| ~ spl2_20
| ~ spl2_1172 ),
inference(superposition,[],[f93556,f274]) ).
fof(f93556,plain,
( ! [X10,X11] : is_a_theorem(necessarily(or(X10,implies(X11,not(X10)))))
| ~ spl2_1172 ),
inference(avatar_component_clause,[],[f93555]) ).
fof(f93876,plain,
( spl2_1174
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1171 ),
inference(avatar_split_clause,[],[f93729,f93459,f373,f286,f273,f93874]) ).
fof(f93874,plain,
( spl2_1174
<=> ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),or(X49,possibly(X48)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1174])]) ).
fof(f93459,plain,
( spl2_1171
<=> ! [X6,X7] : is_a_theorem(necessarily(or(X6,or(X7,not(X6))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1171])]) ).
fof(f93729,plain,
( ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),or(X49,possibly(X48))))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1171 ),
inference(forward_demodulation,[],[f93728,f287]) ).
fof(f93728,plain,
( ! [X48,X49] : is_a_theorem(necessarily(implies(possibly(X48),or(X49,possibly(X48)))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1171 ),
inference(forward_demodulation,[],[f93676,f374]) ).
fof(f93676,plain,
( ! [X48,X49] : is_a_theorem(necessarily(or(necessarily(not(X48)),or(X49,possibly(X48)))))
| ~ spl2_20
| ~ spl2_1171 ),
inference(superposition,[],[f93460,f274]) ).
fof(f93460,plain,
( ! [X6,X7] : is_a_theorem(necessarily(or(X6,or(X7,not(X6)))))
| ~ spl2_1171 ),
inference(avatar_component_clause,[],[f93459]) ).
fof(f93872,plain,
( spl2_1173
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1170 ),
inference(avatar_split_clause,[],[f93626,f93455,f373,f286,f273,f93870]) ).
fof(f93870,plain,
( spl2_1173
<=> ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),or(possibly(X48),X49))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1173])]) ).
fof(f93455,plain,
( spl2_1170
<=> ! [X2,X3] : is_a_theorem(necessarily(or(X2,or(not(X2),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1170])]) ).
fof(f93626,plain,
( ! [X48,X49] : is_a_theorem(strict_implies(possibly(X48),or(possibly(X48),X49)))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1170 ),
inference(forward_demodulation,[],[f93625,f287]) ).
fof(f93625,plain,
( ! [X48,X49] : is_a_theorem(necessarily(implies(possibly(X48),or(possibly(X48),X49))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1170 ),
inference(forward_demodulation,[],[f93572,f374]) ).
fof(f93572,plain,
( ! [X48,X49] : is_a_theorem(necessarily(or(necessarily(not(X48)),or(possibly(X48),X49))))
| ~ spl2_20
| ~ spl2_1170 ),
inference(superposition,[],[f93456,f274]) ).
fof(f93456,plain,
( ! [X2,X3] : is_a_theorem(necessarily(or(X2,or(not(X2),X3))))
| ~ spl2_1170 ),
inference(avatar_component_clause,[],[f93455]) ).
fof(f93557,plain,
( spl2_1172
| ~ spl2_535
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92580,f91295,f28565,f93555]) ).
fof(f92580,plain,
( ! [X10,X11] : is_a_theorem(necessarily(or(X10,implies(X11,not(X10)))))
| ~ spl2_535
| ~ spl2_1162 ),
inference(superposition,[],[f28566,f91296]) ).
fof(f93461,plain,
( spl2_1171
| ~ spl2_331
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92578,f91295,f10620,f93459]) ).
fof(f92578,plain,
( ! [X6,X7] : is_a_theorem(necessarily(or(X6,or(X7,not(X6)))))
| ~ spl2_331
| ~ spl2_1162 ),
inference(superposition,[],[f10621,f91296]) ).
fof(f93457,plain,
( spl2_1170
| ~ spl2_330
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92576,f91295,f10591,f93455]) ).
fof(f92576,plain,
( ! [X2,X3] : is_a_theorem(necessarily(or(X2,or(not(X2),X3))))
| ~ spl2_330
| ~ spl2_1162 ),
inference(superposition,[],[f10592,f91296]) ).
fof(f93374,plain,
( spl2_1169
| ~ spl2_30
| ~ spl2_804 ),
inference(avatar_split_clause,[],[f55403,f53730,f319,f93372]) ).
fof(f93372,plain,
( spl2_1169
<=> ! [X169,X167,X168] :
( ~ is_a_theorem(equiv(and(not(X168),not(X169)),X167))
| is_a_theorem(not(and(X167,or(X168,X169)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1169])]) ).
fof(f319,plain,
( spl2_30
<=> ! [X2,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(and(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f53730,plain,
( spl2_804
<=> ! [X2,X0,X1] : equiv(and(not(X0),not(X1)),X2) = and(not(and(X2,or(X0,X1))),implies(and(not(X0),not(X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_804])]) ).
fof(f55403,plain,
( ! [X168,X169,X167] :
( ~ is_a_theorem(equiv(and(not(X168),not(X169)),X167))
| is_a_theorem(not(and(X167,or(X168,X169)))) )
| ~ spl2_30
| ~ spl2_804 ),
inference(superposition,[],[f320,f53731]) ).
fof(f53731,plain,
( ! [X2,X0,X1] : equiv(and(not(X0),not(X1)),X2) = and(not(and(X2,or(X0,X1))),implies(and(not(X0),not(X1)),X2))
| ~ spl2_804 ),
inference(avatar_component_clause,[],[f53730]) ).
fof(f320,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(X1) )
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f93370,plain,
( spl2_1168
| ~ spl2_983
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92577,f91295,f74343,f93368]) ).
fof(f74343,plain,
( spl2_983
<=> ! [X2,X1] : is_a_theorem(or(not(X1),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_983])]) ).
fof(f92577,plain,
( ! [X4,X5] : is_a_theorem(or(X4,or(X5,not(X4))))
| ~ spl2_983
| ~ spl2_1162 ),
inference(superposition,[],[f74344,f91296]) ).
fof(f74344,plain,
( ! [X2,X1] : is_a_theorem(or(not(X1),or(X2,X1)))
| ~ spl2_983 ),
inference(avatar_component_clause,[],[f74343]) ).
fof(f93206,plain,
( spl2_1167
| ~ spl2_1106
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92579,f91295,f86722,f93204]) ).
fof(f86722,plain,
( spl2_1106
<=> ! [X27,X28] : is_a_theorem(or(not(X27),implies(X28,X27))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1106])]) ).
fof(f92579,plain,
( ! [X8,X9] : is_a_theorem(or(X8,implies(X9,not(X8))))
| ~ spl2_1106
| ~ spl2_1162 ),
inference(superposition,[],[f86723,f91296]) ).
fof(f86723,plain,
( ! [X28,X27] : is_a_theorem(or(not(X27),implies(X28,X27)))
| ~ spl2_1106 ),
inference(avatar_component_clause,[],[f86722]) ).
fof(f93202,plain,
( spl2_1166
| ~ spl2_23
| ~ spl2_29
| ~ spl2_38
| ~ spl2_325
| ~ spl2_652 ),
inference(avatar_split_clause,[],[f41796,f36434,f10415,f377,f315,f286,f93200]) ).
fof(f93200,plain,
( spl2_1166
<=> ! [X22,X24,X23] : necessarily(not(equiv(X24,strict_implies(X22,X23)))) = necessarily(not(equiv(strict_implies(X22,X23),X24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1166])]) ).
fof(f315,plain,
( spl2_29
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f377,plain,
( spl2_38
<=> ! [X4,X3] : possibly(and(X3,not(X4))) = not(strict_implies(X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f10415,plain,
( spl2_325
<=> ! [X9,X8] : strict_implies(implies(X8,X9),and(X9,not(X8))) = necessarily(not(equiv(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_325])]) ).
fof(f36434,plain,
( spl2_652
<=> ! [X11,X10] : necessarily(not(equiv(X10,necessarily(not(X11))))) = strict_implies(implies(necessarily(not(X11)),X10),and(X10,possibly(X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_652])]) ).
fof(f41796,plain,
( ! [X24,X22,X23] : necessarily(not(equiv(X24,strict_implies(X22,X23)))) = necessarily(not(equiv(strict_implies(X22,X23),X24)))
| ~ spl2_23
| ~ spl2_29
| ~ spl2_38
| ~ spl2_325
| ~ spl2_652 ),
inference(forward_demodulation,[],[f41795,f10416]) ).
fof(f10416,plain,
( ! [X8,X9] : strict_implies(implies(X8,X9),and(X9,not(X8))) = necessarily(not(equiv(X8,X9)))
| ~ spl2_325 ),
inference(avatar_component_clause,[],[f10415]) ).
fof(f41795,plain,
( ! [X24,X22,X23] : necessarily(not(equiv(X24,strict_implies(X22,X23)))) = strict_implies(implies(strict_implies(X22,X23),X24),and(X24,not(strict_implies(X22,X23))))
| ~ spl2_23
| ~ spl2_29
| ~ spl2_38
| ~ spl2_652 ),
inference(forward_demodulation,[],[f41794,f287]) ).
fof(f41794,plain,
( ! [X24,X22,X23] : necessarily(not(equiv(X24,necessarily(implies(X22,X23))))) = strict_implies(implies(necessarily(implies(X22,X23)),X24),and(X24,not(strict_implies(X22,X23))))
| ~ spl2_29
| ~ spl2_38
| ~ spl2_652 ),
inference(forward_demodulation,[],[f41710,f378]) ).
fof(f378,plain,
( ! [X3,X4] : possibly(and(X3,not(X4))) = not(strict_implies(X3,X4))
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f41710,plain,
( ! [X24,X22,X23] : necessarily(not(equiv(X24,necessarily(implies(X22,X23))))) = strict_implies(implies(necessarily(implies(X22,X23)),X24),and(X24,possibly(and(X22,not(X23)))))
| ~ spl2_29
| ~ spl2_652 ),
inference(superposition,[],[f36435,f316]) ).
fof(f316,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f36435,plain,
( ! [X10,X11] : necessarily(not(equiv(X10,necessarily(not(X11))))) = strict_implies(implies(necessarily(not(X11)),X10),and(X10,possibly(X11)))
| ~ spl2_652 ),
inference(avatar_component_clause,[],[f36434]) ).
fof(f93198,plain,
( spl2_1165
| ~ spl2_981
| ~ spl2_1162 ),
inference(avatar_split_clause,[],[f92575,f91295,f74264,f93196]) ).
fof(f92575,plain,
( ! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1)))
| ~ spl2_981
| ~ spl2_1162 ),
inference(superposition,[],[f74265,f91296]) ).
fof(f92496,plain,
( spl2_1164
| ~ spl2_20
| ~ spl2_32
| ~ spl2_325
| ~ spl2_652 ),
inference(avatar_split_clause,[],[f41791,f36434,f10415,f336,f273,f92494]) ).
fof(f92494,plain,
( spl2_1164
<=> ! [X0,X1] : necessarily(not(equiv(X1,necessarily(possibly(X0))))) = necessarily(not(equiv(necessarily(possibly(X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1164])]) ).
fof(f336,plain,
( spl2_32
<=> ! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f41791,plain,
( ! [X0,X1] : necessarily(not(equiv(X1,necessarily(possibly(X0))))) = necessarily(not(equiv(necessarily(possibly(X0)),X1)))
| ~ spl2_20
| ~ spl2_32
| ~ spl2_325
| ~ spl2_652 ),
inference(forward_demodulation,[],[f41790,f10416]) ).
fof(f41790,plain,
( ! [X0,X1] : necessarily(not(equiv(X1,necessarily(possibly(X0))))) = strict_implies(implies(necessarily(possibly(X0)),X1),and(X1,not(necessarily(possibly(X0)))))
| ~ spl2_20
| ~ spl2_32
| ~ spl2_652 ),
inference(forward_demodulation,[],[f41703,f337]) ).
fof(f337,plain,
( ! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0)))
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f41703,plain,
( ! [X0,X1] : necessarily(not(equiv(X1,necessarily(possibly(X0))))) = strict_implies(implies(necessarily(possibly(X0)),X1),and(X1,possibly(necessarily(not(X0)))))
| ~ spl2_20
| ~ spl2_652 ),
inference(superposition,[],[f36435,f274]) ).
fof(f91301,plain,
( spl2_1163
| ~ spl2_29
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f89000,f88382,f315,f91299]) ).
fof(f89000,plain,
( ! [X114,X115] : implies(X115,not(not(X114))) = implies(X115,X114)
| ~ spl2_29
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f88460,f316]) ).
fof(f88460,plain,
( ! [X114,X115] : implies(X115,not(not(X114))) = not(and(X115,not(X114)))
| ~ spl2_29
| ~ spl2_1121 ),
inference(superposition,[],[f316,f88383]) ).
fof(f91297,plain,
( spl2_1162
| ~ spl2_24
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88939,f88382,f290,f91295]) ).
fof(f91293,plain,
( spl2_1161
| ~ spl2_382
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88415,f88382,f13556,f91291]) ).
fof(f91291,plain,
( spl2_1161
<=> ! [X7,X8] :
( ~ is_a_theorem(necessarily(not(X7)))
| is_a_theorem(strict_implies(X8,not(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1161])]) ).
fof(f13556,plain,
( spl2_382
<=> ! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(not(not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_382])]) ).
fof(f88415,plain,
( ! [X8,X7] :
( ~ is_a_theorem(necessarily(not(X7)))
| is_a_theorem(strict_implies(X8,not(X7))) )
| ~ spl2_382
| ~ spl2_1121 ),
inference(superposition,[],[f13557,f88383]) ).
fof(f13557,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(strict_implies(X1,X0)) )
| ~ spl2_382 ),
inference(avatar_component_clause,[],[f13556]) ).
fof(f91289,plain,
( spl2_1160
| ~ spl2_504
| ~ spl2_508 ),
inference(avatar_split_clause,[],[f25245,f24819,f23260,f91287]) ).
fof(f91287,plain,
( spl2_1160
<=> ! [X240,X243,X242,X241] : and(X240,and(X243,strict_equiv(X241,X242))) = and(X243,and(X240,strict_equiv(X242,X241))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1160])]) ).
fof(f23260,plain,
( spl2_504
<=> ! [X13,X12,X14] : and(X12,and(X13,X14)) = and(X13,and(X12,X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_504])]) ).
fof(f24819,plain,
( spl2_508
<=> ! [X2,X0,X1] : and(X0,strict_equiv(X1,X2)) = and(X0,strict_equiv(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_508])]) ).
fof(f25245,plain,
( ! [X242,X243,X240,X241] : and(X240,and(X243,strict_equiv(X241,X242))) = and(X243,and(X240,strict_equiv(X242,X241)))
| ~ spl2_504
| ~ spl2_508 ),
inference(superposition,[],[f23261,f24820]) ).
fof(f24820,plain,
( ! [X2,X0,X1] : and(X0,strict_equiv(X1,X2)) = and(X0,strict_equiv(X2,X1))
| ~ spl2_508 ),
inference(avatar_component_clause,[],[f24819]) ).
fof(f23261,plain,
( ! [X14,X12,X13] : and(X12,and(X13,X14)) = and(X13,and(X12,X14))
| ~ spl2_504 ),
inference(avatar_component_clause,[],[f23260]) ).
fof(f91285,plain,
( spl2_1159
| ~ spl2_29
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88387,f88382,f315,f91283]) ).
fof(f91283,plain,
( spl2_1159
<=> ! [X2,X3] : implies(X2,X3) = not(not(implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1159])]) ).
fof(f88387,plain,
( ! [X2,X3] : implies(X2,X3) = not(not(implies(X2,X3)))
| ~ spl2_29
| ~ spl2_1121 ),
inference(superposition,[],[f88383,f316]) ).
fof(f91239,plain,
( spl2_1158
| ~ spl2_24
| ~ spl2_955
| ~ spl2_1114
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88998,f88382,f87090,f70384,f290,f91237]) ).
fof(f91237,plain,
( spl2_1158
<=> ! [X11,X12,X13] : is_a_theorem(or(X11,or(X13,implies(X11,X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1158])]) ).
fof(f70384,plain,
( spl2_955
<=> ! [X4,X5] : not(not(X4)) = implies(implies(X4,X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_955])]) ).
fof(f87090,plain,
( spl2_1114
<=> ! [X2,X4,X3] : is_a_theorem(or(implies(X2,X4),or(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1114])]) ).
fof(f88998,plain,
( ! [X11,X12,X13] : is_a_theorem(or(X11,or(X13,implies(X11,X12))))
| ~ spl2_24
| ~ spl2_955
| ~ spl2_1114
| ~ spl2_1121 ),
inference(backward_demodulation,[],[f87148,f88939]) ).
fof(f87148,plain,
( ! [X11,X12,X13] : is_a_theorem(or(not(not(X11)),or(X13,implies(X11,X12))))
| ~ spl2_955
| ~ spl2_1114 ),
inference(superposition,[],[f87091,f70385]) ).
fof(f70385,plain,
( ! [X4,X5] : not(not(X4)) = implies(implies(X4,X5),X4)
| ~ spl2_955 ),
inference(avatar_component_clause,[],[f70384]) ).
fof(f87091,plain,
( ! [X2,X3,X4] : is_a_theorem(or(implies(X2,X4),or(X3,X2)))
| ~ spl2_1114 ),
inference(avatar_component_clause,[],[f87090]) ).
fof(f91235,plain,
( spl2_1157
| ~ spl2_503
| ~ spl2_508 ),
inference(avatar_split_clause,[],[f25169,f24819,f23256,f91233]) ).
fof(f91233,plain,
( spl2_1157
<=> ! [X29,X27,X28,X26] : and(strict_equiv(X27,X26),strict_equiv(X28,X29)) = and(strict_equiv(X26,X27),strict_equiv(X29,X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1157])]) ).
fof(f23256,plain,
( spl2_503
<=> ! [X2,X0,X1] : and(strict_equiv(X0,X1),X2) = and(strict_equiv(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_503])]) ).
fof(f25169,plain,
( ! [X28,X29,X26,X27] : and(strict_equiv(X27,X26),strict_equiv(X28,X29)) = and(strict_equiv(X26,X27),strict_equiv(X29,X28))
| ~ spl2_503
| ~ spl2_508 ),
inference(superposition,[],[f24820,f23257]) ).
fof(f23257,plain,
( ! [X2,X0,X1] : and(strict_equiv(X0,X1),X2) = and(strict_equiv(X1,X0),X2)
| ~ spl2_503 ),
inference(avatar_component_clause,[],[f23256]) ).
fof(f91186,plain,
( spl2_1156
| ~ spl2_24
| ~ spl2_955
| ~ spl2_1111
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88996,f88382,f87033,f70384,f290,f91184]) ).
fof(f91184,plain,
( spl2_1156
<=> ! [X13,X12,X11] : is_a_theorem(or(X11,or(implies(X11,X12),X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1156])]) ).
fof(f87033,plain,
( spl2_1111
<=> ! [X134,X136,X135] : is_a_theorem(or(implies(X134,X135),or(X134,X136))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1111])]) ).
fof(f88996,plain,
( ! [X11,X12,X13] : is_a_theorem(or(X11,or(implies(X11,X12),X13)))
| ~ spl2_24
| ~ spl2_955
| ~ spl2_1111
| ~ spl2_1121 ),
inference(backward_demodulation,[],[f87041,f88939]) ).
fof(f87041,plain,
( ! [X11,X12,X13] : is_a_theorem(or(not(not(X11)),or(implies(X11,X12),X13)))
| ~ spl2_955
| ~ spl2_1111 ),
inference(superposition,[],[f87034,f70385]) ).
fof(f87034,plain,
( ! [X136,X134,X135] : is_a_theorem(or(implies(X134,X135),or(X134,X136)))
| ~ spl2_1111 ),
inference(avatar_component_clause,[],[f87033]) ).
fof(f91027,plain,
( spl2_1155
| ~ spl2_502
| ~ spl2_508 ),
inference(avatar_split_clause,[],[f25165,f24819,f23252,f91025]) ).
fof(f91025,plain,
( spl2_1155
<=> ! [X17,X14,X16,X15] : and(equiv(X15,X14),strict_equiv(X16,X17)) = and(equiv(X14,X15),strict_equiv(X17,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1155])]) ).
fof(f23252,plain,
( spl2_502
<=> ! [X2,X0,X1] : and(equiv(X0,X1),X2) = and(equiv(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_502])]) ).
fof(f25165,plain,
( ! [X16,X14,X17,X15] : and(equiv(X15,X14),strict_equiv(X16,X17)) = and(equiv(X14,X15),strict_equiv(X17,X16))
| ~ spl2_502
| ~ spl2_508 ),
inference(superposition,[],[f24820,f23253]) ).
fof(f23253,plain,
( ! [X2,X0,X1] : and(equiv(X0,X1),X2) = and(equiv(X1,X0),X2)
| ~ spl2_502 ),
inference(avatar_component_clause,[],[f23252]) ).
fof(f91023,plain,
( spl2_1154
| ~ spl2_1133
| ~ spl2_1151 ),
inference(avatar_split_clause,[],[f90986,f90973,f89967,f91021]) ).
fof(f91021,plain,
( spl2_1154
<=> ! [X18,X17] :
( is_a_theorem(X17)
| ~ is_a_theorem(equiv(X17,implies(X17,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1154])]) ).
fof(f89967,plain,
( spl2_1133
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1133])]) ).
fof(f90973,plain,
( spl2_1151
<=> ! [X9,X8] : is_a_theorem(implies(equiv(X8,implies(X8,X9)),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1151])]) ).
fof(f90986,plain,
( ! [X18,X17] :
( is_a_theorem(X17)
| ~ is_a_theorem(equiv(X17,implies(X17,X18))) )
| ~ spl2_1133
| ~ spl2_1151 ),
inference(resolution,[],[f90974,f89968]) ).
fof(f89968,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ spl2_1133 ),
inference(avatar_component_clause,[],[f89967]) ).
fof(f90974,plain,
( ! [X8,X9] : is_a_theorem(implies(equiv(X8,implies(X8,X9)),X8))
| ~ spl2_1151 ),
inference(avatar_component_clause,[],[f90973]) ).
fof(f91019,plain,
( spl2_1153
| ~ spl2_112
| ~ spl2_134
| ~ spl2_1142 ),
inference(avatar_split_clause,[],[f90658,f90587,f2301,f1558,f91017]) ).
fof(f91017,plain,
( spl2_1153
<=> ! [X0] : ~ is_a_theorem(possibly(and(possibly(X0),necessarily(not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1153])]) ).
fof(f1558,plain,
( spl2_112
<=> ! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_112])]) ).
fof(f2301,plain,
( spl2_134
<=> ! [X0,X1] : possibly(and(X1,possibly(X0))) = possibly(and(possibly(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_134])]) ).
fof(f90587,plain,
( spl2_1142
<=> ! [X4] : ~ is_a_theorem(not(strict_implies(X4,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1142])]) ).
fof(f90658,plain,
( ! [X0] : ~ is_a_theorem(possibly(and(possibly(X0),necessarily(not(X0)))))
| ~ spl2_112
| ~ spl2_134
| ~ spl2_1142 ),
inference(forward_demodulation,[],[f90649,f2302]) ).
fof(f2302,plain,
( ! [X0,X1] : possibly(and(X1,possibly(X0))) = possibly(and(possibly(X0),X1))
| ~ spl2_134 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f90649,plain,
( ! [X0] : ~ is_a_theorem(possibly(and(necessarily(not(X0)),possibly(X0))))
| ~ spl2_112
| ~ spl2_1142 ),
inference(superposition,[],[f90588,f1559]) ).
fof(f1559,plain,
( ! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0)))
| ~ spl2_112 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f90588,plain,
( ! [X4] : ~ is_a_theorem(not(strict_implies(X4,X4)))
| ~ spl2_1142 ),
inference(avatar_component_clause,[],[f90587]) ).
fof(f90979,plain,
( spl2_1152
| ~ spl2_504
| ~ spl2_506 ),
inference(avatar_split_clause,[],[f24911,f24811,f23260,f90977]) ).
fof(f90977,plain,
( spl2_1152
<=> ! [X262,X265,X264,X263] : and(X262,and(X265,equiv(X263,X264))) = and(X265,and(X262,equiv(X264,X263))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1152])]) ).
fof(f24811,plain,
( spl2_506
<=> ! [X2,X0,X1] : and(X0,equiv(X1,X2)) = and(X0,equiv(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_506])]) ).
fof(f24911,plain,
( ! [X263,X262,X264,X265] : and(X262,and(X265,equiv(X263,X264))) = and(X265,and(X262,equiv(X264,X263)))
| ~ spl2_504
| ~ spl2_506 ),
inference(superposition,[],[f23261,f24812]) ).
fof(f24812,plain,
( ! [X2,X0,X1] : and(X0,equiv(X1,X2)) = and(X0,equiv(X2,X1))
| ~ spl2_506 ),
inference(avatar_component_clause,[],[f24811]) ).
fof(f90975,plain,
( spl2_1151
| ~ spl2_29
| ~ spl2_512
| ~ spl2_955
| ~ spl2_1001
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f89013,f88382,f75282,f70384,f25503,f315,f90973]) ).
fof(f25503,plain,
( spl2_512
<=> ! [X400,X398,X399] : implies(equiv(X398,X399),X400) = implies(equiv(X399,X398),X400) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_512])]) ).
fof(f75282,plain,
( spl2_1001
<=> ! [X52,X51] : is_a_theorem(implies(equiv(X51,X52),implies(X51,X52))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1001])]) ).
fof(f89013,plain,
( ! [X8,X9] : is_a_theorem(implies(equiv(X8,implies(X8,X9)),X8))
| ~ spl2_29
| ~ spl2_512
| ~ spl2_955
| ~ spl2_1001
| ~ spl2_1121 ),
inference(backward_demodulation,[],[f75435,f89000]) ).
fof(f75435,plain,
( ! [X8,X9] : is_a_theorem(implies(equiv(X8,implies(X8,X9)),not(not(X8))))
| ~ spl2_512
| ~ spl2_955
| ~ spl2_1001 ),
inference(forward_demodulation,[],[f75420,f25504]) ).
fof(f25504,plain,
( ! [X399,X400,X398] : implies(equiv(X398,X399),X400) = implies(equiv(X399,X398),X400)
| ~ spl2_512 ),
inference(avatar_component_clause,[],[f25503]) ).
fof(f75420,plain,
( ! [X8,X9] : is_a_theorem(implies(equiv(implies(X8,X9),X8),not(not(X8))))
| ~ spl2_955
| ~ spl2_1001 ),
inference(superposition,[],[f75283,f70385]) ).
fof(f75283,plain,
( ! [X51,X52] : is_a_theorem(implies(equiv(X51,X52),implies(X51,X52)))
| ~ spl2_1001 ),
inference(avatar_component_clause,[],[f75282]) ).
fof(f90917,plain,
( spl2_1150
| ~ spl2_20
| ~ spl2_1140 ),
inference(avatar_split_clause,[],[f90622,f90579,f273,f90915]) ).
fof(f90915,plain,
( spl2_1150
<=> ! [X33] :
( ~ is_a_theorem(possibly(X33))
| ~ is_a_theorem(necessarily(not(X33))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1150])]) ).
fof(f90622,plain,
( ! [X33] :
( ~ is_a_theorem(possibly(X33))
| ~ is_a_theorem(necessarily(not(X33))) )
| ~ spl2_20
| ~ spl2_1140 ),
inference(superposition,[],[f90580,f274]) ).
fof(f90913,plain,
( spl2_1149
| ~ spl2_503
| ~ spl2_506 ),
inference(avatar_split_clause,[],[f24829,f24811,f23256,f90911]) ).
fof(f90911,plain,
( spl2_1149
<=> ! [X29,X27,X28,X26] : and(strict_equiv(X27,X26),equiv(X28,X29)) = and(strict_equiv(X26,X27),equiv(X29,X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1149])]) ).
fof(f24829,plain,
( ! [X28,X29,X26,X27] : and(strict_equiv(X27,X26),equiv(X28,X29)) = and(strict_equiv(X26,X27),equiv(X29,X28))
| ~ spl2_503
| ~ spl2_506 ),
inference(superposition,[],[f24812,f23257]) ).
fof(f90681,plain,
( spl2_1148
| ~ spl2_76
| ~ spl2_1065
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90523,f90025,f81126,f810,f90679]) ).
fof(f90679,plain,
( spl2_1148
<=> ! [X0] : ~ is_a_theorem(and(possibly(X0),not(possibly(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1148])]) ).
fof(f81126,plain,
( spl2_1065
<=> ! [X3] : possibly(X3) = not(not(possibly(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1065])]) ).
fof(f90025,plain,
( spl2_1136
<=> ! [X11] : ~ is_a_theorem(and(X11,not(X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1136])]) ).
fof(f90523,plain,
( ! [X0] : ~ is_a_theorem(and(possibly(X0),not(possibly(X0))))
| ~ spl2_76
| ~ spl2_1065
| ~ spl2_1136 ),
inference(forward_demodulation,[],[f90036,f811]) ).
fof(f90036,plain,
( ! [X0] : ~ is_a_theorem(and(not(possibly(X0)),possibly(X0)))
| ~ spl2_1065
| ~ spl2_1136 ),
inference(superposition,[],[f90026,f81127]) ).
fof(f81127,plain,
( ! [X3] : possibly(X3) = not(not(possibly(X3)))
| ~ spl2_1065 ),
inference(avatar_component_clause,[],[f81126]) ).
fof(f90026,plain,
( ! [X11] : ~ is_a_theorem(and(X11,not(X11)))
| ~ spl2_1136 ),
inference(avatar_component_clause,[],[f90025]) ).
fof(f90677,plain,
( spl2_1147
| ~ spl2_502
| ~ spl2_506 ),
inference(avatar_split_clause,[],[f24827,f24811,f23252,f90675]) ).
fof(f90675,plain,
( spl2_1147
<=> ! [X18,X19,X20,X21] : and(equiv(X19,X18),equiv(X20,X21)) = and(equiv(X18,X19),equiv(X21,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1147])]) ).
fof(f24827,plain,
( ! [X21,X18,X19,X20] : and(equiv(X19,X18),equiv(X20,X21)) = and(equiv(X18,X19),equiv(X21,X20))
| ~ spl2_502
| ~ spl2_506 ),
inference(superposition,[],[f24812,f23253]) ).
fof(f90673,plain,
( spl2_1146
| ~ spl2_76
| ~ spl2_1121
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90522,f90025,f88382,f810,f90671]) ).
fof(f90671,plain,
( spl2_1146
<=> ! [X1] : ~ is_a_theorem(and(not(X1),not(not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1146])]) ).
fof(f90522,plain,
( ! [X1] : ~ is_a_theorem(and(not(X1),not(not(X1))))
| ~ spl2_76
| ~ spl2_1121
| ~ spl2_1136 ),
inference(forward_demodulation,[],[f90037,f811]) ).
fof(f90037,plain,
( ! [X1] : ~ is_a_theorem(and(not(not(X1)),not(X1)))
| ~ spl2_1121
| ~ spl2_1136 ),
inference(superposition,[],[f90026,f88383]) ).
fof(f90669,plain,
( spl2_1145
| ~ spl2_20
| ~ spl2_76
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90080,f90025,f810,f273,f90667]) ).
fof(f90667,plain,
( spl2_1145
<=> ! [X33] : ~ is_a_theorem(and(possibly(X33),necessarily(not(X33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1145])]) ).
fof(f90080,plain,
( ! [X33] : ~ is_a_theorem(and(possibly(X33),necessarily(not(X33))))
| ~ spl2_20
| ~ spl2_76
| ~ spl2_1136 ),
inference(forward_demodulation,[],[f90048,f811]) ).
fof(f90048,plain,
( ! [X33] : ~ is_a_theorem(and(necessarily(not(X33)),possibly(X33)))
| ~ spl2_20
| ~ spl2_1136 ),
inference(superposition,[],[f90026,f274]) ).
fof(f90665,plain,
( spl2_1144
| ~ spl2_450
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90034,f90025,f16522,f90663]) ).
fof(f90663,plain,
( spl2_1144
<=> ! [X3] : ~ is_a_theorem(not(necessarily(or(X3,not(X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1144])]) ).
fof(f16522,plain,
( spl2_450
<=> ! [X4,X3] :
( is_a_theorem(and(necessarily(or(X3,not(X3))),X4))
| ~ is_a_theorem(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_450])]) ).
fof(f90034,plain,
( ! [X3] : ~ is_a_theorem(not(necessarily(or(X3,not(X3)))))
| ~ spl2_450
| ~ spl2_1136 ),
inference(resolution,[],[f90026,f16523]) ).
fof(f16523,plain,
( ! [X3,X4] :
( is_a_theorem(and(necessarily(or(X3,not(X3))),X4))
| ~ is_a_theorem(X4) )
| ~ spl2_450 ),
inference(avatar_component_clause,[],[f16522]) ).
fof(f90638,plain,
( spl2_1143
| ~ spl2_503
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24173,f23260,f23256,f90636]) ).
fof(f90636,plain,
( spl2_1143
<=> ! [X65,X64,X67,X66] : and(strict_equiv(X64,X65),and(X67,X66)) = and(X67,and(strict_equiv(X65,X64),X66)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1143])]) ).
fof(f24173,plain,
( ! [X65,X66,X67,X64] : and(strict_equiv(X64,X65),and(X67,X66)) = and(X67,and(strict_equiv(X65,X64),X66))
| ~ spl2_503
| ~ spl2_504 ),
inference(superposition,[],[f23261,f23257]) ).
fof(f90589,plain,
( spl2_1142
| ~ spl2_448
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90035,f90025,f16331,f90587]) ).
fof(f16331,plain,
( spl2_448
<=> ! [X0,X1] :
( is_a_theorem(and(strict_implies(X0,X0),X1))
| ~ is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_448])]) ).
fof(f90035,plain,
( ! [X4] : ~ is_a_theorem(not(strict_implies(X4,X4)))
| ~ spl2_448
| ~ spl2_1136 ),
inference(resolution,[],[f90026,f16332]) ).
fof(f16332,plain,
( ! [X0,X1] :
( is_a_theorem(and(strict_implies(X0,X0),X1))
| ~ is_a_theorem(X1) )
| ~ spl2_448 ),
inference(avatar_component_clause,[],[f16331]) ).
fof(f90585,plain,
( spl2_1141
| ~ spl2_34
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24170,f23260,f344,f90583]) ).
fof(f90583,plain,
( spl2_1141
<=> ! [X57,X55,X56] : and(strict_implies(X55,X56),and(X57,strict_implies(X56,X55))) = and(X57,strict_equiv(X55,X56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1141])]) ).
fof(f344,plain,
( spl2_34
<=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f24170,plain,
( ! [X56,X57,X55] : and(strict_implies(X55,X56),and(X57,strict_implies(X56,X55))) = and(X57,strict_equiv(X55,X56))
| ~ spl2_34
| ~ spl2_504 ),
inference(superposition,[],[f23261,f345]) ).
fof(f345,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f90581,plain,
( spl2_1140
| ~ spl2_26
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90032,f90025,f298,f90579]) ).
fof(f298,plain,
( spl2_26
<=> ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f90032,plain,
( ! [X1] :
( ~ is_a_theorem(not(X1))
| ~ is_a_theorem(X1) )
| ~ spl2_26
| ~ spl2_1136 ),
inference(resolution,[],[f90026,f299]) ).
fof(f299,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f90506,plain,
( spl2_2
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90101]) ).
fof(f90101,plain,
( $false
| spl2_2
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f187]) ).
fof(f90029,plain,
( ! [X10] : is_a_theorem(X10)
| ~ spl2_1137 ),
inference(avatar_component_clause,[],[f90028]) ).
fof(f90028,plain,
( spl2_1137
<=> ! [X10] : is_a_theorem(X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1137])]) ).
fof(f90505,plain,
( ~ spl2_1082
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90192]) ).
fof(f90192,plain,
( $false
| ~ spl2_1082
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f83849]) ).
fof(f83849,plain,
( ! [X2,X1] : ~ is_a_theorem(not(implies(implies(X1,X2),implies(X1,X2))))
| ~ spl2_1082 ),
inference(avatar_component_clause,[],[f83848]) ).
fof(f83848,plain,
( spl2_1082
<=> ! [X2,X1] : ~ is_a_theorem(not(implies(implies(X1,X2),implies(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1082])]) ).
fof(f90504,plain,
( ~ spl2_1083
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90201]) ).
fof(f90201,plain,
( $false
| ~ spl2_1083
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f83934]) ).
fof(f83934,plain,
( ! [X16,X17] : ~ is_a_theorem(not(implies(or(X16,X17),or(X16,X17))))
| ~ spl2_1083 ),
inference(avatar_component_clause,[],[f83933]) ).
fof(f83933,plain,
( spl2_1083
<=> ! [X16,X17] : ~ is_a_theorem(not(implies(or(X16,X17),or(X16,X17)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1083])]) ).
fof(f90503,plain,
( ~ spl2_1084
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90202]) ).
fof(f90202,plain,
( $false
| ~ spl2_1084
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f83964]) ).
fof(f83964,plain,
( ! [X0,X1] : ~ is_a_theorem(not(implies(or(X1,X0),or(X0,X1))))
| ~ spl2_1084 ),
inference(avatar_component_clause,[],[f83963]) ).
fof(f83963,plain,
( spl2_1084
<=> ! [X0,X1] : ~ is_a_theorem(not(implies(or(X1,X0),or(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1084])]) ).
fof(f90502,plain,
( ~ spl2_1081
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90204]) ).
fof(f90204,plain,
( $false
| ~ spl2_1081
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f83821]) ).
fof(f83821,plain,
( ! [X0] : ~ is_a_theorem(not(implies(possibly(X0),possibly(X0))))
| ~ spl2_1081 ),
inference(avatar_component_clause,[],[f83820]) ).
fof(f83820,plain,
( spl2_1081
<=> ! [X0] : ~ is_a_theorem(not(implies(possibly(X0),possibly(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1081])]) ).
fof(f90501,plain,
( ~ spl2_1080
| ~ spl2_1137 ),
inference(avatar_contradiction_clause,[],[f90241]) ).
fof(f90241,plain,
( $false
| ~ spl2_1080
| ~ spl2_1137 ),
inference(resolution,[],[f90029,f83674]) ).
fof(f83674,plain,
( ! [X16] : ~ is_a_theorem(not(or(X16,not(X16))))
| ~ spl2_1080 ),
inference(avatar_component_clause,[],[f83673]) ).
fof(f83673,plain,
( spl2_1080
<=> ! [X16] : ~ is_a_theorem(not(or(X16,not(X16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1080])]) ).
fof(f90090,plain,
( spl2_1139
| ~ spl2_549
| ~ spl2_1136 ),
inference(avatar_split_clause,[],[f90031,f90025,f29220,f90088]) ).
fof(f90088,plain,
( spl2_1139
<=> ! [X0] : ~ is_a_theorem(not(implies(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1139])]) ).
fof(f29220,plain,
( spl2_549
<=> ! [X13,X12] :
( ~ is_a_theorem(not(implies(X12,X13)))
| is_a_theorem(and(X12,not(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_549])]) ).
fof(f90031,plain,
( ! [X0] : ~ is_a_theorem(not(implies(X0,X0)))
| ~ spl2_549
| ~ spl2_1136 ),
inference(resolution,[],[f90026,f29221]) ).
fof(f29221,plain,
( ! [X12,X13] :
( is_a_theorem(and(X12,not(X13)))
| ~ is_a_theorem(not(implies(X12,X13))) )
| ~ spl2_549 ),
inference(avatar_component_clause,[],[f29220]) ).
fof(f90086,plain,
( spl2_1138
| ~ spl2_502
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24163,f23260,f23252,f90084]) ).
fof(f90084,plain,
( spl2_1138
<=> ! [X31,X34,X33,X32] : and(equiv(X31,X32),and(X34,X33)) = and(X34,and(equiv(X32,X31),X33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1138])]) ).
fof(f24163,plain,
( ! [X31,X34,X32,X33] : and(equiv(X31,X32),and(X34,X33)) = and(X34,and(equiv(X32,X31),X33))
| ~ spl2_502
| ~ spl2_504 ),
inference(superposition,[],[f23261,f23253]) ).
fof(f90030,plain,
( spl2_1136
| spl2_1137
| ~ spl2_980
| ~ spl2_1133 ),
inference(avatar_split_clause,[],[f89984,f89967,f74183,f90028,f90025]) ).
fof(f89984,plain,
( ! [X10,X11] :
( is_a_theorem(X10)
| ~ is_a_theorem(and(X11,not(X11))) )
| ~ spl2_980
| ~ spl2_1133 ),
inference(resolution,[],[f89968,f74184]) ).
fof(f89977,plain,
( spl2_1135
| ~ spl2_36
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24160,f23260,f363,f89975]) ).
fof(f89975,plain,
( spl2_1135
<=> ! [X22,X24,X23] : and(X24,equiv(X22,X23)) = and(implies(X22,X23),and(X24,implies(X23,X22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1135])]) ).
fof(f363,plain,
( spl2_36
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f24160,plain,
( ! [X24,X22,X23] : and(X24,equiv(X22,X23)) = and(implies(X22,X23),and(X24,implies(X23,X22)))
| ~ spl2_36
| ~ spl2_504 ),
inference(superposition,[],[f23261,f364]) ).
fof(f364,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f89973,plain,
( spl2_1134
| ~ spl2_448
| ~ spl2_1132 ),
inference(avatar_split_clause,[],[f89940,f89934,f16331,f89971]) ).
fof(f89934,plain,
( spl2_1132
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,implies(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1132])]) ).
fof(f89940,plain,
( ! [X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(implies(strict_implies(X7,X7),X6)) )
| ~ spl2_448
| ~ spl2_1132 ),
inference(resolution,[],[f89935,f16332]) ).
fof(f89935,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X1,implies(X1,X0)))
| is_a_theorem(X0) )
| ~ spl2_1132 ),
inference(avatar_component_clause,[],[f89934]) ).
fof(f89969,plain,
( spl2_1133
| ~ spl2_26
| ~ spl2_1132 ),
inference(avatar_split_clause,[],[f89937,f89934,f298,f89967]) ).
fof(f89937,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X1) )
| ~ spl2_26
| ~ spl2_1132 ),
inference(resolution,[],[f89935,f299]) ).
fof(f89936,plain,
( spl2_1132
| ~ spl2_27
| ~ spl2_1130 ),
inference(avatar_split_clause,[],[f89853,f89850,f302,f89934]) ).
fof(f302,plain,
( spl2_27
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f89850,plain,
( spl2_1130
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(X1,implies(X1,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1130])]) ).
fof(f89853,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,implies(X1,X0))) )
| ~ spl2_27
| ~ spl2_1130 ),
inference(resolution,[],[f89851,f303]) ).
fof(f303,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f89851,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X1,implies(X1,X2)),X2))
| ~ spl2_1130 ),
inference(avatar_component_clause,[],[f89850]) ).
fof(f89932,plain,
( spl2_1131
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24158,f23260,f89930]) ).
fof(f89930,plain,
( spl2_1131
<=> ! [X17,X14,X16,X15] : and(X14,and(X17,and(X15,X16))) = and(X17,and(X15,and(X14,X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1131])]) ).
fof(f24158,plain,
( ! [X16,X14,X17,X15] : and(X14,and(X17,and(X15,X16))) = and(X17,and(X15,and(X14,X16)))
| ~ spl2_504 ),
inference(superposition,[],[f23261,f23261]) ).
fof(f89852,plain,
( spl2_1130
| ~ spl2_23
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_962
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88932,f88382,f73027,f33172,f26955,f1122,f814,f315,f286,f89850]) ).
fof(f33172,plain,
( spl2_617
<=> ! [X420,X419,X418] : implies(and(X419,X420),X418) = implies(and(X420,X419),X418) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_617])]) ).
fof(f73027,plain,
( spl2_962
<=> ! [X0] : is_a_theorem(necessarily(not(not(implies(X0,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_962])]) ).
fof(f88932,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X1,implies(X1,X2)),X2))
| ~ spl2_23
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_962
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f88922,f287]) ).
fof(f88922,plain,
( ! [X2,X1] : is_a_theorem(necessarily(implies(and(X1,implies(X1,X2)),X2)))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_962
| ~ spl2_1121 ),
inference(backward_demodulation,[],[f73046,f88387]) ).
fof(f73046,plain,
( ! [X2,X1] : is_a_theorem(necessarily(not(not(implies(and(X1,implies(X1,X2)),X2)))))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_962 ),
inference(forward_demodulation,[],[f73045,f33173]) ).
fof(f33173,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = implies(and(X420,X419),X418)
| ~ spl2_617 ),
inference(avatar_component_clause,[],[f33172]) ).
fof(f73045,plain,
( ! [X2,X1] : is_a_theorem(necessarily(not(not(implies(and(implies(X1,X2),X1),X2)))))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_962 ),
inference(forward_demodulation,[],[f73044,f27370]) ).
fof(f73044,plain,
( ! [X2,X1] : is_a_theorem(necessarily(not(not(not(and(implies(X1,X2),and(X1,not(X2))))))))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_962 ),
inference(forward_demodulation,[],[f73032,f1196]) ).
fof(f1196,plain,
( ! [X2,X3,X4] : not(and(X4,implies(X2,X3))) = not(and(implies(X2,X3),X4))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96 ),
inference(forward_demodulation,[],[f1167,f815]) ).
fof(f1167,plain,
( ! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = not(and(implies(X2,X3),X4))
| ~ spl2_29
| ~ spl2_96 ),
inference(superposition,[],[f1123,f316]) ).
fof(f73032,plain,
( ! [X2,X1] : is_a_theorem(necessarily(not(not(not(and(and(X1,not(X2)),implies(X1,X2)))))))
| ~ spl2_77
| ~ spl2_962 ),
inference(superposition,[],[f73028,f815]) ).
fof(f73028,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(implies(X0,X0)))))
| ~ spl2_962 ),
inference(avatar_component_clause,[],[f73027]) ).
fof(f89822,plain,
( spl2_1129
| ~ spl2_58
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f24129,f23256,f544,f89820]) ).
fof(f89820,plain,
( spl2_1129
<=> ! [X386,X387,X388,X385] : implies(implies(strict_equiv(X385,X386),X387),X388) = implies(implies(strict_equiv(X386,X385),X387),X388) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1129])]) ).
fof(f544,plain,
( spl2_58
<=> ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).
fof(f24129,plain,
( ! [X387,X386,X385,X388] : implies(implies(strict_equiv(X385,X386),X387),X388) = implies(implies(strict_equiv(X386,X385),X387),X388)
| ~ spl2_58
| ~ spl2_503 ),
inference(forward_demodulation,[],[f23826,f545]) ).
fof(f545,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2)
| ~ spl2_58 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f23826,plain,
( ! [X387,X386,X385,X388] : implies(implies(strict_equiv(X385,X386),X387),X388) = or(and(strict_equiv(X386,X385),not(X387)),X388)
| ~ spl2_58
| ~ spl2_503 ),
inference(superposition,[],[f545,f23257]) ).
fof(f89818,plain,
( spl2_1128
| ~ spl2_591
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88439,f88382,f30695,f89816]) ).
fof(f89816,plain,
( spl2_1128
<=> ! [X68,X67] :
( ~ is_a_theorem(not(X67))
| is_a_theorem(implies(X68,not(X67))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1128])]) ).
fof(f88439,plain,
( ! [X68,X67] :
( ~ is_a_theorem(not(X67))
| is_a_theorem(implies(X68,not(X67))) )
| ~ spl2_591
| ~ spl2_1121 ),
inference(superposition,[],[f30696,f88383]) ).
fof(f89788,plain,
( spl2_1127
| ~ spl2_402
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88424,f88382,f14352,f89786]) ).
fof(f89786,plain,
( spl2_1127
<=> ! [X32,X33] :
( ~ is_a_theorem(not(X32))
| is_a_theorem(or(X33,not(X32))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1127])]) ).
fof(f88424,plain,
( ! [X32,X33] :
( ~ is_a_theorem(not(X32))
| is_a_theorem(or(X33,not(X32))) )
| ~ spl2_402
| ~ spl2_1121 ),
inference(superposition,[],[f14353,f88383]) ).
fof(f89758,plain,
( spl2_1126
| ~ spl2_58
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23690,f23252,f544,f89756]) ).
fof(f89756,plain,
( spl2_1126
<=> ! [X407,X406,X405,X404] : implies(implies(equiv(X404,X405),X406),X407) = implies(implies(equiv(X405,X404),X406),X407) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1126])]) ).
fof(f23690,plain,
( ! [X405,X404,X407,X406] : implies(implies(equiv(X404,X405),X406),X407) = implies(implies(equiv(X405,X404),X406),X407)
| ~ spl2_58
| ~ spl2_502 ),
inference(forward_demodulation,[],[f23384,f545]) ).
fof(f23384,plain,
( ! [X405,X404,X407,X406] : implies(implies(equiv(X404,X405),X406),X407) = or(and(equiv(X405,X404),not(X406)),X407)
| ~ spl2_58
| ~ spl2_502 ),
inference(superposition,[],[f545,f23253]) ).
fof(f89754,plain,
( spl2_1125
| ~ spl2_396
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88420,f88382,f14288,f89752]) ).
fof(f89752,plain,
( spl2_1125
<=> ! [X22,X21] :
( ~ is_a_theorem(not(X21))
| is_a_theorem(or(not(X21),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1125])]) ).
fof(f88420,plain,
( ! [X21,X22] :
( ~ is_a_theorem(not(X21))
| is_a_theorem(or(not(X21),X22)) )
| ~ spl2_396
| ~ spl2_1121 ),
inference(superposition,[],[f14289,f88383]) ).
fof(f89684,plain,
( spl2_1124
| ~ spl2_29
| ~ spl2_1036
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f89014,f88382,f76868,f315,f89682]) ).
fof(f89682,plain,
( spl2_1124
<=> ! [X0] : is_a_theorem(implies(equiv(X0,not(X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1124])]) ).
fof(f76868,plain,
( spl2_1036
<=> ! [X0] : is_a_theorem(implies(equiv(X0,not(X0)),not(not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1036])]) ).
fof(f89014,plain,
( ! [X0] : is_a_theorem(implies(equiv(X0,not(X0)),X0))
| ~ spl2_29
| ~ spl2_1036
| ~ spl2_1121 ),
inference(backward_demodulation,[],[f76869,f89000]) ).
fof(f76869,plain,
( ! [X0] : is_a_theorem(implies(equiv(X0,not(X0)),not(not(X0))))
| ~ spl2_1036 ),
inference(avatar_component_clause,[],[f76868]) ).
fof(f89680,plain,
( spl2_1123
| ~ spl2_22
| ~ spl2_434 ),
inference(avatar_split_clause,[],[f18653,f15123,f281,f89678]) ).
fof(f89678,plain,
( spl2_1123
<=> ! [X18,X19] :
( ~ is_a_theorem(or(X18,not(X19)))
| ~ is_a_theorem(or(X19,not(X18)))
| not(X18) = not(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1123])]) ).
fof(f281,plain,
( spl2_22
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f15123,plain,
( spl2_434
<=> ! [X8,X7] :
( is_a_theorem(equiv(not(X7),not(X8)))
| ~ is_a_theorem(or(X8,not(X7)))
| ~ is_a_theorem(or(X7,not(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_434])]) ).
fof(f18653,plain,
( ! [X18,X19] :
( ~ is_a_theorem(or(X18,not(X19)))
| ~ is_a_theorem(or(X19,not(X18)))
| not(X18) = not(X19) )
| ~ spl2_22
| ~ spl2_434 ),
inference(resolution,[],[f15124,f282]) ).
fof(f282,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f15124,plain,
( ! [X8,X7] :
( is_a_theorem(equiv(not(X7),not(X8)))
| ~ is_a_theorem(or(X8,not(X7)))
| ~ is_a_theorem(or(X7,not(X8))) )
| ~ spl2_434 ),
inference(avatar_component_clause,[],[f15123]) ).
fof(f89443,plain,
( spl2_1122
| ~ spl2_20
| ~ spl2_1121 ),
inference(avatar_split_clause,[],[f88938,f88382,f273,f89441]) ).
fof(f89441,plain,
( spl2_1122
<=> ! [X111] : possibly(X111) = possibly(not(not(X111))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1122])]) ).
fof(f88938,plain,
( ! [X111] : possibly(X111) = possibly(not(not(X111)))
| ~ spl2_20
| ~ spl2_1121 ),
inference(forward_demodulation,[],[f88458,f274]) ).
fof(f88458,plain,
( ! [X111] : possibly(not(not(X111))) = not(necessarily(not(X111)))
| ~ spl2_20
| ~ spl2_1121 ),
inference(superposition,[],[f274,f88383]) ).
fof(f88384,plain,
( spl2_1121
| ~ spl2_307
| ~ spl2_311
| ~ spl2_520
| ~ spl2_1063
| ~ spl2_1119 ),
inference(avatar_split_clause,[],[f87905,f87247,f80899,f27681,f9479,f9463,f88382]) ).
fof(f88380,plain,
( spl2_1120
| ~ spl2_76
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f13928,f12444,f810,f88378]) ).
fof(f88378,plain,
( spl2_1120
<=> ! [X2,X4,X3] : necessarily(not(and(X4,or(X2,X3)))) = necessarily(not(and(X4,or(X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1120])]) ).
fof(f12444,plain,
( spl2_371
<=> ! [X2,X0,X1] : strict_implies(X2,and(not(X0),not(X1))) = necessarily(not(and(X2,or(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_371])]) ).
fof(f13928,plain,
( ! [X2,X3,X4] : necessarily(not(and(X4,or(X2,X3)))) = necessarily(not(and(X4,or(X3,X2))))
| ~ spl2_76
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13804,f12445]) ).
fof(f12445,plain,
( ! [X2,X0,X1] : strict_implies(X2,and(not(X0),not(X1))) = necessarily(not(and(X2,or(X0,X1))))
| ~ spl2_371 ),
inference(avatar_component_clause,[],[f12444]) ).
fof(f13804,plain,
( ! [X2,X3,X4] : necessarily(not(and(X4,or(X2,X3)))) = strict_implies(X4,and(not(X3),not(X2)))
| ~ spl2_76
| ~ spl2_371 ),
inference(superposition,[],[f12445,f811]) ).
fof(f87249,plain,
( spl2_1119
| ~ spl2_24
| ~ spl2_96
| ~ spl2_97
| ~ spl2_1102 ),
inference(avatar_split_clause,[],[f86242,f85844,f1233,f1122,f290,f87247]) ).
fof(f1233,plain,
( spl2_97
<=> ! [X2,X3] : or(X2,X3) = or(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).
fof(f85844,plain,
( spl2_1102
<=> ! [X0,X1] : not(X0) = and(not(X0),not(and(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1102])]) ).
fof(f86242,plain,
( ! [X10,X9] : not(not(X9)) = or(X9,and(X9,X10))
| ~ spl2_24
| ~ spl2_96
| ~ spl2_97
| ~ spl2_1102 ),
inference(forward_demodulation,[],[f86241,f1234]) ).
fof(f1234,plain,
( ! [X2,X3] : or(X2,X3) = or(X3,X2)
| ~ spl2_97 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f86241,plain,
( ! [X10,X9] : not(not(X9)) = or(and(X9,X10),X9)
| ~ spl2_24
| ~ spl2_96
| ~ spl2_1102 ),
inference(forward_demodulation,[],[f85938,f291]) ).
fof(f85938,plain,
( ! [X10,X9] : not(not(X9)) = implies(not(and(X9,X10)),X9)
| ~ spl2_96
| ~ spl2_1102 ),
inference(superposition,[],[f1123,f85845]) ).
fof(f85845,plain,
( ! [X0,X1] : not(X0) = and(not(X0),not(and(X0,X1)))
| ~ spl2_1102 ),
inference(avatar_component_clause,[],[f85844]) ).
fof(f87245,plain,
( spl2_1118
| ~ spl2_76
| ~ spl2_370 ),
inference(avatar_split_clause,[],[f13708,f12373,f810,f87243]) ).
fof(f87243,plain,
( spl2_1118
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X2,and(not(X3),not(X4))),not(and(or(X3,X4),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1118])]) ).
fof(f12373,plain,
( spl2_370
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X2,and(not(X0),not(X1))),not(and(X2,or(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_370])]) ).
fof(f13708,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X2,and(not(X3),not(X4))),not(and(or(X3,X4),X2))))
| ~ spl2_76
| ~ spl2_370 ),
inference(superposition,[],[f12374,f811]) ).
fof(f12374,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X2,and(not(X0),not(X1))),not(and(X2,or(X0,X1)))))
| ~ spl2_370 ),
inference(avatar_component_clause,[],[f12373]) ).
fof(f87241,plain,
( spl2_1117
| ~ spl2_388
| ~ spl2_1102 ),
inference(avatar_split_clause,[],[f86025,f85844,f14079,f87239]) ).
fof(f87239,plain,
( spl2_1117
<=> ! [X259,X257,X258] :
( ~ is_a_theorem(not(X257))
| is_a_theorem(implies(and(X257,X258),X259)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1117])]) ).
fof(f14079,plain,
( spl2_388
<=> ! [X9,X11,X10] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(implies(X9,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_388])]) ).
fof(f86025,plain,
( ! [X259,X258,X257] :
( ~ is_a_theorem(not(X257))
| is_a_theorem(implies(and(X257,X258),X259)) )
| ~ spl2_388
| ~ spl2_1102 ),
inference(superposition,[],[f14080,f85845]) ).
fof(f14080,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(implies(X9,X11)) )
| ~ spl2_388 ),
inference(avatar_component_clause,[],[f14079]) ).
fof(f87191,plain,
( spl2_1116
| ~ spl2_97
| ~ spl2_1113 ),
inference(avatar_split_clause,[],[f87096,f87086,f1233,f87189]) ).
fof(f87189,plain,
( spl2_1116
<=> ! [X4,X2,X3] : is_a_theorem(or(or(X3,X2),implies(X2,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1116])]) ).
fof(f87086,plain,
( spl2_1113
<=> ! [X2,X0,X1] : is_a_theorem(or(or(X0,X1),implies(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1113])]) ).
fof(f87096,plain,
( ! [X2,X3,X4] : is_a_theorem(or(or(X3,X2),implies(X2,X4)))
| ~ spl2_97
| ~ spl2_1113 ),
inference(superposition,[],[f87087,f1234]) ).
fof(f87087,plain,
( ! [X2,X0,X1] : is_a_theorem(or(or(X0,X1),implies(X0,X2)))
| ~ spl2_1113 ),
inference(avatar_component_clause,[],[f87086]) ).
fof(f87142,plain,
( spl2_1115
| ~ spl2_72
| ~ spl2_370 ),
inference(avatar_split_clause,[],[f13707,f12373,f748,f87140]) ).
fof(f87140,plain,
( spl2_1115
<=> ! [X0,X1] : is_a_theorem(strict_implies(equiv(or(X0,X1),and(not(X0),not(X1))),not(or(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1115])]) ).
fof(f13707,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(or(X0,X1),and(not(X0),not(X1))),not(or(X0,X1))))
| ~ spl2_72
| ~ spl2_370 ),
inference(superposition,[],[f12374,f749]) ).
fof(f87092,plain,
( spl2_1114
| ~ spl2_97
| ~ spl2_1111 ),
inference(avatar_split_clause,[],[f87054,f87033,f1233,f87090]) ).
fof(f87054,plain,
( ! [X2,X3,X4] : is_a_theorem(or(implies(X2,X4),or(X3,X2)))
| ~ spl2_97
| ~ spl2_1111 ),
inference(superposition,[],[f87034,f1234]) ).
fof(f87088,plain,
( spl2_1113
| ~ spl2_322
| ~ spl2_1111 ),
inference(avatar_split_clause,[],[f87036,f87033,f10110,f87086]) ).
fof(f87036,plain,
( ! [X2,X0,X1] : is_a_theorem(or(or(X0,X1),implies(X0,X2)))
| ~ spl2_322
| ~ spl2_1111 ),
inference(resolution,[],[f87034,f10111]) ).
fof(f87084,plain,
( spl2_1112
| ~ spl2_75
| ~ spl2_370 ),
inference(avatar_split_clause,[],[f13694,f12373,f806,f87082]) ).
fof(f87082,plain,
( spl2_1112
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(equiv(and(not(X3),not(X4)),X2),not(and(X2,or(X3,X4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1112])]) ).
fof(f13694,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(and(not(X3),not(X4)),X2),not(and(X2,or(X3,X4)))))
| ~ spl2_75
| ~ spl2_370 ),
inference(superposition,[],[f12374,f807]) ).
fof(f87035,plain,
( spl2_1111
| ~ spl2_24
| ~ spl2_954
| ~ spl2_1110 ),
inference(avatar_split_clause,[],[f87027,f86951,f69866,f290,f87033]) ).
fof(f86951,plain,
( spl2_1110
<=> ! [X4,X2,X3] : is_a_theorem(or(X2,implies(and(X3,X2),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1110])]) ).
fof(f87027,plain,
( ! [X136,X134,X135] : is_a_theorem(or(implies(X134,X135),or(X134,X136)))
| ~ spl2_24
| ~ spl2_954
| ~ spl2_1110 ),
inference(forward_demodulation,[],[f86993,f291]) ).
fof(f86993,plain,
( ! [X136,X134,X135] : is_a_theorem(or(implies(X134,X135),implies(not(X134),X136)))
| ~ spl2_954
| ~ spl2_1110 ),
inference(superposition,[],[f86952,f69867]) ).
fof(f86952,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,implies(and(X3,X2),X4)))
| ~ spl2_1110 ),
inference(avatar_component_clause,[],[f86951]) ).
fof(f86953,plain,
( spl2_1110
| ~ spl2_76
| ~ spl2_1108 ),
inference(avatar_split_clause,[],[f86869,f86863,f810,f86951]) ).
fof(f86863,plain,
( spl2_1108
<=> ! [X388,X390,X389] : is_a_theorem(or(X388,implies(and(X388,X389),X390))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1108])]) ).
fof(f86869,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,implies(and(X3,X2),X4)))
| ~ spl2_76
| ~ spl2_1108 ),
inference(superposition,[],[f86864,f811]) ).
fof(f86864,plain,
( ! [X390,X389,X388] : is_a_theorem(or(X388,implies(and(X388,X389),X390)))
| ~ spl2_1108 ),
inference(avatar_component_clause,[],[f86863]) ).
fof(f86949,plain,
( spl2_1109
| ~ spl2_76
| ~ spl2_370 ),
inference(avatar_split_clause,[],[f13691,f12373,f810,f86947]) ).
fof(f86947,plain,
( spl2_1109
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(equiv(X4,and(not(X3),not(X2))),not(and(X4,or(X2,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1109])]) ).
fof(f13691,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X4,and(not(X3),not(X2))),not(and(X4,or(X2,X3)))))
| ~ spl2_76
| ~ spl2_370 ),
inference(superposition,[],[f12374,f811]) ).
fof(f86865,plain,
( spl2_1108
| ~ spl2_24
| ~ spl2_1032
| ~ spl2_1102 ),
inference(avatar_split_clause,[],[f86519,f85844,f76852,f290,f86863]) ).
fof(f76852,plain,
( spl2_1032
<=> ! [X134,X136,X135] : is_a_theorem(implies(and(X136,not(X134)),implies(X134,X135))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1032])]) ).
fof(f86519,plain,
( ! [X390,X389,X388] : is_a_theorem(or(X388,implies(and(X388,X389),X390)))
| ~ spl2_24
| ~ spl2_1032
| ~ spl2_1102 ),
inference(forward_demodulation,[],[f86065,f291]) ).
fof(f86065,plain,
( ! [X390,X389,X388] : is_a_theorem(implies(not(X388),implies(and(X388,X389),X390)))
| ~ spl2_1032
| ~ spl2_1102 ),
inference(superposition,[],[f76853,f85845]) ).
fof(f76853,plain,
( ! [X136,X134,X135] : is_a_theorem(implies(and(X136,not(X134)),implies(X134,X135)))
| ~ spl2_1032 ),
inference(avatar_component_clause,[],[f76852]) ).
fof(f86812,plain,
( spl2_1107
| ~ spl2_27
| ~ spl2_370 ),
inference(avatar_split_clause,[],[f13669,f12373,f302,f86810]) ).
fof(f86810,plain,
( spl2_1107
<=> ! [X25,X24,X26] :
( is_a_theorem(not(and(X24,or(X25,X26))))
| ~ is_a_theorem(equiv(X24,and(not(X25),not(X26)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1107])]) ).
fof(f13669,plain,
( ! [X26,X24,X25] :
( is_a_theorem(not(and(X24,or(X25,X26))))
| ~ is_a_theorem(equiv(X24,and(not(X25),not(X26)))) )
| ~ spl2_27
| ~ spl2_370 ),
inference(resolution,[],[f12374,f303]) ).
fof(f86724,plain,
( spl2_1106
| ~ spl2_96
| ~ spl2_1103 ),
inference(avatar_split_clause,[],[f86695,f86624,f1122,f86722]) ).
fof(f86624,plain,
( spl2_1103
<=> ! [X823,X822] : is_a_theorem(or(X822,not(and(X822,X823)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1103])]) ).
fof(f86695,plain,
( ! [X28,X27] : is_a_theorem(or(not(X27),implies(X28,X27)))
| ~ spl2_96
| ~ spl2_1103 ),
inference(superposition,[],[f86625,f1123]) ).
fof(f86625,plain,
( ! [X823,X822] : is_a_theorem(or(X822,not(and(X822,X823))))
| ~ spl2_1103 ),
inference(avatar_component_clause,[],[f86624]) ).
fof(f86720,plain,
( spl2_1105
| ~ spl2_76
| ~ spl2_1103 ),
inference(avatar_split_clause,[],[f86634,f86624,f810,f86718]) ).
fof(f86718,plain,
( spl2_1105
<=> ! [X2,X1] : is_a_theorem(or(X1,not(and(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1105])]) ).
fof(f86634,plain,
( ! [X2,X1] : is_a_theorem(or(X1,not(and(X2,X1))))
| ~ spl2_76
| ~ spl2_1103 ),
inference(superposition,[],[f86625,f811]) ).
fof(f86630,plain,
( spl2_1104
| ~ spl2_49
| ~ spl2_369 ),
inference(avatar_split_clause,[],[f13574,f12259,f470,f86628]) ).
fof(f86628,plain,
( spl2_1104
<=> ! [X11,X10] :
( ~ is_a_theorem(strict_implies(X10,not(X11)))
| ~ is_a_theorem(necessarily(or(X11,X10)))
| is_a_theorem(strict_equiv(X10,not(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1104])]) ).
fof(f470,plain,
( spl2_49
<=> ! [X2,X3] :
( is_a_theorem(strict_equiv(X3,X2))
| ~ is_a_theorem(strict_equiv(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
fof(f12259,plain,
( spl2_369
<=> ! [X9,X8] :
( is_a_theorem(strict_equiv(not(X8),X9))
| ~ is_a_theorem(strict_implies(X9,not(X8)))
| ~ is_a_theorem(necessarily(or(X8,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_369])]) ).
fof(f13574,plain,
( ! [X10,X11] :
( ~ is_a_theorem(strict_implies(X10,not(X11)))
| ~ is_a_theorem(necessarily(or(X11,X10)))
| is_a_theorem(strict_equiv(X10,not(X11))) )
| ~ spl2_49
| ~ spl2_369 ),
inference(resolution,[],[f12260,f471]) ).
fof(f471,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_equiv(X2,X3))
| is_a_theorem(strict_equiv(X3,X2)) )
| ~ spl2_49 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f12260,plain,
( ! [X8,X9] :
( is_a_theorem(strict_equiv(not(X8),X9))
| ~ is_a_theorem(strict_implies(X9,not(X8)))
| ~ is_a_theorem(necessarily(or(X8,X9))) )
| ~ spl2_369 ),
inference(avatar_component_clause,[],[f12259]) ).
fof(f86626,plain,
( spl2_1103
| ~ spl2_24
| ~ spl2_970
| ~ spl2_1102 ),
inference(avatar_split_clause,[],[f86604,f85844,f73788,f290,f86624]) ).
fof(f86604,plain,
( ! [X823,X822] : is_a_theorem(or(X822,not(and(X822,X823))))
| ~ spl2_24
| ~ spl2_970
| ~ spl2_1102 ),
inference(forward_demodulation,[],[f86206,f291]) ).
fof(f86206,plain,
( ! [X823,X822] : is_a_theorem(implies(not(X822),not(and(X822,X823))))
| ~ spl2_970
| ~ spl2_1102 ),
inference(superposition,[],[f73789,f85845]) ).
fof(f85846,plain,
( spl2_1102
| ~ spl2_520
| ~ spl2_1028 ),
inference(avatar_split_clause,[],[f84801,f76361,f27681,f85844]) ).
fof(f76361,plain,
( spl2_1028
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,X1),X0))
| not(X0) = and(not(X0),not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1028])]) ).
fof(f84801,plain,
( ! [X0,X1] : not(X0) = and(not(X0),not(and(X0,X1)))
| ~ spl2_520
| ~ spl2_1028 ),
inference(resolution,[],[f76362,f27682]) ).
fof(f76362,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,X1),X0))
| not(X0) = and(not(X0),not(X1)) )
| ~ spl2_1028 ),
inference(avatar_component_clause,[],[f76361]) ).
fof(f85842,plain,
( spl2_1101
| ~ spl2_20
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_209
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11658,f10415,f4558,f2750,f1852,f340,f286,f273,f85840]) ).
fof(f85840,plain,
( spl2_1101
<=> ! [X0,X1] : necessarily(not(equiv(necessarily(not(X0)),X1))) = necessarily(not(equiv(X1,necessarily(not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1101])]) ).
fof(f2750,plain,
( spl2_161
<=> ! [X9,X11,X10] : strict_implies(X9,and(X10,not(X11))) = necessarily(not(and(X9,implies(X10,X11)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_161])]) ).
fof(f4558,plain,
( spl2_209
<=> ! [X4,X5] : equiv(X4,necessarily(not(X5))) = and(not(and(X4,possibly(X5))),implies(necessarily(not(X5)),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_209])]) ).
fof(f11658,plain,
( ! [X0,X1] : necessarily(not(equiv(necessarily(not(X0)),X1))) = necessarily(not(equiv(X1,necessarily(not(X0)))))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_209
| ~ spl2_325 ),
inference(forward_demodulation,[],[f11589,f4711]) ).
fof(f4711,plain,
( ! [X10,X11] : necessarily(not(equiv(X10,necessarily(not(X11))))) = strict_implies(implies(necessarily(not(X11)),X10),and(X10,possibly(X11)))
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_209 ),
inference(forward_demodulation,[],[f4710,f287]) ).
fof(f4710,plain,
( ! [X10,X11] : necessarily(not(equiv(X10,necessarily(not(X11))))) = necessarily(implies(implies(necessarily(not(X11)),X10),and(X10,possibly(X11))))
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_209 ),
inference(forward_demodulation,[],[f4709,f1853]) ).
fof(f4709,plain,
( ! [X10,X11] : necessarily(not(equiv(X10,necessarily(not(X11))))) = necessarily(or(and(X10,possibly(X11)),and(necessarily(not(X11)),not(X10))))
| ~ spl2_33
| ~ spl2_161
| ~ spl2_209 ),
inference(forward_demodulation,[],[f4603,f341]) ).
fof(f4603,plain,
( ! [X10,X11] : strict_implies(not(and(X10,possibly(X11))),and(necessarily(not(X11)),not(X10))) = necessarily(not(equiv(X10,necessarily(not(X11)))))
| ~ spl2_161
| ~ spl2_209 ),
inference(superposition,[],[f2751,f4559]) ).
fof(f4559,plain,
( ! [X4,X5] : equiv(X4,necessarily(not(X5))) = and(not(and(X4,possibly(X5))),implies(necessarily(not(X5)),X4))
| ~ spl2_209 ),
inference(avatar_component_clause,[],[f4558]) ).
fof(f2751,plain,
( ! [X10,X11,X9] : strict_implies(X9,and(X10,not(X11))) = necessarily(not(and(X9,implies(X10,X11))))
| ~ spl2_161 ),
inference(avatar_component_clause,[],[f2750]) ).
fof(f11589,plain,
( ! [X0,X1] : strict_implies(implies(necessarily(not(X0)),X1),and(X1,possibly(X0))) = necessarily(not(equiv(necessarily(not(X0)),X1)))
| ~ spl2_20
| ~ spl2_325 ),
inference(superposition,[],[f10416,f274]) ).
fof(f85703,plain,
( spl2_1091
| ~ spl2_72
| ~ spl2_1098 ),
inference(avatar_split_clause,[],[f85669,f85642,f748,f85324]) ).
fof(f85324,plain,
( spl2_1091
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(possibly(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1091])]) ).
fof(f85642,plain,
( spl2_1098
<=> ! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(possibly(X0)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1098])]) ).
fof(f85669,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ spl2_72
| ~ spl2_1098 ),
inference(superposition,[],[f85643,f749]) ).
fof(f85643,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(possibly(X0)),X1),X2))
| ~ spl2_1098 ),
inference(avatar_component_clause,[],[f85642]) ).
fof(f85702,plain,
( spl2_1100
| ~ spl2_40
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11610,f10415,f406,f85700]) ).
fof(f85700,plain,
( spl2_1100
<=> ! [X16,X17] : is_a_theorem(strict_implies(strict_equiv(implies(X16,X17),and(X17,not(X16))),necessarily(not(equiv(X16,X17))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1100])]) ).
fof(f406,plain,
( spl2_40
<=> ! [X13,X12] : is_a_theorem(strict_implies(strict_equiv(X12,X13),strict_implies(X12,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
fof(f11610,plain,
( ! [X16,X17] : is_a_theorem(strict_implies(strict_equiv(implies(X16,X17),and(X17,not(X16))),necessarily(not(equiv(X16,X17)))))
| ~ spl2_40
| ~ spl2_325 ),
inference(superposition,[],[f407,f10416]) ).
fof(f407,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(strict_equiv(X12,X13),strict_implies(X12,X13)))
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f85648,plain,
( spl2_1099
| ~ spl2_761
| ~ spl2_1091 ),
inference(avatar_split_clause,[],[f85611,f85324,f49204,f85646]) ).
fof(f85646,plain,
( spl2_1099
<=> ! [X4,X5,X3] : is_a_theorem(implies(and(X3,necessarily(possibly(X4))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1099])]) ).
fof(f49204,plain,
( spl2_761
<=> ! [X4,X5,X3] :
( is_a_theorem(implies(and(X3,X4),X5))
| ~ is_a_theorem(implies(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_761])]) ).
fof(f85611,plain,
( ! [X3,X4,X5] : is_a_theorem(implies(and(X3,necessarily(possibly(X4))),X5))
| ~ spl2_761
| ~ spl2_1091 ),
inference(resolution,[],[f85325,f49205]) ).
fof(f49205,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(implies(X4,X5))
| is_a_theorem(implies(and(X3,X4),X5)) )
| ~ spl2_761 ),
inference(avatar_component_clause,[],[f49204]) ).
fof(f85325,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ spl2_1091 ),
inference(avatar_component_clause,[],[f85324]) ).
fof(f85644,plain,
( spl2_1098
| ~ spl2_791
| ~ spl2_1091 ),
inference(avatar_split_clause,[],[f85610,f85324,f52768,f85642]) ).
fof(f52768,plain,
( spl2_791
<=> ! [X4,X5,X3] :
( is_a_theorem(implies(and(X3,X4),X5))
| ~ is_a_theorem(implies(X3,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_791])]) ).
fof(f85610,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(possibly(X0)),X1),X2))
| ~ spl2_791
| ~ spl2_1091 ),
inference(resolution,[],[f85325,f52769]) ).
fof(f52769,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(implies(X3,X5))
| is_a_theorem(implies(and(X3,X4),X5)) )
| ~ spl2_791 ),
inference(avatar_component_clause,[],[f52768]) ).
fof(f85640,plain,
( spl2_1097
| ~ spl2_27
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11607,f10415,f302,f85638]) ).
fof(f85638,plain,
( spl2_1097
<=> ! [X11,X10] :
( ~ is_a_theorem(necessarily(not(equiv(X10,X11))))
| is_a_theorem(and(X11,not(X10)))
| ~ is_a_theorem(implies(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1097])]) ).
fof(f11607,plain,
( ! [X10,X11] :
( ~ is_a_theorem(necessarily(not(equiv(X10,X11))))
| is_a_theorem(and(X11,not(X10)))
| ~ is_a_theorem(implies(X10,X11)) )
| ~ spl2_27
| ~ spl2_325 ),
inference(superposition,[],[f303,f10416]) ).
fof(f85636,plain,
( spl2_1096
| ~ spl2_24
| ~ spl2_1073
| ~ spl2_1083 ),
inference(avatar_split_clause,[],[f83961,f83933,f83125,f290,f85634]) ).
fof(f85634,plain,
( spl2_1096
<=> ! [X20] : ~ is_a_theorem(not(or(not(X20),not(not(X20))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1096])]) ).
fof(f83125,plain,
( spl2_1073
<=> ! [X0,X1] : not(not(X0)) = or(X0,and(possibly(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1073])]) ).
fof(f83961,plain,
( ! [X20] : ~ is_a_theorem(not(or(not(X20),not(not(X20)))))
| ~ spl2_24
| ~ spl2_1073
| ~ spl2_1083 ),
inference(forward_demodulation,[],[f83943,f291]) ).
fof(f83943,plain,
( ! [X20] : ~ is_a_theorem(not(implies(not(not(X20)),not(not(X20)))))
| ~ spl2_1073
| ~ spl2_1083 ),
inference(superposition,[],[f83934,f83126]) ).
fof(f83126,plain,
( ! [X0,X1] : not(not(X0)) = or(X0,and(possibly(X1),X0))
| ~ spl2_1073 ),
inference(avatar_component_clause,[],[f83125]) ).
fof(f85609,plain,
( spl2_1095
| ~ spl2_23
| ~ spl2_96
| ~ spl2_1090 ),
inference(avatar_split_clause,[],[f85322,f84897,f1122,f286,f85607]) ).
fof(f85607,plain,
( spl2_1095
<=> ! [X38,X37,X39] : is_a_theorem(implies(strict_implies(X38,X37),X39)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1095])]) ).
fof(f84897,plain,
( spl2_1090
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1090])]) ).
fof(f85322,plain,
( ! [X38,X39,X37] : is_a_theorem(implies(strict_implies(X38,X37),X39))
| ~ spl2_23
| ~ spl2_96
| ~ spl2_1090 ),
inference(forward_demodulation,[],[f85289,f287]) ).
fof(f85289,plain,
( ! [X38,X39,X37] : is_a_theorem(implies(necessarily(implies(X38,X37)),X39))
| ~ spl2_96
| ~ spl2_1090 ),
inference(superposition,[],[f84898,f1123]) ).
fof(f84898,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ spl2_1090 ),
inference(avatar_component_clause,[],[f84897]) ).
fof(f85605,plain,
( spl2_1091
| ~ spl2_20
| ~ spl2_1090 ),
inference(avatar_split_clause,[],[f85291,f84897,f273,f85324]) ).
fof(f85291,plain,
( ! [X44,X43] : is_a_theorem(implies(necessarily(possibly(X43)),X44))
| ~ spl2_20
| ~ spl2_1090 ),
inference(superposition,[],[f84898,f274]) ).
fof(f85604,plain,
( spl2_1094
| ~ spl2_33
| ~ spl2_296 ),
inference(avatar_split_clause,[],[f9449,f9368,f340,f85602]) ).
fof(f85602,plain,
( spl2_1094
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,or(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,equiv(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1094])]) ).
fof(f9368,plain,
( spl2_296
<=> ! [X13,X12,X11] :
( is_a_theorem(strict_implies(X11,or(X12,X13)))
| ~ is_a_theorem(strict_implies(X11,equiv(not(X12),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_296])]) ).
fof(f9449,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,or(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,equiv(not(X1),X2)))) )
| ~ spl2_33
| ~ spl2_296 ),
inference(forward_demodulation,[],[f9440,f341]) ).
fof(f9440,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,equiv(not(X1),X2))))
| is_a_theorem(strict_implies(not(X0),or(X1,X2))) )
| ~ spl2_33
| ~ spl2_296 ),
inference(superposition,[],[f9369,f341]) ).
fof(f9369,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(strict_implies(X11,equiv(not(X12),X13)))
| is_a_theorem(strict_implies(X11,or(X12,X13))) )
| ~ spl2_296 ),
inference(avatar_component_clause,[],[f9368]) ).
fof(f85600,plain,
( spl2_1093
| ~ spl2_20
| ~ spl2_38
| ~ spl2_1085 ),
inference(avatar_split_clause,[],[f85428,f84174,f377,f273,f85598]) ).
fof(f85598,plain,
( spl2_1093
<=> ! [X6,X5] : is_a_theorem(possibly(strict_implies(X5,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1093])]) ).
fof(f84174,plain,
( spl2_1085
<=> ! [X0] : is_a_theorem(not(necessarily(possibly(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1085])]) ).
fof(f85428,plain,
( ! [X6,X5] : is_a_theorem(possibly(strict_implies(X5,X6)))
| ~ spl2_20
| ~ spl2_38
| ~ spl2_1085 ),
inference(forward_demodulation,[],[f84528,f274]) ).
fof(f84528,plain,
( ! [X6,X5] : is_a_theorem(not(necessarily(not(strict_implies(X5,X6)))))
| ~ spl2_38
| ~ spl2_1085 ),
inference(superposition,[],[f84175,f378]) ).
fof(f84175,plain,
( ! [X0] : is_a_theorem(not(necessarily(possibly(X0))))
| ~ spl2_1085 ),
inference(avatar_component_clause,[],[f84174]) ).
fof(f85546,plain,
( spl2_1092
| ~ spl2_20
| ~ spl2_1059
| ~ spl2_1086 ),
inference(avatar_split_clause,[],[f84608,f84178,f80219,f273,f85544]) ).
fof(f85544,plain,
( spl2_1092
<=> ! [X14] : is_a_theorem(possibly(not(X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1092])]) ).
fof(f80219,plain,
( spl2_1059
<=> ! [X11,X10] : strict_implies(implies(X10,X11),X10) = necessarily(not(not(X10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1059])]) ).
fof(f84178,plain,
( spl2_1086
<=> ! [X6,X5] : is_a_theorem(not(strict_implies(X5,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1086])]) ).
fof(f84608,plain,
( ! [X14] : is_a_theorem(possibly(not(X14)))
| ~ spl2_20
| ~ spl2_1059
| ~ spl2_1086 ),
inference(forward_demodulation,[],[f84581,f274]) ).
fof(f84581,plain,
( ! [X14] : is_a_theorem(not(necessarily(not(not(X14)))))
| ~ spl2_1059
| ~ spl2_1086 ),
inference(superposition,[],[f84179,f80220]) ).
fof(f80220,plain,
( ! [X10,X11] : strict_implies(implies(X10,X11),X10) = necessarily(not(not(X10)))
| ~ spl2_1059 ),
inference(avatar_component_clause,[],[f80219]) ).
fof(f84179,plain,
( ! [X6,X5] : is_a_theorem(not(strict_implies(X5,X6)))
| ~ spl2_1086 ),
inference(avatar_component_clause,[],[f84178]) ).
fof(f85430,plain,
( spl2_1079
| ~ spl2_955
| ~ spl2_1065
| ~ spl2_1089 ),
inference(avatar_split_clause,[],[f85416,f84733,f81126,f70384,f83670]) ).
fof(f83670,plain,
( spl2_1079
<=> ! [X17] : is_a_theorem(possibly(X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1079])]) ).
fof(f84733,plain,
( spl2_1089
<=> ! [X25,X24] : is_a_theorem(implies(X24,possibly(X25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1089])]) ).
fof(f85416,plain,
( ! [X0] : is_a_theorem(possibly(X0))
| ~ spl2_955
| ~ spl2_1065
| ~ spl2_1089 ),
inference(forward_demodulation,[],[f84883,f81127]) ).
fof(f84883,plain,
( ! [X0] : is_a_theorem(not(not(possibly(X0))))
| ~ spl2_955
| ~ spl2_1089 ),
inference(superposition,[],[f84734,f70385]) ).
fof(f84734,plain,
( ! [X24,X25] : is_a_theorem(implies(X24,possibly(X25)))
| ~ spl2_1089 ),
inference(avatar_component_clause,[],[f84733]) ).
fof(f85415,plain,
( spl2_1079
| ~ spl2_83
| ~ spl2_1065
| ~ spl2_1088 ),
inference(avatar_split_clause,[],[f84800,f84617,f81126,f1024,f83670]) ).
fof(f84617,plain,
( spl2_1088
<=> ! [X22,X23] : is_a_theorem(or(X22,possibly(X23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1088])]) ).
fof(f84800,plain,
( ! [X0] : is_a_theorem(possibly(X0))
| ~ spl2_83
| ~ spl2_1065
| ~ spl2_1088 ),
inference(forward_demodulation,[],[f84788,f81127]) ).
fof(f84788,plain,
( ! [X0] : is_a_theorem(not(not(possibly(X0))))
| ~ spl2_83
| ~ spl2_1088 ),
inference(superposition,[],[f84618,f1025]) ).
fof(f84618,plain,
( ! [X22,X23] : is_a_theorem(or(X22,possibly(X23)))
| ~ spl2_1088 ),
inference(avatar_component_clause,[],[f84617]) ).
fof(f85414,plain,
( spl2_1079
| ~ spl2_521
| ~ spl2_1087 ),
inference(avatar_split_clause,[],[f84738,f84613,f27806,f83670]) ).
fof(f27806,plain,
( spl2_521
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,and(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_521])]) ).
fof(f84613,plain,
( spl2_1087
<=> ! [X20,X21] : is_a_theorem(or(possibly(X20),X21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1087])]) ).
fof(f84738,plain,
( ! [X4] : is_a_theorem(possibly(X4))
| ~ spl2_521
| ~ spl2_1087 ),
inference(resolution,[],[f84614,f27807]) ).
fof(f27807,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,and(X0,X1)))
| is_a_theorem(X0) )
| ~ spl2_521 ),
inference(avatar_component_clause,[],[f27806]) ).
fof(f84614,plain,
( ! [X21,X20] : is_a_theorem(or(possibly(X20),X21))
| ~ spl2_1087 ),
inference(avatar_component_clause,[],[f84613]) ).
fof(f85326,plain,
( spl2_1091
| ~ spl2_362
| ~ spl2_1085 ),
inference(avatar_split_clause,[],[f84503,f84174,f12231,f85324]) ).
fof(f12231,plain,
( spl2_362
<=> ! [X0,X1] :
( is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(not(necessarily(possibly(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_362])]) ).
fof(f84503,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ spl2_362
| ~ spl2_1085 ),
inference(resolution,[],[f84175,f12232]) ).
fof(f12232,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(necessarily(possibly(X0))))
| is_a_theorem(implies(necessarily(possibly(X0)),X1)) )
| ~ spl2_362 ),
inference(avatar_component_clause,[],[f12231]) ).
fof(f84913,plain,
( spl2_1079
| ~ spl2_955
| ~ spl2_1065
| ~ spl2_1089 ),
inference(avatar_split_clause,[],[f84895,f84733,f81126,f70384,f83670]) ).
fof(f84895,plain,
( ! [X0] : is_a_theorem(possibly(X0))
| ~ spl2_955
| ~ spl2_1065
| ~ spl2_1089 ),
inference(forward_demodulation,[],[f84883,f81127]) ).
fof(f84899,plain,
( spl2_1090
| ~ spl2_336
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84146,f83670,f11086,f84897]) ).
fof(f11086,plain,
( spl2_336
<=> ! [X9,X10] :
( is_a_theorem(implies(necessarily(not(X9)),X10))
| ~ is_a_theorem(possibly(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_336])]) ).
fof(f84146,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ spl2_336
| ~ spl2_1079 ),
inference(resolution,[],[f83671,f11087]) ).
fof(f11087,plain,
( ! [X10,X9] :
( ~ is_a_theorem(possibly(X9))
| is_a_theorem(implies(necessarily(not(X9)),X10)) )
| ~ spl2_336 ),
inference(avatar_component_clause,[],[f11086]) ).
fof(f83671,plain,
( ! [X17] : is_a_theorem(possibly(X17))
| ~ spl2_1079 ),
inference(avatar_component_clause,[],[f83670]) ).
fof(f84735,plain,
( spl2_1089
| ~ spl2_1068
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84158,f83670,f82422,f84733]) ).
fof(f82422,plain,
( spl2_1068
<=> ! [X70,X69] :
( ~ is_a_theorem(possibly(X69))
| is_a_theorem(implies(X70,possibly(X69))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1068])]) ).
fof(f84158,plain,
( ! [X24,X25] : is_a_theorem(implies(X24,possibly(X25)))
| ~ spl2_1068
| ~ spl2_1079 ),
inference(resolution,[],[f83671,f82423]) ).
fof(f82423,plain,
( ! [X70,X69] :
( ~ is_a_theorem(possibly(X69))
| is_a_theorem(implies(X70,possibly(X69))) )
| ~ spl2_1068 ),
inference(avatar_component_clause,[],[f82422]) ).
fof(f84619,plain,
( spl2_1088
| ~ spl2_1067
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84157,f83670,f82418,f84617]) ).
fof(f82418,plain,
( spl2_1067
<=> ! [X32,X33] :
( ~ is_a_theorem(possibly(X32))
| is_a_theorem(or(X33,possibly(X32))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1067])]) ).
fof(f84157,plain,
( ! [X22,X23] : is_a_theorem(or(X22,possibly(X23)))
| ~ spl2_1067
| ~ spl2_1079 ),
inference(resolution,[],[f83671,f82419]) ).
fof(f82419,plain,
( ! [X32,X33] :
( ~ is_a_theorem(possibly(X32))
| is_a_theorem(or(X33,possibly(X32))) )
| ~ spl2_1067 ),
inference(avatar_component_clause,[],[f82418]) ).
fof(f84615,plain,
( spl2_1087
| ~ spl2_1066
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84156,f83670,f82414,f84613]) ).
fof(f82414,plain,
( spl2_1066
<=> ! [X22,X21] :
( ~ is_a_theorem(possibly(X21))
| is_a_theorem(or(possibly(X21),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1066])]) ).
fof(f84156,plain,
( ! [X21,X20] : is_a_theorem(or(possibly(X20),X21))
| ~ spl2_1066
| ~ spl2_1079 ),
inference(resolution,[],[f83671,f82415]) ).
fof(f82415,plain,
( ! [X21,X22] :
( ~ is_a_theorem(possibly(X21))
| is_a_theorem(or(possibly(X21),X22)) )
| ~ spl2_1066 ),
inference(avatar_component_clause,[],[f82414]) ).
fof(f84180,plain,
( spl2_1086
| ~ spl2_38
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84162,f83670,f377,f84178]) ).
fof(f84162,plain,
( ! [X6,X5] : is_a_theorem(not(strict_implies(X5,X6)))
| ~ spl2_38
| ~ spl2_1079 ),
inference(superposition,[],[f83671,f378]) ).
fof(f84176,plain,
( spl2_1085
| ~ spl2_32
| ~ spl2_1079 ),
inference(avatar_split_clause,[],[f84159,f83670,f336,f84174]) ).
fof(f84159,plain,
( ! [X0] : is_a_theorem(not(necessarily(possibly(X0))))
| ~ spl2_32
| ~ spl2_1079 ),
inference(superposition,[],[f83671,f337]) ).
fof(f83965,plain,
( spl2_1084
| ~ spl2_318
| ~ spl2_1083 ),
inference(avatar_split_clause,[],[f83958,f83933,f9826,f83963]) ).
fof(f9826,plain,
( spl2_318
<=> ! [X4,X5,X3] : implies(or(X4,X3),X5) = implies(or(X3,X4),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_318])]) ).
fof(f83958,plain,
( ! [X0,X1] : ~ is_a_theorem(not(implies(or(X1,X0),or(X0,X1))))
| ~ spl2_318
| ~ spl2_1083 ),
inference(superposition,[],[f83934,f9827]) ).
fof(f9827,plain,
( ! [X3,X4,X5] : implies(or(X4,X3),X5) = implies(or(X3,X4),X5)
| ~ spl2_318 ),
inference(avatar_component_clause,[],[f9826]) ).
fof(f83935,plain,
( spl2_1083
| ~ spl2_24
| ~ spl2_1082 ),
inference(avatar_split_clause,[],[f83919,f83848,f290,f83933]) ).
fof(f83919,plain,
( ! [X16,X17] : ~ is_a_theorem(not(implies(or(X16,X17),or(X16,X17))))
| ~ spl2_24
| ~ spl2_1082 ),
inference(superposition,[],[f83849,f291]) ).
fof(f83850,plain,
( spl2_1082
| ~ spl2_29
| ~ spl2_58
| ~ spl2_1080 ),
inference(avatar_split_clause,[],[f83710,f83673,f544,f315,f83848]) ).
fof(f83710,plain,
( ! [X2,X1] : ~ is_a_theorem(not(implies(implies(X1,X2),implies(X1,X2))))
| ~ spl2_29
| ~ spl2_58
| ~ spl2_1080 ),
inference(forward_demodulation,[],[f83677,f545]) ).
fof(f83677,plain,
( ! [X2,X1] : ~ is_a_theorem(not(or(and(X1,not(X2)),implies(X1,X2))))
| ~ spl2_29
| ~ spl2_1080 ),
inference(superposition,[],[f83674,f316]) ).
fof(f83822,plain,
( spl2_1081
| ~ spl2_24
| ~ spl2_1065
| ~ spl2_1080 ),
inference(avatar_split_clause,[],[f83709,f83673,f81126,f290,f83820]) ).
fof(f83709,plain,
( ! [X0] : ~ is_a_theorem(not(implies(possibly(X0),possibly(X0))))
| ~ spl2_24
| ~ spl2_1065
| ~ spl2_1080 ),
inference(forward_demodulation,[],[f83676,f81394]) ).
fof(f81394,plain,
( ! [X136,X137] : or(not(possibly(X136)),X137) = implies(possibly(X136),X137)
| ~ spl2_24
| ~ spl2_1065 ),
inference(superposition,[],[f291,f81127]) ).
fof(f83676,plain,
( ! [X0] : ~ is_a_theorem(not(or(not(possibly(X0)),possibly(X0))))
| ~ spl2_1065
| ~ spl2_1080 ),
inference(superposition,[],[f83674,f81127]) ).
fof(f83675,plain,
( spl2_1079
| spl2_1080
| ~ spl2_24
| ~ spl2_97
| ~ spl2_884
| ~ spl2_1073 ),
inference(avatar_split_clause,[],[f83588,f83125,f62610,f1233,f290,f83673,f83670]) ).
fof(f62610,plain,
( spl2_884
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(X1,and(X0,X2)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_884])]) ).
fof(f83588,plain,
( ! [X16,X17] :
( ~ is_a_theorem(not(or(X16,not(X16))))
| is_a_theorem(possibly(X17)) )
| ~ spl2_24
| ~ spl2_97
| ~ spl2_884
| ~ spl2_1073 ),
inference(forward_demodulation,[],[f83587,f1234]) ).
fof(f83587,plain,
( ! [X16,X17] :
( ~ is_a_theorem(not(or(not(X16),X16)))
| is_a_theorem(possibly(X17)) )
| ~ spl2_24
| ~ spl2_884
| ~ spl2_1073 ),
inference(forward_demodulation,[],[f83383,f291]) ).
fof(f83383,plain,
( ! [X16,X17] :
( ~ is_a_theorem(not(implies(not(not(X16)),X16)))
| is_a_theorem(possibly(X17)) )
| ~ spl2_884
| ~ spl2_1073 ),
inference(superposition,[],[f62611,f83126]) ).
fof(f62611,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(or(X1,and(X0,X2)),X1)))
| is_a_theorem(X0) )
| ~ spl2_884 ),
inference(avatar_component_clause,[],[f62610]) ).
fof(f83328,plain,
( spl2_1078
| ~ spl2_27
| ~ spl2_1060 ),
inference(avatar_split_clause,[],[f80800,f80450,f302,f83326]) ).
fof(f83326,plain,
( spl2_1078
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(not(not(X0)))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1078])]) ).
fof(f80450,plain,
( spl2_1060
<=> ! [X102,X103] : is_a_theorem(strict_implies(and(not(not(not(not(X102)))),X103),X102)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1060])]) ).
fof(f80800,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(not(not(X0)))),X1)) )
| ~ spl2_27
| ~ spl2_1060 ),
inference(resolution,[],[f80451,f303]) ).
fof(f80451,plain,
( ! [X102,X103] : is_a_theorem(strict_implies(and(not(not(not(not(X102)))),X103),X102))
| ~ spl2_1060 ),
inference(avatar_component_clause,[],[f80450]) ).
fof(f83214,plain,
( spl2_1077
| ~ spl2_249
| ~ spl2_954
| ~ spl2_1059 ),
inference(avatar_split_clause,[],[f80676,f80219,f69866,f6955,f83212]) ).
fof(f6955,plain,
( spl2_249
<=> ! [X2,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(and(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_249])]) ).
fof(f80676,plain,
( ! [X76] :
( ~ is_a_theorem(not(X76))
| ~ is_a_theorem(necessarily(not(not(X76))))
| is_a_theorem(X76) )
| ~ spl2_249
| ~ spl2_954
| ~ spl2_1059 ),
inference(forward_demodulation,[],[f80552,f69867]) ).
fof(f80552,plain,
( ! [X76,X77] :
( ~ is_a_theorem(necessarily(not(not(X76))))
| is_a_theorem(X76)
| ~ is_a_theorem(and(not(X76),implies(X76,X77))) )
| ~ spl2_249
| ~ spl2_1059 ),
inference(superposition,[],[f6956,f80220]) ).
fof(f6956,plain,
( ! [X2,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(and(not(X1),X2)) )
| ~ spl2_249 ),
inference(avatar_component_clause,[],[f6955]) ).
fof(f83210,plain,
( spl2_1076
| ~ spl2_665
| ~ spl2_1055 ),
inference(avatar_split_clause,[],[f79549,f79232,f37546,f83208]) ).
fof(f83208,plain,
( spl2_1076
<=> ! [X36,X37] : is_a_theorem(strict_implies(and(X36,not(not(not(not(X37))))),X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1076])]) ).
fof(f37546,plain,
( spl2_665
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(X2,not(not(X1))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_665])]) ).
fof(f79232,plain,
( spl2_1055
<=> ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X6,not(not(X7))))
| is_a_theorem(strict_implies(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1055])]) ).
fof(f79549,plain,
( ! [X36,X37] : is_a_theorem(strict_implies(and(X36,not(not(not(not(X37))))),X37))
| ~ spl2_665
| ~ spl2_1055 ),
inference(resolution,[],[f79233,f37547]) ).
fof(f37547,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X2,not(not(X1))),X1))
| ~ spl2_665 ),
inference(avatar_component_clause,[],[f37546]) ).
fof(f79233,plain,
( ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X6,not(not(X7))))
| is_a_theorem(strict_implies(X6,X7)) )
| ~ spl2_1055 ),
inference(avatar_component_clause,[],[f79232]) ).
fof(f83206,plain,
( spl2_1075
| ~ spl2_24
| ~ spl2_956 ),
inference(avatar_split_clause,[],[f70837,f70388,f290,f83204]) ).
fof(f83204,plain,
( spl2_1075
<=> ! [X22,X24,X23] : is_a_theorem(necessarily(or(or(X22,X23),or(not(X22),X24)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1075])]) ).
fof(f70388,plain,
( spl2_956
<=> ! [X29,X30,X31] : is_a_theorem(necessarily(or(implies(X29,X30),or(X29,X31)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_956])]) ).
fof(f70837,plain,
( ! [X24,X22,X23] : is_a_theorem(necessarily(or(or(X22,X23),or(not(X22),X24))))
| ~ spl2_24
| ~ spl2_956 ),
inference(superposition,[],[f70389,f291]) ).
fof(f70389,plain,
( ! [X31,X29,X30] : is_a_theorem(necessarily(or(implies(X29,X30),or(X29,X31))))
| ~ spl2_956 ),
inference(avatar_component_clause,[],[f70388]) ).
fof(f83131,plain,
( spl2_1074
| ~ spl2_44
| ~ spl2_655
| ~ spl2_955 ),
inference(avatar_split_clause,[],[f70667,f70384,f37077,f440,f83129]) ).
fof(f83129,plain,
( spl2_1074
<=> ! [X20,X21] : is_a_theorem(strict_implies(equiv(X20,implies(X20,X21)),not(not(X20)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1074])]) ).
fof(f440,plain,
( spl2_44
<=> ! [X13,X12] : is_a_theorem(strict_implies(equiv(X12,X13),implies(X12,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
fof(f37077,plain,
( spl2_655
<=> ! [X420,X419,X421] : strict_implies(equiv(X419,X420),X421) = strict_implies(equiv(X420,X419),X421) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_655])]) ).
fof(f70667,plain,
( ! [X21,X20] : is_a_theorem(strict_implies(equiv(X20,implies(X20,X21)),not(not(X20))))
| ~ spl2_44
| ~ spl2_655
| ~ spl2_955 ),
inference(forward_demodulation,[],[f70487,f37078]) ).
fof(f37078,plain,
( ! [X421,X420,X419] : strict_implies(equiv(X419,X420),X421) = strict_implies(equiv(X420,X419),X421)
| ~ spl2_655 ),
inference(avatar_component_clause,[],[f37077]) ).
fof(f70487,plain,
( ! [X21,X20] : is_a_theorem(strict_implies(equiv(implies(X20,X21),X20),not(not(X20))))
| ~ spl2_44
| ~ spl2_955 ),
inference(superposition,[],[f441,f70385]) ).
fof(f441,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(equiv(X12,X13),implies(X12,X13)))
| ~ spl2_44 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f83127,plain,
( spl2_1073
| ~ spl2_20
| ~ spl2_24
| ~ spl2_54
| ~ spl2_311
| ~ spl2_955 ),
inference(avatar_split_clause,[],[f70613,f70384,f9479,f505,f290,f273,f83125]) ).
fof(f70613,plain,
( ! [X0,X1] : not(not(X0)) = or(X0,and(possibly(X1),X0))
| ~ spl2_20
| ~ spl2_24
| ~ spl2_54
| ~ spl2_311
| ~ spl2_955 ),
inference(forward_demodulation,[],[f70612,f13032]) ).
fof(f13032,plain,
( ! [X2,X0,X1] : or(and(X1,possibly(X0)),X2) = or(X2,and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_24
| ~ spl2_54
| ~ spl2_311 ),
inference(forward_demodulation,[],[f13031,f291]) ).
fof(f13031,plain,
( ! [X2,X0,X1] : implies(not(and(X1,possibly(X0))),X2) = or(X2,and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_54
| ~ spl2_311 ),
inference(forward_demodulation,[],[f12940,f506]) ).
fof(f12940,plain,
( ! [X2,X0,X1] : implies(implies(X1,necessarily(not(X0))),X2) = or(X2,and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_311 ),
inference(superposition,[],[f9480,f274]) ).
fof(f70612,plain,
( ! [X0,X1] : not(not(X0)) = or(and(X0,possibly(X1)),X0)
| ~ spl2_24
| ~ spl2_54
| ~ spl2_955 ),
inference(forward_demodulation,[],[f70458,f291]) ).
fof(f70458,plain,
( ! [X0,X1] : not(not(X0)) = implies(not(and(X0,possibly(X1))),X0)
| ~ spl2_54
| ~ spl2_955 ),
inference(superposition,[],[f70385,f506]) ).
fof(f82906,plain,
( spl2_1072
| ~ spl2_983
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81796,f81126,f74343,f82904]) ).
fof(f82904,plain,
( spl2_1072
<=> ! [X1141,X1142] : is_a_theorem(or(possibly(X1141),or(X1142,not(possibly(X1141))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1072])]) ).
fof(f81796,plain,
( ! [X1141,X1142] : is_a_theorem(or(possibly(X1141),or(X1142,not(possibly(X1141)))))
| ~ spl2_983
| ~ spl2_1065 ),
inference(superposition,[],[f74344,f81127]) ).
fof(f82564,plain,
( spl2_1071
| ~ spl2_20
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81393,f81126,f273,f82562]) ).
fof(f82562,plain,
( spl2_1071
<=> ! [X135] : possibly(not(possibly(X135))) = not(necessarily(possibly(X135))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1071])]) ).
fof(f81393,plain,
( ! [X135] : possibly(not(possibly(X135))) = not(necessarily(possibly(X135)))
| ~ spl2_20
| ~ spl2_1065 ),
inference(superposition,[],[f274,f81127]) ).
fof(f82560,plain,
( spl2_1070
| ~ spl2_433
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81353,f81126,f15091,f82558]) ).
fof(f82558,plain,
( spl2_1070
<=> ! [X50,X51] :
( ~ is_a_theorem(possibly(X50))
| is_a_theorem(implies(possibly(X51),possibly(X50))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1070])]) ).
fof(f15091,plain,
( spl2_433
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(implies(possibly(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_433])]) ).
fof(f81353,plain,
( ! [X50,X51] :
( ~ is_a_theorem(possibly(X50))
| is_a_theorem(implies(possibly(X51),possibly(X50))) )
| ~ spl2_433
| ~ spl2_1065 ),
inference(superposition,[],[f15092,f81127]) ).
fof(f15092,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(implies(possibly(X1),X0)) )
| ~ spl2_433 ),
inference(avatar_component_clause,[],[f15091]) ).
fof(f82556,plain,
( spl2_1069
| ~ spl2_382
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81337,f81126,f13556,f82554]) ).
fof(f82554,plain,
( spl2_1069
<=> ! [X7,X8] :
( ~ is_a_theorem(necessarily(possibly(X7)))
| is_a_theorem(strict_implies(X8,possibly(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1069])]) ).
fof(f81337,plain,
( ! [X8,X7] :
( ~ is_a_theorem(necessarily(possibly(X7)))
| is_a_theorem(strict_implies(X8,possibly(X7))) )
| ~ spl2_382
| ~ spl2_1065 ),
inference(superposition,[],[f13557,f81127]) ).
fof(f82424,plain,
( spl2_1068
| ~ spl2_591
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81362,f81126,f30695,f82422]) ).
fof(f81362,plain,
( ! [X70,X69] :
( ~ is_a_theorem(possibly(X69))
| is_a_theorem(implies(X70,possibly(X69))) )
| ~ spl2_591
| ~ spl2_1065 ),
inference(superposition,[],[f30696,f81127]) ).
fof(f82420,plain,
( spl2_1067
| ~ spl2_402
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81346,f81126,f14352,f82418]) ).
fof(f81346,plain,
( ! [X32,X33] :
( ~ is_a_theorem(possibly(X32))
| is_a_theorem(or(X33,possibly(X32))) )
| ~ spl2_402
| ~ spl2_1065 ),
inference(superposition,[],[f14353,f81127]) ).
fof(f82416,plain,
( spl2_1066
| ~ spl2_396
| ~ spl2_1065 ),
inference(avatar_split_clause,[],[f81342,f81126,f14288,f82414]) ).
fof(f81342,plain,
( ! [X21,X22] :
( ~ is_a_theorem(possibly(X21))
| is_a_theorem(or(possibly(X21),X22)) )
| ~ spl2_396
| ~ spl2_1065 ),
inference(superposition,[],[f14289,f81127]) ).
fof(f81128,plain,
( spl2_1065
| ~ spl2_73
| ~ spl2_97
| ~ spl2_307
| ~ spl2_1064 ),
inference(avatar_split_clause,[],[f81055,f81028,f9463,f1233,f780,f81126]) ).
fof(f780,plain,
( spl2_73
<=> ! [X0] : is_a_theorem(necessarily(or(X0,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_73])]) ).
fof(f81028,plain,
( spl2_1064
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),not(not(possibly(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1064])]) ).
fof(f81055,plain,
( ! [X3] : possibly(X3) = not(not(possibly(X3)))
| ~ spl2_73
| ~ spl2_97
| ~ spl2_307
| ~ spl2_1064 ),
inference(subsumption_resolution,[],[f81054,f781]) ).
fof(f781,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(X0))))
| ~ spl2_73 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f81054,plain,
( ! [X3] :
( ~ is_a_theorem(necessarily(or(possibly(X3),not(possibly(X3)))))
| possibly(X3) = not(not(possibly(X3))) )
| ~ spl2_97
| ~ spl2_307
| ~ spl2_1064 ),
inference(forward_demodulation,[],[f81033,f1234]) ).
fof(f81033,plain,
( ! [X3] :
( ~ is_a_theorem(necessarily(or(not(possibly(X3)),possibly(X3))))
| possibly(X3) = not(not(possibly(X3))) )
| ~ spl2_307
| ~ spl2_1064 ),
inference(resolution,[],[f81029,f9464]) ).
fof(f81029,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),not(not(possibly(X0)))))
| ~ spl2_1064 ),
inference(avatar_component_clause,[],[f81028]) ).
fof(f81030,plain,
( spl2_1064
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1063 ),
inference(avatar_split_clause,[],[f80936,f80899,f373,f286,f273,f81028]) ).
fof(f80936,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),not(not(possibly(X0)))))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_1063 ),
inference(forward_demodulation,[],[f80935,f287]) ).
fof(f80935,plain,
( ! [X0] : is_a_theorem(necessarily(implies(possibly(X0),not(not(possibly(X0))))))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_1063 ),
inference(forward_demodulation,[],[f80903,f374]) ).
fof(f80903,plain,
( ! [X0] : is_a_theorem(necessarily(or(necessarily(not(X0)),not(not(possibly(X0))))))
| ~ spl2_20
| ~ spl2_1063 ),
inference(superposition,[],[f80900,f274]) ).
fof(f80901,plain,
( spl2_1063
| ~ spl2_33
| ~ spl2_97
| ~ spl2_954
| ~ spl2_1060 ),
inference(avatar_split_clause,[],[f80888,f80450,f69866,f1233,f340,f80899]) ).
fof(f80888,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(not(not(X0))))))
| ~ spl2_33
| ~ spl2_97
| ~ spl2_954
| ~ spl2_1060 ),
inference(forward_demodulation,[],[f80887,f1234]) ).
fof(f80887,plain,
( ! [X0] : is_a_theorem(necessarily(or(not(not(not(X0))),X0)))
| ~ spl2_33
| ~ spl2_954
| ~ spl2_1060 ),
inference(forward_demodulation,[],[f80857,f341]) ).
fof(f80857,plain,
( ! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0))
| ~ spl2_954
| ~ spl2_1060 ),
inference(superposition,[],[f80451,f69867]) ).
fof(f80460,plain,
( spl2_1062
| ~ spl2_97
| ~ spl2_1058 ),
inference(avatar_split_clause,[],[f80203,f79529,f1233,f80458]) ).
fof(f80458,plain,
( spl2_1062
<=> ! [X6,X5] : is_a_theorem(necessarily(or(strict_implies(X6,X6),not(strict_equiv(X5,X6))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1062])]) ).
fof(f79529,plain,
( spl2_1058
<=> ! [X52,X53] : is_a_theorem(necessarily(or(not(strict_equiv(X52,X53)),strict_implies(X53,X53)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1058])]) ).
fof(f80203,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(strict_implies(X6,X6),not(strict_equiv(X5,X6)))))
| ~ spl2_97
| ~ spl2_1058 ),
inference(superposition,[],[f79530,f1234]) ).
fof(f79530,plain,
( ! [X52,X53] : is_a_theorem(necessarily(or(not(strict_equiv(X52,X53)),strict_implies(X53,X53))))
| ~ spl2_1058 ),
inference(avatar_component_clause,[],[f79529]) ).
fof(f80456,plain,
( spl2_1061
| ~ spl2_97
| ~ spl2_1057 ),
inference(avatar_split_clause,[],[f80172,f79525,f1233,f80454]) ).
fof(f80454,plain,
( spl2_1061
<=> ! [X6,X5] : is_a_theorem(necessarily(or(strict_implies(X5,X5),not(strict_equiv(X5,X6))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1061])]) ).
fof(f79525,plain,
( spl2_1057
<=> ! [X59,X58] : is_a_theorem(necessarily(or(not(strict_equiv(X58,X59)),strict_implies(X58,X58)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1057])]) ).
fof(f80172,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(strict_implies(X5,X5),not(strict_equiv(X5,X6)))))
| ~ spl2_97
| ~ spl2_1057 ),
inference(superposition,[],[f79526,f1234]) ).
fof(f79526,plain,
( ! [X58,X59] : is_a_theorem(necessarily(or(not(strict_equiv(X58,X59)),strict_implies(X58,X58))))
| ~ spl2_1057 ),
inference(avatar_component_clause,[],[f79525]) ).
fof(f80452,plain,
( spl2_1060
| ~ spl2_663
| ~ spl2_1055 ),
inference(avatar_split_clause,[],[f79571,f79232,f37227,f80450]) ).
fof(f37227,plain,
( spl2_663
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_663])]) ).
fof(f79571,plain,
( ! [X102,X103] : is_a_theorem(strict_implies(and(not(not(not(not(X102)))),X103),X102))
| ~ spl2_663
| ~ spl2_1055 ),
inference(resolution,[],[f79233,f37228]) ).
fof(f37228,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))
| ~ spl2_663 ),
inference(avatar_component_clause,[],[f37227]) ).
fof(f80221,plain,
( spl2_1059
| ~ spl2_33
| ~ spl2_83
| ~ spl2_126
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70218,f69866,f1856,f1024,f340,f80219]) ).
fof(f1856,plain,
( spl2_126
<=> ! [X0,X1] : strict_implies(X1,X0) = strict_implies(and(not(X0),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_126])]) ).
fof(f70218,plain,
( ! [X10,X11] : strict_implies(implies(X10,X11),X10) = necessarily(not(not(X10)))
| ~ spl2_33
| ~ spl2_83
| ~ spl2_126
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70217,f1025]) ).
fof(f70217,plain,
( ! [X10,X11] : strict_implies(implies(X10,X11),X10) = necessarily(or(X10,X10))
| ~ spl2_33
| ~ spl2_126
| ~ spl2_954 ),
inference(forward_demodulation,[],[f69907,f341]) ).
fof(f69907,plain,
( ! [X10,X11] : strict_implies(implies(X10,X11),X10) = strict_implies(not(X10),X10)
| ~ spl2_126
| ~ spl2_954 ),
inference(superposition,[],[f1857,f69867]) ).
fof(f1857,plain,
( ! [X0,X1] : strict_implies(X1,X0) = strict_implies(and(not(X0),X1),X0)
| ~ spl2_126 ),
inference(avatar_component_clause,[],[f1856]) ).
fof(f79531,plain,
( spl2_1058
| ~ spl2_33
| ~ spl2_96
| ~ spl2_459
| ~ spl2_524
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70211,f69866,f27818,f17441,f1122,f340,f79529]) ).
fof(f17441,plain,
( spl2_459
<=> ! [X69,X67,X68] :
( is_a_theorem(strict_implies(X67,strict_implies(X68,X68)))
| ~ is_a_theorem(strict_implies(X67,strict_equiv(X69,X68))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_459])]) ).
fof(f70211,plain,
( ! [X52,X53] : is_a_theorem(necessarily(or(not(strict_equiv(X52,X53)),strict_implies(X53,X53))))
| ~ spl2_33
| ~ spl2_96
| ~ spl2_459
| ~ spl2_524
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70163,f341]) ).
fof(f70163,plain,
( ! [X52,X53] : is_a_theorem(strict_implies(not(not(strict_equiv(X52,X53))),strict_implies(X53,X53)))
| ~ spl2_96
| ~ spl2_459
| ~ spl2_524
| ~ spl2_954 ),
inference(backward_demodulation,[],[f28007,f69904]) ).
fof(f28007,plain,
( ! [X54,X52,X53] : is_a_theorem(strict_implies(implies(implies(strict_equiv(X52,X53),X54),strict_equiv(X52,X53)),strict_implies(X53,X53)))
| ~ spl2_459
| ~ spl2_524 ),
inference(resolution,[],[f27819,f17442]) ).
fof(f17442,plain,
( ! [X68,X69,X67] :
( ~ is_a_theorem(strict_implies(X67,strict_equiv(X69,X68)))
| is_a_theorem(strict_implies(X67,strict_implies(X68,X68))) )
| ~ spl2_459 ),
inference(avatar_component_clause,[],[f17441]) ).
fof(f79527,plain,
( spl2_1057
| ~ spl2_33
| ~ spl2_96
| ~ spl2_278
| ~ spl2_524
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70208,f69866,f27818,f8184,f1122,f340,f79525]) ).
fof(f8184,plain,
( spl2_278
<=> ! [X66,X64,X65] :
( is_a_theorem(strict_implies(X64,strict_implies(X65,X65)))
| ~ is_a_theorem(strict_implies(X64,strict_equiv(X65,X66))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_278])]) ).
fof(f70208,plain,
( ! [X58,X59] : is_a_theorem(necessarily(or(not(strict_equiv(X58,X59)),strict_implies(X58,X58))))
| ~ spl2_33
| ~ spl2_96
| ~ spl2_278
| ~ spl2_524
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70161,f341]) ).
fof(f70161,plain,
( ! [X58,X59] : is_a_theorem(strict_implies(not(not(strict_equiv(X58,X59))),strict_implies(X58,X58)))
| ~ spl2_96
| ~ spl2_278
| ~ spl2_524
| ~ spl2_954 ),
inference(backward_demodulation,[],[f28009,f69904]) ).
fof(f28009,plain,
( ! [X58,X59,X60] : is_a_theorem(strict_implies(implies(implies(strict_equiv(X58,X59),X60),strict_equiv(X58,X59)),strict_implies(X58,X58)))
| ~ spl2_278
| ~ spl2_524 ),
inference(resolution,[],[f27819,f8185]) ).
fof(f8185,plain,
( ! [X65,X66,X64] :
( ~ is_a_theorem(strict_implies(X64,strict_equiv(X65,X66)))
| is_a_theorem(strict_implies(X64,strict_implies(X65,X65))) )
| ~ spl2_278 ),
inference(avatar_component_clause,[],[f8184]) ).
fof(f79238,plain,
( spl2_1056
| ~ spl2_33
| ~ spl2_96
| ~ spl2_97
| ~ spl2_275
| ~ spl2_524
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70189,f69866,f27818,f8172,f1233,f1122,f340,f79236]) ).
fof(f79236,plain,
( spl2_1056
<=> ! [X39,X40] : is_a_theorem(necessarily(or(and(X40,X39),not(and(X39,X40))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1056])]) ).
fof(f8172,plain,
( spl2_275
<=> ! [X32,X31,X33] :
( is_a_theorem(strict_implies(X31,and(X32,X33)))
| ~ is_a_theorem(strict_implies(X31,and(X33,X32))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_275])]) ).
fof(f70189,plain,
( ! [X40,X39] : is_a_theorem(necessarily(or(and(X40,X39),not(and(X39,X40)))))
| ~ spl2_33
| ~ spl2_96
| ~ spl2_97
| ~ spl2_275
| ~ spl2_524
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70188,f1234]) ).
fof(f70188,plain,
( ! [X40,X39] : is_a_theorem(necessarily(or(not(and(X39,X40)),and(X40,X39))))
| ~ spl2_33
| ~ spl2_96
| ~ spl2_275
| ~ spl2_524
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70151,f341]) ).
fof(f70151,plain,
( ! [X40,X39] : is_a_theorem(strict_implies(not(not(and(X39,X40))),and(X40,X39)))
| ~ spl2_96
| ~ spl2_275
| ~ spl2_524
| ~ spl2_954 ),
inference(backward_demodulation,[],[f28003,f69904]) ).
fof(f28003,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(implies(implies(and(X39,X40),X41),and(X39,X40)),and(X40,X39)))
| ~ spl2_275
| ~ spl2_524 ),
inference(resolution,[],[f27819,f8173]) ).
fof(f8173,plain,
( ! [X31,X32,X33] :
( ~ is_a_theorem(strict_implies(X31,and(X33,X32)))
| is_a_theorem(strict_implies(X31,and(X32,X33))) )
| ~ spl2_275 ),
inference(avatar_component_clause,[],[f8172]) ).
fof(f79234,plain,
( spl2_1055
| ~ spl2_96
| ~ spl2_122
| ~ spl2_524
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70138,f69866,f27818,f1831,f1122,f79232]) ).
fof(f1831,plain,
( spl2_122
<=> ! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_122])]) ).
fof(f70138,plain,
( ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X6,not(not(X7))))
| is_a_theorem(strict_implies(X6,X7)) )
| ~ spl2_96
| ~ spl2_122
| ~ spl2_524
| ~ spl2_954 ),
inference(backward_demodulation,[],[f27991,f69904]) ).
fof(f27991,plain,
( ! [X8,X6,X7] :
( is_a_theorem(strict_implies(X6,X7))
| ~ is_a_theorem(strict_implies(X6,implies(implies(X7,X8),X7))) )
| ~ spl2_122
| ~ spl2_524 ),
inference(resolution,[],[f27819,f1832]) ).
fof(f1832,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X2)) )
| ~ spl2_122 ),
inference(avatar_component_clause,[],[f1831]) ).
fof(f79124,plain,
( spl2_1054
| ~ spl2_97
| ~ spl2_1050 ),
inference(avatar_split_clause,[],[f78533,f78362,f1233,f79122]) ).
fof(f79122,plain,
( spl2_1054
<=> ! [X2,X1] : is_a_theorem(or(or(X2,X1),not(not(not(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1054])]) ).
fof(f78362,plain,
( spl2_1050
<=> ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(not(not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1050])]) ).
fof(f78533,plain,
( ! [X2,X1] : is_a_theorem(or(or(X2,X1),not(not(not(X1)))))
| ~ spl2_97
| ~ spl2_1050 ),
inference(superposition,[],[f78363,f1234]) ).
fof(f78363,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(not(not(X0)))))
| ~ spl2_1050 ),
inference(avatar_component_clause,[],[f78362]) ).
fof(f78470,plain,
( spl2_1053
| ~ spl2_36
| ~ spl2_1045 ),
inference(avatar_split_clause,[],[f77990,f77459,f363,f78468]) ).
fof(f78468,plain,
( spl2_1053
<=> ! [X0,X1] : is_a_theorem(or(implies(X1,X0),not(equiv(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1053])]) ).
fof(f77459,plain,
( spl2_1045
<=> ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(implies(X3,X4),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1045])]) ).
fof(f77990,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X1,X0),not(equiv(X0,X1))))
| ~ spl2_36
| ~ spl2_1045 ),
inference(superposition,[],[f77460,f364]) ).
fof(f77460,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(implies(X3,X4),X2))))
| ~ spl2_1045 ),
inference(avatar_component_clause,[],[f77459]) ).
fof(f78466,plain,
( spl2_1052
| ~ spl2_76
| ~ spl2_1043 ),
inference(avatar_split_clause,[],[f77784,f77451,f810,f78464]) ).
fof(f78464,plain,
( spl2_1052
<=> ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(or(X3,X4),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1052])]) ).
fof(f77451,plain,
( spl2_1043
<=> ! [X22,X24,X23] : is_a_theorem(or(X24,not(and(X24,or(X22,X23))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1043])]) ).
fof(f77784,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(or(X3,X4),X2))))
| ~ spl2_76
| ~ spl2_1043 ),
inference(superposition,[],[f77452,f811]) ).
fof(f77452,plain,
( ! [X24,X22,X23] : is_a_theorem(or(X24,not(and(X24,or(X22,X23)))))
| ~ spl2_1043 ),
inference(avatar_component_clause,[],[f77451]) ).
fof(f78368,plain,
( spl2_1051
| ~ spl2_97
| ~ spl2_1042 ),
inference(avatar_split_clause,[],[f77713,f77447,f1233,f78366]) ).
fof(f78366,plain,
( spl2_1051
<=> ! [X2,X1] : is_a_theorem(or(not(not(not(X1))),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1051])]) ).
fof(f77447,plain,
( spl2_1042
<=> ! [X16,X17] : is_a_theorem(or(not(not(not(X16))),or(X16,X17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1042])]) ).
fof(f77713,plain,
( ! [X2,X1] : is_a_theorem(or(not(not(not(X1))),or(X2,X1)))
| ~ spl2_97
| ~ spl2_1042 ),
inference(superposition,[],[f77448,f1234]) ).
fof(f77448,plain,
( ! [X16,X17] : is_a_theorem(or(not(not(not(X16))),or(X16,X17)))
| ~ spl2_1042 ),
inference(avatar_component_clause,[],[f77447]) ).
fof(f78364,plain,
( spl2_1050
| ~ spl2_322
| ~ spl2_1042 ),
inference(avatar_split_clause,[],[f77687,f77447,f10110,f78362]) ).
fof(f77687,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(not(not(X0)))))
| ~ spl2_322
| ~ spl2_1042 ),
inference(resolution,[],[f77448,f10111]) ).
fof(f78360,plain,
( spl2_1049
| ~ spl2_24
| ~ spl2_1041 ),
inference(avatar_split_clause,[],[f77663,f77443,f290,f78358]) ).
fof(f78358,plain,
( spl2_1049
<=> ! [X22,X24,X23] : is_a_theorem(or(not(X24),implies(or(X22,X23),X24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1049])]) ).
fof(f77443,plain,
( spl2_1041
<=> ! [X6,X5,X7] : is_a_theorem(or(not(X5),implies(implies(X6,X7),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1041])]) ).
fof(f77663,plain,
( ! [X24,X22,X23] : is_a_theorem(or(not(X24),implies(or(X22,X23),X24)))
| ~ spl2_24
| ~ spl2_1041 ),
inference(superposition,[],[f77444,f291]) ).
fof(f77444,plain,
( ! [X6,X7,X5] : is_a_theorem(or(not(X5),implies(implies(X6,X7),X5)))
| ~ spl2_1041 ),
inference(avatar_component_clause,[],[f77443]) ).
fof(f77473,plain,
( spl2_1048
| ~ spl2_97
| ~ spl2_1034 ),
inference(avatar_split_clause,[],[f77160,f76860,f1233,f77471]) ).
fof(f77471,plain,
( spl2_1048
<=> ! [X2,X1] : is_a_theorem(implies(equiv(X2,not(X1)),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1048])]) ).
fof(f76860,plain,
( spl2_1034
<=> ! [X16,X17] : is_a_theorem(implies(equiv(X17,not(X16)),or(X16,X17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1034])]) ).
fof(f77160,plain,
( ! [X2,X1] : is_a_theorem(implies(equiv(X2,not(X1)),or(X2,X1)))
| ~ spl2_97
| ~ spl2_1034 ),
inference(superposition,[],[f76861,f1234]) ).
fof(f76861,plain,
( ! [X16,X17] : is_a_theorem(implies(equiv(X17,not(X16)),or(X16,X17)))
| ~ spl2_1034 ),
inference(avatar_component_clause,[],[f76860]) ).
fof(f77469,plain,
( spl2_1047
| ~ spl2_76
| ~ spl2_1032 ),
inference(avatar_split_clause,[],[f77085,f76852,f810,f77467]) ).
fof(f77467,plain,
( spl2_1047
<=> ! [X4,X2,X3] : is_a_theorem(implies(and(not(X3),X2),implies(X3,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1047])]) ).
fof(f77085,plain,
( ! [X2,X3,X4] : is_a_theorem(implies(and(not(X3),X2),implies(X3,X4)))
| ~ spl2_76
| ~ spl2_1032 ),
inference(superposition,[],[f76853,f811]) ).
fof(f77465,plain,
( spl2_1046
| ~ spl2_36
| ~ spl2_1030 ),
inference(avatar_split_clause,[],[f76899,f76844,f363,f77463]) ).
fof(f77463,plain,
( spl2_1046
<=> ! [X9,X8] : is_a_theorem(or(implies(X8,X9),not(equiv(X8,X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1046])]) ).
fof(f76844,plain,
( spl2_1030
<=> ! [X4,X2,X3] : is_a_theorem(or(X2,not(and(X2,implies(X3,X4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1030])]) ).
fof(f76899,plain,
( ! [X8,X9] : is_a_theorem(or(implies(X8,X9),not(equiv(X8,X9))))
| ~ spl2_36
| ~ spl2_1030 ),
inference(superposition,[],[f76845,f364]) ).
fof(f76845,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(X2,implies(X3,X4)))))
| ~ spl2_1030 ),
inference(avatar_component_clause,[],[f76844]) ).
fof(f77461,plain,
( spl2_1045
| ~ spl2_76
| ~ spl2_1030 ),
inference(avatar_split_clause,[],[f76897,f76844,f810,f77459]) ).
fof(f76897,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(implies(X3,X4),X2))))
| ~ spl2_76
| ~ spl2_1030 ),
inference(superposition,[],[f76845,f811]) ).
fof(f77457,plain,
( spl2_1044
| ~ spl2_30
| ~ spl2_769 ),
inference(avatar_split_clause,[],[f51195,f49236,f319,f77455]) ).
fof(f77455,plain,
( spl2_1044
<=> ! [X29,X27,X28] :
( ~ is_a_theorem(strict_equiv(not(X29),and(X27,not(X28))))
| is_a_theorem(strict_implies(implies(X27,X28),X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1044])]) ).
fof(f49236,plain,
( spl2_769
<=> ! [X11,X12,X10] : strict_equiv(not(X10),and(X11,not(X12))) = and(strict_implies(implies(X11,X12),X10),strict_implies(and(X11,not(X12)),not(X10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_769])]) ).
fof(f51195,plain,
( ! [X28,X29,X27] :
( ~ is_a_theorem(strict_equiv(not(X29),and(X27,not(X28))))
| is_a_theorem(strict_implies(implies(X27,X28),X29)) )
| ~ spl2_30
| ~ spl2_769 ),
inference(superposition,[],[f320,f49237]) ).
fof(f49237,plain,
( ! [X10,X11,X12] : strict_equiv(not(X10),and(X11,not(X12))) = and(strict_implies(implies(X11,X12),X10),strict_implies(and(X11,not(X12)),not(X10)))
| ~ spl2_769 ),
inference(avatar_component_clause,[],[f49236]) ).
fof(f77453,plain,
( spl2_1043
| ~ spl2_24
| ~ spl2_1030 ),
inference(avatar_split_clause,[],[f76887,f76844,f290,f77451]) ).
fof(f76887,plain,
( ! [X24,X22,X23] : is_a_theorem(or(X24,not(and(X24,or(X22,X23)))))
| ~ spl2_24
| ~ spl2_1030 ),
inference(superposition,[],[f76845,f291]) ).
fof(f77449,plain,
( spl2_1042
| ~ spl2_24
| ~ spl2_1011 ),
inference(avatar_split_clause,[],[f75769,f75674,f290,f77447]) ).
fof(f75674,plain,
( spl2_1011
<=> ! [X9,X8] : is_a_theorem(or(not(not(X8)),implies(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1011])]) ).
fof(f75769,plain,
( ! [X16,X17] : is_a_theorem(or(not(not(not(X16))),or(X16,X17)))
| ~ spl2_24
| ~ spl2_1011 ),
inference(superposition,[],[f75675,f291]) ).
fof(f75675,plain,
( ! [X8,X9] : is_a_theorem(or(not(not(X8)),implies(X8,X9)))
| ~ spl2_1011 ),
inference(avatar_component_clause,[],[f75674]) ).
fof(f77445,plain,
( spl2_1041
| ~ spl2_125
| ~ spl2_981 ),
inference(avatar_split_clause,[],[f74299,f74264,f1852,f77443]) ).
fof(f74299,plain,
( ! [X6,X7,X5] : is_a_theorem(or(not(X5),implies(implies(X6,X7),X5)))
| ~ spl2_125
| ~ spl2_981 ),
inference(superposition,[],[f74265,f1853]) ).
fof(f77441,plain,
( spl2_1040
| ~ spl2_30
| ~ spl2_765 ),
inference(avatar_split_clause,[],[f50704,f49220,f319,f77439]) ).
fof(f77439,plain,
( spl2_1040
<=> ! [X64,X65,X63] :
( ~ is_a_theorem(equiv(not(X65),and(X63,not(X64))))
| is_a_theorem(implies(implies(X63,X64),X65)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1040])]) ).
fof(f49220,plain,
( spl2_765
<=> ! [X9,X8,X10] : equiv(not(X8),and(X9,not(X10))) = and(implies(implies(X9,X10),X8),implies(and(X9,not(X10)),not(X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_765])]) ).
fof(f50704,plain,
( ! [X65,X63,X64] :
( ~ is_a_theorem(equiv(not(X65),and(X63,not(X64))))
| is_a_theorem(implies(implies(X63,X64),X65)) )
| ~ spl2_30
| ~ spl2_765 ),
inference(superposition,[],[f320,f49221]) ).
fof(f49221,plain,
( ! [X10,X8,X9] : equiv(not(X8),and(X9,not(X10))) = and(implies(implies(X9,X10),X8),implies(and(X9,not(X10)),not(X8)))
| ~ spl2_765 ),
inference(avatar_component_clause,[],[f49220]) ).
fof(f77126,plain,
( spl2_1039
| ~ spl2_19
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21366,f19362,f14372,f810,f269,f77124]) ).
fof(f77124,plain,
( spl2_1039
<=> ! [X10,X11,X13,X12] : is_a_theorem(strict_implies(and(X12,and(X10,and(X11,X13))),and(X10,and(X11,X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1039])]) ).
fof(f269,plain,
( spl2_19
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f14372,plain,
( spl2_403
<=> ! [X48,X47,X46,X45] :
( is_a_theorem(strict_implies(X45,and(X46,and(X47,X48))))
| ~ is_a_theorem(strict_implies(X45,and(and(X46,X47),X48))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_403])]) ).
fof(f19362,plain,
( spl2_486
<=> ! [X20,X18,X19] : and(and(X18,X19),X20) = and(and(X18,X20),X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_486])]) ).
fof(f21366,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X12,and(X10,and(X11,X13))),and(X10,and(X11,X12))))
| ~ spl2_19
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21365,f19383]) ).
fof(f19383,plain,
( ! [X10,X8,X9] : and(X10,and(X8,X9)) = and(and(X8,X10),X9)
| ~ spl2_76
| ~ spl2_486 ),
inference(superposition,[],[f19363,f811]) ).
fof(f19363,plain,
( ! [X18,X19,X20] : and(and(X18,X19),X20) = and(and(X18,X20),X19)
| ~ spl2_486 ),
inference(avatar_component_clause,[],[f19362]) ).
fof(f21365,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(X10,X12),and(X11,X13)),and(X10,and(X11,X12))))
| ~ spl2_19
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20314,f19383]) ).
fof(f20314,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(X11,and(X10,X12)),X13),and(X10,and(X11,X12))))
| ~ spl2_19
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(backward_demodulation,[],[f16623,f19383]) ).
fof(f16623,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(and(X10,X11),X12),X13),and(X10,and(X11,X12))))
| ~ spl2_19
| ~ spl2_403 ),
inference(resolution,[],[f14373,f270]) ).
fof(f270,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f14373,plain,
( ! [X48,X46,X47,X45] :
( ~ is_a_theorem(strict_implies(X45,and(and(X46,X47),X48)))
| is_a_theorem(strict_implies(X45,and(X46,and(X47,X48)))) )
| ~ spl2_403 ),
inference(avatar_component_clause,[],[f14372]) ).
fof(f76878,plain,
( spl2_1038
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_241
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21066,f19362,f18075,f6149,f2474,f810,f681,f436,f76876]) ).
fof(f76876,plain,
( spl2_1038
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(strict_equiv(not(X4),X3),X2),and(X2,strict_equiv(X3,not(X4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1038])]) ).
fof(f436,plain,
( spl2_43
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
fof(f2474,plain,
( spl2_141
<=> ! [X0,X1] : strict_equiv(not(X0),X1) = and(necessarily(or(X0,X1)),strict_implies(X1,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_141])]) ).
fof(f6149,plain,
( spl2_241
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),and(X2,strict_implies(X1,not(X0)))),and(X2,strict_equiv(X1,not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_241])]) ).
fof(f18075,plain,
( spl2_471
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,and(X4,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_471])]) ).
fof(f21066,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(strict_equiv(not(X4),X3),X2),and(X2,strict_equiv(X3,not(X4)))))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_241
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f6753,f20837]) ).
fof(f20837,plain,
( ! [X46,X44,X45] : and(strict_equiv(not(X44),X45),X46) = and(necessarily(or(X44,X45)),and(strict_implies(X45,not(X44)),X46))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f20136,f20741]) ).
fof(f20741,plain,
( ! [X14,X12,X13] : and(X12,and(X13,X14)) = and(X13,and(X12,X14))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20740,f19383]) ).
fof(f20740,plain,
( ! [X14,X12,X13] : and(X12,and(X13,X14)) = and(and(X12,X13),X14)
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_471
| ~ spl2_486 ),
inference(subsumption_resolution,[],[f20195,f18076]) ).
fof(f18076,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,and(X4,X3))))
| ~ spl2_471 ),
inference(avatar_component_clause,[],[f18075]) ).
fof(f20195,plain,
( ! [X14,X12,X13] :
( ~ is_a_theorem(strict_implies(and(X12,and(X13,X14)),and(X13,and(X12,X14))))
| and(X12,and(X13,X14)) = and(and(X12,X13),X14) )
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_486 ),
inference(backward_demodulation,[],[f696,f19383]) ).
fof(f696,plain,
( ! [X14,X12,X13] :
( ~ is_a_theorem(strict_implies(and(X12,and(X13,X14)),and(and(X12,X13),X14)))
| and(X12,and(X13,X14)) = and(and(X12,X13),X14) )
| ~ spl2_43
| ~ spl2_70 ),
inference(resolution,[],[f682,f437]) ).
fof(f437,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f20136,plain,
( ! [X46,X44,X45] : and(strict_equiv(not(X44),X45),X46) = and(strict_implies(X45,not(X44)),and(necessarily(or(X44,X45)),X46))
| ~ spl2_76
| ~ spl2_141
| ~ spl2_486 ),
inference(forward_demodulation,[],[f19379,f811]) ).
fof(f19379,plain,
( ! [X46,X44,X45] : and(and(necessarily(or(X44,X45)),X46),strict_implies(X45,not(X44))) = and(strict_equiv(not(X44),X45),X46)
| ~ spl2_141
| ~ spl2_486 ),
inference(superposition,[],[f19363,f2475]) ).
fof(f2475,plain,
( ! [X0,X1] : strict_equiv(not(X0),X1) = and(necessarily(or(X0,X1)),strict_implies(X1,not(X0)))
| ~ spl2_141 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f6753,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(necessarily(or(X4,X3)),and(strict_implies(X3,not(X4)),X2)),and(X2,strict_equiv(X3,not(X4)))))
| ~ spl2_76
| ~ spl2_241 ),
inference(superposition,[],[f6150,f811]) ).
fof(f6150,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),and(X2,strict_implies(X1,not(X0)))),and(X2,strict_equiv(X1,not(X0)))))
| ~ spl2_241 ),
inference(avatar_component_clause,[],[f6149]) ).
fof(f76874,plain,
( spl2_1037
| ~ spl2_97
| ~ spl2_1024 ),
inference(avatar_split_clause,[],[f76765,f75997,f1233,f76872]) ).
fof(f76872,plain,
( spl2_1037
<=> ! [X2,X1] : is_a_theorem(implies(and(not(X1),or(X2,X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1037])]) ).
fof(f75997,plain,
( spl2_1024
<=> ! [X16,X17] : is_a_theorem(implies(and(not(X16),or(X16,X17)),X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1024])]) ).
fof(f76765,plain,
( ! [X2,X1] : is_a_theorem(implies(and(not(X1),or(X2,X1)),X2))
| ~ spl2_97
| ~ spl2_1024 ),
inference(superposition,[],[f75998,f1234]) ).
fof(f75998,plain,
( ! [X16,X17] : is_a_theorem(implies(and(not(X16),or(X16,X17)),X17))
| ~ spl2_1024 ),
inference(avatar_component_clause,[],[f75997]) ).
fof(f76870,plain,
( spl2_1036
| ~ spl2_83
| ~ spl2_512
| ~ spl2_1017 ),
inference(avatar_split_clause,[],[f76072,f75969,f25503,f1024,f76868]) ).
fof(f75969,plain,
( spl2_1017
<=> ! [X105,X104] : is_a_theorem(implies(equiv(not(X104),X105),or(X104,X105))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1017])]) ).
fof(f76072,plain,
( ! [X0] : is_a_theorem(implies(equiv(X0,not(X0)),not(not(X0))))
| ~ spl2_83
| ~ spl2_512
| ~ spl2_1017 ),
inference(forward_demodulation,[],[f76032,f25504]) ).
fof(f76032,plain,
( ! [X0] : is_a_theorem(implies(equiv(not(X0),X0),not(not(X0))))
| ~ spl2_83
| ~ spl2_1017 ),
inference(superposition,[],[f75970,f1025]) ).
fof(f75970,plain,
( ! [X104,X105] : is_a_theorem(implies(equiv(not(X104),X105),or(X104,X105)))
| ~ spl2_1017 ),
inference(avatar_component_clause,[],[f75969]) ).
fof(f76866,plain,
( spl2_1035
| ~ spl2_97
| ~ spl2_1017 ),
inference(avatar_split_clause,[],[f76033,f75969,f1233,f76864]) ).
fof(f76864,plain,
( spl2_1035
<=> ! [X2,X1] : is_a_theorem(implies(equiv(not(X1),X2),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1035])]) ).
fof(f76033,plain,
( ! [X2,X1] : is_a_theorem(implies(equiv(not(X1),X2),or(X2,X1)))
| ~ spl2_97
| ~ spl2_1017 ),
inference(superposition,[],[f75970,f1234]) ).
fof(f76862,plain,
( spl2_1034
| ~ spl2_24
| ~ spl2_1002 ),
inference(avatar_split_clause,[],[f75453,f75286,f290,f76860]) ).
fof(f75286,plain,
( spl2_1002
<=> ! [X55,X56] : is_a_theorem(implies(equiv(X56,X55),implies(X55,X56))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1002])]) ).
fof(f75453,plain,
( ! [X16,X17] : is_a_theorem(implies(equiv(X17,not(X16)),or(X16,X17)))
| ~ spl2_24
| ~ spl2_1002 ),
inference(superposition,[],[f75287,f291]) ).
fof(f75287,plain,
( ! [X56,X55] : is_a_theorem(implies(equiv(X56,X55),implies(X55,X56)))
| ~ spl2_1002 ),
inference(avatar_component_clause,[],[f75286]) ).
fof(f76858,plain,
( spl2_1033
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_80
| ~ spl2_222
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20871,f19362,f18075,f4968,f856,f810,f681,f436,f76856]) ).
fof(f76856,plain,
( spl2_1033
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(equiv(not(X4),X3),X2),and(X2,equiv(X3,not(X4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1033])]) ).
fof(f856,plain,
( spl2_80
<=> ! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).
fof(f4968,plain,
( spl2_222
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(or(X0,X1),and(X2,implies(X1,not(X0)))),and(X2,equiv(X1,not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_222])]) ).
fof(f20871,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(equiv(not(X4),X3),X2),and(X2,equiv(X3,not(X4)))))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_80
| ~ spl2_222
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f5945,f20745]) ).
fof(f20745,plain,
( ! [X40,X38,X39] : and(equiv(not(X38),X39),X40) = and(or(X38,X39),and(implies(X39,not(X38)),X40))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_80
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f20101,f20741]) ).
fof(f20101,plain,
( ! [X40,X38,X39] : and(equiv(not(X38),X39),X40) = and(implies(X39,not(X38)),and(or(X38,X39),X40))
| ~ spl2_76
| ~ spl2_80
| ~ spl2_486 ),
inference(forward_demodulation,[],[f19377,f811]) ).
fof(f19377,plain,
( ! [X40,X38,X39] : and(and(or(X38,X39),X40),implies(X39,not(X38))) = and(equiv(not(X38),X39),X40)
| ~ spl2_80
| ~ spl2_486 ),
inference(superposition,[],[f19363,f857]) ).
fof(f857,plain,
( ! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0)))
| ~ spl2_80 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f5945,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(or(X4,X3),and(implies(X3,not(X4)),X2)),and(X2,equiv(X3,not(X4)))))
| ~ spl2_76
| ~ spl2_222 ),
inference(superposition,[],[f4969,f811]) ).
fof(f4969,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(or(X0,X1),and(X2,implies(X1,not(X0)))),and(X2,equiv(X1,not(X0)))))
| ~ spl2_222 ),
inference(avatar_component_clause,[],[f4968]) ).
fof(f76854,plain,
( spl2_1032
| ~ spl2_954
| ~ spl2_1000 ),
inference(avatar_split_clause,[],[f75352,f75278,f69866,f76852]) ).
fof(f75278,plain,
( spl2_1000
<=> ! [X29,X27,X28] : is_a_theorem(implies(and(X28,and(X29,X27)),X27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1000])]) ).
fof(f75352,plain,
( ! [X136,X134,X135] : is_a_theorem(implies(and(X136,not(X134)),implies(X134,X135)))
| ~ spl2_954
| ~ spl2_1000 ),
inference(superposition,[],[f75279,f69867]) ).
fof(f75279,plain,
( ! [X28,X29,X27] : is_a_theorem(implies(and(X28,and(X29,X27)),X27))
| ~ spl2_1000 ),
inference(avatar_component_clause,[],[f75278]) ).
fof(f76850,plain,
( spl2_1031
| ~ spl2_37
| ~ spl2_973 ),
inference(avatar_split_clause,[],[f73986,f73958,f373,f76848]) ).
fof(f76848,plain,
( spl2_1031
<=> ! [X20,X19] : is_a_theorem(implies(possibly(X19),implies(necessarily(not(X19)),X20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1031])]) ).
fof(f73958,plain,
( spl2_973
<=> ! [X98,X97] : is_a_theorem(or(X97,implies(X97,X98))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_973])]) ).
fof(f73986,plain,
( ! [X19,X20] : is_a_theorem(implies(possibly(X19),implies(necessarily(not(X19)),X20)))
| ~ spl2_37
| ~ spl2_973 ),
inference(superposition,[],[f73959,f374]) ).
fof(f73959,plain,
( ! [X98,X97] : is_a_theorem(or(X97,implies(X97,X98)))
| ~ spl2_973 ),
inference(avatar_component_clause,[],[f73958]) ).
fof(f76846,plain,
( spl2_1030
| ~ spl2_77
| ~ spl2_973 ),
inference(avatar_split_clause,[],[f73968,f73958,f814,f76844]) ).
fof(f73968,plain,
( ! [X2,X3,X4] : is_a_theorem(or(X2,not(and(X2,implies(X3,X4)))))
| ~ spl2_77
| ~ spl2_973 ),
inference(superposition,[],[f73959,f815]) ).
fof(f76842,plain,
( spl2_1029
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20143,f19362,f6129,f2474,f810,f76840]) ).
fof(f76840,plain,
( spl2_1029
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,not(X3))),and(strict_equiv(not(X3),X2),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1029])]) ).
fof(f6129,plain,
( spl2_236
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X1,not(X0)),X2),and(strict_implies(X1,not(X0)),and(necessarily(or(X0,X1)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_236])]) ).
fof(f20143,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,not(X3))),and(strict_equiv(not(X3),X2),X4)))
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(backward_demodulation,[],[f6556,f20136]) ).
fof(f6556,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,not(X3))),and(strict_implies(X2,not(X3)),and(necessarily(or(X3,X2)),X4))))
| ~ spl2_76
| ~ spl2_236 ),
inference(superposition,[],[f6130,f811]) ).
fof(f6130,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X1,not(X0)),X2),and(strict_implies(X1,not(X0)),and(necessarily(or(X0,X1)),X2))))
| ~ spl2_236 ),
inference(avatar_component_clause,[],[f6129]) ).
fof(f76363,plain,
( spl2_1028
| ~ spl2_23
| ~ spl2_96
| ~ spl2_129
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f13948,f12444,f2138,f1122,f286,f76361]) ).
fof(f2138,plain,
( spl2_129
<=> ! [X9,X8] :
( ~ is_a_theorem(strict_implies(X8,and(X8,X9)))
| and(X8,X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_129])]) ).
fof(f13948,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,X1),X0))
| not(X0) = and(not(X0),not(X1)) )
| ~ spl2_23
| ~ spl2_96
| ~ spl2_129
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13947,f287]) ).
fof(f13947,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(or(X0,X1),X0)))
| not(X0) = and(not(X0),not(X1)) )
| ~ spl2_96
| ~ spl2_129
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13812,f1123]) ).
fof(f13812,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(and(not(X0),or(X0,X1)))))
| not(X0) = and(not(X0),not(X1)) )
| ~ spl2_129
| ~ spl2_371 ),
inference(superposition,[],[f2139,f12445]) ).
fof(f2139,plain,
( ! [X8,X9] :
( ~ is_a_theorem(strict_implies(X8,and(X8,X9)))
| and(X8,X9) = X8 )
| ~ spl2_129 ),
inference(avatar_component_clause,[],[f2138]) ).
fof(f76276,plain,
( spl2_1027
| ~ spl2_76
| ~ spl2_1025 ),
inference(avatar_split_clause,[],[f76232,f76195,f810,f76274]) ).
fof(f76274,plain,
( spl2_1027
<=> ! [X2,X1] : is_a_theorem(implies(and(not(not(X2)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1027])]) ).
fof(f76195,plain,
( spl2_1025
<=> ! [X0,X1] : is_a_theorem(implies(and(X1,not(not(X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1025])]) ).
fof(f76232,plain,
( ! [X2,X1] : is_a_theorem(implies(and(not(not(X2)),X1),X2))
| ~ spl2_76
| ~ spl2_1025 ),
inference(superposition,[],[f76196,f811]) ).
fof(f76196,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X1,not(not(X0))),X0))
| ~ spl2_1025 ),
inference(avatar_component_clause,[],[f76195]) ).
fof(f76201,plain,
( spl2_1026
| ~ spl2_76
| ~ spl2_329 ),
inference(avatar_split_clause,[],[f11875,f10587,f810,f76199]) ).
fof(f76199,plain,
( spl2_1026
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(equiv(and(not(X3),X2),X4))
| is_a_theorem(not(and(X4,implies(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1026])]) ).
fof(f10587,plain,
( spl2_329
<=> ! [X44,X43,X42] :
( ~ is_a_theorem(equiv(and(X43,not(X44)),X42))
| is_a_theorem(not(and(X42,implies(X43,X44)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_329])]) ).
fof(f11875,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(equiv(and(not(X3),X2),X4))
| is_a_theorem(not(and(X4,implies(X2,X3)))) )
| ~ spl2_76
| ~ spl2_329 ),
inference(superposition,[],[f10588,f811]) ).
fof(f10588,plain,
( ! [X44,X42,X43] :
( ~ is_a_theorem(equiv(and(X43,not(X44)),X42))
| is_a_theorem(not(and(X42,implies(X43,X44)))) )
| ~ spl2_329 ),
inference(avatar_component_clause,[],[f10587]) ).
fof(f76197,plain,
( spl2_1025
| ~ spl2_118
| ~ spl2_1018 ),
inference(avatar_split_clause,[],[f76134,f75973,f1704,f76195]) ).
fof(f1704,plain,
( spl2_118
<=> ! [X41,X42] : implies(and(not(X41),X42),X41) = implies(X42,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_118])]) ).
fof(f75973,plain,
( spl2_1018
<=> ! [X9,X11,X10] : is_a_theorem(implies(and(X9,and(X10,not(X9))),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1018])]) ).
fof(f76134,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X1,not(not(X0))),X0))
| ~ spl2_118
| ~ spl2_1018 ),
inference(superposition,[],[f75974,f1705]) ).
fof(f1705,plain,
( ! [X41,X42] : implies(and(not(X41),X42),X41) = implies(X42,X41)
| ~ spl2_118 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f75974,plain,
( ! [X10,X11,X9] : is_a_theorem(implies(and(X9,and(X10,not(X9))),X11))
| ~ spl2_1018 ),
inference(avatar_component_clause,[],[f75973]) ).
fof(f75999,plain,
( spl2_1024
| ~ spl2_24
| ~ spl2_992 ),
inference(avatar_split_clause,[],[f75046,f74513,f290,f75997]) ).
fof(f74513,plain,
( spl2_992
<=> ! [X2,X1] : is_a_theorem(implies(and(X1,implies(X1,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_992])]) ).
fof(f75046,plain,
( ! [X16,X17] : is_a_theorem(implies(and(not(X16),or(X16,X17)),X17))
| ~ spl2_24
| ~ spl2_992 ),
inference(superposition,[],[f74514,f291]) ).
fof(f74514,plain,
( ! [X2,X1] : is_a_theorem(implies(and(X1,implies(X1,X2)),X2))
| ~ spl2_992 ),
inference(avatar_component_clause,[],[f74513]) ).
fof(f75995,plain,
( spl2_1023
| ~ spl2_76
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11600,f10415,f810,f75993]) ).
fof(f75993,plain,
( spl2_1023
<=> ! [X2,X1] : necessarily(not(equiv(X2,X1))) = strict_implies(implies(X2,X1),and(not(X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1023])]) ).
fof(f11600,plain,
( ! [X2,X1] : necessarily(not(equiv(X2,X1))) = strict_implies(implies(X2,X1),and(not(X2),X1))
| ~ spl2_76
| ~ spl2_325 ),
inference(superposition,[],[f10416,f811]) ).
fof(f75991,plain,
( spl2_1022
| ~ spl2_20
| ~ spl2_617
| ~ spl2_980 ),
inference(avatar_split_clause,[],[f74231,f74183,f33172,f273,f75989]) ).
fof(f75989,plain,
( spl2_1022
<=> ! [X0,X1] : is_a_theorem(implies(and(possibly(X0),necessarily(not(X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1022])]) ).
fof(f74231,plain,
( ! [X0,X1] : is_a_theorem(implies(and(possibly(X0),necessarily(not(X0))),X1))
| ~ spl2_20
| ~ spl2_617
| ~ spl2_980 ),
inference(forward_demodulation,[],[f74192,f33173]) ).
fof(f74192,plain,
( ! [X0,X1] : is_a_theorem(implies(and(necessarily(not(X0)),possibly(X0)),X1))
| ~ spl2_20
| ~ spl2_980 ),
inference(superposition,[],[f74184,f274]) ).
fof(f75987,plain,
( spl2_1021
| ~ spl2_761
| ~ spl2_980 ),
inference(avatar_split_clause,[],[f74187,f74183,f49204,f75985]) ).
fof(f75985,plain,
( spl2_1021
<=> ! [X4,X5,X3] : is_a_theorem(implies(and(X3,and(X4,not(X4))),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1021])]) ).
fof(f74187,plain,
( ! [X3,X4,X5] : is_a_theorem(implies(and(X3,and(X4,not(X4))),X5))
| ~ spl2_761
| ~ spl2_980 ),
inference(resolution,[],[f74184,f49205]) ).
fof(f75983,plain,
( spl2_1020
| ~ spl2_76
| ~ spl2_358
| ~ spl2_486
| ~ spl2_616
| ~ spl2_617
| ~ spl2_970 ),
inference(avatar_split_clause,[],[f73940,f73788,f33172,f33168,f19362,f12088,f810,f75981]) ).
fof(f75981,plain,
( spl2_1020
<=> ! [X9,X11,X10] : is_a_theorem(implies(and(X9,and(not(X9),X10)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1020])]) ).
fof(f12088,plain,
( spl2_358
<=> ! [X22,X20,X21] :
( is_a_theorem(implies(and(not(X20),X21),X22))
| ~ is_a_theorem(implies(X21,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_358])]) ).
fof(f33168,plain,
( spl2_616
<=> ! [X20,X18,X19] : and(X20,and(X19,X18)) = and(X20,and(X18,X19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_616])]) ).
fof(f73940,plain,
( ! [X10,X11,X9] : is_a_theorem(implies(and(X9,and(not(X9),X10)),X11))
| ~ spl2_76
| ~ spl2_358
| ~ spl2_486
| ~ spl2_616
| ~ spl2_617
| ~ spl2_970 ),
inference(forward_demodulation,[],[f73877,f34276]) ).
fof(f34276,plain,
( ! [X28,X29,X26,X27] : implies(and(X26,and(X28,X27)),X29) = implies(and(X28,and(X27,X26)),X29)
| ~ spl2_76
| ~ spl2_486
| ~ spl2_616
| ~ spl2_617 ),
inference(forward_demodulation,[],[f34063,f19383]) ).
fof(f34063,plain,
( ! [X28,X29,X26,X27] : implies(and(and(X27,X28),X26),X29) = implies(and(X26,and(X28,X27)),X29)
| ~ spl2_616
| ~ spl2_617 ),
inference(superposition,[],[f33173,f33169]) ).
fof(f33169,plain,
( ! [X18,X19,X20] : and(X20,and(X19,X18)) = and(X20,and(X18,X19))
| ~ spl2_616 ),
inference(avatar_component_clause,[],[f33168]) ).
fof(f73877,plain,
( ! [X10,X11,X9] : is_a_theorem(implies(and(not(X9),and(X10,X9)),X11))
| ~ spl2_358
| ~ spl2_970 ),
inference(resolution,[],[f73789,f12089]) ).
fof(f12089,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(implies(X21,X20))
| is_a_theorem(implies(and(not(X20),X21),X22)) )
| ~ spl2_358 ),
inference(avatar_component_clause,[],[f12088]) ).
fof(f75979,plain,
( spl2_1019
| ~ spl2_72
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11599,f10415,f748,f75977]) ).
fof(f11599,plain,
( ! [X0] : necessarily(not(equiv(X0,not(X0)))) = strict_implies(implies(X0,not(X0)),not(X0))
| ~ spl2_72
| ~ spl2_325 ),
inference(superposition,[],[f10416,f749]) ).
fof(f75975,plain,
( spl2_1018
| ~ spl2_76
| ~ spl2_358
| ~ spl2_486
| ~ spl2_616
| ~ spl2_617
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73861,f73202,f33172,f33168,f19362,f12088,f810,f75973]) ).
fof(f73861,plain,
( ! [X10,X11,X9] : is_a_theorem(implies(and(X9,and(X10,not(X9))),X11))
| ~ spl2_76
| ~ spl2_358
| ~ spl2_486
| ~ spl2_616
| ~ spl2_617
| ~ spl2_968 ),
inference(forward_demodulation,[],[f73798,f34276]) ).
fof(f73798,plain,
( ! [X10,X11,X9] : is_a_theorem(implies(and(not(X9),and(X9,X10)),X11))
| ~ spl2_358
| ~ spl2_968 ),
inference(resolution,[],[f73203,f12089]) ).
fof(f75971,plain,
( spl2_1017
| ~ spl2_80
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73841,f73202,f856,f75969]) ).
fof(f73841,plain,
( ! [X104,X105] : is_a_theorem(implies(equiv(not(X104),X105),or(X104,X105)))
| ~ spl2_80
| ~ spl2_968 ),
inference(superposition,[],[f73203,f857]) ).
fof(f75928,plain,
( spl2_1016
| ~ spl2_97
| ~ spl2_961 ),
inference(avatar_split_clause,[],[f73021,f72986,f1233,f75926]) ).
fof(f75926,plain,
( spl2_1016
<=> ! [X2,X1,X3] : is_a_theorem(necessarily(or(implies(X3,X1),implies(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1016])]) ).
fof(f72986,plain,
( spl2_961
<=> ! [X550,X548,X549] : is_a_theorem(necessarily(or(implies(X548,X549),implies(X550,X548)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_961])]) ).
fof(f73021,plain,
( ! [X2,X3,X1] : is_a_theorem(necessarily(or(implies(X3,X1),implies(X1,X2))))
| ~ spl2_97
| ~ spl2_961 ),
inference(superposition,[],[f72987,f1234]) ).
fof(f72987,plain,
( ! [X549,X548,X550] : is_a_theorem(necessarily(or(implies(X548,X549),implies(X550,X548))))
| ~ spl2_961 ),
inference(avatar_component_clause,[],[f72986]) ).
fof(f75924,plain,
( spl2_1015
| ~ spl2_72
| ~ spl2_75
| ~ spl2_324 ),
inference(avatar_split_clause,[],[f11541,f10240,f806,f748,f75922]) ).
fof(f75922,plain,
( spl2_1015
<=> ! [X0] : is_a_theorem(strict_implies(equiv(not(X0),implies(X0,not(X0))),not(equiv(X0,not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1015])]) ).
fof(f10240,plain,
( spl2_324
<=> ! [X9,X8] : is_a_theorem(strict_implies(equiv(implies(X8,X9),and(X9,not(X8))),not(equiv(X8,X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_324])]) ).
fof(f11541,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(not(X0),implies(X0,not(X0))),not(equiv(X0,not(X0)))))
| ~ spl2_72
| ~ spl2_75
| ~ spl2_324 ),
inference(forward_demodulation,[],[f11526,f807]) ).
fof(f11526,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(implies(X0,not(X0)),not(X0)),not(equiv(X0,not(X0)))))
| ~ spl2_72
| ~ spl2_324 ),
inference(superposition,[],[f10241,f749]) ).
fof(f10241,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(equiv(implies(X8,X9),and(X9,not(X8))),not(equiv(X8,X9))))
| ~ spl2_324 ),
inference(avatar_component_clause,[],[f10240]) ).
fof(f75795,plain,
( spl2_1014
| ~ spl2_76
| ~ spl2_1009 ),
inference(avatar_split_clause,[],[f75693,f75666,f810,f75793]) ).
fof(f75793,plain,
( spl2_1014
<=> ! [X2,X1] : is_a_theorem(or(X1,not(and(possibly(X2),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1014])]) ).
fof(f75666,plain,
( spl2_1009
<=> ! [X0,X1] : is_a_theorem(or(X0,not(and(X0,possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1009])]) ).
fof(f75693,plain,
( ! [X2,X1] : is_a_theorem(or(X1,not(and(possibly(X2),X1))))
| ~ spl2_76
| ~ spl2_1009 ),
inference(superposition,[],[f75667,f811]) ).
fof(f75667,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(and(X0,possibly(X1)))))
| ~ spl2_1009 ),
inference(avatar_component_clause,[],[f75666]) ).
fof(f75791,plain,
( spl2_1013
| ~ spl2_75
| ~ spl2_324 ),
inference(avatar_split_clause,[],[f11530,f10240,f806,f75789]) ).
fof(f75789,plain,
( spl2_1013
<=> ! [X2,X1] : is_a_theorem(strict_implies(equiv(implies(X1,X2),and(X2,not(X1))),not(equiv(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1013])]) ).
fof(f11530,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(equiv(implies(X1,X2),and(X2,not(X1))),not(equiv(X2,X1))))
| ~ spl2_75
| ~ spl2_324 ),
inference(superposition,[],[f10241,f807]) ).
fof(f75787,plain,
( spl2_1012
| ~ spl2_104
| ~ spl2_981 ),
inference(avatar_split_clause,[],[f74303,f74264,f1388,f75785]) ).
fof(f75785,plain,
( spl2_1012
<=> ! [X20,X21] : is_a_theorem(or(not(X20),implies(possibly(X21),X20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1012])]) ).
fof(f74303,plain,
( ! [X21,X20] : is_a_theorem(or(not(X20),implies(possibly(X21),X20)))
| ~ spl2_104
| ~ spl2_981 ),
inference(superposition,[],[f74265,f1389]) ).
fof(f75676,plain,
( spl2_1011
| ~ spl2_97
| ~ spl2_955
| ~ spl2_973 ),
inference(avatar_split_clause,[],[f73992,f73958,f70384,f1233,f75674]) ).
fof(f73992,plain,
( ! [X8,X9] : is_a_theorem(or(not(not(X8)),implies(X8,X9)))
| ~ spl2_97
| ~ spl2_955
| ~ spl2_973 ),
inference(forward_demodulation,[],[f73970,f1234]) ).
fof(f73970,plain,
( ! [X8,X9] : is_a_theorem(or(implies(X8,X9),not(not(X8))))
| ~ spl2_955
| ~ spl2_973 ),
inference(superposition,[],[f73959,f70385]) ).
fof(f75672,plain,
( spl2_1010
| ~ spl2_76
| ~ spl2_324 ),
inference(avatar_split_clause,[],[f11527,f10240,f810,f75670]) ).
fof(f75670,plain,
( spl2_1010
<=> ! [X2,X1] : is_a_theorem(strict_implies(equiv(implies(X2,X1),and(not(X2),X1)),not(equiv(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1010])]) ).
fof(f11527,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(equiv(implies(X2,X1),and(not(X2),X1)),not(equiv(X2,X1))))
| ~ spl2_76
| ~ spl2_324 ),
inference(superposition,[],[f10241,f811]) ).
fof(f75668,plain,
( spl2_1009
| ~ spl2_54
| ~ spl2_973 ),
inference(avatar_split_clause,[],[f73967,f73958,f505,f75666]) ).
fof(f73967,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(and(X0,possibly(X1)))))
| ~ spl2_54
| ~ spl2_973 ),
inference(superposition,[],[f73959,f506]) ).
fof(f75513,plain,
( spl2_1008
| ~ spl2_27
| ~ spl2_324 ),
inference(avatar_split_clause,[],[f11508,f10240,f302,f75511]) ).
fof(f75511,plain,
( spl2_1008
<=> ! [X18,X17] :
( is_a_theorem(not(equiv(X17,X18)))
| ~ is_a_theorem(equiv(implies(X17,X18),and(X18,not(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1008])]) ).
fof(f11508,plain,
( ! [X18,X17] :
( is_a_theorem(not(equiv(X17,X18)))
| ~ is_a_theorem(equiv(implies(X17,X18),and(X18,not(X17)))) )
| ~ spl2_27
| ~ spl2_324 ),
inference(resolution,[],[f10241,f303]) ).
fof(f75308,plain,
( spl2_1007
| ~ spl2_76
| ~ spl2_323 ),
inference(avatar_split_clause,[],[f11422,f10114,f810,f75306]) ).
fof(f75306,plain,
( spl2_1007
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(equiv(X4,and(not(X3),X2)))
| is_a_theorem(not(and(X4,implies(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1007])]) ).
fof(f10114,plain,
( spl2_323
<=> ! [X9,X8,X7] :
( is_a_theorem(not(and(X7,implies(X8,X9))))
| ~ is_a_theorem(equiv(X7,and(X8,not(X9)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_323])]) ).
fof(f11422,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(equiv(X4,and(not(X3),X2)))
| is_a_theorem(not(and(X4,implies(X2,X3)))) )
| ~ spl2_76
| ~ spl2_323 ),
inference(superposition,[],[f10115,f811]) ).
fof(f10115,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(equiv(X7,and(X8,not(X9))))
| is_a_theorem(not(and(X7,implies(X8,X9)))) )
| ~ spl2_323 ),
inference(avatar_component_clause,[],[f10114]) ).
fof(f75304,plain,
( spl2_1006
| ~ spl2_625
| ~ spl2_791
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73860,f73202,f52768,f34595,f75302]) ).
fof(f75302,plain,
( spl2_1006
<=> ! [X2,X0,X1] : is_a_theorem(implies(and(X1,and(X0,X2)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1006])]) ).
fof(f34595,plain,
( spl2_625
<=> ! [X9,X8,X10] : and(X10,and(X8,X9)) = and(and(X8,X10),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_625])]) ).
fof(f73860,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X1,and(X0,X2)),X0))
| ~ spl2_625
| ~ spl2_791
| ~ spl2_968 ),
inference(forward_demodulation,[],[f73795,f34596]) ).
fof(f34596,plain,
( ! [X10,X8,X9] : and(X10,and(X8,X9)) = and(and(X8,X10),X9)
| ~ spl2_625 ),
inference(avatar_component_clause,[],[f34595]) ).
fof(f73795,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X0))
| ~ spl2_791
| ~ spl2_968 ),
inference(resolution,[],[f73203,f52769]) ).
fof(f75300,plain,
( spl2_1005
| ~ spl2_235
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73847,f73202,f6125,f75298]) ).
fof(f75298,plain,
( spl2_1005
<=> ! [X116,X117] : is_a_theorem(implies(strict_equiv(X117,X116),strict_implies(X116,X117))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1005])]) ).
fof(f6125,plain,
( spl2_235
<=> ! [X13,X14] : strict_equiv(X13,X14) = and(strict_implies(X14,X13),strict_equiv(X13,X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_235])]) ).
fof(f73847,plain,
( ! [X116,X117] : is_a_theorem(implies(strict_equiv(X117,X116),strict_implies(X116,X117)))
| ~ spl2_235
| ~ spl2_968 ),
inference(superposition,[],[f73203,f6126]) ).
fof(f6126,plain,
( ! [X14,X13] : strict_equiv(X13,X14) = and(strict_implies(X14,X13),strict_equiv(X13,X14))
| ~ spl2_235 ),
inference(avatar_component_clause,[],[f6125]) ).
fof(f75296,plain,
( spl2_1004
| ~ spl2_34
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73845,f73202,f344,f75294]) ).
fof(f75294,plain,
( spl2_1004
<=> ! [X112,X113] : is_a_theorem(implies(strict_equiv(X112,X113),strict_implies(X112,X113))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1004])]) ).
fof(f73845,plain,
( ! [X113,X112] : is_a_theorem(implies(strict_equiv(X112,X113),strict_implies(X112,X113)))
| ~ spl2_34
| ~ spl2_968 ),
inference(superposition,[],[f73203,f345]) ).
fof(f75292,plain,
( spl2_1003
| ~ spl2_33
| ~ spl2_279 ),
inference(avatar_split_clause,[],[f9290,f8188,f340,f75290]) ).
fof(f75290,plain,
( spl2_1003
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_equiv(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1003])]) ).
fof(f8188,plain,
( spl2_279
<=> ! [X73,X75,X74] :
( is_a_theorem(strict_implies(X73,strict_equiv(X74,X75)))
| ~ is_a_theorem(strict_implies(X73,strict_equiv(X75,X74))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_279])]) ).
fof(f9290,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_equiv(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) )
| ~ spl2_33
| ~ spl2_279 ),
inference(forward_demodulation,[],[f9287,f341]) ).
fof(f9287,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2))))
| is_a_theorem(strict_implies(not(X0),strict_equiv(X2,X1))) )
| ~ spl2_33
| ~ spl2_279 ),
inference(superposition,[],[f8189,f341]) ).
fof(f8189,plain,
( ! [X73,X74,X75] :
( ~ is_a_theorem(strict_implies(X73,strict_equiv(X75,X74)))
| is_a_theorem(strict_implies(X73,strict_equiv(X74,X75))) )
| ~ spl2_279 ),
inference(avatar_component_clause,[],[f8188]) ).
fof(f75288,plain,
( spl2_1002
| ~ spl2_234
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73822,f73202,f6121,f75286]) ).
fof(f6121,plain,
( spl2_234
<=> ! [X9,X10] : equiv(X9,X10) = and(implies(X10,X9),equiv(X9,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_234])]) ).
fof(f73822,plain,
( ! [X56,X55] : is_a_theorem(implies(equiv(X56,X55),implies(X55,X56)))
| ~ spl2_234
| ~ spl2_968 ),
inference(superposition,[],[f73203,f6122]) ).
fof(f6122,plain,
( ! [X10,X9] : equiv(X9,X10) = and(implies(X10,X9),equiv(X9,X10))
| ~ spl2_234 ),
inference(avatar_component_clause,[],[f6121]) ).
fof(f75284,plain,
( spl2_1001
| ~ spl2_36
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73820,f73202,f363,f75282]) ).
fof(f73820,plain,
( ! [X51,X52] : is_a_theorem(implies(equiv(X51,X52),implies(X51,X52)))
| ~ spl2_36
| ~ spl2_968 ),
inference(superposition,[],[f73203,f364]) ).
fof(f75280,plain,
( spl2_1000
| ~ spl2_517
| ~ spl2_968 ),
inference(avatar_split_clause,[],[f73812,f73202,f26955,f75278]) ).
fof(f73812,plain,
( ! [X28,X29,X27] : is_a_theorem(implies(and(X28,and(X29,X27)),X27))
| ~ spl2_517
| ~ spl2_968 ),
inference(superposition,[],[f73203,f26956]) ).
fof(f75276,plain,
( spl2_999
| ~ spl2_96
| ~ spl2_300
| ~ spl2_967 ),
inference(avatar_split_clause,[],[f73193,f73133,f9395,f1122,f75274]) ).
fof(f75274,plain,
( spl2_999
<=> ! [X4,X5] : is_a_theorem(implies(implies(X5,X4),implies(X5,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_999])]) ).
fof(f9395,plain,
( spl2_300
<=> ! [X22,X24,X23] : implies(implies(X22,X23),X24) = or(and(not(X23),X22),X24) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_300])]) ).
fof(f73133,plain,
( spl2_967
<=> ! [X9] : is_a_theorem(or(X9,not(X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_967])]) ).
fof(f73193,plain,
( ! [X4,X5] : is_a_theorem(implies(implies(X5,X4),implies(X5,X4)))
| ~ spl2_96
| ~ spl2_300
| ~ spl2_967 ),
inference(forward_demodulation,[],[f73162,f1123]) ).
fof(f73162,plain,
( ! [X4,X5] : is_a_theorem(implies(implies(X5,X4),not(and(not(X4),X5))))
| ~ spl2_300
| ~ spl2_967 ),
inference(superposition,[],[f73134,f9396]) ).
fof(f9396,plain,
( ! [X24,X22,X23] : implies(implies(X22,X23),X24) = or(and(not(X23),X22),X24)
| ~ spl2_300 ),
inference(avatar_component_clause,[],[f9395]) ).
fof(f73134,plain,
( ! [X9] : is_a_theorem(or(X9,not(X9)))
| ~ spl2_967 ),
inference(avatar_component_clause,[],[f73133]) ).
fof(f75272,plain,
( spl2_998
| ~ spl2_33
| ~ spl2_278 ),
inference(avatar_split_clause,[],[f9261,f8184,f340,f75270]) ).
fof(f75270,plain,
( spl2_998
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_implies(X1,X1))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_998])]) ).
fof(f9261,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_implies(X1,X1))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) )
| ~ spl2_33
| ~ spl2_278 ),
inference(forward_demodulation,[],[f9258,f341]) ).
fof(f9258,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2))))
| is_a_theorem(strict_implies(not(X0),strict_implies(X1,X1))) )
| ~ spl2_33
| ~ spl2_278 ),
inference(superposition,[],[f8185,f341]) ).
fof(f75033,plain,
( spl2_997
| ~ spl2_33
| ~ spl2_277 ),
inference(avatar_split_clause,[],[f9236,f8180,f340,f75031]) ).
fof(f75031,plain,
( spl2_997
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_implies(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_997])]) ).
fof(f8180,plain,
( spl2_277
<=> ! [X61,X62,X63] :
( is_a_theorem(strict_implies(X61,strict_implies(X62,X63)))
| ~ is_a_theorem(strict_implies(X61,strict_equiv(X62,X63))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_277])]) ).
fof(f9236,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,strict_implies(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2)))) )
| ~ spl2_33
| ~ spl2_277 ),
inference(forward_demodulation,[],[f9233,f341]) ).
fof(f9233,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,strict_equiv(X1,X2))))
| is_a_theorem(strict_implies(not(X0),strict_implies(X1,X2))) )
| ~ spl2_33
| ~ spl2_277 ),
inference(superposition,[],[f8181,f341]) ).
fof(f8181,plain,
( ! [X62,X63,X61] :
( ~ is_a_theorem(strict_implies(X61,strict_equiv(X62,X63)))
| is_a_theorem(strict_implies(X61,strict_implies(X62,X63))) )
| ~ spl2_277 ),
inference(avatar_component_clause,[],[f8180]) ).
fof(f74546,plain,
( spl2_996
| ~ spl2_33
| ~ spl2_275 ),
inference(avatar_split_clause,[],[f8549,f8172,f340,f74544]) ).
fof(f74544,plain,
( spl2_996
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,and(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,and(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_996])]) ).
fof(f8549,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,and(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,and(X1,X2)))) )
| ~ spl2_33
| ~ spl2_275 ),
inference(forward_demodulation,[],[f8515,f341]) ).
fof(f8515,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(X1,X2))))
| is_a_theorem(strict_implies(not(X0),and(X2,X1))) )
| ~ spl2_33
| ~ spl2_275 ),
inference(superposition,[],[f8173,f341]) ).
fof(f74527,plain,
( spl2_995
| ~ spl2_33
| ~ spl2_976 ),
inference(avatar_split_clause,[],[f74098,f74000,f340,f74525]) ).
fof(f74525,plain,
( spl2_995
<=> ! [X6,X7] : is_a_theorem(necessarily(or(X6,or(X7,not(X7))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_995])]) ).
fof(f74000,plain,
( spl2_976
<=> ! [X14,X15] : is_a_theorem(strict_implies(X15,or(X14,not(X14)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_976])]) ).
fof(f74098,plain,
( ! [X6,X7] : is_a_theorem(necessarily(or(X6,or(X7,not(X7)))))
| ~ spl2_33
| ~ spl2_976 ),
inference(superposition,[],[f74001,f341]) ).
fof(f74001,plain,
( ! [X14,X15] : is_a_theorem(strict_implies(X15,or(X14,not(X14))))
| ~ spl2_976 ),
inference(avatar_component_clause,[],[f74000]) ).
fof(f74523,plain,
( spl2_994
| ~ spl2_24
| ~ spl2_975 ),
inference(avatar_split_clause,[],[f74018,f73996,f290,f74521]) ).
fof(f74521,plain,
( spl2_994
<=> ! [X14,X15] : is_a_theorem(necessarily(or(or(X14,not(X14)),X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_994])]) ).
fof(f73996,plain,
( spl2_975
<=> ! [X18,X17] : is_a_theorem(necessarily(or(implies(X17,X17),X18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_975])]) ).
fof(f74018,plain,
( ! [X14,X15] : is_a_theorem(necessarily(or(or(X14,not(X14)),X15)))
| ~ spl2_24
| ~ spl2_975 ),
inference(superposition,[],[f73997,f291]) ).
fof(f73997,plain,
( ! [X18,X17] : is_a_theorem(necessarily(or(implies(X17,X17),X18)))
| ~ spl2_975 ),
inference(avatar_component_clause,[],[f73996]) ).
fof(f74519,plain,
( spl2_993
| ~ spl2_33
| ~ spl2_274 ),
inference(avatar_split_clause,[],[f8405,f8168,f340,f74517]) ).
fof(f74517,plain,
( spl2_993
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,equiv(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_993])]) ).
fof(f8168,plain,
( spl2_274
<=> ! [X9,X8,X10] :
( is_a_theorem(strict_implies(X8,equiv(X9,X10)))
| ~ is_a_theorem(strict_implies(X8,equiv(X10,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_274])]) ).
fof(f8405,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,equiv(X2,X1))))
| ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2)))) )
| ~ spl2_33
| ~ spl2_274 ),
inference(forward_demodulation,[],[f8402,f341]) ).
fof(f8402,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2))))
| is_a_theorem(strict_implies(not(X0),equiv(X2,X1))) )
| ~ spl2_33
| ~ spl2_274 ),
inference(superposition,[],[f8169,f341]) ).
fof(f8169,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(strict_implies(X8,equiv(X10,X9)))
| is_a_theorem(strict_implies(X8,equiv(X9,X10))) )
| ~ spl2_274 ),
inference(avatar_component_clause,[],[f8168]) ).
fof(f74515,plain,
( spl2_992
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73745,f73098,f33172,f26955,f1122,f814,f315,f74513]) ).
fof(f73098,plain,
( spl2_965
<=> ! [X0] : is_a_theorem(implies(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_965])]) ).
fof(f73745,plain,
( ! [X2,X1] : is_a_theorem(implies(and(X1,implies(X1,X2)),X2))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_617
| ~ spl2_965 ),
inference(forward_demodulation,[],[f73127,f33173]) ).
fof(f73127,plain,
( ! [X2,X1] : is_a_theorem(implies(and(implies(X1,X2),X1),X2))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_517
| ~ spl2_965 ),
inference(forward_demodulation,[],[f73126,f27370]) ).
fof(f73126,plain,
( ! [X2,X1] : is_a_theorem(not(and(implies(X1,X2),and(X1,not(X2)))))
| ~ spl2_29
| ~ spl2_77
| ~ spl2_96
| ~ spl2_965 ),
inference(forward_demodulation,[],[f73112,f1196]) ).
fof(f73112,plain,
( ! [X2,X1] : is_a_theorem(not(and(and(X1,not(X2)),implies(X1,X2))))
| ~ spl2_77
| ~ spl2_965 ),
inference(superposition,[],[f73099,f815]) ).
fof(f73099,plain,
( ! [X0] : is_a_theorem(implies(X0,X0))
| ~ spl2_965 ),
inference(avatar_component_clause,[],[f73098]) ).
fof(f74511,plain,
( spl2_991
| ~ spl2_54
| ~ spl2_133
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73125,f73098,f2297,f505,f74509]) ).
fof(f74509,plain,
( spl2_991
<=> ! [X0] : is_a_theorem(not(and(possibly(X0),necessarily(not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_991])]) ).
fof(f2297,plain,
( spl2_133
<=> ! [X0,X1] : not(and(X1,possibly(X0))) = not(and(possibly(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_133])]) ).
fof(f73125,plain,
( ! [X0] : is_a_theorem(not(and(possibly(X0),necessarily(not(X0)))))
| ~ spl2_54
| ~ spl2_133
| ~ spl2_965 ),
inference(forward_demodulation,[],[f73111,f2298]) ).
fof(f2298,plain,
( ! [X0,X1] : not(and(X1,possibly(X0))) = not(and(possibly(X0),X1))
| ~ spl2_133 ),
inference(avatar_component_clause,[],[f2297]) ).
fof(f73111,plain,
( ! [X0] : is_a_theorem(not(and(necessarily(not(X0)),possibly(X0))))
| ~ spl2_54
| ~ spl2_965 ),
inference(superposition,[],[f73099,f506]) ).
fof(f74507,plain,
( spl2_990
| ~ spl2_515
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73121,f73098,f25559,f74505]) ).
fof(f74505,plain,
( spl2_990
<=> ! [X18,X19] : is_a_theorem(implies(strict_equiv(X19,X18),strict_equiv(X18,X19))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_990])]) ).
fof(f25559,plain,
( spl2_515
<=> ! [X379,X381,X380] : implies(strict_equiv(X379,X380),X381) = implies(strict_equiv(X380,X379),X381) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_515])]) ).
fof(f73121,plain,
( ! [X18,X19] : is_a_theorem(implies(strict_equiv(X19,X18),strict_equiv(X18,X19)))
| ~ spl2_515
| ~ spl2_965 ),
inference(superposition,[],[f73099,f25560]) ).
fof(f25560,plain,
( ! [X381,X380,X379] : implies(strict_equiv(X379,X380),X381) = implies(strict_equiv(X380,X379),X381)
| ~ spl2_515 ),
inference(avatar_component_clause,[],[f25559]) ).
fof(f74503,plain,
( spl2_989
| ~ spl2_318
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73119,f73098,f9826,f74501]) ).
fof(f74501,plain,
( spl2_989
<=> ! [X14,X15] : is_a_theorem(implies(or(X15,X14),or(X14,X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_989])]) ).
fof(f73119,plain,
( ! [X14,X15] : is_a_theorem(implies(or(X15,X14),or(X14,X15)))
| ~ spl2_318
| ~ spl2_965 ),
inference(superposition,[],[f73099,f9827]) ).
fof(f74499,plain,
( spl2_988
| ~ spl2_33
| ~ spl2_273 ),
inference(avatar_split_clause,[],[f8378,f8164,f340,f74497]) ).
fof(f74497,plain,
( spl2_988
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,implies(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_988])]) ).
fof(f8164,plain,
( spl2_273
<=> ! [X4,X2,X3] :
( is_a_theorem(strict_implies(X2,implies(X3,X4)))
| ~ is_a_theorem(strict_implies(X2,equiv(X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_273])]) ).
fof(f8378,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,implies(X1,X2))))
| ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2)))) )
| ~ spl2_33
| ~ spl2_273 ),
inference(forward_demodulation,[],[f8375,f341]) ).
fof(f8375,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,equiv(X1,X2))))
| is_a_theorem(strict_implies(not(X0),implies(X1,X2))) )
| ~ spl2_33
| ~ spl2_273 ),
inference(superposition,[],[f8165,f341]) ).
fof(f8165,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(strict_implies(X2,equiv(X3,X4)))
| is_a_theorem(strict_implies(X2,implies(X3,X4))) )
| ~ spl2_273 ),
inference(avatar_component_clause,[],[f8164]) ).
fof(f74495,plain,
( spl2_987
| ~ spl2_617
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73117,f73098,f33172,f74493]) ).
fof(f74493,plain,
( spl2_987
<=> ! [X11,X10] : is_a_theorem(implies(and(X11,X10),and(X10,X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_987])]) ).
fof(f73117,plain,
( ! [X10,X11] : is_a_theorem(implies(and(X11,X10),and(X10,X11)))
| ~ spl2_617
| ~ spl2_965 ),
inference(superposition,[],[f73099,f33173]) ).
fof(f74491,plain,
( spl2_986
| ~ spl2_512
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73114,f73098,f25503,f74489]) ).
fof(f74489,plain,
( spl2_986
<=> ! [X6,X5] : is_a_theorem(implies(equiv(X6,X5),equiv(X5,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_986])]) ).
fof(f73114,plain,
( ! [X6,X5] : is_a_theorem(implies(equiv(X6,X5),equiv(X5,X6)))
| ~ spl2_512
| ~ spl2_965 ),
inference(superposition,[],[f73099,f25504]) ).
fof(f74424,plain,
( spl2_985
| ~ spl2_20
| ~ spl2_270 ),
inference(avatar_split_clause,[],[f8200,f8072,f273,f74422]) ).
fof(f74422,plain,
( spl2_985
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(possibly(X0),necessarily(not(X1))),strict_implies(possibly(X1),necessarily(not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_985])]) ).
fof(f8072,plain,
( spl2_270
<=> ! [X4,X3] : is_a_theorem(strict_implies(strict_equiv(not(X3),necessarily(not(X4))),strict_implies(possibly(X4),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_270])]) ).
fof(f8200,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(possibly(X0),necessarily(not(X1))),strict_implies(possibly(X1),necessarily(not(X0)))))
| ~ spl2_20
| ~ spl2_270 ),
inference(superposition,[],[f8073,f274]) ).
fof(f8073,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(strict_equiv(not(X3),necessarily(not(X4))),strict_implies(possibly(X4),X3)))
| ~ spl2_270 ),
inference(avatar_component_clause,[],[f8072]) ).
fof(f74420,plain,
( spl2_984
| ~ spl2_24
| ~ spl2_962 ),
inference(avatar_split_clause,[],[f73036,f73027,f290,f74418]) ).
fof(f74418,plain,
( spl2_984
<=> ! [X9] : is_a_theorem(necessarily(not(not(or(X9,not(X9)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_984])]) ).
fof(f73036,plain,
( ! [X9] : is_a_theorem(necessarily(not(not(or(X9,not(X9))))))
| ~ spl2_24
| ~ spl2_962 ),
inference(superposition,[],[f73028,f291]) ).
fof(f74345,plain,
( spl2_983
| ~ spl2_97
| ~ spl2_981 ),
inference(avatar_split_clause,[],[f74297,f74264,f1233,f74343]) ).
fof(f74297,plain,
( ! [X2,X1] : is_a_theorem(or(not(X1),or(X2,X1)))
| ~ spl2_97
| ~ spl2_981 ),
inference(superposition,[],[f74265,f1234]) ).
fof(f74270,plain,
( spl2_982
| ~ spl2_76
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3520,f2750,f810,f74268]) ).
fof(f74268,plain,
( spl2_982
<=> ! [X2,X3,X4] : strict_implies(X2,and(X3,not(X4))) = necessarily(not(and(implies(X3,X4),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_982])]) ).
fof(f3520,plain,
( ! [X2,X3,X4] : strict_implies(X2,and(X3,not(X4))) = necessarily(not(and(implies(X3,X4),X2)))
| ~ spl2_76
| ~ spl2_161 ),
inference(superposition,[],[f2751,f811]) ).
fof(f74266,plain,
( spl2_981
| ~ spl2_24
| ~ spl2_973 ),
inference(avatar_split_clause,[],[f73973,f73958,f290,f74264]) ).
fof(f73973,plain,
( ! [X16,X17] : is_a_theorem(or(not(X16),or(X16,X17)))
| ~ spl2_24
| ~ spl2_973 ),
inference(superposition,[],[f73959,f291]) ).
fof(f74185,plain,
( spl2_980
| ~ spl2_358
| ~ spl2_617
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73124,f73098,f33172,f12088,f74183]) ).
fof(f73124,plain,
( ! [X6,X7] : is_a_theorem(implies(and(X6,not(X6)),X7))
| ~ spl2_358
| ~ spl2_617
| ~ spl2_965 ),
inference(forward_demodulation,[],[f73108,f33173]) ).
fof(f73108,plain,
( ! [X6,X7] : is_a_theorem(implies(and(not(X6),X6),X7))
| ~ spl2_358
| ~ spl2_965 ),
inference(resolution,[],[f73099,f12089]) ).
fof(f74181,plain,
( spl2_979
| ~ spl2_72
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3519,f2750,f748,f74179]) ).
fof(f74179,plain,
( spl2_979
<=> ! [X0,X1] : necessarily(not(implies(X0,X1))) = strict_implies(implies(X0,X1),and(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_979])]) ).
fof(f3519,plain,
( ! [X0,X1] : necessarily(not(implies(X0,X1))) = strict_implies(implies(X0,X1),and(X0,not(X1)))
| ~ spl2_72
| ~ spl2_161 ),
inference(superposition,[],[f2751,f749]) ).
fof(f74010,plain,
( spl2_978
| ~ spl2_33
| ~ spl2_964 ),
inference(avatar_split_clause,[],[f73081,f73055,f340,f74008]) ).
fof(f74008,plain,
( spl2_978
<=> ! [X6,X7] : is_a_theorem(necessarily(or(X6,implies(X7,X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_978])]) ).
fof(f73055,plain,
( spl2_964
<=> ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_964])]) ).
fof(f73081,plain,
( ! [X6,X7] : is_a_theorem(necessarily(or(X6,implies(X7,X7))))
| ~ spl2_33
| ~ spl2_964 ),
inference(superposition,[],[f73056,f341]) ).
fof(f73056,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1)))
| ~ spl2_964 ),
inference(avatar_component_clause,[],[f73055]) ).
fof(f74006,plain,
( spl2_977
| ~ spl2_76
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3473,f2734,f810,f74004]) ).
fof(f74004,plain,
( spl2_977
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X2,and(X3,not(X4))),not(and(implies(X3,X4),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_977])]) ).
fof(f3473,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X2,and(X3,not(X4))),not(and(implies(X3,X4),X2))))
| ~ spl2_76
| ~ spl2_157 ),
inference(superposition,[],[f2735,f811]) ).
fof(f74002,plain,
( spl2_976
| ~ spl2_24
| ~ spl2_964 ),
inference(avatar_split_clause,[],[f73072,f73055,f290,f74000]) ).
fof(f73072,plain,
( ! [X14,X15] : is_a_theorem(strict_implies(X15,or(X14,not(X14))))
| ~ spl2_24
| ~ spl2_964 ),
inference(superposition,[],[f73056,f291]) ).
fof(f73998,plain,
( spl2_975
| ~ spl2_327
| ~ spl2_964 ),
inference(avatar_split_clause,[],[f73065,f73055,f10547,f73996]) ).
fof(f10547,plain,
( spl2_327
<=> ! [X13,X12,X11] :
( ~ is_a_theorem(strict_implies(implies(X12,X13),X11))
| is_a_theorem(necessarily(or(X11,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_327])]) ).
fof(f73065,plain,
( ! [X18,X17] : is_a_theorem(necessarily(or(implies(X17,X17),X18)))
| ~ spl2_327
| ~ spl2_964 ),
inference(resolution,[],[f73056,f10548]) ).
fof(f10548,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(strict_implies(implies(X12,X13),X11))
| is_a_theorem(necessarily(or(X11,X12))) )
| ~ spl2_327 ),
inference(avatar_component_clause,[],[f10547]) ).
fof(f73964,plain,
( spl2_974
| ~ spl2_76
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3462,f2734,f810,f73962]) ).
fof(f73962,plain,
( spl2_974
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(equiv(X4,and(not(X3),X2)),not(and(X4,implies(X2,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_974])]) ).
fof(f3462,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(equiv(X4,and(not(X3),X2)),not(and(X4,implies(X2,X3)))))
| ~ spl2_76
| ~ spl2_157 ),
inference(superposition,[],[f2735,f811]) ).
fof(f73960,plain,
( spl2_973
| ~ spl2_24
| ~ spl2_954
| ~ spl2_970 ),
inference(avatar_split_clause,[],[f73943,f73788,f69866,f290,f73958]) ).
fof(f73943,plain,
( ! [X98,X97] : is_a_theorem(or(X97,implies(X97,X98)))
| ~ spl2_24
| ~ spl2_954
| ~ spl2_970 ),
inference(forward_demodulation,[],[f73917,f291]) ).
fof(f73917,plain,
( ! [X98,X97] : is_a_theorem(implies(not(X97),implies(X97,X98)))
| ~ spl2_954
| ~ spl2_970 ),
inference(superposition,[],[f73789,f69867]) ).
fof(f73956,plain,
( spl2_972
| ~ spl2_20
| ~ spl2_37
| ~ spl2_967 ),
inference(avatar_split_clause,[],[f73196,f73133,f373,f273,f73954]) ).
fof(f73954,plain,
( spl2_972
<=> ! [X13] : is_a_theorem(implies(possibly(X13),possibly(X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_972])]) ).
fof(f73196,plain,
( ! [X13] : is_a_theorem(implies(possibly(X13),possibly(X13)))
| ~ spl2_20
| ~ spl2_37
| ~ spl2_967 ),
inference(forward_demodulation,[],[f73165,f274]) ).
fof(f73165,plain,
( ! [X13] : is_a_theorem(implies(possibly(X13),not(necessarily(not(X13)))))
| ~ spl2_37
| ~ spl2_967 ),
inference(superposition,[],[f73134,f374]) ).
fof(f73794,plain,
( spl2_971
| ~ spl2_76
| ~ spl2_154 ),
inference(avatar_split_clause,[],[f3418,f2673,f810,f73792]) ).
fof(f73792,plain,
( spl2_971
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(strict_implies(X3,X4),necessarily(or(X2,X3))))
| is_a_theorem(necessarily(or(X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_971])]) ).
fof(f2673,plain,
( spl2_154
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X2)))
| ~ is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_154])]) ).
fof(f3418,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(strict_implies(X3,X4),necessarily(or(X2,X3))))
| is_a_theorem(necessarily(or(X2,X4))) )
| ~ spl2_76
| ~ spl2_154 ),
inference(superposition,[],[f2674,f811]) ).
fof(f2674,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X1,X2)))
| is_a_theorem(necessarily(or(X0,X2))) )
| ~ spl2_154 ),
inference(avatar_component_clause,[],[f2673]) ).
fof(f73790,plain,
( spl2_970
| ~ spl2_761
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73106,f73098,f49204,f73788]) ).
fof(f73106,plain,
( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3))
| ~ spl2_761
| ~ spl2_965 ),
inference(resolution,[],[f73099,f49205]) ).
fof(f73744,plain,
( ~ spl2_387
| ~ spl2_458 ),
inference(avatar_contradiction_clause,[],[f73222]) ).
fof(f73222,plain,
( $false
| ~ spl2_387
| ~ spl2_458 ),
inference(resolution,[],[f14076,f17195]) ).
fof(f17195,plain,
( ! [X3,X4] : is_a_theorem(and(strict_implies(X4,X4),necessarily(or(X3,not(X3)))))
| ~ spl2_458 ),
inference(avatar_component_clause,[],[f17194]) ).
fof(f17194,plain,
( spl2_458
<=> ! [X4,X3] : is_a_theorem(and(strict_implies(X4,X4),necessarily(or(X3,not(X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_458])]) ).
fof(f14076,plain,
( ! [X2] : ~ is_a_theorem(X2)
| ~ spl2_387 ),
inference(avatar_component_clause,[],[f14075]) ).
fof(f14075,plain,
( spl2_387
<=> ! [X2] : ~ is_a_theorem(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_387])]) ).
fof(f73743,plain,
( ~ spl2_387
| ~ spl2_455 ),
inference(avatar_contradiction_clause,[],[f73224]) ).
fof(f73224,plain,
( $false
| ~ spl2_387
| ~ spl2_455 ),
inference(resolution,[],[f14076,f16878]) ).
fof(f16878,plain,
( ! [X31,X30] : is_a_theorem(and(strict_implies(X30,X30),strict_implies(X31,X31)))
| ~ spl2_455 ),
inference(avatar_component_clause,[],[f16877]) ).
fof(f16877,plain,
( spl2_455
<=> ! [X30,X31] : is_a_theorem(and(strict_implies(X30,X30),strict_implies(X31,X31))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_455])]) ).
fof(f73742,plain,
( ~ spl2_387
| ~ spl2_457 ),
inference(avatar_contradiction_clause,[],[f73225]) ).
fof(f73225,plain,
( $false
| ~ spl2_387
| ~ spl2_457 ),
inference(resolution,[],[f14076,f17191]) ).
fof(f17191,plain,
( ! [X3,X4] : is_a_theorem(and(necessarily(or(X3,not(X3))),strict_implies(X4,X4)))
| ~ spl2_457 ),
inference(avatar_component_clause,[],[f17190]) ).
fof(f17190,plain,
( spl2_457
<=> ! [X4,X3] : is_a_theorem(and(necessarily(or(X3,not(X3))),strict_implies(X4,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_457])]) ).
fof(f73741,plain,
( ~ spl2_387
| ~ spl2_967 ),
inference(avatar_contradiction_clause,[],[f73226]) ).
fof(f73226,plain,
( $false
| ~ spl2_387
| ~ spl2_967 ),
inference(resolution,[],[f14076,f73134]) ).
fof(f73740,plain,
( ~ spl2_73
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73227]) ).
fof(f73227,plain,
( $false
| ~ spl2_73
| ~ spl2_387 ),
inference(resolution,[],[f14076,f781]) ).
fof(f73739,plain,
( ~ spl2_387
| ~ spl2_683 ),
inference(avatar_contradiction_clause,[],[f73228]) ).
fof(f73228,plain,
( $false
| ~ spl2_387
| ~ spl2_683 ),
inference(resolution,[],[f14076,f40979]) ).
fof(f40979,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(X2,not(and(X2,X1)))))
| ~ spl2_683 ),
inference(avatar_component_clause,[],[f40978]) ).
fof(f40978,plain,
( spl2_683
<=> ! [X2,X1] : is_a_theorem(necessarily(or(X2,not(and(X2,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_683])]) ).
fof(f73738,plain,
( ~ spl2_337
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73229]) ).
fof(f73229,plain,
( $false
| ~ spl2_337
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11207]) ).
fof(f11207,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(X2,implies(X3,X4))))))
| ~ spl2_337 ),
inference(avatar_component_clause,[],[f11206]) ).
fof(f11206,plain,
( spl2_337
<=> ! [X4,X2,X3] : is_a_theorem(necessarily(or(X2,not(and(X2,implies(X3,X4)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_337])]) ).
fof(f73737,plain,
( ~ spl2_339
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73230]) ).
fof(f73230,plain,
( $false
| ~ spl2_339
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11373]) ).
fof(f11373,plain,
( ! [X8,X9,X7] : is_a_theorem(necessarily(or(X9,not(and(X9,or(X7,X8))))))
| ~ spl2_339 ),
inference(avatar_component_clause,[],[f11372]) ).
fof(f11372,plain,
( spl2_339
<=> ! [X9,X8,X7] : is_a_theorem(necessarily(or(X9,not(and(X9,or(X7,X8)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_339])]) ).
fof(f73736,plain,
( ~ spl2_332
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73231]) ).
fof(f73231,plain,
( $false
| ~ spl2_332
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10703]) ).
fof(f10703,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X0,not(and(X0,possibly(X1))))))
| ~ spl2_332 ),
inference(avatar_component_clause,[],[f10702]) ).
fof(f10702,plain,
( spl2_332
<=> ! [X0,X1] : is_a_theorem(necessarily(or(X0,not(and(X0,possibly(X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_332])]) ).
fof(f73735,plain,
( ~ spl2_387
| ~ spl2_682 ),
inference(avatar_contradiction_clause,[],[f73232]) ).
fof(f73232,plain,
( $false
| ~ spl2_387
| ~ spl2_682 ),
inference(resolution,[],[f14076,f40363]) ).
fof(f40363,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X1,not(and(X0,X1)))))
| ~ spl2_682 ),
inference(avatar_component_clause,[],[f40362]) ).
fof(f40362,plain,
( spl2_682
<=> ! [X0,X1] : is_a_theorem(necessarily(or(X1,not(and(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_682])]) ).
fof(f73734,plain,
( ~ spl2_387
| ~ spl2_721 ),
inference(avatar_contradiction_clause,[],[f73233]) ).
fof(f73233,plain,
( $false
| ~ spl2_387
| ~ spl2_721 ),
inference(resolution,[],[f14076,f45038]) ).
fof(f45038,plain,
( ! [X76,X77,X75] : is_a_theorem(necessarily(or(X77,not(and(X76,and(X75,X77))))))
| ~ spl2_721 ),
inference(avatar_component_clause,[],[f45037]) ).
fof(f45037,plain,
( spl2_721
<=> ! [X77,X76,X75] : is_a_theorem(necessarily(or(X77,not(and(X76,and(X75,X77)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_721])]) ).
fof(f73733,plain,
( ~ spl2_387
| ~ spl2_748 ),
inference(avatar_contradiction_clause,[],[f73234]) ).
fof(f73234,plain,
( $false
| ~ spl2_387
| ~ spl2_748 ),
inference(resolution,[],[f14076,f48852]) ).
fof(f48852,plain,
( ! [X18,X19,X20] : is_a_theorem(necessarily(or(X18,not(and(X19,and(X18,X20))))))
| ~ spl2_748 ),
inference(avatar_component_clause,[],[f48851]) ).
fof(f48851,plain,
( spl2_748
<=> ! [X20,X19,X18] : is_a_theorem(necessarily(or(X18,not(and(X19,and(X18,X20)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_748])]) ).
fof(f73732,plain,
( ~ spl2_340
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73235]) ).
fof(f73235,plain,
( $false
| ~ spl2_340
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11377]) ).
fof(f11377,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(implies(X3,X4),X2)))))
| ~ spl2_340 ),
inference(avatar_component_clause,[],[f11376]) ).
fof(f11376,plain,
( spl2_340
<=> ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(implies(X3,X4),X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_340])]) ).
fof(f73731,plain,
( ~ spl2_343
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73236]) ).
fof(f73236,plain,
( $false
| ~ spl2_343
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11548]) ).
fof(f11548,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(or(X3,X4),X2)))))
| ~ spl2_343 ),
inference(avatar_component_clause,[],[f11547]) ).
fof(f11547,plain,
( spl2_343
<=> ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(or(X3,X4),X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_343])]) ).
fof(f73730,plain,
( ~ spl2_335
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73237]) ).
fof(f73237,plain,
( $false
| ~ spl2_335
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11033]) ).
fof(f11033,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(X1,not(and(possibly(X2),X1)))))
| ~ spl2_335 ),
inference(avatar_component_clause,[],[f11032]) ).
fof(f11032,plain,
( spl2_335
<=> ! [X2,X1] : is_a_theorem(necessarily(or(X1,not(and(possibly(X2),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_335])]) ).
fof(f73729,plain,
( ~ spl2_387
| ~ spl2_953 ),
inference(avatar_contradiction_clause,[],[f73238]) ).
fof(f73238,plain,
( $false
| ~ spl2_387
| ~ spl2_953 ),
inference(resolution,[],[f14076,f68784]) ).
fof(f68784,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(equiv(X0,not(X0))))))
| ~ spl2_953 ),
inference(avatar_component_clause,[],[f68783]) ).
fof(f68783,plain,
( spl2_953
<=> ! [X0] : is_a_theorem(necessarily(or(X0,not(equiv(X0,not(X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_953])]) ).
fof(f73728,plain,
( ~ spl2_328
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73239]) ).
fof(f73239,plain,
( $false
| ~ spl2_328
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10567]) ).
fof(f10567,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X0,implies(X0,X1))))
| ~ spl2_328 ),
inference(avatar_component_clause,[],[f10566]) ).
fof(f10566,plain,
( spl2_328
<=> ! [X0,X1] : is_a_theorem(necessarily(or(X0,implies(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_328])]) ).
fof(f73727,plain,
( ~ spl2_348
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73240]) ).
fof(f73240,plain,
( $false
| ~ spl2_348
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11898]) ).
fof(f11898,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X0,not(X1)),X2))))
| ~ spl2_348 ),
inference(avatar_component_clause,[],[f11897]) ).
fof(f11897,plain,
( spl2_348
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X0,not(X1)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_348])]) ).
fof(f73726,plain,
( ~ spl2_349
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73241]) ).
fof(f73241,plain,
( $false
| ~ spl2_349
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11926]) ).
fof(f11926,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X1,implies(and(X1,possibly(X0)),X2))))
| ~ spl2_349 ),
inference(avatar_component_clause,[],[f11925]) ).
fof(f11925,plain,
( spl2_349
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(X1,implies(and(X1,possibly(X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_349])]) ).
fof(f73725,plain,
( ~ spl2_387
| ~ spl2_547 ),
inference(avatar_contradiction_clause,[],[f73242]) ).
fof(f73242,plain,
( $false
| ~ spl2_387
| ~ spl2_547 ),
inference(resolution,[],[f14076,f29010]) ).
fof(f29010,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X3,implies(and(X3,X2),X4))))
| ~ spl2_547 ),
inference(avatar_component_clause,[],[f29009]) ).
fof(f29009,plain,
( spl2_547
<=> ! [X4,X2,X3] : is_a_theorem(necessarily(or(X3,implies(and(X3,X2),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_547])]) ).
fof(f73724,plain,
( ~ spl2_387
| ~ spl2_546 ),
inference(avatar_contradiction_clause,[],[f73243]) ).
fof(f73243,plain,
( $false
| ~ spl2_387
| ~ spl2_546 ),
inference(resolution,[],[f14076,f28952]) ).
fof(f28952,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X1,X0),X2))))
| ~ spl2_546 ),
inference(avatar_component_clause,[],[f28951]) ).
fof(f28951,plain,
( spl2_546
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X1,X0),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_546])]) ).
fof(f73723,plain,
( ~ spl2_351
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73244]) ).
fof(f73244,plain,
( $false
| ~ spl2_351
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11934]) ).
fof(f11934,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,implies(and(not(X3),X2),X4))))
| ~ spl2_351 ),
inference(avatar_component_clause,[],[f11933]) ).
fof(f11933,plain,
( spl2_351
<=> ! [X4,X2,X3] : is_a_theorem(necessarily(or(X2,implies(and(not(X3),X2),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_351])]) ).
fof(f73722,plain,
( ~ spl2_352
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73245]) ).
fof(f73245,plain,
( $false
| ~ spl2_352
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11985]) ).
fof(f11985,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,implies(and(possibly(X3),X2),X4))))
| ~ spl2_352 ),
inference(avatar_component_clause,[],[f11984]) ).
fof(f11984,plain,
( spl2_352
<=> ! [X4,X2,X3] : is_a_theorem(necessarily(or(X2,implies(and(possibly(X3),X2),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_352])]) ).
fof(f73721,plain,
( ~ spl2_373
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73246]) ).
fof(f73246,plain,
( $false
| ~ spl2_373
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12453]) ).
fof(f12453,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(necessarily(or(X17,implies(and(implies(X15,X16),X17),X18))))
| ~ spl2_373 ),
inference(avatar_component_clause,[],[f12452]) ).
fof(f12452,plain,
( spl2_373
<=> ! [X18,X17,X16,X15] : is_a_theorem(necessarily(or(X17,implies(and(implies(X15,X16),X17),X18)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_373])]) ).
fof(f73720,plain,
( ~ spl2_378
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73247]) ).
fof(f73247,plain,
( $false
| ~ spl2_378
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12656]) ).
fof(f12656,plain,
( ! [X10,X11,X9,X12] : is_a_theorem(necessarily(or(X11,implies(and(or(X9,X10),X11),X12))))
| ~ spl2_378 ),
inference(avatar_component_clause,[],[f12655]) ).
fof(f12655,plain,
( spl2_378
<=> ! [X10,X11,X12,X9] : is_a_theorem(necessarily(or(X11,implies(and(or(X9,X10),X11),X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_378])]) ).
fof(f73719,plain,
( ~ spl2_364
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73248]) ).
fof(f73248,plain,
( $false
| ~ spl2_364
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12240]) ).
fof(f12240,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(necessarily(or(X17,implies(and(X17,implies(X15,X16)),X18))))
| ~ spl2_364 ),
inference(avatar_component_clause,[],[f12239]) ).
fof(f12239,plain,
( spl2_364
<=> ! [X18,X17,X16,X15] : is_a_theorem(necessarily(or(X17,implies(and(X17,implies(X15,X16)),X18)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_364])]) ).
fof(f73718,plain,
( ~ spl2_387
| ~ spl2_917 ),
inference(avatar_contradiction_clause,[],[f73249]) ).
fof(f73249,plain,
( $false
| ~ spl2_387
| ~ spl2_917 ),
inference(resolution,[],[f14076,f66724]) ).
fof(f66724,plain,
( ! [X28,X29,X26,X27] : is_a_theorem(necessarily(or(X26,implies(and(X27,and(X28,X26)),X29))))
| ~ spl2_917 ),
inference(avatar_component_clause,[],[f66723]) ).
fof(f66723,plain,
( spl2_917
<=> ! [X29,X27,X28,X26] : is_a_theorem(necessarily(or(X26,implies(and(X27,and(X28,X26)),X29)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_917])]) ).
fof(f73717,plain,
( ~ spl2_387
| ~ spl2_918 ),
inference(avatar_contradiction_clause,[],[f73250]) ).
fof(f73250,plain,
( $false
| ~ spl2_387
| ~ spl2_918 ),
inference(resolution,[],[f14076,f66728]) ).
fof(f66728,plain,
( ! [X31,X32,X30,X33] : is_a_theorem(necessarily(or(X30,implies(and(X32,and(X30,X31)),X33))))
| ~ spl2_918 ),
inference(avatar_component_clause,[],[f66727]) ).
fof(f66727,plain,
( spl2_918
<=> ! [X31,X33,X30,X32] : is_a_theorem(necessarily(or(X30,implies(and(X32,and(X30,X31)),X33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_918])]) ).
fof(f73716,plain,
( ~ spl2_375
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73251]) ).
fof(f73251,plain,
( $false
| ~ spl2_375
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12461]) ).
fof(f12461,plain,
( ! [X10,X11,X9,X12] : is_a_theorem(necessarily(or(X11,implies(and(X11,or(X9,X10)),X12))))
| ~ spl2_375 ),
inference(avatar_component_clause,[],[f12460]) ).
fof(f12460,plain,
( spl2_375
<=> ! [X10,X11,X12,X9] : is_a_theorem(necessarily(or(X11,implies(and(X11,or(X9,X10)),X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_375])]) ).
fof(f73715,plain,
( ~ spl2_341
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73252]) ).
fof(f73252,plain,
( $false
| ~ spl2_341
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11381]) ).
fof(f11381,plain,
( ! [X8,X9] : is_a_theorem(necessarily(or(implies(X8,X9),not(equiv(X8,X9)))))
| ~ spl2_341 ),
inference(avatar_component_clause,[],[f11380]) ).
fof(f11380,plain,
( spl2_341
<=> ! [X9,X8] : is_a_theorem(necessarily(or(implies(X8,X9),not(equiv(X8,X9))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_341])]) ).
fof(f73714,plain,
( ~ spl2_344
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73253]) ).
fof(f73253,plain,
( $false
| ~ spl2_344
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11552]) ).
fof(f11552,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),not(equiv(X0,X1)))))
| ~ spl2_344 ),
inference(avatar_component_clause,[],[f11551]) ).
fof(f11551,plain,
( spl2_344
<=> ! [X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),not(equiv(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_344])]) ).
fof(f73713,plain,
( ~ spl2_376
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73254]) ).
fof(f73254,plain,
( $false
| ~ spl2_376
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12481]) ).
fof(f12481,plain,
( ! [X11,X12,X13] : is_a_theorem(necessarily(or(implies(X11,X12),implies(equiv(X11,X12),X13))))
| ~ spl2_376 ),
inference(avatar_component_clause,[],[f12480]) ).
fof(f12480,plain,
( spl2_376
<=> ! [X13,X12,X11] : is_a_theorem(necessarily(or(implies(X11,X12),implies(equiv(X11,X12),X13)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_376])]) ).
fof(f73712,plain,
( ~ spl2_379
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73255]) ).
fof(f73255,plain,
( $false
| ~ spl2_379
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12660]) ).
fof(f12660,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),implies(equiv(X0,X1),X2))))
| ~ spl2_379 ),
inference(avatar_component_clause,[],[f12659]) ).
fof(f12659,plain,
( spl2_379
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),implies(equiv(X0,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_379])]) ).
fof(f73711,plain,
( ~ spl2_387
| ~ spl2_961 ),
inference(avatar_contradiction_clause,[],[f73256]) ).
fof(f73256,plain,
( $false
| ~ spl2_387
| ~ spl2_961 ),
inference(resolution,[],[f14076,f72987]) ).
fof(f73710,plain,
( ~ spl2_387
| ~ spl2_956 ),
inference(avatar_contradiction_clause,[],[f73257]) ).
fof(f73257,plain,
( $false
| ~ spl2_387
| ~ spl2_956 ),
inference(resolution,[],[f14076,f70389]) ).
fof(f73709,plain,
( ~ spl2_387
| ~ spl2_957 ),
inference(avatar_contradiction_clause,[],[f73258]) ).
fof(f73258,plain,
( $false
| ~ spl2_387
| ~ spl2_957 ),
inference(resolution,[],[f14076,f70874]) ).
fof(f70874,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(implies(X2,X4),or(X3,X2))))
| ~ spl2_957 ),
inference(avatar_component_clause,[],[f70873]) ).
fof(f70873,plain,
( spl2_957
<=> ! [X2,X4,X3] : is_a_theorem(necessarily(or(implies(X2,X4),or(X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_957])]) ).
fof(f73708,plain,
( ~ spl2_387
| ~ spl2_628 ),
inference(avatar_contradiction_clause,[],[f73259]) ).
fof(f73259,plain,
( $false
| ~ spl2_387
| ~ spl2_628 ),
inference(resolution,[],[f14076,f34608]) ).
fof(f34608,plain,
( ! [X78,X76,X77] : is_a_theorem(necessarily(or(equiv(X76,X77),implies(equiv(X77,X76),X78))))
| ~ spl2_628 ),
inference(avatar_component_clause,[],[f34607]) ).
fof(f34607,plain,
( spl2_628
<=> ! [X77,X76,X78] : is_a_theorem(necessarily(or(equiv(X76,X77),implies(equiv(X77,X76),X78)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_628])]) ).
fof(f73707,plain,
( ~ spl2_387
| ~ spl2_749 ),
inference(avatar_contradiction_clause,[],[f73260]) ).
fof(f73260,plain,
( $false
| ~ spl2_387
| ~ spl2_749 ),
inference(resolution,[],[f14076,f48856]) ).
fof(f48856,plain,
( ! [X68,X69] : is_a_theorem(necessarily(or(equiv(X68,X69),not(equiv(X69,X68)))))
| ~ spl2_749 ),
inference(avatar_component_clause,[],[f48855]) ).
fof(f48855,plain,
( spl2_749
<=> ! [X69,X68] : is_a_theorem(necessarily(or(equiv(X68,X69),not(equiv(X69,X68))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_749])]) ).
fof(f73706,plain,
( ~ spl2_330
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73261]) ).
fof(f73261,plain,
( $false
| ~ spl2_330
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10592]) ).
fof(f73705,plain,
( ~ spl2_331
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73262]) ).
fof(f73262,plain,
( $false
| ~ spl2_331
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10621]) ).
fof(f73704,plain,
( ~ spl2_387
| ~ spl2_535 ),
inference(avatar_contradiction_clause,[],[f73263]) ).
fof(f73263,plain,
( $false
| ~ spl2_387
| ~ spl2_535 ),
inference(resolution,[],[f14076,f28566]) ).
fof(f73703,plain,
( ~ spl2_338
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73264]) ).
fof(f73264,plain,
( $false
| ~ spl2_338
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11235]) ).
fof(f11235,plain,
( ! [X14,X15,X13] : is_a_theorem(necessarily(or(not(X13),implies(implies(X14,X15),X13))))
| ~ spl2_338 ),
inference(avatar_component_clause,[],[f11234]) ).
fof(f11234,plain,
( spl2_338
<=> ! [X13,X14,X15] : is_a_theorem(necessarily(or(not(X13),implies(implies(X14,X15),X13)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_338])]) ).
fof(f73702,plain,
( ~ spl2_342
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73265]) ).
fof(f73265,plain,
( $false
| ~ spl2_342
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11544]) ).
fof(f11544,plain,
( ! [X8,X9,X7] : is_a_theorem(necessarily(or(not(X9),implies(or(X7,X8),X9))))
| ~ spl2_342 ),
inference(avatar_component_clause,[],[f11543]) ).
fof(f11543,plain,
( spl2_342
<=> ! [X9,X8,X7] : is_a_theorem(necessarily(or(not(X9),implies(or(X7,X8),X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_342])]) ).
fof(f73701,plain,
( ~ spl2_334
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73266]) ).
fof(f73266,plain,
( $false
| ~ spl2_334
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11029]) ).
fof(f11029,plain,
( ! [X16,X17] : is_a_theorem(necessarily(or(not(X16),implies(possibly(X17),X16))))
| ~ spl2_334 ),
inference(avatar_component_clause,[],[f11028]) ).
fof(f11028,plain,
( spl2_334
<=> ! [X16,X17] : is_a_theorem(necessarily(or(not(X16),implies(possibly(X17),X16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_334])]) ).
fof(f73700,plain,
( ~ spl2_368
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73267]) ).
fof(f73267,plain,
( $false
| ~ spl2_368
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12256]) ).
fof(f12256,plain,
( ! [X8] : is_a_theorem(necessarily(or(not(not(X8)),not(equiv(X8,not(X8))))))
| ~ spl2_368 ),
inference(avatar_component_clause,[],[f12255]) ).
fof(f12255,plain,
( spl2_368
<=> ! [X8] : is_a_theorem(necessarily(or(not(not(X8)),not(equiv(X8,not(X8)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_368])]) ).
fof(f73699,plain,
( ~ spl2_387
| ~ spl2_959 ),
inference(avatar_contradiction_clause,[],[f73268]) ).
fof(f73268,plain,
( $false
| ~ spl2_387
| ~ spl2_959 ),
inference(resolution,[],[f14076,f71127]) ).
fof(f71127,plain,
( ! [X526,X525] : is_a_theorem(necessarily(or(not(not(X525)),implies(X525,X526))))
| ~ spl2_959 ),
inference(avatar_component_clause,[],[f71126]) ).
fof(f71126,plain,
( spl2_959
<=> ! [X525,X526] : is_a_theorem(necessarily(or(not(not(X525)),implies(X525,X526)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_959])]) ).
fof(f73698,plain,
( ~ spl2_387
| ~ spl2_634 ),
inference(avatar_contradiction_clause,[],[f73269]) ).
fof(f73269,plain,
( $false
| ~ spl2_387
| ~ spl2_634 ),
inference(resolution,[],[f14076,f34632]) ).
fof(f34632,plain,
( ! [X136,X137,X135] : is_a_theorem(necessarily(or(and(X135,X136),implies(and(X136,X135),X137))))
| ~ spl2_634 ),
inference(avatar_component_clause,[],[f34631]) ).
fof(f34631,plain,
( spl2_634
<=> ! [X136,X137,X135] : is_a_theorem(necessarily(or(and(X135,X136),implies(and(X136,X135),X137)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_634])]) ).
fof(f73697,plain,
( ~ spl2_345
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73270]) ).
fof(f73270,plain,
( $false
| ~ spl2_345
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11737]) ).
fof(f11737,plain,
( ! [X11,X12,X13] : is_a_theorem(necessarily(or(or(X11,X12),implies(or(X12,X11),X13))))
| ~ spl2_345 ),
inference(avatar_component_clause,[],[f11736]) ).
fof(f11736,plain,
( spl2_345
<=> ! [X13,X12,X11] : is_a_theorem(necessarily(or(or(X11,X12),implies(or(X12,X11),X13)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_345])]) ).
fof(f73696,plain,
( ~ spl2_387
| ~ spl2_958 ),
inference(avatar_contradiction_clause,[],[f73271]) ).
fof(f73271,plain,
( $false
| ~ spl2_387
| ~ spl2_958 ),
inference(resolution,[],[f14076,f71037]) ).
fof(f71037,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X0,X2),implies(X0,X1))))
| ~ spl2_958 ),
inference(avatar_component_clause,[],[f71036]) ).
fof(f71036,plain,
( spl2_958
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X0,X2),implies(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_958])]) ).
fof(f73695,plain,
( ~ spl2_387
| ~ spl2_960 ),
inference(avatar_contradiction_clause,[],[f73272]) ).
fof(f73272,plain,
( $false
| ~ spl2_387
| ~ spl2_960 ),
inference(resolution,[],[f14076,f72013]) ).
fof(f72013,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X2,X0),implies(X0,X1))))
| ~ spl2_960 ),
inference(avatar_component_clause,[],[f72012]) ).
fof(f72012,plain,
( spl2_960
<=> ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X2,X0),implies(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_960])]) ).
fof(f73694,plain,
( ~ spl2_356
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73273]) ).
fof(f73273,plain,
( $false
| ~ spl2_356
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12081]) ).
fof(f12081,plain,
( ! [X16,X15] : is_a_theorem(necessarily(or(or(X15,X16),not(equiv(not(X15),X16)))))
| ~ spl2_356 ),
inference(avatar_component_clause,[],[f12080]) ).
fof(f12080,plain,
( spl2_356
<=> ! [X16,X15] : is_a_theorem(necessarily(or(or(X15,X16),not(equiv(not(X15),X16))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_356])]) ).
fof(f73693,plain,
( ~ spl2_367
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73274]) ).
fof(f73274,plain,
( $false
| ~ spl2_367
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12252]) ).
fof(f12252,plain,
( ! [X10,X9] : is_a_theorem(necessarily(or(or(X10,X9),not(equiv(not(X9),X10)))))
| ~ spl2_367 ),
inference(avatar_component_clause,[],[f12251]) ).
fof(f12251,plain,
( spl2_367
<=> ! [X9,X10] : is_a_theorem(necessarily(or(or(X10,X9),not(equiv(not(X9),X10))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_367])]) ).
fof(f73692,plain,
( ~ spl2_372
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73275]) ).
fof(f73275,plain,
( $false
| ~ spl2_372
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12449]) ).
fof(f12449,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(or(X5,X6),not(equiv(X6,not(X5))))))
| ~ spl2_372 ),
inference(avatar_component_clause,[],[f12448]) ).
fof(f12448,plain,
( spl2_372
<=> ! [X6,X5] : is_a_theorem(necessarily(or(or(X5,X6),not(equiv(X6,not(X5)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_372])]) ).
fof(f73691,plain,
( ~ spl2_377
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73276]) ).
fof(f73276,plain,
( $false
| ~ spl2_377
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12485]) ).
fof(f12485,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(or(X2,X1),not(equiv(X2,not(X1))))))
| ~ spl2_377 ),
inference(avatar_component_clause,[],[f12484]) ).
fof(f12484,plain,
( spl2_377
<=> ! [X2,X1] : is_a_theorem(necessarily(or(or(X2,X1),not(equiv(X2,not(X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_377])]) ).
fof(f73690,plain,
( ~ spl2_387
| ~ spl2_722 ),
inference(avatar_contradiction_clause,[],[f73277]) ).
fof(f73277,plain,
( $false
| ~ spl2_387
| ~ spl2_722 ),
inference(resolution,[],[f14076,f45042]) ).
fof(f45042,plain,
( ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X87,X86),not(strict_equiv(X86,X87)))))
| ~ spl2_722 ),
inference(avatar_component_clause,[],[f45041]) ).
fof(f45041,plain,
( spl2_722
<=> ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X87,X86),not(strict_equiv(X86,X87))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_722])]) ).
fof(f73689,plain,
( ~ spl2_387
| ~ spl2_750 ),
inference(avatar_contradiction_clause,[],[f73278]) ).
fof(f73278,plain,
( $false
| ~ spl2_387
| ~ spl2_750 ),
inference(resolution,[],[f14076,f49059]) ).
fof(f49059,plain,
( ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X86,X87),not(strict_equiv(X86,X87)))))
| ~ spl2_750 ),
inference(avatar_component_clause,[],[f49058]) ).
fof(f49058,plain,
( spl2_750
<=> ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X86,X87),not(strict_equiv(X86,X87))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_750])]) ).
fof(f73688,plain,
( ~ spl2_387
| ~ spl2_856 ),
inference(avatar_contradiction_clause,[],[f73279]) ).
fof(f73279,plain,
( $false
| ~ spl2_387
| ~ spl2_856 ),
inference(resolution,[],[f14076,f62031]) ).
fof(f62031,plain,
( ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X95,X94),implies(strict_equiv(X94,X95),X96))))
| ~ spl2_856 ),
inference(avatar_component_clause,[],[f62030]) ).
fof(f62030,plain,
( spl2_856
<=> ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X95,X94),implies(strict_equiv(X94,X95),X96)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_856])]) ).
fof(f73687,plain,
( ~ spl2_387
| ~ spl2_919 ),
inference(avatar_contradiction_clause,[],[f73280]) ).
fof(f73280,plain,
( $false
| ~ spl2_387
| ~ spl2_919 ),
inference(resolution,[],[f14076,f66732]) ).
fof(f66732,plain,
( ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X94,X95),implies(strict_equiv(X94,X95),X96))))
| ~ spl2_919 ),
inference(avatar_component_clause,[],[f66731]) ).
fof(f66731,plain,
( spl2_919
<=> ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X94,X95),implies(strict_equiv(X94,X95),X96)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_919])]) ).
fof(f73686,plain,
( ~ spl2_387
| ~ spl2_630 ),
inference(avatar_contradiction_clause,[],[f73281]) ).
fof(f73281,plain,
( $false
| ~ spl2_387
| ~ spl2_630 ),
inference(resolution,[],[f14076,f34616]) ).
fof(f34616,plain,
( ! [X72,X70,X71] : is_a_theorem(necessarily(or(strict_equiv(X70,X71),implies(strict_equiv(X71,X70),X72))))
| ~ spl2_630 ),
inference(avatar_component_clause,[],[f34615]) ).
fof(f34615,plain,
( spl2_630
<=> ! [X70,X72,X71] : is_a_theorem(necessarily(or(strict_equiv(X70,X71),implies(strict_equiv(X71,X70),X72)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_630])]) ).
fof(f73685,plain,
( ~ spl2_387
| ~ spl2_751 ),
inference(avatar_contradiction_clause,[],[f73282]) ).
fof(f73282,plain,
( $false
| ~ spl2_387
| ~ spl2_751 ),
inference(resolution,[],[f14076,f49063]) ).
fof(f49063,plain,
( ! [X104,X103] : is_a_theorem(necessarily(or(strict_equiv(X103,X104),not(strict_equiv(X104,X103)))))
| ~ spl2_751 ),
inference(avatar_component_clause,[],[f49062]) ).
fof(f49062,plain,
( spl2_751
<=> ! [X104,X103] : is_a_theorem(necessarily(or(strict_equiv(X103,X104),not(strict_equiv(X104,X103))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_751])]) ).
fof(f73684,plain,
( ~ spl2_387
| ~ spl2_554 ),
inference(avatar_contradiction_clause,[],[f73283]) ).
fof(f73283,plain,
( $false
| ~ spl2_387
| ~ spl2_554 ),
inference(resolution,[],[f14076,f29241]) ).
fof(f29241,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(possibly(X0),not(and(X1,possibly(X0))))))
| ~ spl2_554 ),
inference(avatar_component_clause,[],[f29240]) ).
fof(f29240,plain,
( spl2_554
<=> ! [X0,X1] : is_a_theorem(necessarily(or(possibly(X0),not(and(X1,possibly(X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_554])]) ).
fof(f73683,plain,
( ~ spl2_387
| ~ spl2_588 ),
inference(avatar_contradiction_clause,[],[f73284]) ).
fof(f73284,plain,
( $false
| ~ spl2_387
| ~ spl2_588 ),
inference(resolution,[],[f14076,f30526]) ).
fof(f30526,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(possibly(X2),not(and(possibly(X2),X1)))))
| ~ spl2_588 ),
inference(avatar_component_clause,[],[f30525]) ).
fof(f30525,plain,
( spl2_588
<=> ! [X2,X1] : is_a_theorem(necessarily(or(possibly(X2),not(and(possibly(X2),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_588])]) ).
fof(f73682,plain,
( ~ spl2_387
| ~ spl2_962 ),
inference(avatar_contradiction_clause,[],[f73286]) ).
fof(f73286,plain,
( $false
| ~ spl2_387
| ~ spl2_962 ),
inference(resolution,[],[f14076,f73028]) ).
fof(f73681,plain,
( ~ spl2_71
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73287]) ).
fof(f73287,plain,
( $false
| ~ spl2_71
| ~ spl2_387 ),
inference(resolution,[],[f14076,f739]) ).
fof(f73680,plain,
( ~ spl2_387
| ~ spl2_964 ),
inference(avatar_contradiction_clause,[],[f73288]) ).
fof(f73288,plain,
( $false
| ~ spl2_387
| ~ spl2_964 ),
inference(resolution,[],[f14076,f73056]) ).
fof(f73679,plain,
( ~ spl2_346
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73289]) ).
fof(f73289,plain,
( $false
| ~ spl2_346
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11773]) ).
fof(f11773,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,not(X3)),X4)))
| ~ spl2_346 ),
inference(avatar_component_clause,[],[f11772]) ).
fof(f11772,plain,
( spl2_346
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,not(X3)),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_346])]) ).
fof(f73678,plain,
( ~ spl2_347
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73290]) ).
fof(f73290,plain,
( $false
| ~ spl2_347
| ~ spl2_387 ),
inference(resolution,[],[f14076,f11777]) ).
fof(f11777,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(not(X5),X6),X7)))
| ~ spl2_347 ),
inference(avatar_component_clause,[],[f11776]) ).
fof(f11776,plain,
( spl2_347
<=> ! [X6,X5,X7] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(not(X5),X6),X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_347])]) ).
fof(f73677,plain,
( ~ spl2_387
| ~ spl2_642 ),
inference(avatar_contradiction_clause,[],[f73291]) ).
fof(f73291,plain,
( $false
| ~ spl2_387
| ~ spl2_642 ),
inference(resolution,[],[f14076,f36244]) ).
fof(f36244,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,possibly(X4)),X3)))
| ~ spl2_642 ),
inference(avatar_component_clause,[],[f36243]) ).
fof(f36243,plain,
( spl2_642
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,possibly(X4)),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_642])]) ).
fof(f73676,plain,
( ~ spl2_387
| ~ spl2_752 ),
inference(avatar_contradiction_clause,[],[f73292]) ).
fof(f73292,plain,
( $false
| ~ spl2_387
| ~ spl2_752 ),
inference(resolution,[],[f14076,f49067]) ).
fof(f49067,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X4,X6),X5)))
| ~ spl2_752 ),
inference(avatar_component_clause,[],[f49066]) ).
fof(f49066,plain,
( spl2_752
<=> ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X4,X6),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_752])]) ).
fof(f73675,plain,
( ~ spl2_387
| ~ spl2_723 ),
inference(avatar_contradiction_clause,[],[f73293]) ).
fof(f73293,plain,
( $false
| ~ spl2_387
| ~ spl2_723 ),
inference(resolution,[],[f14076,f45046]) ).
fof(f45046,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X6,X4),X5)))
| ~ spl2_723 ),
inference(avatar_component_clause,[],[f45045]) ).
fof(f45045,plain,
( spl2_723
<=> ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X6,X4),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_723])]) ).
fof(f73674,plain,
( ~ spl2_387
| ~ spl2_659 ),
inference(avatar_contradiction_clause,[],[f73294]) ).
fof(f73294,plain,
( $false
| ~ spl2_387
| ~ spl2_659 ),
inference(resolution,[],[f14076,f37094]) ).
fof(f37094,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(possibly(X7),X6),X5)))
| ~ spl2_659 ),
inference(avatar_component_clause,[],[f37093]) ).
fof(f37093,plain,
( spl2_659
<=> ! [X6,X5,X7] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(possibly(X7),X6),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_659])]) ).
fof(f73673,plain,
( ~ spl2_387
| ~ spl2_533 ),
inference(avatar_contradiction_clause,[],[f73296]) ).
fof(f73296,plain,
( $false
| ~ spl2_387
| ~ spl2_533 ),
inference(resolution,[],[f14076,f28314]) ).
fof(f28314,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(implies(implies(X3,X2),not(X2)),not(X2)))
| ~ spl2_533 ),
inference(avatar_component_clause,[],[f28313]) ).
fof(f28313,plain,
( spl2_533
<=> ! [X2,X3] : is_a_theorem(strict_implies(implies(implies(X3,X2),not(X2)),not(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_533])]) ).
fof(f73672,plain,
( ~ spl2_387
| ~ spl2_542 ),
inference(avatar_contradiction_clause,[],[f73297]) ).
fof(f73297,plain,
( $false
| ~ spl2_387
| ~ spl2_542 ),
inference(resolution,[],[f14076,f28624]) ).
fof(f28624,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X2,X0),X1),X0),X0))
| ~ spl2_542 ),
inference(avatar_component_clause,[],[f28623]) ).
fof(f28623,plain,
( spl2_542
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X2,X0),X1),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_542])]) ).
fof(f73671,plain,
( ~ spl2_387
| ~ spl2_543 ),
inference(avatar_contradiction_clause,[],[f73298]) ).
fof(f73298,plain,
( $false
| ~ spl2_387
| ~ spl2_543 ),
inference(resolution,[],[f14076,f28628]) ).
fof(f28628,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X0,X2),X1),X0),X0))
| ~ spl2_543 ),
inference(avatar_component_clause,[],[f28627]) ).
fof(f28627,plain,
( spl2_543
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X0,X2),X1),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_543])]) ).
fof(f73670,plain,
( ~ spl2_387
| ~ spl2_545 ),
inference(avatar_contradiction_clause,[],[f73299]) ).
fof(f73299,plain,
( $false
| ~ spl2_387
| ~ spl2_545 ),
inference(resolution,[],[f14076,f28636]) ).
fof(f28636,plain,
( ! [X11,X12] : is_a_theorem(strict_implies(implies(or(X11,X12),not(X12)),not(X12)))
| ~ spl2_545 ),
inference(avatar_component_clause,[],[f28635]) ).
fof(f28635,plain,
( spl2_545
<=> ! [X11,X12] : is_a_theorem(strict_implies(implies(or(X11,X12),not(X12)),not(X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_545])]) ).
fof(f73669,plain,
( ~ spl2_44
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73300]) ).
fof(f73300,plain,
( $false
| ~ spl2_44
| ~ spl2_387 ),
inference(resolution,[],[f14076,f441]) ).
fof(f73668,plain,
( ~ spl2_84
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73301]) ).
fof(f73301,plain,
( $false
| ~ spl2_84
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1047]) ).
fof(f1047,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(equiv(X3,X2),implies(X2,X3)))
| ~ spl2_84 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1046,plain,
( spl2_84
<=> ! [X2,X3] : is_a_theorem(strict_implies(equiv(X3,X2),implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_84])]) ).
fof(f73667,plain,
( ~ spl2_45
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73302]) ).
fof(f73302,plain,
( $false
| ~ spl2_45
| ~ spl2_387 ),
inference(resolution,[],[f14076,f445]) ).
fof(f445,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(equiv(X9,X8),equiv(X8,X9)))
| ~ spl2_45 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f444,plain,
( spl2_45
<=> ! [X9,X8] : is_a_theorem(strict_implies(equiv(X9,X8),equiv(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
fof(f73666,plain,
( ~ spl2_56
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73303]) ).
fof(f73303,plain,
( $false
| ~ spl2_56
| ~ spl2_387 ),
inference(resolution,[],[f14076,f530]) ).
fof(f530,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(not(X0),X1),or(X0,X1)))
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f529,plain,
( spl2_56
<=> ! [X0,X1] : is_a_theorem(strict_implies(equiv(not(X0),X1),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
fof(f73665,plain,
( ~ spl2_100
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73304]) ).
fof(f73304,plain,
( $false
| ~ spl2_100
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1307]) ).
fof(f1307,plain,
( ! [X10,X9] : is_a_theorem(strict_implies(equiv(not(X9),X10),or(X10,X9)))
| ~ spl2_100 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f1306,plain,
( spl2_100
<=> ! [X9,X10] : is_a_theorem(strict_implies(equiv(not(X9),X10),or(X10,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_100])]) ).
fof(f73664,plain,
( ~ spl2_387
| ~ spl2_444 ),
inference(avatar_contradiction_clause,[],[f73305]) ).
fof(f73305,plain,
( $false
| ~ spl2_387
| ~ spl2_444 ),
inference(resolution,[],[f14076,f16308]) ).
fof(f16308,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(equiv(necessarily(not(X3)),X2),not(and(X2,possibly(X3)))))
| ~ spl2_444 ),
inference(avatar_component_clause,[],[f16307]) ).
fof(f16307,plain,
( spl2_444
<=> ! [X2,X3] : is_a_theorem(strict_implies(equiv(necessarily(not(X3)),X2),not(and(X2,possibly(X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_444])]) ).
fof(f73663,plain,
( ~ spl2_95
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73306]) ).
fof(f73306,plain,
( $false
| ~ spl2_95
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1119]) ).
fof(f1119,plain,
( ! [X18,X17] : is_a_theorem(strict_implies(equiv(X18,not(X17)),or(X17,X18)))
| ~ spl2_95 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f1118,plain,
( spl2_95
<=> ! [X18,X17] : is_a_theorem(strict_implies(equiv(X18,not(X17)),or(X17,X18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).
fof(f73662,plain,
( ~ spl2_99
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73307]) ).
fof(f73307,plain,
( $false
| ~ spl2_99
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1287]) ).
fof(f1287,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(equiv(X4,not(X3)),or(X4,X3)))
| ~ spl2_99 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f1286,plain,
( spl2_99
<=> ! [X4,X3] : is_a_theorem(strict_implies(equiv(X4,not(X3)),or(X4,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_99])]) ).
fof(f73661,plain,
( ~ spl2_98
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73308]) ).
fof(f73308,plain,
( $false
| ~ spl2_98
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1274]) ).
fof(f1274,plain,
( ! [X2] : is_a_theorem(strict_implies(equiv(X2,not(X2)),not(not(X2))))
| ~ spl2_98 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1273,plain,
( spl2_98
<=> ! [X2] : is_a_theorem(strict_implies(equiv(X2,not(X2)),not(not(X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).
fof(f73660,plain,
( ~ spl2_387
| ~ spl2_672 ),
inference(avatar_contradiction_clause,[],[f73309]) ).
fof(f73309,plain,
( $false
| ~ spl2_387
| ~ spl2_672 ),
inference(resolution,[],[f14076,f39163]) ).
fof(f39163,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(X0,not(X0)),X0))
| ~ spl2_672 ),
inference(avatar_component_clause,[],[f39162]) ).
fof(f39162,plain,
( spl2_672
<=> ! [X0] : is_a_theorem(strict_implies(equiv(X0,not(X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_672])]) ).
fof(f73659,plain,
( ~ spl2_387
| ~ spl2_889 ),
inference(avatar_contradiction_clause,[],[f73310]) ).
fof(f73310,plain,
( $false
| ~ spl2_387
| ~ spl2_889 ),
inference(resolution,[],[f14076,f62819]) ).
fof(f62819,plain,
( ! [X26,X25] : is_a_theorem(strict_implies(equiv(and(X25,X26),not(and(X25,X26))),X26))
| ~ spl2_889 ),
inference(avatar_component_clause,[],[f62818]) ).
fof(f62818,plain,
( spl2_889
<=> ! [X25,X26] : is_a_theorem(strict_implies(equiv(and(X25,X26),not(and(X25,X26))),X26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_889])]) ).
fof(f73658,plain,
( ~ spl2_387
| ~ spl2_891 ),
inference(avatar_contradiction_clause,[],[f73311]) ).
fof(f73311,plain,
( $false
| ~ spl2_387
| ~ spl2_891 ),
inference(resolution,[],[f14076,f62827]) ).
fof(f62827,plain,
( ! [X28,X27] : is_a_theorem(strict_implies(equiv(and(X27,X28),not(and(X27,X28))),X27))
| ~ spl2_891 ),
inference(avatar_component_clause,[],[f62826]) ).
fof(f62826,plain,
( spl2_891
<=> ! [X27,X28] : is_a_theorem(strict_implies(equiv(and(X27,X28),not(and(X27,X28))),X27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_891])]) ).
fof(f73657,plain,
( ~ spl2_157
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73312]) ).
fof(f73312,plain,
( $false
| ~ spl2_157
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2735]) ).
fof(f73656,plain,
( ~ spl2_370
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73313]) ).
fof(f73313,plain,
( $false
| ~ spl2_370
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12374]) ).
fof(f73655,plain,
( ~ spl2_237
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73314]) ).
fof(f73314,plain,
( $false
| ~ spl2_237
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6134]) ).
fof(f6134,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(equiv(X6,and(not(X6),X7)),implies(X7,X6)))
| ~ spl2_237 ),
inference(avatar_component_clause,[],[f6133]) ).
fof(f6133,plain,
( spl2_237
<=> ! [X6,X7] : is_a_theorem(strict_implies(equiv(X6,and(not(X6),X7)),implies(X7,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_237])]) ).
fof(f73654,plain,
( ~ spl2_248
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73315]) ).
fof(f73315,plain,
( $false
| ~ spl2_248
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6952]) ).
fof(f6952,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(equiv(X8,and(X7,not(X8))),implies(X7,X8)))
| ~ spl2_248 ),
inference(avatar_component_clause,[],[f6951]) ).
fof(f6951,plain,
( spl2_248
<=> ! [X8,X7] : is_a_theorem(strict_implies(equiv(X8,and(X7,not(X8))),implies(X7,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_248])]) ).
fof(f73653,plain,
( ~ spl2_324
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73316]) ).
fof(f73316,plain,
( $false
| ~ spl2_324
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10241]) ).
fof(f73652,plain,
( ~ spl2_387
| ~ spl2_742 ),
inference(avatar_contradiction_clause,[],[f73317]) ).
fof(f73317,plain,
( $false
| ~ spl2_387
| ~ spl2_742 ),
inference(resolution,[],[f14076,f46195]) ).
fof(f46195,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(equiv(not(and(X12,possibly(X13))),and(necessarily(not(X13)),not(X12))),not(equiv(X12,necessarily(not(X13))))))
| ~ spl2_742 ),
inference(avatar_component_clause,[],[f46194]) ).
fof(f46194,plain,
( spl2_742
<=> ! [X13,X12] : is_a_theorem(strict_implies(equiv(not(and(X12,possibly(X13))),and(necessarily(not(X13)),not(X12))),not(equiv(X12,necessarily(not(X13)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_742])]) ).
fof(f73651,plain,
( ~ spl2_387
| ~ spl2_829 ),
inference(avatar_contradiction_clause,[],[f73318]) ).
fof(f73318,plain,
( $false
| ~ spl2_387
| ~ spl2_829 ),
inference(resolution,[],[f14076,f57347]) ).
fof(f57347,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(equiv(not(and(X21,implies(X22,X23))),and(not(X23),and(X22,not(X21)))),not(equiv(and(X22,not(X23)),X21))))
| ~ spl2_829 ),
inference(avatar_component_clause,[],[f57346]) ).
fof(f57346,plain,
( spl2_829
<=> ! [X22,X21,X23] : is_a_theorem(strict_implies(equiv(not(and(X21,implies(X22,X23))),and(not(X23),and(X22,not(X21)))),not(equiv(and(X22,not(X23)),X21)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_829])]) ).
fof(f73650,plain,
( ~ spl2_387
| ~ spl2_430 ),
inference(avatar_contradiction_clause,[],[f73319]) ).
fof(f73319,plain,
( $false
| ~ spl2_387
| ~ spl2_430 ),
inference(resolution,[],[f14076,f15001]) ).
fof(f15001,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(equiv(or(X10,X11),and(X11,not(not(X10)))),not(equiv(not(X10),X11))))
| ~ spl2_430 ),
inference(avatar_component_clause,[],[f15000]) ).
fof(f15000,plain,
( spl2_430
<=> ! [X11,X10] : is_a_theorem(strict_implies(equiv(or(X10,X11),and(X11,not(not(X10)))),not(equiv(not(X10),X11)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_430])]) ).
fof(f73649,plain,
( ~ spl2_114
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73320]) ).
fof(f73320,plain,
( $false
| ~ spl2_114
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1641]) ).
fof(f73648,plain,
( ~ spl2_306
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73321]) ).
fof(f73321,plain,
( $false
| ~ spl2_306
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9460]) ).
fof(f9460,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(equiv(X1,necessarily(not(X2))),not(and(possibly(X2),X1))))
| ~ spl2_306 ),
inference(avatar_component_clause,[],[f9459]) ).
fof(f9459,plain,
( spl2_306
<=> ! [X2,X1] : is_a_theorem(strict_implies(equiv(X1,necessarily(not(X2))),not(and(possibly(X2),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_306])]) ).
fof(f73647,plain,
( ~ spl2_224
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73322]) ).
fof(f73322,plain,
( $false
| ~ spl2_224
| ~ spl2_387 ),
inference(resolution,[],[f14076,f5463]) ).
fof(f5463,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),not(possibly(X0))))
| ~ spl2_224 ),
inference(avatar_component_clause,[],[f5462]) ).
fof(f5462,plain,
( spl2_224
<=> ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),not(possibly(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_224])]) ).
fof(f73646,plain,
( ~ spl2_387
| ~ spl2_892 ),
inference(avatar_contradiction_clause,[],[f73323]) ).
fof(f73323,plain,
( $false
| ~ spl2_387
| ~ spl2_892 ),
inference(resolution,[],[f14076,f62831]) ).
fof(f62831,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),necessarily(not(X0))))
| ~ spl2_892 ),
inference(avatar_component_clause,[],[f62830]) ).
fof(f62830,plain,
( spl2_892
<=> ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),necessarily(not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_892])]) ).
fof(f73645,plain,
( ~ spl2_19
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73324]) ).
fof(f73324,plain,
( $false
| ~ spl2_19
| ~ spl2_387 ),
inference(resolution,[],[f14076,f270]) ).
fof(f73644,plain,
( ~ spl2_25
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73325]) ).
fof(f73325,plain,
( $false
| ~ spl2_25
| ~ spl2_387 ),
inference(resolution,[],[f14076,f295]) ).
fof(f295,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f294,plain,
( spl2_25
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f73643,plain,
( ~ spl2_81
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73326]) ).
fof(f73326,plain,
( $false
| ~ spl2_81
| ~ spl2_387 ),
inference(resolution,[],[f14076,f912]) ).
fof(f912,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X2,X1),X1))
| ~ spl2_81 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f911,plain,
( spl2_81
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(X2,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
fof(f73642,plain,
( ~ spl2_156
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73327]) ).
fof(f73327,plain,
( $false
| ~ spl2_156
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2731]) ).
fof(f2731,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X14,X15)))
| ~ spl2_156 ),
inference(avatar_component_clause,[],[f2730]) ).
fof(f2730,plain,
( spl2_156
<=> ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X14,X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_156])]) ).
fof(f73641,plain,
( ~ spl2_175
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73328]) ).
fof(f73328,plain,
( $false
| ~ spl2_175
| ~ spl2_387 ),
inference(resolution,[],[f14076,f3355]) ).
fof(f3355,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X15,X14)))
| ~ spl2_175 ),
inference(avatar_component_clause,[],[f3354]) ).
fof(f3354,plain,
( spl2_175
<=> ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X15,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_175])]) ).
fof(f73640,plain,
( ~ spl2_284
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73329]) ).
fof(f73329,plain,
( $false
| ~ spl2_284
| ~ spl2_387 ),
inference(resolution,[],[f14076,f8436]) ).
fof(f8436,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,equiv(X8,X9)),equiv(X9,X8)))
| ~ spl2_284 ),
inference(avatar_component_clause,[],[f8435]) ).
fof(f8435,plain,
( spl2_284
<=> ! [X9,X8,X7] : is_a_theorem(strict_implies(and(X7,equiv(X8,X9)),equiv(X9,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_284])]) ).
fof(f73639,plain,
( ~ spl2_387
| ~ spl2_507 ),
inference(avatar_contradiction_clause,[],[f73330]) ).
fof(f73330,plain,
( $false
| ~ spl2_387
| ~ spl2_507 ),
inference(resolution,[],[f14076,f24816]) ).
fof(f24816,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(X5,equiv(X4,X3)),and(X5,equiv(X3,X4))))
| ~ spl2_507 ),
inference(avatar_component_clause,[],[f24815]) ).
fof(f24815,plain,
( spl2_507
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(X5,equiv(X4,X3)),and(X5,equiv(X3,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_507])]) ).
fof(f73638,plain,
( ~ spl2_387
| ~ spl2_901 ),
inference(avatar_contradiction_clause,[],[f73331]) ).
fof(f73331,plain,
( $false
| ~ spl2_387
| ~ spl2_901 ),
inference(resolution,[],[f14076,f64149]) ).
fof(f64149,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,equiv(X2,X3)),and(equiv(X3,X2),X4)))
| ~ spl2_901 ),
inference(avatar_component_clause,[],[f64148]) ).
fof(f64148,plain,
( spl2_901
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,equiv(X2,X3)),and(equiv(X3,X2),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_901])]) ).
fof(f73637,plain,
( ~ spl2_227
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73332]) ).
fof(f73332,plain,
( $false
| ~ spl2_227
| ~ spl2_387 ),
inference(resolution,[],[f14076,f5535]) ).
fof(f5535,plain,
( ! [X18,X19,X17] : is_a_theorem(strict_implies(and(X19,equiv(not(X17),X18)),or(X17,X18)))
| ~ spl2_227 ),
inference(avatar_component_clause,[],[f5534]) ).
fof(f5534,plain,
( spl2_227
<=> ! [X18,X17,X19] : is_a_theorem(strict_implies(and(X19,equiv(not(X17),X18)),or(X17,X18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_227])]) ).
fof(f73636,plain,
( ~ spl2_240
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73333]) ).
fof(f73333,plain,
( $false
| ~ spl2_240
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6146]) ).
fof(f6146,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X11,equiv(not(X9),X10)),or(X10,X9)))
| ~ spl2_240 ),
inference(avatar_component_clause,[],[f6145]) ).
fof(f6145,plain,
( spl2_240
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(X11,equiv(not(X9),X10)),or(X10,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_240])]) ).
fof(f73635,plain,
( ~ spl2_242
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73334]) ).
fof(f73334,plain,
( $false
| ~ spl2_242
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6154]) ).
fof(f6154,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(X8,equiv(X7,not(X7))),not(not(X7))))
| ~ spl2_242 ),
inference(avatar_component_clause,[],[f6153]) ).
fof(f6153,plain,
( spl2_242
<=> ! [X7,X8] : is_a_theorem(strict_implies(and(X8,equiv(X7,not(X7))),not(not(X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_242])]) ).
fof(f73634,plain,
( ~ spl2_251
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73335]) ).
fof(f73335,plain,
( $false
| ~ spl2_251
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6964]) ).
fof(f6964,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,equiv(X1,not(X0))),or(X0,X1)))
| ~ spl2_251 ),
inference(avatar_component_clause,[],[f6963]) ).
fof(f6963,plain,
( spl2_251
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,equiv(X1,not(X0))),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_251])]) ).
fof(f73633,plain,
( ~ spl2_256
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73336]) ).
fof(f73336,plain,
( $false
| ~ spl2_256
| ~ spl2_387 ),
inference(resolution,[],[f14076,f7157]) ).
fof(f7157,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,equiv(X3,not(X2))),or(X3,X2)))
| ~ spl2_256 ),
inference(avatar_component_clause,[],[f7156]) ).
fof(f7156,plain,
( spl2_256
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(X4,equiv(X3,not(X2))),or(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_256])]) ).
fof(f73632,plain,
( ~ spl2_387
| ~ spl2_909 ),
inference(avatar_contradiction_clause,[],[f73337]) ).
fof(f73337,plain,
( $false
| ~ spl2_387
| ~ spl2_909 ),
inference(resolution,[],[f14076,f65191]) ).
fof(f65191,plain,
( ! [X16,X15] : is_a_theorem(strict_implies(and(X15,equiv(X16,not(X16))),X16))
| ~ spl2_909 ),
inference(avatar_component_clause,[],[f65190]) ).
fof(f65190,plain,
( spl2_909
<=> ! [X16,X15] : is_a_theorem(strict_implies(and(X15,equiv(X16,not(X16))),X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_909])]) ).
fof(f73631,plain,
( ~ spl2_387
| ~ spl2_665 ),
inference(avatar_contradiction_clause,[],[f73338]) ).
fof(f73338,plain,
( $false
| ~ spl2_387
| ~ spl2_665 ),
inference(resolution,[],[f14076,f37547]) ).
fof(f73630,plain,
( ~ spl2_387
| ~ spl2_699 ),
inference(avatar_contradiction_clause,[],[f73339]) ).
fof(f73339,plain,
( $false
| ~ spl2_387
| ~ spl2_699 ),
inference(resolution,[],[f14076,f42478]) ).
fof(f42478,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(X43,not(not(and(X44,X45)))),X44))
| ~ spl2_699 ),
inference(avatar_component_clause,[],[f42477]) ).
fof(f42477,plain,
( spl2_699
<=> ! [X45,X44,X43] : is_a_theorem(strict_implies(and(X43,not(not(and(X44,X45)))),X44)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_699])]) ).
fof(f73629,plain,
( ~ spl2_387
| ~ spl2_936 ),
inference(avatar_contradiction_clause,[],[f73340]) ).
fof(f73340,plain,
( $false
| ~ spl2_387
| ~ spl2_936 ),
inference(resolution,[],[f14076,f67051]) ).
fof(f67051,plain,
( ! [X19,X20] : is_a_theorem(strict_implies(and(X19,not(not(equiv(X20,not(X20))))),X20))
| ~ spl2_936 ),
inference(avatar_component_clause,[],[f67050]) ).
fof(f67050,plain,
( spl2_936
<=> ! [X20,X19] : is_a_theorem(strict_implies(and(X19,not(not(equiv(X20,not(X20))))),X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_936])]) ).
fof(f73628,plain,
( ~ spl2_387
| ~ spl2_686 ),
inference(avatar_contradiction_clause,[],[f73341]) ).
fof(f73341,plain,
( $false
| ~ spl2_387
| ~ spl2_686 ),
inference(resolution,[],[f14076,f41209]) ).
fof(f41209,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,not(implies(X2,X3))),X2))
| ~ spl2_686 ),
inference(avatar_component_clause,[],[f41208]) ).
fof(f41208,plain,
( spl2_686
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(X4,not(implies(X2,X3))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_686])]) ).
fof(f73627,plain,
( ~ spl2_387
| ~ spl2_698 ),
inference(avatar_contradiction_clause,[],[f73342]) ).
fof(f73342,plain,
( $false
| ~ spl2_387
| ~ spl2_698 ),
inference(resolution,[],[f14076,f42474]) ).
fof(f42474,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(X40,not(not(and(X41,X42)))),X42))
| ~ spl2_698 ),
inference(avatar_component_clause,[],[f42473]) ).
fof(f42473,plain,
( spl2_698
<=> ! [X41,X40,X42] : is_a_theorem(strict_implies(and(X40,not(not(and(X41,X42)))),X42)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_698])]) ).
fof(f73626,plain,
( ~ spl2_385
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73343]) ).
fof(f73343,plain,
( $false
| ~ spl2_385
| ~ spl2_387 ),
inference(resolution,[],[f14076,f13748]) ).
fof(f13748,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),implies(X9,X11)))
| ~ spl2_385 ),
inference(avatar_component_clause,[],[f13747]) ).
fof(f13747,plain,
( spl2_385
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(X10,not(X9)),implies(X9,X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_385])]) ).
fof(f73625,plain,
( ~ spl2_387
| ~ spl2_934 ),
inference(avatar_contradiction_clause,[],[f73344]) ).
fof(f73344,plain,
( $false
| ~ spl2_387
| ~ spl2_934 ),
inference(resolution,[],[f14076,f67043]) ).
fof(f67043,plain,
( ! [X40,X38,X41,X39] : is_a_theorem(strict_implies(and(X39,not(X38)),implies(and(X40,X38),X41)))
| ~ spl2_934 ),
inference(avatar_component_clause,[],[f67042]) ).
fof(f67042,plain,
( spl2_934
<=> ! [X38,X41,X40,X39] : is_a_theorem(strict_implies(and(X39,not(X38)),implies(and(X40,X38),X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_934])]) ).
fof(f73624,plain,
( ~ spl2_387
| ~ spl2_423 ),
inference(avatar_contradiction_clause,[],[f73345]) ).
fof(f73345,plain,
( $false
| ~ spl2_387
| ~ spl2_423 ),
inference(resolution,[],[f14076,f14893]) ).
fof(f14893,plain,
( ! [X18,X16,X17] : is_a_theorem(strict_implies(and(X18,not(not(X16))),implies(possibly(X17),X16)))
| ~ spl2_423 ),
inference(avatar_component_clause,[],[f14892]) ).
fof(f14892,plain,
( spl2_423
<=> ! [X18,X16,X17] : is_a_theorem(strict_implies(and(X18,not(not(X16))),implies(possibly(X17),X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_423])]) ).
fof(f73623,plain,
( ~ spl2_387
| ~ spl2_587 ),
inference(avatar_contradiction_clause,[],[f73346]) ).
fof(f73346,plain,
( $false
| ~ spl2_387
| ~ spl2_587 ),
inference(resolution,[],[f14076,f30522]) ).
fof(f30522,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),implies(X4,X2)))
| ~ spl2_587 ),
inference(avatar_component_clause,[],[f30521]) ).
fof(f30521,plain,
( spl2_587
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),implies(X4,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_587])]) ).
fof(f73622,plain,
( ~ spl2_387
| ~ spl2_416 ),
inference(avatar_contradiction_clause,[],[f73347]) ).
fof(f73347,plain,
( $false
| ~ spl2_387
| ~ spl2_416 ),
inference(resolution,[],[f14076,f14626]) ).
fof(f14626,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(X0)),not(and(X0,possibly(X1)))))
| ~ spl2_416 ),
inference(avatar_component_clause,[],[f14625]) ).
fof(f14625,plain,
( spl2_416
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(X0)),not(and(X0,possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_416])]) ).
fof(f73621,plain,
( ~ spl2_387
| ~ spl2_790 ),
inference(avatar_contradiction_clause,[],[f73348]) ).
fof(f73348,plain,
( $false
| ~ spl2_387
| ~ spl2_790 ),
inference(resolution,[],[f14076,f52765]) ).
fof(f52765,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X9,X11))))
| ~ spl2_790 ),
inference(avatar_component_clause,[],[f52764]) ).
fof(f52764,plain,
( spl2_790
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X9,X11)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_790])]) ).
fof(f73620,plain,
( ~ spl2_387
| ~ spl2_426 ),
inference(avatar_contradiction_clause,[],[f73349]) ).
fof(f73349,plain,
( $false
| ~ spl2_387
| ~ spl2_426 ),
inference(resolution,[],[f14076,f14905]) ).
fof(f14905,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(possibly(X11),X9))))
| ~ spl2_426 ),
inference(avatar_component_clause,[],[f14904]) ).
fof(f14904,plain,
( spl2_426
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(possibly(X11),X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_426])]) ).
fof(f73619,plain,
( ~ spl2_387
| ~ spl2_759 ),
inference(avatar_contradiction_clause,[],[f73350]) ).
fof(f73350,plain,
( $false
| ~ spl2_387
| ~ spl2_759 ),
inference(resolution,[],[f14076,f49197]) ).
fof(f49197,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X11,X9))))
| ~ spl2_759 ),
inference(avatar_component_clause,[],[f49196]) ).
fof(f49196,plain,
( spl2_759
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X11,X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_759])]) ).
fof(f73618,plain,
( ~ spl2_387
| ~ spl2_727 ),
inference(avatar_contradiction_clause,[],[f73351]) ).
fof(f73351,plain,
( $false
| ~ spl2_387
| ~ spl2_727 ),
inference(resolution,[],[f14076,f45383]) ).
fof(f45383,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(implies(X0,X1))),not(X1)))
| ~ spl2_727 ),
inference(avatar_component_clause,[],[f45382]) ).
fof(f45382,plain,
( spl2_727
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(implies(X0,X1))),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_727])]) ).
fof(f73617,plain,
( ~ spl2_387
| ~ spl2_764 ),
inference(avatar_contradiction_clause,[],[f73352]) ).
fof(f73352,plain,
( $false
| ~ spl2_387
| ~ spl2_764 ),
inference(resolution,[],[f14076,f49217]) ).
fof(f49217,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X16)))
| ~ spl2_764 ),
inference(avatar_component_clause,[],[f49216]) ).
fof(f49216,plain,
( spl2_764
<=> ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_764])]) ).
fof(f73616,plain,
( ~ spl2_387
| ~ spl2_755 ),
inference(avatar_contradiction_clause,[],[f73353]) ).
fof(f73353,plain,
( $false
| ~ spl2_387
| ~ spl2_755 ),
inference(resolution,[],[f14076,f49130]) ).
fof(f49130,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X15)))
| ~ spl2_755 ),
inference(avatar_component_clause,[],[f49129]) ).
fof(f49129,plain,
( spl2_755
<=> ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_755])]) ).
fof(f73615,plain,
( ~ spl2_387
| ~ spl2_393 ),
inference(avatar_contradiction_clause,[],[f73354]) ).
fof(f73354,plain,
( $false
| ~ spl2_387
| ~ spl2_393 ),
inference(resolution,[],[f14076,f14162]) ).
fof(f14162,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X9,not(not(X7))),or(X7,X8)))
| ~ spl2_393 ),
inference(avatar_component_clause,[],[f14161]) ).
fof(f14161,plain,
( spl2_393
<=> ! [X9,X8,X7] : is_a_theorem(strict_implies(and(X9,not(not(X7))),or(X7,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_393])]) ).
fof(f73614,plain,
( ~ spl2_387
| ~ spl2_399 ),
inference(avatar_contradiction_clause,[],[f73355]) ).
fof(f73355,plain,
( $false
| ~ spl2_387
| ~ spl2_399 ),
inference(resolution,[],[f14076,f14317]) ).
fof(f14317,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),or(X4,X2)))
| ~ spl2_399 ),
inference(avatar_component_clause,[],[f14316]) ).
fof(f14316,plain,
( spl2_399
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),or(X4,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_399])]) ).
fof(f73613,plain,
( ~ spl2_387
| ~ spl2_700 ),
inference(avatar_contradiction_clause,[],[f73356]) ).
fof(f73356,plain,
( $false
| ~ spl2_387
| ~ spl2_700 ),
inference(resolution,[],[f14076,f42482]) ).
fof(f42482,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X1,not(possibly(X0))),necessarily(not(X0))))
| ~ spl2_700 ),
inference(avatar_component_clause,[],[f42481]) ).
fof(f42481,plain,
( spl2_700
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X1,not(possibly(X0))),necessarily(not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_700])]) ).
fof(f73612,plain,
( ~ spl2_138
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73357]) ).
fof(f73357,plain,
( $false
| ~ spl2_138
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2463]) ).
fof(f2463,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),X8))
| ~ spl2_138 ),
inference(avatar_component_clause,[],[f2462]) ).
fof(f2462,plain,
( spl2_138
<=> ! [X9,X8,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_138])]) ).
fof(f73611,plain,
( ~ spl2_144
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73358]) ).
fof(f73358,plain,
( $false
| ~ spl2_144
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2537]) ).
fof(f2537,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X3,X2)),X2))
| ~ spl2_144 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f2536,plain,
( spl2_144
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(X4,and(X3,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_144])]) ).
fof(f73610,plain,
( ~ spl2_185
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73359]) ).
fof(f73359,plain,
( $false
| ~ spl2_185
| ~ spl2_387 ),
inference(resolution,[],[f14076,f3512]) ).
fof(f3512,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X3,X4)))
| ~ spl2_185 ),
inference(avatar_component_clause,[],[f3511]) ).
fof(f3511,plain,
( spl2_185
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X3,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_185])]) ).
fof(f73609,plain,
( ~ spl2_200
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73360]) ).
fof(f73360,plain,
( $false
| ~ spl2_200
| ~ spl2_387 ),
inference(resolution,[],[f14076,f4157]) ).
fof(f4157,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,X4)))
| ~ spl2_200 ),
inference(avatar_component_clause,[],[f4156]) ).
fof(f4156,plain,
( spl2_200
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_200])]) ).
fof(f73608,plain,
( ~ spl2_207
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73361]) ).
fof(f73361,plain,
( $false
| ~ spl2_207
| ~ spl2_387 ),
inference(resolution,[],[f14076,f4551]) ).
fof(f4551,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,and(X2,X4)),and(X3,X2)))
| ~ spl2_207 ),
inference(avatar_component_clause,[],[f4550]) ).
fof(f4550,plain,
( spl2_207
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(X3,and(X2,X4)),and(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_207])]) ).
fof(f73607,plain,
( ~ spl2_286
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73362]) ).
fof(f73362,plain,
( $false
| ~ spl2_286
| ~ spl2_387 ),
inference(resolution,[],[f14076,f8726]) ).
fof(f8726,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),and(X9,X8)))
| ~ spl2_286 ),
inference(avatar_component_clause,[],[f8725]) ).
fof(f8725,plain,
( spl2_286
<=> ! [X9,X8,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),and(X9,X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_286])]) ).
fof(f73606,plain,
( ~ spl2_203
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73363]) ).
fof(f73363,plain,
( $false
| ~ spl2_203
| ~ spl2_387 ),
inference(resolution,[],[f14076,f4169]) ).
fof(f4169,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,and(X4,X2)),and(X3,X2)))
| ~ spl2_203 ),
inference(avatar_component_clause,[],[f4168]) ).
fof(f4168,plain,
( spl2_203
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(X3,and(X4,X2)),and(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_203])]) ).
fof(f73605,plain,
( ~ spl2_303
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73364]) ).
fof(f73364,plain,
( $false
| ~ spl2_303
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9408]) ).
fof(f9408,plain,
( ! [X38,X39,X37] : is_a_theorem(strict_implies(and(X39,and(X37,X38)),and(X37,and(X38,X39))))
| ~ spl2_303 ),
inference(avatar_component_clause,[],[f9407]) ).
fof(f9407,plain,
( spl2_303
<=> ! [X38,X37,X39] : is_a_theorem(strict_implies(and(X39,and(X37,X38)),and(X37,and(X38,X39)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_303])]) ).
fof(f73604,plain,
( ~ spl2_387
| ~ spl2_903 ),
inference(avatar_contradiction_clause,[],[f73365]) ).
fof(f73365,plain,
( $false
| ~ spl2_387
| ~ spl2_903 ),
inference(resolution,[],[f14076,f64385]) ).
fof(f64385,plain,
( ! [X31,X29,X30] : is_a_theorem(strict_implies(and(X30,and(X29,X31)),and(X31,and(X30,X29))))
| ~ spl2_903 ),
inference(avatar_component_clause,[],[f64384]) ).
fof(f64384,plain,
( spl2_903
<=> ! [X29,X30,X31] : is_a_theorem(strict_implies(and(X30,and(X29,X31)),and(X31,and(X30,X29)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_903])]) ).
fof(f73603,plain,
( ~ spl2_387
| ~ spl2_938 ),
inference(avatar_contradiction_clause,[],[f73366]) ).
fof(f73366,plain,
( $false
| ~ spl2_387
| ~ spl2_938 ),
inference(resolution,[],[f14076,f67064]) ).
fof(f67064,plain,
( ! [X34,X35,X33] : is_a_theorem(strict_implies(and(X33,and(X34,equiv(X35,not(X35)))),X35))
| ~ spl2_938 ),
inference(avatar_component_clause,[],[f67063]) ).
fof(f67063,plain,
( spl2_938
<=> ! [X34,X35,X33] : is_a_theorem(strict_implies(and(X33,and(X34,equiv(X35,not(X35)))),X35)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_938])]) ).
fof(f73602,plain,
( ~ spl2_387
| ~ spl2_646 ),
inference(avatar_contradiction_clause,[],[f73367]) ).
fof(f73367,plain,
( $false
| ~ spl2_387
| ~ spl2_646 ),
inference(resolution,[],[f14076,f36260]) ).
fof(f36260,plain,
( ! [X461,X460,X459,X458] : is_a_theorem(strict_implies(and(X459,and(X460,not(X458))),implies(X458,X461)))
| ~ spl2_646 ),
inference(avatar_component_clause,[],[f36259]) ).
fof(f36259,plain,
( spl2_646
<=> ! [X459,X458,X461,X460] : is_a_theorem(strict_implies(and(X459,and(X460,not(X458))),implies(X458,X461))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_646])]) ).
fof(f73601,plain,
( ~ spl2_387
| ~ spl2_678 ),
inference(avatar_contradiction_clause,[],[f73368]) ).
fof(f73368,plain,
( $false
| ~ spl2_387
| ~ spl2_678 ),
inference(resolution,[],[f14076,f39529]) ).
fof(f39529,plain,
( ! [X28,X29,X27] : is_a_theorem(strict_implies(and(X28,and(X29,not(not(X27)))),X27))
| ~ spl2_678 ),
inference(avatar_component_clause,[],[f39528]) ).
fof(f39528,plain,
( spl2_678
<=> ! [X29,X27,X28] : is_a_theorem(strict_implies(and(X28,and(X29,not(not(X27)))),X27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_678])]) ).
fof(f73600,plain,
( ~ spl2_387
| ~ spl2_930 ),
inference(avatar_contradiction_clause,[],[f73369]) ).
fof(f73369,plain,
( $false
| ~ spl2_387
| ~ spl2_930 ),
inference(resolution,[],[f14076,f66972]) ).
fof(f66972,plain,
( ! [X40,X38,X41,X39] : is_a_theorem(strict_implies(and(X40,and(X41,not(implies(X38,X39)))),X38))
| ~ spl2_930 ),
inference(avatar_component_clause,[],[f66971]) ).
fof(f66971,plain,
( spl2_930
<=> ! [X38,X41,X40,X39] : is_a_theorem(strict_implies(and(X40,and(X41,not(implies(X38,X39)))),X38)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_930])]) ).
fof(f73599,plain,
( ~ spl2_174
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73370]) ).
fof(f73370,plain,
( $false
| ~ spl2_174
| ~ spl2_387 ),
inference(resolution,[],[f14076,f3351]) ).
fof(f3351,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(X11,and(X12,X13))),X12))
| ~ spl2_174 ),
inference(avatar_component_clause,[],[f3350]) ).
fof(f3350,plain,
( spl2_174
<=> ! [X13,X12,X11,X10] : is_a_theorem(strict_implies(and(X10,and(X11,and(X12,X13))),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_174])]) ).
fof(f73598,plain,
( ~ spl2_179
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73371]) ).
fof(f73371,plain,
( $false
| ~ spl2_179
| ~ spl2_387 ),
inference(resolution,[],[f14076,f3439]) ).
fof(f3439,plain,
( ! [X16,X14,X17,X15] : is_a_theorem(strict_implies(and(X14,and(X15,and(X16,X17))),X17))
| ~ spl2_179 ),
inference(avatar_component_clause,[],[f3438]) ).
fof(f3438,plain,
( spl2_179
<=> ! [X16,X17,X14,X15] : is_a_theorem(strict_implies(and(X14,and(X15,and(X16,X17))),X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_179])]) ).
fof(f73597,plain,
( ~ spl2_387
| ~ spl2_644 ),
inference(avatar_contradiction_clause,[],[f73372]) ).
fof(f73372,plain,
( $false
| ~ spl2_387
| ~ spl2_644 ),
inference(resolution,[],[f14076,f36252]) ).
fof(f36252,plain,
( ! [X452,X451,X450,X449] : is_a_theorem(strict_implies(and(X450,and(not(X449),X451)),implies(X449,X452)))
| ~ spl2_644 ),
inference(avatar_component_clause,[],[f36251]) ).
fof(f36251,plain,
( spl2_644
<=> ! [X452,X451,X449,X450] : is_a_theorem(strict_implies(and(X450,and(not(X449),X451)),implies(X449,X452))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_644])]) ).
fof(f73596,plain,
( ~ spl2_387
| ~ spl2_677 ),
inference(avatar_contradiction_clause,[],[f73373]) ).
fof(f73373,plain,
( $false
| ~ spl2_387
| ~ spl2_677 ),
inference(resolution,[],[f14076,f39525]) ).
fof(f39525,plain,
( ! [X18,X19,X20] : is_a_theorem(strict_implies(and(X19,and(not(not(X18)),X20)),X18))
| ~ spl2_677 ),
inference(avatar_component_clause,[],[f39524]) ).
fof(f39524,plain,
( spl2_677
<=> ! [X20,X18,X19] : is_a_theorem(strict_implies(and(X19,and(not(not(X18)),X20)),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_677])]) ).
fof(f73595,plain,
( ~ spl2_387
| ~ spl2_828 ),
inference(avatar_contradiction_clause,[],[f73374]) ).
fof(f73374,plain,
( $false
| ~ spl2_387
| ~ spl2_828 ),
inference(resolution,[],[f14076,f57343]) ).
fof(f57343,plain,
( ! [X10,X8,X9] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X8,X9))),X9))
| ~ spl2_828 ),
inference(avatar_component_clause,[],[f57342]) ).
fof(f57342,plain,
( spl2_828
<=> ! [X9,X8,X10] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X8,X9))),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_828])]) ).
fof(f73594,plain,
( ~ spl2_387
| ~ spl2_844 ),
inference(avatar_contradiction_clause,[],[f73375]) ).
fof(f73375,plain,
( $false
| ~ spl2_387
| ~ spl2_844 ),
inference(resolution,[],[f14076,f60557]) ).
fof(f60557,plain,
( ! [X10,X8,X9] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X9,X8))),X9))
| ~ spl2_844 ),
inference(avatar_component_clause,[],[f60556]) ).
fof(f60556,plain,
( spl2_844
<=> ! [X9,X8,X10] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X9,X8))),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_844])]) ).
fof(f73593,plain,
( ~ spl2_387
| ~ spl2_929 ),
inference(avatar_contradiction_clause,[],[f73376]) ).
fof(f73376,plain,
( $false
| ~ spl2_387
| ~ spl2_929 ),
inference(resolution,[],[f14076,f66968]) ).
fof(f66968,plain,
( ! [X28,X29,X26,X27] : is_a_theorem(strict_implies(and(X28,and(not(implies(X26,X27)),X29)),X26))
| ~ spl2_929 ),
inference(avatar_component_clause,[],[f66967]) ).
fof(f66967,plain,
( spl2_929
<=> ! [X29,X27,X28,X26] : is_a_theorem(strict_implies(and(X28,and(not(implies(X26,X27)),X29)),X26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_929])]) ).
fof(f73592,plain,
( ~ spl2_387
| ~ spl2_937 ),
inference(avatar_contradiction_clause,[],[f73377]) ).
fof(f73377,plain,
( $false
| ~ spl2_387
| ~ spl2_937 ),
inference(resolution,[],[f14076,f67055]) ).
fof(f67055,plain,
( ! [X31,X32,X30] : is_a_theorem(strict_implies(and(X30,and(equiv(X31,not(X31)),X32)),X31))
| ~ spl2_937 ),
inference(avatar_component_clause,[],[f67054]) ).
fof(f67054,plain,
( spl2_937
<=> ! [X32,X30,X31] : is_a_theorem(strict_implies(and(X30,and(equiv(X31,not(X31)),X32)),X31)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_937])]) ).
fof(f73591,plain,
( ~ spl2_158
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73378]) ).
fof(f73378,plain,
( $false
| ~ spl2_158
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2739]) ).
fof(f2739,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X20,X21)))
| ~ spl2_158 ),
inference(avatar_component_clause,[],[f2738]) ).
fof(f2738,plain,
( spl2_158
<=> ! [X22,X20,X21] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X20,X21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_158])]) ).
fof(f73590,plain,
( ~ spl2_292
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73379]) ).
fof(f73379,plain,
( $false
| ~ spl2_292
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9308]) ).
fof(f9308,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(and(X5,strict_equiv(X6,X7)),strict_implies(X6,X6)))
| ~ spl2_292 ),
inference(avatar_component_clause,[],[f9307]) ).
fof(f9307,plain,
( spl2_292
<=> ! [X6,X5,X7] : is_a_theorem(strict_implies(and(X5,strict_equiv(X6,X7)),strict_implies(X6,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_292])]) ).
fof(f73589,plain,
( ~ spl2_176
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73380]) ).
fof(f73380,plain,
( $false
| ~ spl2_176
| ~ spl2_387 ),
inference(resolution,[],[f14076,f3395]) ).
fof(f3395,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X21,X20)))
| ~ spl2_176 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f3394,plain,
( spl2_176
<=> ! [X22,X20,X21] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X21,X20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_176])]) ).
fof(f73588,plain,
( ~ spl2_295
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73381]) ).
fof(f73381,plain,
( $false
| ~ spl2_295
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9350]) ).
fof(f9350,plain,
( ! [X38,X36,X37] : is_a_theorem(strict_implies(and(X36,strict_equiv(X37,X38)),strict_implies(X38,X38)))
| ~ spl2_295 ),
inference(avatar_component_clause,[],[f9349]) ).
fof(f9349,plain,
( spl2_295
<=> ! [X38,X36,X37] : is_a_theorem(strict_implies(and(X36,strict_equiv(X37,X38)),strict_implies(X38,X38))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_295])]) ).
fof(f73587,plain,
( ~ spl2_290
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73382]) ).
fof(f73382,plain,
( $false
| ~ spl2_290
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9065]) ).
fof(f9065,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(X41,strict_equiv(X39,X40)),strict_equiv(X40,X39)))
| ~ spl2_290 ),
inference(avatar_component_clause,[],[f9064]) ).
fof(f9064,plain,
( spl2_290
<=> ! [X41,X40,X39] : is_a_theorem(strict_implies(and(X41,strict_equiv(X39,X40)),strict_equiv(X40,X39))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_290])]) ).
fof(f73586,plain,
( ~ spl2_387
| ~ spl2_509 ),
inference(avatar_contradiction_clause,[],[f73383]) ).
fof(f73383,plain,
( $false
| ~ spl2_387
| ~ spl2_509 ),
inference(resolution,[],[f14076,f25492]) ).
fof(f25492,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,strict_equiv(X1,X0)),and(X2,strict_equiv(X0,X1))))
| ~ spl2_509 ),
inference(avatar_component_clause,[],[f25491]) ).
fof(f25491,plain,
( spl2_509
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,strict_equiv(X1,X0)),and(X2,strict_equiv(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_509])]) ).
fof(f73585,plain,
( ~ spl2_387
| ~ spl2_902 ),
inference(avatar_contradiction_clause,[],[f73384]) ).
fof(f73384,plain,
( $false
| ~ spl2_387
| ~ spl2_902 ),
inference(resolution,[],[f14076,f64331]) ).
fof(f64331,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,X3)),and(strict_equiv(X3,X2),X4)))
| ~ spl2_902 ),
inference(avatar_component_clause,[],[f64330]) ).
fof(f64330,plain,
( spl2_902
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,X3)),and(strict_equiv(X3,X2),X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_902])]) ).
fof(f73584,plain,
( ~ spl2_387
| ~ spl2_415 ),
inference(avatar_contradiction_clause,[],[f73385]) ).
fof(f73385,plain,
( $false
| ~ spl2_387
| ~ spl2_415 ),
inference(resolution,[],[f14076,f14622]) ).
fof(f14622,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X1,possibly(X0)),implies(necessarily(not(X0)),X2)))
| ~ spl2_415 ),
inference(avatar_component_clause,[],[f14621]) ).
fof(f14621,plain,
( spl2_415
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X1,possibly(X0)),implies(necessarily(not(X0)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_415])]) ).
fof(f73583,plain,
( ~ spl2_282
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73386]) ).
fof(f73386,plain,
( $false
| ~ spl2_282
| ~ spl2_387 ),
inference(resolution,[],[f14076,f8408]) ).
fof(f8408,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(equiv(X4,X5),X6),equiv(X5,X4)))
| ~ spl2_282 ),
inference(avatar_component_clause,[],[f8407]) ).
fof(f8407,plain,
( spl2_282
<=> ! [X6,X4,X5] : is_a_theorem(strict_implies(and(equiv(X4,X5),X6),equiv(X5,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_282])]) ).
fof(f73582,plain,
( ~ spl2_149
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73387]) ).
fof(f73387,plain,
( $false
| ~ spl2_149
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2617]) ).
fof(f2617,plain,
( ! [X14,X15,X13] : is_a_theorem(strict_implies(and(equiv(X13,X14),X15),implies(X13,X14)))
| ~ spl2_149 ),
inference(avatar_component_clause,[],[f2616]) ).
fof(f2616,plain,
( spl2_149
<=> ! [X13,X14,X15] : is_a_theorem(strict_implies(and(equiv(X13,X14),X15),implies(X13,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_149])]) ).
fof(f73581,plain,
( ~ spl2_163
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73388]) ).
fof(f73388,plain,
( $false
| ~ spl2_163
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2759]) ).
fof(f2759,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(equiv(X14,X15),X16),implies(X15,X14)))
| ~ spl2_163 ),
inference(avatar_component_clause,[],[f2758]) ).
fof(f2758,plain,
( spl2_163
<=> ! [X16,X14,X15] : is_a_theorem(strict_implies(and(equiv(X14,X15),X16),implies(X15,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_163])]) ).
fof(f73580,plain,
( ~ spl2_387
| ~ spl2_488 ),
inference(avatar_contradiction_clause,[],[f73389]) ).
fof(f73389,plain,
( $false
| ~ spl2_387
| ~ spl2_488 ),
inference(resolution,[],[f14076,f22736]) ).
fof(f22736,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(equiv(X4,X3),X5)))
| ~ spl2_488 ),
inference(avatar_component_clause,[],[f22735]) ).
fof(f22735,plain,
( spl2_488
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(equiv(X4,X3),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_488])]) ).
fof(f73579,plain,
( ~ spl2_387
| ~ spl2_904 ),
inference(avatar_contradiction_clause,[],[f73390]) ).
fof(f73390,plain,
( $false
| ~ spl2_387
| ~ spl2_904 ),
inference(resolution,[],[f14076,f64410]) ).
fof(f64410,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X0,X1),X2),and(X2,equiv(X1,X0))))
| ~ spl2_904 ),
inference(avatar_component_clause,[],[f64409]) ).
fof(f64409,plain,
( spl2_904
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X0,X1),X2),and(X2,equiv(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_904])]) ).
fof(f73578,plain,
( ~ spl2_223
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73391]) ).
fof(f73391,plain,
( $false
| ~ spl2_223
| ~ spl2_387 ),
inference(resolution,[],[f14076,f5422]) ).
fof(f5422,plain,
( ! [X18,X19,X17] : is_a_theorem(strict_implies(and(equiv(not(X17),X18),X19),or(X17,X18)))
| ~ spl2_223 ),
inference(avatar_component_clause,[],[f5421]) ).
fof(f5421,plain,
( spl2_223
<=> ! [X18,X17,X19] : is_a_theorem(strict_implies(and(equiv(not(X17),X18),X19),or(X17,X18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_223])]) ).
fof(f73577,plain,
( ~ spl2_230
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73392]) ).
fof(f73392,plain,
( $false
| ~ spl2_230
| ~ spl2_387 ),
inference(resolution,[],[f14076,f5600]) ).
fof(f5600,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(equiv(not(X9),X10),X11),or(X10,X9)))
| ~ spl2_230 ),
inference(avatar_component_clause,[],[f5599]) ).
fof(f5599,plain,
( spl2_230
<=> ! [X9,X11,X10] : is_a_theorem(strict_implies(and(equiv(not(X9),X10),X11),or(X10,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_230])]) ).
fof(f73576,plain,
( ~ spl2_239
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73393]) ).
fof(f73393,plain,
( $false
| ~ spl2_239
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6142]) ).
fof(f6142,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X1,not(X0)),X2),or(X0,X1)))
| ~ spl2_239 ),
inference(avatar_component_clause,[],[f6141]) ).
fof(f6141,plain,
( spl2_239
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X1,not(X0)),X2),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_239])]) ).
fof(f73575,plain,
( ~ spl2_246
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73394]) ).
fof(f73394,plain,
( $false
| ~ spl2_246
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6170]) ).
fof(f6170,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(equiv(X3,not(X2)),X4),or(X3,X2)))
| ~ spl2_246 ),
inference(avatar_component_clause,[],[f6169]) ).
fof(f6169,plain,
( spl2_246
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(equiv(X3,not(X2)),X4),or(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_246])]) ).
fof(f73574,plain,
( ~ spl2_231
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73395]) ).
fof(f73395,plain,
( $false
| ~ spl2_231
| ~ spl2_387 ),
inference(resolution,[],[f14076,f5604]) ).
fof(f5604,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(equiv(X7,not(X7)),X8),not(not(X7))))
| ~ spl2_231 ),
inference(avatar_component_clause,[],[f5603]) ).
fof(f5603,plain,
( spl2_231
<=> ! [X7,X8] : is_a_theorem(strict_implies(and(equiv(X7,not(X7)),X8),not(not(X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_231])]) ).
fof(f73573,plain,
( ~ spl2_387
| ~ spl2_908 ),
inference(avatar_contradiction_clause,[],[f73396]) ).
fof(f73396,plain,
( $false
| ~ spl2_387
| ~ spl2_908 ),
inference(resolution,[],[f14076,f65187]) ).
fof(f65187,plain,
( ! [X14,X13] : is_a_theorem(strict_implies(and(equiv(X13,not(X13)),X14),X13))
| ~ spl2_908 ),
inference(avatar_component_clause,[],[f65186]) ).
fof(f65186,plain,
( spl2_908
<=> ! [X13,X14] : is_a_theorem(strict_implies(and(equiv(X13,not(X13)),X14),X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_908])]) ).
fof(f73572,plain,
( ~ spl2_387
| ~ spl2_663 ),
inference(avatar_contradiction_clause,[],[f73397]) ).
fof(f73397,plain,
( $false
| ~ spl2_387
| ~ spl2_663 ),
inference(resolution,[],[f14076,f37228]) ).
fof(f73571,plain,
( ~ spl2_387
| ~ spl2_684 ),
inference(avatar_contradiction_clause,[],[f73398]) ).
fof(f73398,plain,
( $false
| ~ spl2_387
| ~ spl2_684 ),
inference(resolution,[],[f14076,f41049]) ).
fof(f41049,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(not(implies(X20,X19)),X21),X20))
| ~ spl2_684 ),
inference(avatar_component_clause,[],[f41048]) ).
fof(f41048,plain,
( spl2_684
<=> ! [X20,X21,X19] : is_a_theorem(strict_implies(and(not(implies(X20,X19)),X21),X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_684])]) ).
fof(f73570,plain,
( ~ spl2_387
| ~ spl2_675 ),
inference(avatar_contradiction_clause,[],[f73399]) ).
fof(f73399,plain,
( $false
| ~ spl2_387
| ~ spl2_675 ),
inference(resolution,[],[f14076,f39386]) ).
fof(f39386,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(not(and(X43,X44))),X45),X43))
| ~ spl2_675 ),
inference(avatar_component_clause,[],[f39385]) ).
fof(f39385,plain,
( spl2_675
<=> ! [X45,X43,X44] : is_a_theorem(strict_implies(and(not(not(and(X43,X44))),X45),X43)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_675])]) ).
fof(f73569,plain,
( ~ spl2_387
| ~ spl2_928 ),
inference(avatar_contradiction_clause,[],[f73400]) ).
fof(f73400,plain,
( $false
| ~ spl2_387
| ~ spl2_928 ),
inference(resolution,[],[f14076,f66964]) ).
fof(f66964,plain,
( ! [X59,X62,X60,X61] : is_a_theorem(strict_implies(and(not(implies(and(X59,X60),X61)),X62),X59))
| ~ spl2_928 ),
inference(avatar_component_clause,[],[f66963]) ).
fof(f66963,plain,
( spl2_928
<=> ! [X61,X60,X59,X62] : is_a_theorem(strict_implies(and(not(implies(and(X59,X60),X61)),X62),X59)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_928])]) ).
fof(f73568,plain,
( ~ spl2_387
| ~ spl2_620 ),
inference(avatar_contradiction_clause,[],[f73401]) ).
fof(f73401,plain,
( $false
| ~ spl2_387
| ~ spl2_620 ),
inference(resolution,[],[f14076,f33185]) ).
fof(f33185,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X2),implies(implies(X0,X1),X2)),X0))
| ~ spl2_620 ),
inference(avatar_component_clause,[],[f33184]) ).
fof(f33184,plain,
( spl2_620
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X2),implies(implies(X0,X1),X2)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_620])]) ).
fof(f73567,plain,
( ~ spl2_387
| ~ spl2_671 ),
inference(avatar_contradiction_clause,[],[f73402]) ).
fof(f73402,plain,
( $false
| ~ spl2_387
| ~ spl2_671 ),
inference(resolution,[],[f14076,f38977]) ).
fof(f38977,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),equiv(not(X0),X1)),X1))
| ~ spl2_671 ),
inference(avatar_component_clause,[],[f38976]) ).
fof(f38976,plain,
( spl2_671
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),equiv(not(X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_671])]) ).
fof(f73566,plain,
( ~ spl2_387
| ~ spl2_830 ),
inference(avatar_contradiction_clause,[],[f73403]) ).
fof(f73403,plain,
( $false
| ~ spl2_387
| ~ spl2_830 ),
inference(resolution,[],[f14076,f57492]) ).
fof(f57492,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(not(X0),X1)),X0))
| ~ spl2_830 ),
inference(avatar_component_clause,[],[f57491]) ).
fof(f57491,plain,
( spl2_830
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(not(X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_830])]) ).
fof(f73565,plain,
( ~ spl2_387
| ~ spl2_681 ),
inference(avatar_contradiction_clause,[],[f73404]) ).
fof(f73404,plain,
( $false
| ~ spl2_387
| ~ spl2_681 ),
inference(resolution,[],[f14076,f40239]) ).
fof(f40239,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(X2,not(X1))),X2))
| ~ spl2_681 ),
inference(avatar_component_clause,[],[f40238]) ).
fof(f40238,plain,
( spl2_681
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(X2,not(X1))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_681])]) ).
fof(f73564,plain,
( ~ spl2_387
| ~ spl2_832 ),
inference(avatar_contradiction_clause,[],[f73405]) ).
fof(f73405,plain,
( $false
| ~ spl2_387
| ~ spl2_832 ),
inference(resolution,[],[f14076,f57683]) ).
fof(f57683,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(not(X2),equiv(X2,not(X1))),X1))
| ~ spl2_832 ),
inference(avatar_component_clause,[],[f57682]) ).
fof(f57682,plain,
( spl2_832
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(not(X2),equiv(X2,not(X1))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_832])]) ).
fof(f73563,plain,
( ~ spl2_387
| ~ spl2_654 ),
inference(avatar_contradiction_clause,[],[f73406]) ).
fof(f73406,plain,
( $false
| ~ spl2_387
| ~ spl2_654 ),
inference(resolution,[],[f14076,f37074]) ).
fof(f37074,plain,
( ! [X218,X219,X217] : is_a_theorem(strict_implies(and(not(X218),and(or(X218,X217),X219)),X217))
| ~ spl2_654 ),
inference(avatar_component_clause,[],[f37073]) ).
fof(f37073,plain,
( spl2_654
<=> ! [X219,X217,X218] : is_a_theorem(strict_implies(and(not(X218),and(or(X218,X217),X219)),X217)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_654])]) ).
fof(f73562,plain,
( ~ spl2_387
| ~ spl2_822 ),
inference(avatar_contradiction_clause,[],[f73407]) ).
fof(f73407,plain,
( $false
| ~ spl2_387
| ~ spl2_822 ),
inference(resolution,[],[f14076,f57319]) ).
fof(f57319,plain,
( ! [X222,X220,X221] : is_a_theorem(strict_implies(and(not(X221),and(or(X220,X221),X222)),X220))
| ~ spl2_822 ),
inference(avatar_component_clause,[],[f57318]) ).
fof(f57318,plain,
( spl2_822
<=> ! [X221,X220,X222] : is_a_theorem(strict_implies(and(not(X221),and(or(X220,X221),X222)),X220)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_822])]) ).
fof(f73561,plain,
( ~ spl2_387
| ~ spl2_487 ),
inference(avatar_contradiction_clause,[],[f73408]) ).
fof(f73408,plain,
( $false
| ~ spl2_387
| ~ spl2_487 ),
inference(resolution,[],[f14076,f22732]) ).
fof(f22732,plain,
( ! [X19,X20] : is_a_theorem(strict_implies(and(not(X20),or(X19,X20)),X19))
| ~ spl2_487 ),
inference(avatar_component_clause,[],[f22731]) ).
fof(f22731,plain,
( spl2_487
<=> ! [X20,X19] : is_a_theorem(strict_implies(and(not(X20),or(X19,X20)),X19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_487])]) ).
fof(f73560,plain,
( ~ spl2_387
| ~ spl2_489 ),
inference(avatar_contradiction_clause,[],[f73409]) ).
fof(f73409,plain,
( $false
| ~ spl2_387
| ~ spl2_489 ),
inference(resolution,[],[f14076,f22740]) ).
fof(f22740,plain,
( ! [X203,X204] : is_a_theorem(strict_implies(and(not(X204),or(X204,X203)),X203))
| ~ spl2_489 ),
inference(avatar_component_clause,[],[f22739]) ).
fof(f22739,plain,
( spl2_489
<=> ! [X203,X204] : is_a_theorem(strict_implies(and(not(X204),or(X204,X203)),X203)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_489])]) ).
fof(f73559,plain,
( ~ spl2_387
| ~ spl2_519 ),
inference(avatar_contradiction_clause,[],[f73410]) ).
fof(f73410,plain,
( $false
| ~ spl2_387
| ~ spl2_519 ),
inference(resolution,[],[f14076,f26992]) ).
fof(f26992,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(X43),or(X43,and(X44,X45))),X44))
| ~ spl2_519 ),
inference(avatar_component_clause,[],[f26991]) ).
fof(f26991,plain,
( spl2_519
<=> ! [X45,X44,X43] : is_a_theorem(strict_implies(and(not(X43),or(X43,and(X44,X45))),X44)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_519])]) ).
fof(f73558,plain,
( ~ spl2_387
| ~ spl2_518 ),
inference(avatar_contradiction_clause,[],[f73411]) ).
fof(f73411,plain,
( $false
| ~ spl2_387
| ~ spl2_518 ),
inference(resolution,[],[f14076,f26960]) ).
fof(f26960,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(X43),or(and(X44,X45),X43)),X44))
| ~ spl2_518 ),
inference(avatar_component_clause,[],[f26959]) ).
fof(f26959,plain,
( spl2_518
<=> ! [X45,X44,X43] : is_a_theorem(strict_implies(and(not(X43),or(and(X44,X45),X43)),X44)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_518])]) ).
fof(f73557,plain,
( ~ spl2_387
| ~ spl2_674 ),
inference(avatar_contradiction_clause,[],[f73412]) ).
fof(f73412,plain,
( $false
| ~ spl2_387
| ~ spl2_674 ),
inference(resolution,[],[f14076,f39382]) ).
fof(f39382,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(not(and(X40,X41))),X42),X41))
| ~ spl2_674 ),
inference(avatar_component_clause,[],[f39381]) ).
fof(f39381,plain,
( spl2_674
<=> ! [X41,X40,X42] : is_a_theorem(strict_implies(and(not(not(and(X40,X41))),X42),X41)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_674])]) ).
fof(f73556,plain,
( ~ spl2_387
| ~ spl2_927 ),
inference(avatar_contradiction_clause,[],[f73413]) ).
fof(f73413,plain,
( $false
| ~ spl2_387
| ~ spl2_927 ),
inference(resolution,[],[f14076,f66960]) ).
fof(f66960,plain,
( ! [X58,X56,X57,X55] : is_a_theorem(strict_implies(and(not(implies(and(X55,X56),X57)),X58),X56))
| ~ spl2_927 ),
inference(avatar_component_clause,[],[f66959]) ).
fof(f66959,plain,
( spl2_927
<=> ! [X57,X55,X56,X58] : is_a_theorem(strict_implies(and(not(implies(and(X55,X56),X57)),X58),X56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_927])]) ).
fof(f73555,plain,
( ~ spl2_387
| ~ spl2_614 ),
inference(avatar_contradiction_clause,[],[f73414]) ).
fof(f73414,plain,
( $false
| ~ spl2_387
| ~ spl2_614 ),
inference(resolution,[],[f14076,f33161]) ).
fof(f33161,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(X40),or(and(X41,X42),X40)),X42))
| ~ spl2_614 ),
inference(avatar_component_clause,[],[f33160]) ).
fof(f33160,plain,
( spl2_614
<=> ! [X41,X40,X42] : is_a_theorem(strict_implies(and(not(X40),or(and(X41,X42),X40)),X42)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_614])]) ).
fof(f73554,plain,
( ~ spl2_387
| ~ spl2_615 ),
inference(avatar_contradiction_clause,[],[f73415]) ).
fof(f73415,plain,
( $false
| ~ spl2_387
| ~ spl2_615 ),
inference(resolution,[],[f14076,f33165]) ).
fof(f33165,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(X40),or(X40,and(X41,X42))),X42))
| ~ spl2_615 ),
inference(avatar_component_clause,[],[f33164]) ).
fof(f33164,plain,
( spl2_615
<=> ! [X41,X40,X42] : is_a_theorem(strict_implies(and(not(X40),or(X40,and(X41,X42))),X42)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_615])]) ).
fof(f73553,plain,
( ~ spl2_387
| ~ spl2_827 ),
inference(avatar_contradiction_clause,[],[f73416]) ).
fof(f73416,plain,
( $false
| ~ spl2_387
| ~ spl2_827 ),
inference(resolution,[],[f14076,f57339]) ).
fof(f57339,plain,
( ! [X8,X6,X7] : is_a_theorem(strict_implies(and(not(X6),and(X8,or(X6,X7))),X7))
| ~ spl2_827 ),
inference(avatar_component_clause,[],[f57338]) ).
fof(f57338,plain,
( spl2_827
<=> ! [X6,X7,X8] : is_a_theorem(strict_implies(and(not(X6),and(X8,or(X6,X7))),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_827])]) ).
fof(f73552,plain,
( ~ spl2_387
| ~ spl2_843 ),
inference(avatar_contradiction_clause,[],[f73417]) ).
fof(f73417,plain,
( $false
| ~ spl2_387
| ~ spl2_843 ),
inference(resolution,[],[f14076,f60553]) ).
fof(f60553,plain,
( ! [X8,X6,X7] : is_a_theorem(strict_implies(and(not(X7),and(X8,or(X6,X7))),X6))
| ~ spl2_843 ),
inference(avatar_component_clause,[],[f60552]) ).
fof(f60552,plain,
( spl2_843
<=> ! [X6,X7,X8] : is_a_theorem(strict_implies(and(not(X7),and(X8,or(X6,X7))),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_843])]) ).
fof(f73551,plain,
( ~ spl2_383
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73418]) ).
fof(f73418,plain,
( $false
| ~ spl2_383
| ~ spl2_387 ),
inference(resolution,[],[f14076,f13619]) ).
fof(f13619,plain,
( ! [X26,X24,X25] : is_a_theorem(strict_implies(and(not(X24),X25),implies(X24,X26)))
| ~ spl2_383 ),
inference(avatar_component_clause,[],[f13618]) ).
fof(f13618,plain,
( spl2_383
<=> ! [X25,X24,X26] : is_a_theorem(strict_implies(and(not(X24),X25),implies(X24,X26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_383])]) ).
fof(f73550,plain,
( ~ spl2_387
| ~ spl2_855 ),
inference(avatar_contradiction_clause,[],[f73419]) ).
fof(f73419,plain,
( $false
| ~ spl2_387
| ~ spl2_855 ),
inference(resolution,[],[f14076,f62027]) ).
fof(f62027,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X2,X0),X3)))
| ~ spl2_855 ),
inference(avatar_component_clause,[],[f62026]) ).
fof(f62026,plain,
( spl2_855
<=> ! [X0,X3,X2,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X2,X0),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_855])]) ).
fof(f73549,plain,
( ~ spl2_387
| ~ spl2_916 ),
inference(avatar_contradiction_clause,[],[f73420]) ).
fof(f73420,plain,
( $false
| ~ spl2_387
| ~ spl2_916 ),
inference(resolution,[],[f14076,f66456]) ).
fof(f66456,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X0,X2),X3)))
| ~ spl2_916 ),
inference(avatar_component_clause,[],[f66455]) ).
fof(f66455,plain,
( spl2_916
<=> ! [X0,X3,X2,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X0,X2),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_916])]) ).
fof(f73548,plain,
( ~ spl2_387
| ~ spl2_412 ),
inference(avatar_contradiction_clause,[],[f73421]) ).
fof(f73421,plain,
( $false
| ~ spl2_387
| ~ spl2_412 ),
inference(resolution,[],[f14076,f14610]) ).
fof(f14610,plain,
( ! [X83,X84,X85] : is_a_theorem(strict_implies(and(not(not(X83)),X84),implies(possibly(X85),X83)))
| ~ spl2_412 ),
inference(avatar_component_clause,[],[f14609]) ).
fof(f14609,plain,
( spl2_412
<=> ! [X84,X85,X83] : is_a_theorem(strict_implies(and(not(not(X83)),X84),implies(possibly(X85),X83))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_412])]) ).
fof(f73547,plain,
( ~ spl2_387
| ~ spl2_553 ),
inference(avatar_contradiction_clause,[],[f73422]) ).
fof(f73422,plain,
( $false
| ~ spl2_387
| ~ spl2_553 ),
inference(resolution,[],[f14076,f29237]) ).
fof(f29237,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),implies(X2,X0)))
| ~ spl2_553 ),
inference(avatar_component_clause,[],[f29236]) ).
fof(f29236,plain,
( spl2_553
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),implies(X2,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_553])]) ).
fof(f73546,plain,
( ~ spl2_387
| ~ spl2_408 ),
inference(avatar_contradiction_clause,[],[f73423]) ).
fof(f73423,plain,
( $false
| ~ spl2_387
| ~ spl2_408 ),
inference(resolution,[],[f14076,f14495]) ).
fof(f14495,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(not(X2),X3),not(and(X2,possibly(X4)))))
| ~ spl2_408 ),
inference(avatar_component_clause,[],[f14494]) ).
fof(f14494,plain,
( spl2_408
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(not(X2),X3),not(and(X2,possibly(X4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_408])]) ).
fof(f73545,plain,
( ~ spl2_387
| ~ spl2_747 ),
inference(avatar_contradiction_clause,[],[f73424]) ).
fof(f73424,plain,
( $false
| ~ spl2_387
| ~ spl2_747 ),
inference(resolution,[],[f14076,f48848]) ).
fof(f48848,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X0,X2))))
| ~ spl2_747 ),
inference(avatar_component_clause,[],[f48847]) ).
fof(f48847,plain,
( spl2_747
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_747])]) ).
fof(f73544,plain,
( ~ spl2_387
| ~ spl2_411 ),
inference(avatar_contradiction_clause,[],[f73425]) ).
fof(f73425,plain,
( $false
| ~ spl2_387
| ~ spl2_411 ),
inference(resolution,[],[f14076,f14606]) ).
fof(f14606,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(and(not(X21),X22),not(and(possibly(X23),X21))))
| ~ spl2_411 ),
inference(avatar_component_clause,[],[f14605]) ).
fof(f14605,plain,
( spl2_411
<=> ! [X22,X21,X23] : is_a_theorem(strict_implies(and(not(X21),X22),not(and(possibly(X23),X21)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_411])]) ).
fof(f73543,plain,
( ~ spl2_387
| ~ spl2_720 ),
inference(avatar_contradiction_clause,[],[f73426]) ).
fof(f73426,plain,
( $false
| ~ spl2_387
| ~ spl2_720 ),
inference(resolution,[],[f14076,f44644]) ).
fof(f44644,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X2,X0))))
| ~ spl2_720 ),
inference(avatar_component_clause,[],[f44643]) ).
fof(f44643,plain,
( spl2_720
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X2,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_720])]) ).
fof(f73542,plain,
( ~ spl2_387
| ~ spl2_704 ),
inference(avatar_contradiction_clause,[],[f73427]) ).
fof(f73427,plain,
( $false
| ~ spl2_387
| ~ spl2_704 ),
inference(resolution,[],[f14076,f42498]) ).
fof(f42498,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(implies(X0,X1)),X2),not(X1)))
| ~ spl2_704 ),
inference(avatar_component_clause,[],[f42497]) ).
fof(f42497,plain,
( spl2_704
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(implies(X0,X1)),X2),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_704])]) ).
fof(f73541,plain,
( ~ spl2_387
| ~ spl2_732 ),
inference(avatar_contradiction_clause,[],[f73428]) ).
fof(f73428,plain,
( $false
| ~ spl2_387
| ~ spl2_732 ),
inference(resolution,[],[f14076,f45812]) ).
fof(f45812,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X16)))
| ~ spl2_732 ),
inference(avatar_component_clause,[],[f45811]) ).
fof(f45811,plain,
( spl2_732
<=> ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_732])]) ).
fof(f73540,plain,
( ~ spl2_387
| ~ spl2_725 ),
inference(avatar_contradiction_clause,[],[f73429]) ).
fof(f73429,plain,
( $false
| ~ spl2_387
| ~ spl2_725 ),
inference(resolution,[],[f14076,f45375]) ).
fof(f45375,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X15)))
| ~ spl2_725 ),
inference(avatar_component_clause,[],[f45374]) ).
fof(f45374,plain,
( spl2_725
<=> ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_725])]) ).
fof(f73539,plain,
( ~ spl2_387
| ~ spl2_390 ),
inference(avatar_contradiction_clause,[],[f73430]) ).
fof(f73430,plain,
( $false
| ~ spl2_387
| ~ spl2_390 ),
inference(resolution,[],[f14076,f14103]) ).
fof(f14103,plain,
( ! [X78,X79,X77] : is_a_theorem(strict_implies(and(not(not(X77)),X78),or(X77,X79)))
| ~ spl2_390 ),
inference(avatar_component_clause,[],[f14102]) ).
fof(f14102,plain,
( spl2_390
<=> ! [X77,X78,X79] : is_a_theorem(strict_implies(and(not(not(X77)),X78),or(X77,X79))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_390])]) ).
fof(f73538,plain,
( ~ spl2_387
| ~ spl2_391 ),
inference(avatar_contradiction_clause,[],[f73431]) ).
fof(f73431,plain,
( $false
| ~ spl2_387
| ~ spl2_391 ),
inference(resolution,[],[f14076,f14154]) ).
fof(f14154,plain,
( ! [X82,X80,X81] : is_a_theorem(strict_implies(and(not(not(X80)),X81),or(X82,X80)))
| ~ spl2_391 ),
inference(avatar_component_clause,[],[f14153]) ).
fof(f14153,plain,
( spl2_391
<=> ! [X82,X80,X81] : is_a_theorem(strict_implies(and(not(not(X80)),X81),or(X82,X80))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_391])]) ).
fof(f73537,plain,
( ~ spl2_387
| ~ spl2_676 ),
inference(avatar_contradiction_clause,[],[f73432]) ).
fof(f73432,plain,
( $false
| ~ spl2_387
| ~ spl2_676 ),
inference(resolution,[],[f14076,f39390]) ).
fof(f39390,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(possibly(X0)),X1),necessarily(not(X0))))
| ~ spl2_676 ),
inference(avatar_component_clause,[],[f39389]) ).
fof(f39389,plain,
( spl2_676
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(not(possibly(X0)),X1),necessarily(not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_676])]) ).
fof(f73536,plain,
( ~ spl2_146
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73433]) ).
fof(f73433,plain,
( $false
| ~ spl2_146
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2559]) ).
fof(f2559,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),strict_implies(X1,X2)),necessarily(or(X0,X2))))
| ~ spl2_146 ),
inference(avatar_component_clause,[],[f2558]) ).
fof(f2558,plain,
( spl2_146
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),strict_implies(X1,X2)),necessarily(or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_146])]) ).
fof(f73535,plain,
( ~ spl2_387
| ~ spl2_418 ),
inference(avatar_contradiction_clause,[],[f73434]) ).
fof(f73434,plain,
( $false
| ~ spl2_387
| ~ spl2_418 ),
inference(resolution,[],[f14076,f14634]) ).
fof(f14634,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(necessarily(or(X19,X21)),strict_implies(X21,necessarily(not(X20)))),strict_implies(possibly(X20),X19)))
| ~ spl2_418 ),
inference(avatar_component_clause,[],[f14633]) ).
fof(f14633,plain,
( spl2_418
<=> ! [X20,X21,X19] : is_a_theorem(strict_implies(and(necessarily(or(X19,X21)),strict_implies(X21,necessarily(not(X20)))),strict_implies(possibly(X20),X19))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_418])]) ).
fof(f73534,plain,
( ~ spl2_387
| ~ spl2_633 ),
inference(avatar_contradiction_clause,[],[f73435]) ).
fof(f73435,plain,
( $false
| ~ spl2_387
| ~ spl2_633 ),
inference(resolution,[],[f14076,f34628]) ).
fof(f34628,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(necessarily(or(X15,X18)),strict_implies(X18,and(X16,not(X17)))),strict_implies(implies(X16,X17),X15)))
| ~ spl2_633 ),
inference(avatar_component_clause,[],[f34627]) ).
fof(f34627,plain,
( spl2_633
<=> ! [X18,X17,X16,X15] : is_a_theorem(strict_implies(and(necessarily(or(X15,X18)),strict_implies(X18,and(X16,not(X17)))),strict_implies(implies(X16,X17),X15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_633])]) ).
fof(f73533,plain,
( ~ spl2_387
| ~ spl2_407 ),
inference(avatar_contradiction_clause,[],[f73436]) ).
fof(f73436,plain,
( $false
| ~ spl2_387
| ~ spl2_407 ),
inference(resolution,[],[f14076,f14491]) ).
fof(f14491,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2))),necessarily(or(X0,X2))))
| ~ spl2_407 ),
inference(avatar_component_clause,[],[f14490]) ).
fof(f14490,plain,
( spl2_407
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2))),necessarily(or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_407])]) ).
fof(f73532,plain,
( ~ spl2_46
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73437]) ).
fof(f73437,plain,
( $false
| ~ spl2_46
| ~ spl2_387 ),
inference(resolution,[],[f14076,f451]) ).
fof(f451,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f450,plain,
( spl2_46
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
fof(f73531,plain,
( ~ spl2_305
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73438]) ).
fof(f73438,plain,
( $false
| ~ spl2_305
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9456]) ).
fof(f9456,plain,
( ! [X46,X47,X45] : is_a_theorem(strict_implies(and(strict_implies(X46,X47),strict_implies(X45,X46)),strict_implies(X45,X47)))
| ~ spl2_305 ),
inference(avatar_component_clause,[],[f9455]) ).
fof(f9455,plain,
( spl2_305
<=> ! [X45,X46,X47] : is_a_theorem(strict_implies(and(strict_implies(X46,X47),strict_implies(X45,X46)),strict_implies(X45,X47))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_305])]) ).
fof(f73530,plain,
( ~ spl2_142
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73439]) ).
fof(f73439,plain,
( $false
| ~ spl2_142
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2529]) ).
fof(f2529,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))),strict_implies(X2,X1)))
| ~ spl2_142 ),
inference(avatar_component_clause,[],[f2528]) ).
fof(f2528,plain,
( spl2_142
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))),strict_implies(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_142])]) ).
fof(f73529,plain,
( ~ spl2_387
| ~ spl2_410 ),
inference(avatar_contradiction_clause,[],[f73440]) ).
fof(f73440,plain,
( $false
| ~ spl2_387
| ~ spl2_410 ),
inference(resolution,[],[f14076,f14554]) ).
fof(f14554,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(strict_implies(X21,not(X19)),strict_implies(possibly(X20),X19)),strict_implies(X21,necessarily(not(X20)))))
| ~ spl2_410 ),
inference(avatar_component_clause,[],[f14553]) ).
fof(f14553,plain,
( spl2_410
<=> ! [X20,X21,X19] : is_a_theorem(strict_implies(and(strict_implies(X21,not(X19)),strict_implies(possibly(X20),X19)),strict_implies(X21,necessarily(not(X20))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_410])]) ).
fof(f73528,plain,
( ~ spl2_387
| ~ spl2_623 ),
inference(avatar_contradiction_clause,[],[f73441]) ).
fof(f73441,plain,
( $false
| ~ spl2_387
| ~ spl2_623 ),
inference(resolution,[],[f14076,f34354]) ).
fof(f34354,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(strict_implies(X18,not(X15)),strict_implies(implies(X16,X17),X15)),strict_implies(X18,and(X16,not(X17)))))
| ~ spl2_623 ),
inference(avatar_component_clause,[],[f34353]) ).
fof(f34353,plain,
( spl2_623
<=> ! [X18,X17,X16,X15] : is_a_theorem(strict_implies(and(strict_implies(X18,not(X15)),strict_implies(implies(X16,X17),X15)),strict_implies(X18,and(X16,not(X17))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_623])]) ).
fof(f73527,plain,
( ~ spl2_387
| ~ spl2_414 ),
inference(avatar_contradiction_clause,[],[f73442]) ).
fof(f73442,plain,
( $false
| ~ spl2_387
| ~ spl2_414 ),
inference(resolution,[],[f14076,f14618]) ).
fof(f14618,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(strict_implies(possibly(X20),X19),strict_implies(necessarily(not(X20)),X21)),necessarily(or(X19,X21))))
| ~ spl2_414 ),
inference(avatar_component_clause,[],[f14617]) ).
fof(f14617,plain,
( spl2_414
<=> ! [X20,X21,X19] : is_a_theorem(strict_implies(and(strict_implies(possibly(X20),X19),strict_implies(necessarily(not(X20)),X21)),necessarily(or(X19,X21)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_414])]) ).
fof(f73526,plain,
( ~ spl2_387
| ~ spl2_629 ),
inference(avatar_contradiction_clause,[],[f73443]) ).
fof(f73443,plain,
( $false
| ~ spl2_387
| ~ spl2_629 ),
inference(resolution,[],[f14076,f34612]) ).
fof(f34612,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(strict_implies(implies(X16,X17),X15),strict_implies(and(X16,not(X17)),X18)),necessarily(or(X15,X18))))
| ~ spl2_629 ),
inference(avatar_component_clause,[],[f34611]) ).
fof(f34611,plain,
( spl2_629
<=> ! [X18,X17,X16,X15] : is_a_theorem(strict_implies(and(strict_implies(implies(X16,X17),X15),strict_implies(and(X16,not(X17)),X18)),necessarily(or(X15,X18)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_629])]) ).
fof(f73525,plain,
( ~ spl2_288
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73444]) ).
fof(f73444,plain,
( $false
| ~ spl2_288
| ~ spl2_387 ),
inference(resolution,[],[f14076,f8823]) ).
fof(f8823,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(strict_equiv(X39,X40),X41),strict_equiv(X40,X39)))
| ~ spl2_288 ),
inference(avatar_component_clause,[],[f8822]) ).
fof(f8822,plain,
( spl2_288
<=> ! [X41,X40,X39] : is_a_theorem(strict_implies(and(strict_equiv(X39,X40),X41),strict_equiv(X40,X39))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_288])]) ).
fof(f73524,plain,
( ~ spl2_150
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73445]) ).
fof(f73445,plain,
( $false
| ~ spl2_150
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2621]) ).
fof(f2621,plain,
( ! [X24,X22,X23] : is_a_theorem(strict_implies(and(strict_equiv(X22,X23),X24),strict_implies(X22,X23)))
| ~ spl2_150 ),
inference(avatar_component_clause,[],[f2620]) ).
fof(f2620,plain,
( spl2_150
<=> ! [X22,X24,X23] : is_a_theorem(strict_implies(and(strict_equiv(X22,X23),X24),strict_implies(X22,X23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_150])]) ).
fof(f73523,plain,
( ~ spl2_291
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73446]) ).
fof(f73446,plain,
( $false
| ~ spl2_291
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9264]) ).
fof(f9264,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(strict_equiv(X2,X3),X4),strict_implies(X2,X2)))
| ~ spl2_291 ),
inference(avatar_component_clause,[],[f9263]) ).
fof(f9263,plain,
( spl2_291
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(and(strict_equiv(X2,X3),X4),strict_implies(X2,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_291])]) ).
fof(f73522,plain,
( ~ spl2_164
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73447]) ).
fof(f73447,plain,
( $false
| ~ spl2_164
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2763]) ).
fof(f2763,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(strict_equiv(X20,X21),X22),strict_implies(X21,X20)))
| ~ spl2_164 ),
inference(avatar_component_clause,[],[f2762]) ).
fof(f2762,plain,
( spl2_164
<=> ! [X22,X20,X21] : is_a_theorem(strict_implies(and(strict_equiv(X20,X21),X22),strict_implies(X21,X20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_164])]) ).
fof(f73521,plain,
( ~ spl2_294
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73448]) ).
fof(f73448,plain,
( $false
| ~ spl2_294
| ~ spl2_387 ),
inference(resolution,[],[f14076,f9331]) ).
fof(f9331,plain,
( ! [X68,X69,X67] : is_a_theorem(strict_implies(and(strict_equiv(X67,X68),X69),strict_implies(X68,X68)))
| ~ spl2_294 ),
inference(avatar_component_clause,[],[f9330]) ).
fof(f9330,plain,
( spl2_294
<=> ! [X69,X68,X67] : is_a_theorem(strict_implies(and(strict_equiv(X67,X68),X69),strict_implies(X68,X68))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_294])]) ).
fof(f73520,plain,
( ~ spl2_387
| ~ spl2_490 ),
inference(avatar_contradiction_clause,[],[f73449]) ).
fof(f73449,plain,
( $false
| ~ spl2_387
| ~ spl2_490 ),
inference(resolution,[],[f14076,f22902]) ).
fof(f22902,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_equiv(X1,X0),X2)))
| ~ spl2_490 ),
inference(avatar_component_clause,[],[f22901]) ).
fof(f22901,plain,
( spl2_490
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_equiv(X1,X0),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_490])]) ).
fof(f73519,plain,
( ~ spl2_387
| ~ spl2_905 ),
inference(avatar_contradiction_clause,[],[f73450]) ).
fof(f73450,plain,
( $false
| ~ spl2_387
| ~ spl2_905 ),
inference(resolution,[],[f14076,f64631]) ).
fof(f64631,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(X2,strict_equiv(X1,X0))))
| ~ spl2_905 ),
inference(avatar_component_clause,[],[f64630]) ).
fof(f64630,plain,
( spl2_905
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(X2,strict_equiv(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_905])]) ).
fof(f73518,plain,
( ~ spl2_387
| ~ spl2_461 ),
inference(avatar_contradiction_clause,[],[f73451]) ).
fof(f73451,plain,
( $false
| ~ spl2_387
| ~ spl2_461 ),
inference(resolution,[],[f14076,f17552]) ).
fof(f17552,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(not(X0),X1),X2),necessarily(or(X0,X1))))
| ~ spl2_461 ),
inference(avatar_component_clause,[],[f17551]) ).
fof(f17551,plain,
( spl2_461
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(not(X0),X1),X2),necessarily(or(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_461])]) ).
fof(f73517,plain,
( ~ spl2_387
| ~ spl2_409 ),
inference(avatar_contradiction_clause,[],[f73452]) ).
fof(f73452,plain,
( $false
| ~ spl2_387
| ~ spl2_409 ),
inference(resolution,[],[f14076,f14499]) ).
fof(f14499,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),X1),implies(necessarily(not(X0)),X2)))
| ~ spl2_409 ),
inference(avatar_component_clause,[],[f14498]) ).
fof(f14498,plain,
( spl2_409
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),X1),implies(necessarily(not(X0)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_409])]) ).
fof(f73516,plain,
( ~ spl2_387
| ~ spl2_498 ),
inference(avatar_contradiction_clause,[],[f73453]) ).
fof(f73453,plain,
( $false
| ~ spl2_387
| ~ spl2_498 ),
inference(resolution,[],[f14076,f23139]) ).
fof(f23139,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),implies(possibly(X0),X1)),X1))
| ~ spl2_498 ),
inference(avatar_component_clause,[],[f23138]) ).
fof(f23138,plain,
( spl2_498
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),implies(possibly(X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_498])]) ).
fof(f73515,plain,
( ~ spl2_387
| ~ spl2_680 ),
inference(avatar_contradiction_clause,[],[f73454]) ).
fof(f73454,plain,
( $false
| ~ spl2_387
| ~ spl2_680 ),
inference(resolution,[],[f14076,f39537]) ).
fof(f39537,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),equiv(possibly(X0),X1)),X1))
| ~ spl2_680 ),
inference(avatar_component_clause,[],[f39536]) ).
fof(f39536,plain,
( spl2_680
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),equiv(possibly(X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_680])]) ).
fof(f73514,plain,
( ~ spl2_387
| ~ spl2_712 ),
inference(avatar_contradiction_clause,[],[f73455]) ).
fof(f73455,plain,
( $false
| ~ spl2_387
| ~ spl2_712 ),
inference(resolution,[],[f14076,f42530]) ).
fof(f42530,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(possibly(X1),equiv(X2,possibly(X1))),X2))
| ~ spl2_712 ),
inference(avatar_component_clause,[],[f42529]) ).
fof(f42529,plain,
( spl2_712
<=> ! [X2,X1] : is_a_theorem(strict_implies(and(possibly(X1),equiv(X2,possibly(X1))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_712])]) ).
fof(f73513,plain,
( ~ spl2_321
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73456]) ).
fof(f73456,plain,
( $false
| ~ spl2_321
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10073]) ).
fof(f10073,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(or(X4,X3),or(X3,X4)))
| ~ spl2_321 ),
inference(avatar_component_clause,[],[f10072]) ).
fof(f10072,plain,
( spl2_321
<=> ! [X4,X3] : is_a_theorem(strict_implies(or(X4,X3),or(X3,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_321])]) ).
fof(f73512,plain,
( ~ spl2_387
| ~ spl2_520 ),
inference(avatar_contradiction_clause,[],[f73457]) ).
fof(f73457,plain,
( $false
| ~ spl2_387
| ~ spl2_520 ),
inference(resolution,[],[f14076,f27682]) ).
fof(f73511,plain,
( ~ spl2_387
| ~ spl2_522 ),
inference(avatar_contradiction_clause,[],[f73458]) ).
fof(f73458,plain,
( $false
| ~ spl2_387
| ~ spl2_522 ),
inference(resolution,[],[f14076,f27811]) ).
fof(f27811,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(or(X1,and(X2,X1)),X1))
| ~ spl2_522 ),
inference(avatar_component_clause,[],[f27810]) ).
fof(f27810,plain,
( spl2_522
<=> ! [X2,X1] : is_a_theorem(strict_implies(or(X1,and(X2,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_522])]) ).
fof(f73510,plain,
( ~ spl2_387
| ~ spl2_531 ),
inference(avatar_contradiction_clause,[],[f73459]) ).
fof(f73459,plain,
( $false
| ~ spl2_387
| ~ spl2_531 ),
inference(resolution,[],[f14076,f28306]) ).
fof(f28306,plain,
( ! [X18,X19,X20] : is_a_theorem(strict_implies(or(X18,and(X19,and(X20,X18))),X18))
| ~ spl2_531 ),
inference(avatar_component_clause,[],[f28305]) ).
fof(f28305,plain,
( spl2_531
<=> ! [X20,X18,X19] : is_a_theorem(strict_implies(or(X18,and(X19,and(X20,X18))),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_531])]) ).
fof(f73509,plain,
( ~ spl2_387
| ~ spl2_532 ),
inference(avatar_contradiction_clause,[],[f73460]) ).
fof(f73460,plain,
( $false
| ~ spl2_387
| ~ spl2_532 ),
inference(resolution,[],[f14076,f28310]) ).
fof(f28310,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(or(X21,and(X23,and(X21,X22))),X21))
| ~ spl2_532 ),
inference(avatar_component_clause,[],[f28309]) ).
fof(f28309,plain,
( spl2_532
<=> ! [X22,X21,X23] : is_a_theorem(strict_implies(or(X21,and(X23,and(X21,X22))),X21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_532])]) ).
fof(f73508,plain,
( ~ spl2_40
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73461]) ).
fof(f73461,plain,
( $false
| ~ spl2_40
| ~ spl2_387 ),
inference(resolution,[],[f14076,f407]) ).
fof(f73507,plain,
( ~ spl2_52
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73462]) ).
fof(f73462,plain,
( $false
| ~ spl2_52
| ~ spl2_387 ),
inference(resolution,[],[f14076,f490]) ).
fof(f490,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0)))
| ~ spl2_52 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f489,plain,
( spl2_52
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
fof(f73506,plain,
( ~ spl2_87
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73463]) ).
fof(f73463,plain,
( $false
| ~ spl2_87
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1059]) ).
fof(f1059,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(strict_equiv(X13,X12),strict_implies(X12,X12)))
| ~ spl2_87 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1058,plain,
( spl2_87
<=> ! [X13,X12] : is_a_theorem(strict_implies(strict_equiv(X13,X12),strict_implies(X12,X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
fof(f73505,plain,
( ~ spl2_89
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73464]) ).
fof(f73464,plain,
( $false
| ~ spl2_89
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1085]) ).
fof(f1085,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X1,X0)))
| ~ spl2_89 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1084,plain,
( spl2_89
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
fof(f73504,plain,
( ~ spl2_41
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73465]) ).
fof(f73465,plain,
( $false
| ~ spl2_41
| ~ spl2_387 ),
inference(resolution,[],[f14076,f411]) ).
fof(f411,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(strict_equiv(X9,X8),strict_equiv(X8,X9)))
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f410,plain,
( spl2_41
<=> ! [X9,X8] : is_a_theorem(strict_implies(strict_equiv(X9,X8),strict_equiv(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f73503,plain,
( ~ spl2_60
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73466]) ).
fof(f73466,plain,
( $false
| ~ spl2_60
| ~ spl2_387 ),
inference(resolution,[],[f14076,f559]) ).
fof(f559,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,X1))))
| ~ spl2_60 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f558,plain,
( spl2_60
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_60])]) ).
fof(f73502,plain,
( ~ spl2_65
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73467]) ).
fof(f73467,plain,
( $false
| ~ spl2_65
| ~ spl2_387 ),
inference(resolution,[],[f14076,f603]) ).
fof(f73501,plain,
( ~ spl2_117
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73468]) ).
fof(f73468,plain,
( $false
| ~ spl2_117
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1701]) ).
fof(f1701,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(strict_equiv(not(X7),X8),necessarily(or(X8,X7))))
| ~ spl2_117 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f1700,plain,
( spl2_117
<=> ! [X7,X8] : is_a_theorem(strict_implies(strict_equiv(not(X7),X8),necessarily(or(X8,X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_117])]) ).
fof(f73500,plain,
( ~ spl2_110
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73469]) ).
fof(f73469,plain,
( $false
| ~ spl2_110
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1482]) ).
fof(f1482,plain,
( ! [X26,X25] : is_a_theorem(strict_implies(strict_equiv(X26,not(X25)),necessarily(or(X25,X26))))
| ~ spl2_110 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f1481,plain,
( spl2_110
<=> ! [X25,X26] : is_a_theorem(strict_implies(strict_equiv(X26,not(X25)),necessarily(or(X25,X26)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_110])]) ).
fof(f73499,plain,
( ~ spl2_130
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73470]) ).
fof(f73470,plain,
( $false
| ~ spl2_130
| ~ spl2_387 ),
inference(resolution,[],[f14076,f2152]) ).
fof(f2152,plain,
( ! [X21,X22] : is_a_theorem(strict_implies(strict_equiv(X22,not(X21)),necessarily(or(X21,not(X21)))))
| ~ spl2_130 ),
inference(avatar_component_clause,[],[f2151]) ).
fof(f2151,plain,
( spl2_130
<=> ! [X22,X21] : is_a_theorem(strict_implies(strict_equiv(X22,not(X21)),necessarily(or(X21,not(X21))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_130])]) ).
fof(f73498,plain,
( ~ spl2_119
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73471]) ).
fof(f73471,plain,
( $false
| ~ spl2_119
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1709]) ).
fof(f1709,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(strict_equiv(X7,not(X6)),necessarily(or(X7,X6))))
| ~ spl2_119 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f1708,plain,
( spl2_119
<=> ! [X6,X7] : is_a_theorem(strict_implies(strict_equiv(X7,not(X6)),necessarily(or(X7,X6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_119])]) ).
fof(f73497,plain,
( ~ spl2_115
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73472]) ).
fof(f73472,plain,
( $false
| ~ spl2_115
| ~ spl2_387 ),
inference(resolution,[],[f14076,f1685]) ).
fof(f1685,plain,
( ! [X1] : is_a_theorem(strict_implies(strict_equiv(X1,not(X1)),necessarily(not(not(X1)))))
| ~ spl2_115 ),
inference(avatar_component_clause,[],[f1684]) ).
fof(f1684,plain,
( spl2_115
<=> ! [X1] : is_a_theorem(strict_implies(strict_equiv(X1,not(X1)),necessarily(not(not(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_115])]) ).
fof(f73496,plain,
( ~ spl2_387
| ~ spl2_445 ),
inference(avatar_contradiction_clause,[],[f73473]) ).
fof(f73473,plain,
( $false
| ~ spl2_387
| ~ spl2_445 ),
inference(resolution,[],[f14076,f16312]) ).
fof(f16312,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(strict_equiv(necessarily(not(X11)),not(X10)),strict_implies(possibly(X11),X10)))
| ~ spl2_445 ),
inference(avatar_component_clause,[],[f16311]) ).
fof(f16311,plain,
( spl2_445
<=> ! [X11,X10] : is_a_theorem(strict_implies(strict_equiv(necessarily(not(X11)),not(X10)),strict_implies(possibly(X11),X10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_445])]) ).
fof(f73495,plain,
( ~ spl2_250
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73474]) ).
fof(f73474,plain,
( $false
| ~ spl2_250
| ~ spl2_387 ),
inference(resolution,[],[f14076,f6960]) ).
fof(f6960,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(strict_equiv(X7,and(not(X7),X8)),strict_implies(X8,X7)))
| ~ spl2_250 ),
inference(avatar_component_clause,[],[f6959]) ).
fof(f6959,plain,
( spl2_250
<=> ! [X7,X8] : is_a_theorem(strict_implies(strict_equiv(X7,and(not(X7),X8)),strict_implies(X8,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_250])]) ).
fof(f73494,plain,
( ~ spl2_264
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73475]) ).
fof(f73475,plain,
( $false
| ~ spl2_264
| ~ spl2_387 ),
inference(resolution,[],[f14076,f7547]) ).
fof(f7547,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(strict_equiv(X9,and(X8,not(X9))),strict_implies(X8,X9)))
| ~ spl2_264 ),
inference(avatar_component_clause,[],[f7546]) ).
fof(f7546,plain,
( spl2_264
<=> ! [X9,X8] : is_a_theorem(strict_implies(strict_equiv(X9,and(X8,not(X9))),strict_implies(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_264])]) ).
fof(f73493,plain,
( ~ spl2_270
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73476]) ).
fof(f73476,plain,
( $false
| ~ spl2_270
| ~ spl2_387 ),
inference(resolution,[],[f14076,f8073]) ).
fof(f73492,plain,
( ~ spl2_333
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73477]) ).
fof(f73477,plain,
( $false
| ~ spl2_333
| ~ spl2_387 ),
inference(resolution,[],[f14076,f10707]) ).
fof(f10707,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),implies(necessarily(not(X0)),X1)))
| ~ spl2_333 ),
inference(avatar_component_clause,[],[f10706]) ).
fof(f10706,plain,
( spl2_333
<=> ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),implies(necessarily(not(X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_333])]) ).
fof(f73491,plain,
( ~ spl2_387
| ~ spl2_859 ),
inference(avatar_contradiction_clause,[],[f73478]) ).
fof(f73478,plain,
( $false
| ~ spl2_387
| ~ spl2_859 ),
inference(resolution,[],[f14076,f62043]) ).
fof(f62043,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(X15,necessarily(not(X14))),X16)))
| ~ spl2_859 ),
inference(avatar_component_clause,[],[f62042]) ).
fof(f62042,plain,
( spl2_859
<=> ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(X15,necessarily(not(X14))),X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_859])]) ).
fof(f73490,plain,
( ~ spl2_387
| ~ spl2_921 ),
inference(avatar_contradiction_clause,[],[f73479]) ).
fof(f73479,plain,
( $false
| ~ spl2_387
| ~ spl2_921 ),
inference(resolution,[],[f14076,f66815]) ).
fof(f66815,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(necessarily(not(X14)),X15),X16)))
| ~ spl2_921 ),
inference(avatar_component_clause,[],[f66814]) ).
fof(f66814,plain,
( spl2_921
<=> ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(necessarily(not(X14)),X15),X16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_921])]) ).
fof(f73489,plain,
( ~ spl2_354
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73480]) ).
fof(f73480,plain,
( $false
| ~ spl2_354
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12073]) ).
fof(f12073,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(necessarily(not(X0)),possibly(X1)))))
| ~ spl2_354 ),
inference(avatar_component_clause,[],[f12072]) ).
fof(f12072,plain,
( spl2_354
<=> ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(necessarily(not(X0)),possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_354])]) ).
fof(f73488,plain,
( ~ spl2_387
| ~ spl2_753 ),
inference(avatar_contradiction_clause,[],[f73481]) ).
fof(f73481,plain,
( $false
| ~ spl2_387
| ~ spl2_753 ),
inference(resolution,[],[f14076,f49122]) ).
fof(f49122,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(possibly(X10),not(and(necessarily(not(X10)),X11))))
| ~ spl2_753 ),
inference(avatar_component_clause,[],[f49121]) ).
fof(f49121,plain,
( spl2_753
<=> ! [X11,X10] : is_a_theorem(strict_implies(possibly(X10),not(and(necessarily(not(X10)),X11)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_753])]) ).
fof(f73487,plain,
( ~ spl2_361
| ~ spl2_387 ),
inference(avatar_contradiction_clause,[],[f73482]) ).
fof(f73482,plain,
( $false
| ~ spl2_361
| ~ spl2_387 ),
inference(resolution,[],[f14076,f12228]) ).
fof(f12228,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(possibly(X1),necessarily(not(X0))))))
| ~ spl2_361 ),
inference(avatar_component_clause,[],[f12227]) ).
fof(f12227,plain,
( spl2_361
<=> ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(possibly(X1),necessarily(not(X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_361])]) ).
fof(f73486,plain,
( ~ spl2_387
| ~ spl2_724 ),
inference(avatar_contradiction_clause,[],[f73483]) ).
fof(f73483,plain,
( $false
| ~ spl2_387
| ~ spl2_724 ),
inference(resolution,[],[f14076,f45050]) ).
fof(f45050,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(possibly(X10),not(and(X11,necessarily(not(X10))))))
| ~ spl2_724 ),
inference(avatar_component_clause,[],[f45049]) ).
fof(f45049,plain,
( spl2_724
<=> ! [X11,X10] : is_a_theorem(strict_implies(possibly(X10),not(and(X11,necessarily(not(X10)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_724])]) ).
fof(f73208,plain,
( spl2_969
| ~ spl2_76
| ~ spl2_151 ),
inference(avatar_split_clause,[],[f3373,f2643,f810,f73206]) ).
fof(f73206,plain,
( spl2_969
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X1,X2)),strict_implies(X0,not(X1))))
| is_a_theorem(strict_implies(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_969])]) ).
fof(f2643,plain,
( spl2_151
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))))
| is_a_theorem(strict_implies(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_151])]) ).
fof(f3373,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X1,X2)),strict_implies(X0,not(X1))))
| is_a_theorem(strict_implies(X0,X2)) )
| ~ spl2_76
| ~ spl2_151 ),
inference(superposition,[],[f2644,f811]) ).
fof(f2644,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))))
| is_a_theorem(strict_implies(X2,X1)) )
| ~ spl2_151 ),
inference(avatar_component_clause,[],[f2643]) ).
fof(f73204,plain,
( spl2_968
| ~ spl2_791
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73105,f73098,f52768,f73202]) ).
fof(f73105,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_791
| ~ spl2_965 ),
inference(resolution,[],[f73099,f52769]) ).
fof(f73135,plain,
( spl2_967
| ~ spl2_24
| ~ spl2_965 ),
inference(avatar_split_clause,[],[f73116,f73098,f290,f73133]) ).
fof(f73116,plain,
( ! [X9] : is_a_theorem(or(X9,not(X9)))
| ~ spl2_24
| ~ spl2_965 ),
inference(superposition,[],[f73099,f291]) ).
fof(f73104,plain,
( spl2_966
| ~ spl2_76
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3129,f2558,f810,f73102]) ).
fof(f73102,plain,
( spl2_966
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X3,X4),necessarily(or(X2,X3))),necessarily(or(X2,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_966])]) ).
fof(f3129,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(strict_implies(X3,X4),necessarily(or(X2,X3))),necessarily(or(X2,X4))))
| ~ spl2_76
| ~ spl2_146 ),
inference(superposition,[],[f2559,f811]) ).
fof(f73100,plain,
( spl2_387
| spl2_965
| ~ spl2_27
| ~ spl2_964 ),
inference(avatar_split_clause,[],[f73058,f73055,f302,f73098,f14075]) ).
fof(f73058,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(X1) )
| ~ spl2_27
| ~ spl2_964 ),
inference(resolution,[],[f73056,f303]) ).
fof(f73057,plain,
( spl2_964
| ~ spl2_382
| ~ spl2_962 ),
inference(avatar_split_clause,[],[f73030,f73027,f13556,f73055]) ).
fof(f73030,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1)))
| ~ spl2_382
| ~ spl2_962 ),
inference(resolution,[],[f73028,f13557]) ).
fof(f73053,plain,
( spl2_963
| ~ spl2_76
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f2994,f2528,f810,f73051]) ).
fof(f73051,plain,
( spl2_963
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X1,X2)),strict_implies(X0,not(X1))),strict_implies(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_963])]) ).
fof(f2994,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X1,X2)),strict_implies(X0,not(X1))),strict_implies(X0,X2)))
| ~ spl2_76
| ~ spl2_142 ),
inference(superposition,[],[f2529,f811]) ).
fof(f73029,plain,
( spl2_962
| ~ spl2_83
| ~ spl2_961 ),
inference(avatar_split_clause,[],[f73020,f72986,f1024,f73027]) ).
fof(f73020,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(implies(X0,X0)))))
| ~ spl2_83
| ~ spl2_961 ),
inference(superposition,[],[f72987,f1025]) ).
fof(f72988,plain,
( spl2_961
| ~ spl2_29
| ~ spl2_721
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70372,f69866,f45037,f315,f72986]) ).
fof(f70372,plain,
( ! [X549,X548,X550] : is_a_theorem(necessarily(or(implies(X548,X549),implies(X550,X548))))
| ~ spl2_29
| ~ spl2_721
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70087,f316]) ).
fof(f70087,plain,
( ! [X549,X548,X550] : is_a_theorem(necessarily(or(implies(X548,X549),not(and(X550,not(X548))))))
| ~ spl2_721
| ~ spl2_954 ),
inference(superposition,[],[f45038,f69867]) ).
fof(f72014,plain,
( spl2_960
| ~ spl2_97
| ~ spl2_957 ),
inference(avatar_split_clause,[],[f71076,f70873,f1233,f72012]) ).
fof(f71076,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X2,X0),implies(X0,X1))))
| ~ spl2_97
| ~ spl2_957 ),
inference(superposition,[],[f70874,f1234]) ).
fof(f71128,plain,
( spl2_959
| ~ spl2_97
| ~ spl2_682
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70371,f69866,f40362,f1233,f71126]) ).
fof(f70371,plain,
( ! [X526,X525] : is_a_theorem(necessarily(or(not(not(X525)),implies(X525,X526))))
| ~ spl2_97
| ~ spl2_682
| ~ spl2_954 ),
inference(forward_demodulation,[],[f70078,f1234]) ).
fof(f70078,plain,
( ! [X526,X525] : is_a_theorem(necessarily(or(implies(X525,X526),not(not(X525)))))
| ~ spl2_682
| ~ spl2_954 ),
inference(superposition,[],[f40363,f69867]) ).
fof(f71038,plain,
( spl2_958
| ~ spl2_97
| ~ spl2_956 ),
inference(avatar_split_clause,[],[f70867,f70388,f1233,f71036]) ).
fof(f70867,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(or(X0,X2),implies(X0,X1))))
| ~ spl2_97
| ~ spl2_956 ),
inference(superposition,[],[f70389,f1234]) ).
fof(f70875,plain,
( spl2_957
| ~ spl2_97
| ~ spl2_956 ),
inference(avatar_split_clause,[],[f70847,f70388,f1233,f70873]) ).
fof(f70847,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(implies(X2,X4),or(X3,X2))))
| ~ spl2_97
| ~ spl2_956 ),
inference(superposition,[],[f70389,f1234]) ).
fof(f70390,plain,
( spl2_956
| ~ spl2_24
| ~ spl2_351
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f70230,f69866,f11933,f290,f70388]) ).
fof(f70230,plain,
( ! [X31,X29,X30] : is_a_theorem(necessarily(or(implies(X29,X30),or(X29,X31))))
| ~ spl2_24
| ~ spl2_351
| ~ spl2_954 ),
inference(forward_demodulation,[],[f69915,f291]) ).
fof(f69915,plain,
( ! [X31,X29,X30] : is_a_theorem(necessarily(or(implies(X29,X30),implies(not(X29),X31))))
| ~ spl2_351
| ~ spl2_954 ),
inference(superposition,[],[f11934,f69867]) ).
fof(f70386,plain,
( spl2_955
| ~ spl2_96
| ~ spl2_954 ),
inference(avatar_split_clause,[],[f69904,f69866,f1122,f70384]) ).
fof(f69868,plain,
( spl2_954
| ~ spl2_524
| ~ spl2_947 ),
inference(avatar_split_clause,[],[f69821,f67422,f27818,f69866]) ).
fof(f67422,plain,
( spl2_947
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X1,X0),X0))
| not(X0) = and(not(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_947])]) ).
fof(f69821,plain,
( ! [X2,X3] : not(X2) = and(not(X2),implies(X2,X3))
| ~ spl2_524
| ~ spl2_947 ),
inference(resolution,[],[f67423,f27819]) ).
fof(f67423,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X1,X0),X0))
| not(X0) = and(not(X0),X1) )
| ~ spl2_947 ),
inference(avatar_component_clause,[],[f67422]) ).
fof(f68785,plain,
( spl2_953
| ~ spl2_33
| ~ spl2_72
| ~ spl2_97
| ~ spl2_936 ),
inference(avatar_split_clause,[],[f68773,f67050,f1233,f748,f340,f68783]) ).
fof(f68773,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(equiv(X0,not(X0))))))
| ~ spl2_33
| ~ spl2_72
| ~ spl2_97
| ~ spl2_936 ),
inference(forward_demodulation,[],[f68772,f1234]) ).
fof(f68772,plain,
( ! [X0] : is_a_theorem(necessarily(or(not(equiv(X0,not(X0))),X0)))
| ~ spl2_33
| ~ spl2_72
| ~ spl2_936 ),
inference(forward_demodulation,[],[f68741,f341]) ).
fof(f68741,plain,
( ! [X0] : is_a_theorem(strict_implies(not(not(equiv(X0,not(X0)))),X0))
| ~ spl2_72
| ~ spl2_936 ),
inference(superposition,[],[f67051,f749]) ).
fof(f68550,plain,
( spl2_952
| ~ spl2_38
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f24128,f23256,f377,f68548]) ).
fof(f68548,plain,
( spl2_952
<=> ! [X384,X382,X383] : not(strict_implies(strict_equiv(X382,X383),X384)) = not(strict_implies(strict_equiv(X383,X382),X384)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_952])]) ).
fof(f24128,plain,
( ! [X384,X383,X382] : not(strict_implies(strict_equiv(X382,X383),X384)) = not(strict_implies(strict_equiv(X383,X382),X384))
| ~ spl2_38
| ~ spl2_503 ),
inference(forward_demodulation,[],[f23825,f378]) ).
fof(f23825,plain,
( ! [X384,X383,X382] : not(strict_implies(strict_equiv(X382,X383),X384)) = possibly(and(strict_equiv(X383,X382),not(X384)))
| ~ spl2_38
| ~ spl2_503 ),
inference(superposition,[],[f378,f23257]) ).
fof(f68527,plain,
( spl2_951
| ~ spl2_451
| ~ spl2_933 ),
inference(avatar_split_clause,[],[f68475,f67029,f16617,f68525]) ).
fof(f68525,plain,
( spl2_951
<=> ! [X18,X17,X19] :
( is_a_theorem(implies(and(X17,X18),X19))
| ~ is_a_theorem(not(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_951])]) ).
fof(f16617,plain,
( spl2_451
<=> ! [X4,X3] :
( is_a_theorem(and(X4,necessarily(or(X3,not(X3)))))
| ~ is_a_theorem(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_451])]) ).
fof(f67029,plain,
( spl2_933
<=> ! [X0,X3,X2,X1] :
( is_a_theorem(implies(and(X0,X1),X2))
| ~ is_a_theorem(and(not(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_933])]) ).
fof(f68475,plain,
( ! [X18,X19,X17] :
( is_a_theorem(implies(and(X17,X18),X19))
| ~ is_a_theorem(not(X18)) )
| ~ spl2_451
| ~ spl2_933 ),
inference(resolution,[],[f67030,f16618]) ).
fof(f16618,plain,
( ! [X3,X4] :
( is_a_theorem(and(X4,necessarily(or(X3,not(X3)))))
| ~ is_a_theorem(X4) )
| ~ spl2_451 ),
inference(avatar_component_clause,[],[f16617]) ).
fof(f67030,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(and(not(X1),X3))
| is_a_theorem(implies(and(X0,X1),X2)) )
| ~ spl2_933 ),
inference(avatar_component_clause,[],[f67029]) ).
fof(f68470,plain,
( spl2_950
| ~ spl2_38
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23689,f23252,f377,f68468]) ).
fof(f68468,plain,
( spl2_950
<=> ! [X403,X401,X402] : not(strict_implies(equiv(X401,X402),X403)) = not(strict_implies(equiv(X402,X401),X403)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_950])]) ).
fof(f23689,plain,
( ! [X403,X402,X401] : not(strict_implies(equiv(X401,X402),X403)) = not(strict_implies(equiv(X402,X401),X403))
| ~ spl2_38
| ~ spl2_502 ),
inference(forward_demodulation,[],[f23383,f378]) ).
fof(f23383,plain,
( ! [X403,X402,X401] : not(strict_implies(equiv(X401,X402),X403)) = possibly(and(equiv(X402,X401),not(X403)))
| ~ spl2_38
| ~ spl2_502 ),
inference(superposition,[],[f378,f23253]) ).
fof(f68174,plain,
( spl2_949
| ~ spl2_76
| ~ spl2_80
| ~ spl2_161
| ~ spl2_325
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f13931,f12444,f10415,f2750,f856,f810,f68172]) ).
fof(f13931,plain,
( ! [X3,X4] : necessarily(not(equiv(X3,not(X4)))) = necessarily(not(equiv(not(X4),X3)))
| ~ spl2_76
| ~ spl2_80
| ~ spl2_161
| ~ spl2_325
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13930,f3523]) ).
fof(f3523,plain,
( ! [X10,X11] : strict_implies(or(X10,X11),and(X11,not(not(X10)))) = necessarily(not(equiv(not(X10),X11)))
| ~ spl2_80
| ~ spl2_161 ),
inference(superposition,[],[f2751,f857]) ).
fof(f13930,plain,
( ! [X3,X4] : necessarily(not(equiv(X3,not(X4)))) = strict_implies(or(X4,X3),and(X3,not(not(X4))))
| ~ spl2_76
| ~ spl2_161
| ~ spl2_325
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13806,f3520]) ).
fof(f13806,plain,
( ! [X3,X4] : necessarily(not(equiv(X3,not(X4)))) = necessarily(not(and(implies(X3,not(X4)),or(X4,X3))))
| ~ spl2_325
| ~ spl2_371 ),
inference(superposition,[],[f12445,f10416]) ).
fof(f67752,plain,
( spl2_948
| ~ spl2_136
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f13816,f12444,f2344,f67750]) ).
fof(f67750,plain,
( spl2_948
<=> ! [X13,X12,X11] :
( ~ is_a_theorem(necessarily(not(and(X11,or(X12,X13)))))
| is_a_theorem(strict_implies(X11,not(X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_948])]) ).
fof(f2344,plain,
( spl2_136
<=> ! [X29,X28,X30] :
( is_a_theorem(strict_implies(X28,X29))
| ~ is_a_theorem(strict_implies(X28,and(X29,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_136])]) ).
fof(f13816,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(necessarily(not(and(X11,or(X12,X13)))))
| is_a_theorem(strict_implies(X11,not(X12))) )
| ~ spl2_136
| ~ spl2_371 ),
inference(superposition,[],[f2345,f12445]) ).
fof(f2345,plain,
( ! [X28,X29,X30] :
( ~ is_a_theorem(strict_implies(X28,and(X29,X30)))
| is_a_theorem(strict_implies(X28,X29)) )
| ~ spl2_136 ),
inference(avatar_component_clause,[],[f2344]) ).
fof(f67424,plain,
( spl2_947
| ~ spl2_23
| ~ spl2_33
| ~ spl2_76
| ~ spl2_125
| ~ spl2_129 ),
inference(avatar_split_clause,[],[f2422,f2138,f1852,f810,f340,f286,f67422]) ).
fof(f2422,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X1,X0),X0))
| not(X0) = and(not(X0),X1) )
| ~ spl2_23
| ~ spl2_33
| ~ spl2_76
| ~ spl2_125
| ~ spl2_129 ),
inference(forward_demodulation,[],[f2416,f287]) ).
fof(f2416,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(implies(X1,X0),X0)))
| not(X0) = and(not(X0),X1) )
| ~ spl2_33
| ~ spl2_76
| ~ spl2_125
| ~ spl2_129 ),
inference(backward_demodulation,[],[f2149,f2377]) ).
fof(f2377,plain,
( ! [X2,X3,X4] : implies(implies(X2,X3),X4) = or(X4,and(not(X3),X2))
| ~ spl2_76
| ~ spl2_125 ),
inference(superposition,[],[f1853,f811]) ).
fof(f2149,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(not(X0),X1))))
| not(X0) = and(not(X0),X1) )
| ~ spl2_33
| ~ spl2_129 ),
inference(superposition,[],[f2139,f341]) ).
fof(f67178,plain,
( spl2_946
| ~ spl2_26
| ~ spl2_896 ),
inference(avatar_split_clause,[],[f66115,f63354,f298,f67176]) ).
fof(f67176,plain,
( spl2_946
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(X7,or(X6,X8)))
| ~ is_a_theorem(not(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_946])]) ).
fof(f63354,plain,
( spl2_896
<=> ! [X6,X7,X8] :
( ~ is_a_theorem(and(not(X7),and(X8,or(X6,X7))))
| is_a_theorem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_896])]) ).
fof(f66115,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(X7,or(X6,X8)))
| ~ is_a_theorem(not(X8)) )
| ~ spl2_26
| ~ spl2_896 ),
inference(resolution,[],[f63355,f299]) ).
fof(f63355,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(and(not(X7),and(X8,or(X6,X7))))
| is_a_theorem(X6) )
| ~ spl2_896 ),
inference(avatar_component_clause,[],[f63354]) ).
fof(f67174,plain,
( spl2_945
| ~ spl2_76
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f921,f814,f810,f67172]) ).
fof(f67172,plain,
( spl2_945
<=> ! [X2,X4,X3] : not(and(X4,implies(X2,X3))) = implies(X4,and(not(X3),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_945])]) ).
fof(f921,plain,
( ! [X2,X3,X4] : not(and(X4,implies(X2,X3))) = implies(X4,and(not(X3),X2))
| ~ spl2_76
| ~ spl2_77 ),
inference(superposition,[],[f815,f811]) ).
fof(f67170,plain,
( spl2_944
| ~ spl2_76
| ~ spl2_894 ),
inference(avatar_split_clause,[],[f66046,f63346,f810,f67168]) ).
fof(f67168,plain,
( spl2_944
<=> ! [X6,X7,X8] :
( ~ is_a_theorem(not(implies(and(X8,or(X6,X7)),X7)))
| is_a_theorem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_944])]) ).
fof(f63346,plain,
( spl2_894
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(or(X3,X4),X5),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_894])]) ).
fof(f66046,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(implies(and(X8,or(X6,X7)),X7)))
| is_a_theorem(X6) )
| ~ spl2_76
| ~ spl2_894 ),
inference(superposition,[],[f63347,f811]) ).
fof(f63347,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(not(implies(and(or(X3,X4),X5),X4)))
| is_a_theorem(X3) )
| ~ spl2_894 ),
inference(avatar_component_clause,[],[f63346]) ).
fof(f67166,plain,
( spl2_943
| ~ spl2_29
| ~ spl2_655
| ~ spl2_891 ),
inference(avatar_split_clause,[],[f65770,f62826,f37077,f315,f67164]) ).
fof(f67164,plain,
( spl2_943
<=> ! [X0,X1] : is_a_theorem(strict_implies(equiv(implies(X0,X1),and(X0,not(X1))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_943])]) ).
fof(f65770,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(implies(X0,X1),and(X0,not(X1))),X0))
| ~ spl2_29
| ~ spl2_655
| ~ spl2_891 ),
inference(forward_demodulation,[],[f65739,f37078]) ).
fof(f65739,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(and(X0,not(X1)),implies(X0,X1)),X0))
| ~ spl2_29
| ~ spl2_891 ),
inference(superposition,[],[f62827,f316]) ).
fof(f67162,plain,
( spl2_942
| ~ spl2_27
| ~ spl2_891 ),
inference(avatar_split_clause,[],[f65654,f62826,f302,f67160]) ).
fof(f67160,plain,
( spl2_942
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(and(X0,X1),not(and(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_942])]) ).
fof(f65654,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(and(X0,X1),not(and(X0,X1)))) )
| ~ spl2_27
| ~ spl2_891 ),
inference(resolution,[],[f62827,f303]) ).
fof(f67158,plain,
( spl2_941
| ~ spl2_96
| ~ spl2_655
| ~ spl2_889 ),
inference(avatar_split_clause,[],[f65650,f62818,f37077,f1122,f67156]) ).
fof(f67156,plain,
( spl2_941
<=> ! [X27,X28] : is_a_theorem(strict_implies(equiv(implies(X28,X27),and(not(X27),X28)),X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_941])]) ).
fof(f65650,plain,
( ! [X28,X27] : is_a_theorem(strict_implies(equiv(implies(X28,X27),and(not(X27),X28)),X28))
| ~ spl2_96
| ~ spl2_655
| ~ spl2_889 ),
inference(forward_demodulation,[],[f65632,f37078]) ).
fof(f65632,plain,
( ! [X28,X27] : is_a_theorem(strict_implies(equiv(and(not(X27),X28),implies(X28,X27)),X28))
| ~ spl2_96
| ~ spl2_889 ),
inference(superposition,[],[f62819,f1123]) ).
fof(f67073,plain,
( spl2_940
| ~ spl2_27
| ~ spl2_889 ),
inference(avatar_split_clause,[],[f65539,f62818,f302,f67071]) ).
fof(f67071,plain,
( spl2_940
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(and(X1,X0),not(and(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_940])]) ).
fof(f65539,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(and(X1,X0),not(and(X1,X0)))) )
| ~ spl2_27
| ~ spl2_889 ),
inference(resolution,[],[f62819,f303]) ).
fof(f67069,plain,
( spl2_939
| ~ spl2_663
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65110,f62814,f37227,f67067]) ).
fof(f67067,plain,
( spl2_939
<=> ! [X59,X58] : is_a_theorem(strict_implies(and(not(not(equiv(X58,not(X58)))),X59),X58)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_939])]) ).
fof(f62814,plain,
( spl2_888
<=> ! [X2,X3] :
( is_a_theorem(strict_implies(X2,X3))
| ~ is_a_theorem(strict_implies(X2,equiv(X3,not(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_888])]) ).
fof(f65110,plain,
( ! [X58,X59] : is_a_theorem(strict_implies(and(not(not(equiv(X58,not(X58)))),X59),X58))
| ~ spl2_663
| ~ spl2_888 ),
inference(resolution,[],[f62815,f37228]) ).
fof(f62815,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_implies(X2,equiv(X3,not(X3))))
| is_a_theorem(strict_implies(X2,X3)) )
| ~ spl2_888 ),
inference(avatar_component_clause,[],[f62814]) ).
fof(f67065,plain,
( spl2_938
| ~ spl2_144
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65102,f62814,f2536,f67063]) ).
fof(f65102,plain,
( ! [X34,X35,X33] : is_a_theorem(strict_implies(and(X33,and(X34,equiv(X35,not(X35)))),X35))
| ~ spl2_144
| ~ spl2_888 ),
inference(resolution,[],[f62815,f2537]) ).
fof(f67056,plain,
( spl2_937
| ~ spl2_138
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65101,f62814,f2462,f67054]) ).
fof(f65101,plain,
( ! [X31,X32,X30] : is_a_theorem(strict_implies(and(X30,and(equiv(X31,not(X31)),X32)),X31))
| ~ spl2_138
| ~ spl2_888 ),
inference(resolution,[],[f62815,f2463]) ).
fof(f67052,plain,
( spl2_936
| ~ spl2_665
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65097,f62814,f37546,f67050]) ).
fof(f65097,plain,
( ! [X19,X20] : is_a_theorem(strict_implies(and(X19,not(not(equiv(X20,not(X20))))),X20))
| ~ spl2_665
| ~ spl2_888 ),
inference(resolution,[],[f62815,f37547]) ).
fof(f67048,plain,
( spl2_935
| ~ spl2_27
| ~ spl2_859 ),
inference(avatar_split_clause,[],[f64195,f62042,f302,f67046]) ).
fof(f67046,plain,
( spl2_935
<=> ! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(possibly(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_935])]) ).
fof(f64195,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(possibly(X1)) )
| ~ spl2_27
| ~ spl2_859 ),
inference(resolution,[],[f62043,f303]) ).
fof(f67044,plain,
( spl2_934
| ~ spl2_76
| ~ spl2_855 ),
inference(avatar_split_clause,[],[f64060,f62026,f810,f67042]) ).
fof(f64060,plain,
( ! [X40,X38,X41,X39] : is_a_theorem(strict_implies(and(X39,not(X38)),implies(and(X40,X38),X41)))
| ~ spl2_76
| ~ spl2_855 ),
inference(superposition,[],[f62027,f811]) ).
fof(f67031,plain,
( spl2_933
| ~ spl2_27
| ~ spl2_855 ),
inference(avatar_split_clause,[],[f64025,f62026,f302,f67029]) ).
fof(f64025,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(and(X0,X1),X2))
| ~ is_a_theorem(and(not(X1),X3)) )
| ~ spl2_27
| ~ spl2_855 ),
inference(resolution,[],[f62027,f303]) ).
fof(f67027,plain,
( spl2_932
| ~ spl2_550
| ~ spl2_697 ),
inference(avatar_split_clause,[],[f42645,f42469,f29224,f67025]) ).
fof(f67025,plain,
( spl2_932
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(and(X7,not(not(X6))),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_932])]) ).
fof(f29224,plain,
( spl2_550
<=> ! [X20,X19] :
( ~ is_a_theorem(not(implies(X20,X19)))
| is_a_theorem(and(not(X19),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_550])]) ).
fof(f42469,plain,
( spl2_697
<=> ! [X29,X27,X28] :
( ~ is_a_theorem(and(X28,and(X29,not(not(X27)))))
| is_a_theorem(X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_697])]) ).
fof(f42645,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(and(X7,not(not(X6))),X8))) )
| ~ spl2_550
| ~ spl2_697 ),
inference(resolution,[],[f42470,f29225]) ).
fof(f29225,plain,
( ! [X19,X20] :
( is_a_theorem(and(not(X19),X20))
| ~ is_a_theorem(not(implies(X20,X19))) )
| ~ spl2_550 ),
inference(avatar_component_clause,[],[f29224]) ).
fof(f42470,plain,
( ! [X28,X29,X27] :
( ~ is_a_theorem(and(X28,and(X29,not(not(X27)))))
| is_a_theorem(X27) )
| ~ spl2_697 ),
inference(avatar_component_clause,[],[f42469]) ).
fof(f67023,plain,
( spl2_931
| ~ spl2_550
| ~ spl2_695 ),
inference(avatar_split_clause,[],[f42581,f42461,f29224,f67021]) ).
fof(f67021,plain,
( spl2_931
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(and(not(not(X6)),X7),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_931])]) ).
fof(f42461,plain,
( spl2_695
<=> ! [X20,X19,X18] :
( ~ is_a_theorem(and(X19,and(not(not(X18)),X20)))
| is_a_theorem(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_695])]) ).
fof(f42581,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(and(not(not(X6)),X7),X8))) )
| ~ spl2_550
| ~ spl2_695 ),
inference(resolution,[],[f42462,f29225]) ).
fof(f42462,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(and(X19,and(not(not(X18)),X20)))
| is_a_theorem(X18) )
| ~ spl2_695 ),
inference(avatar_component_clause,[],[f42461]) ).
fof(f66973,plain,
( spl2_930
| ~ spl2_517
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41175,f41048,f26955,f66971]) ).
fof(f41175,plain,
( ! [X40,X38,X41,X39] : is_a_theorem(strict_implies(and(X40,and(X41,not(implies(X38,X39)))),X38))
| ~ spl2_517
| ~ spl2_684 ),
inference(superposition,[],[f41049,f26956]) ).
fof(f66969,plain,
( spl2_929
| ~ spl2_504
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41172,f41048,f23260,f66967]) ).
fof(f41172,plain,
( ! [X28,X29,X26,X27] : is_a_theorem(strict_implies(and(X28,and(not(implies(X26,X27)),X29)),X26))
| ~ spl2_504
| ~ spl2_684 ),
inference(superposition,[],[f41049,f23261]) ).
fof(f66965,plain,
( spl2_928
| ~ spl2_136
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41136,f41048,f2344,f66963]) ).
fof(f41136,plain,
( ! [X59,X62,X60,X61] : is_a_theorem(strict_implies(and(not(implies(and(X59,X60),X61)),X62),X59))
| ~ spl2_136
| ~ spl2_684 ),
inference(resolution,[],[f41049,f2345]) ).
fof(f66961,plain,
( spl2_927
| ~ spl2_152
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41135,f41048,f2665,f66959]) ).
fof(f2665,plain,
( spl2_152
<=> ! [X34,X36,X35] :
( is_a_theorem(strict_implies(X34,X35))
| ~ is_a_theorem(strict_implies(X34,and(X36,X35))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_152])]) ).
fof(f41135,plain,
( ! [X58,X56,X57,X55] : is_a_theorem(strict_implies(and(not(implies(and(X55,X56),X57)),X58),X56))
| ~ spl2_152
| ~ spl2_684 ),
inference(resolution,[],[f41049,f2666]) ).
fof(f2666,plain,
( ! [X36,X34,X35] :
( ~ is_a_theorem(strict_implies(X34,and(X36,X35)))
| is_a_theorem(strict_implies(X34,X35)) )
| ~ spl2_152 ),
inference(avatar_component_clause,[],[f2665]) ).
fof(f66911,plain,
( spl2_926
| ~ spl2_20
| ~ spl2_75
| ~ spl2_673 ),
inference(avatar_split_clause,[],[f39251,f39224,f806,f273,f66909]) ).
fof(f66909,plain,
( spl2_926
<=> ! [X0] :
( ~ is_a_theorem(equiv(possibly(X0),necessarily(not(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_926])]) ).
fof(f39224,plain,
( spl2_673
<=> ! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_673])]) ).
fof(f39251,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(possibly(X0),necessarily(not(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_75
| ~ spl2_673 ),
inference(forward_demodulation,[],[f39231,f807]) ).
fof(f39231,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(necessarily(not(X0)),possibly(X0)))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_673 ),
inference(superposition,[],[f39225,f274]) ).
fof(f39225,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(X0,not(X0)))
| is_a_theorem(X0) )
| ~ spl2_673 ),
inference(avatar_component_clause,[],[f39224]) ).
fof(f66907,plain,
( spl2_925
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_577 ),
inference(avatar_split_clause,[],[f30217,f30019,f19362,f810,f505,f66905]) ).
fof(f66905,plain,
( spl2_925
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(X5,and(X4,possibly(X6))))))
| is_a_theorem(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_925])]) ).
fof(f30019,plain,
( spl2_577
<=> ! [X109,X110,X111] :
( ~ is_a_theorem(not(implies(and(X109,X110),X111)))
| is_a_theorem(X110) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_577])]) ).
fof(f30217,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(X5,and(X4,possibly(X6))))))
| is_a_theorem(X5) )
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_577 ),
inference(forward_demodulation,[],[f30215,f19383]) ).
fof(f30215,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(and(X4,X5),possibly(X6)))))
| is_a_theorem(X5) )
| ~ spl2_54
| ~ spl2_577 ),
inference(superposition,[],[f30020,f506]) ).
fof(f30020,plain,
( ! [X111,X109,X110] :
( ~ is_a_theorem(not(implies(and(X109,X110),X111)))
| is_a_theorem(X110) )
| ~ spl2_577 ),
inference(avatar_component_clause,[],[f30019]) ).
fof(f66903,plain,
( spl2_924
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_576 ),
inference(avatar_split_clause,[],[f30177,f30015,f19362,f810,f505,f66901]) ).
fof(f66901,plain,
( spl2_924
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(X5,and(X4,possibly(X6))))))
| is_a_theorem(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_924])]) ).
fof(f30015,plain,
( spl2_576
<=> ! [X108,X107,X106] :
( ~ is_a_theorem(not(implies(and(X106,X107),X108)))
| is_a_theorem(X106) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_576])]) ).
fof(f30177,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(X5,and(X4,possibly(X6))))))
| is_a_theorem(X4) )
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_576 ),
inference(forward_demodulation,[],[f30175,f19383]) ).
fof(f30175,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(not(not(and(and(X4,X5),possibly(X6)))))
| is_a_theorem(X4) )
| ~ spl2_54
| ~ spl2_576 ),
inference(superposition,[],[f30016,f506]) ).
fof(f30016,plain,
( ! [X108,X106,X107] :
( ~ is_a_theorem(not(implies(and(X106,X107),X108)))
| is_a_theorem(X106) )
| ~ spl2_576 ),
inference(avatar_component_clause,[],[f30015]) ).
fof(f66824,plain,
( spl2_923
| ~ spl2_20
| ~ spl2_37
| ~ spl2_562 ),
inference(avatar_split_clause,[],[f29393,f29356,f373,f273,f66822]) ).
fof(f66822,plain,
( spl2_923
<=> ! [X0] :
( ~ is_a_theorem(not(implies(possibly(X0),possibly(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_923])]) ).
fof(f29356,plain,
( spl2_562
<=> ! [X83] :
( ~ is_a_theorem(not(or(X83,not(X83))))
| is_a_theorem(X83) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_562])]) ).
fof(f29393,plain,
( ! [X0] :
( ~ is_a_theorem(not(implies(possibly(X0),possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_37
| ~ spl2_562 ),
inference(forward_demodulation,[],[f29376,f374]) ).
fof(f29376,plain,
( ! [X0] :
( ~ is_a_theorem(not(or(necessarily(not(X0)),possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_562 ),
inference(superposition,[],[f29357,f274]) ).
fof(f29357,plain,
( ! [X83] :
( ~ is_a_theorem(not(or(X83,not(X83))))
| is_a_theorem(X83) )
| ~ spl2_562 ),
inference(avatar_component_clause,[],[f29356]) ).
fof(f66820,plain,
( spl2_922
| ~ spl2_318
| ~ spl2_560 ),
inference(avatar_split_clause,[],[f29347,f29337,f9826,f66818]) ).
fof(f66818,plain,
( spl2_922
<=> ! [X18,X17,X19] :
( ~ is_a_theorem(not(implies(or(X18,X17),X19)))
| is_a_theorem(or(X17,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_922])]) ).
fof(f29337,plain,
( spl2_560
<=> ! [X18,X19] :
( ~ is_a_theorem(not(implies(X18,X19)))
| is_a_theorem(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_560])]) ).
fof(f29347,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(not(implies(or(X18,X17),X19)))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_318
| ~ spl2_560 ),
inference(superposition,[],[f29338,f9827]) ).
fof(f29338,plain,
( ! [X18,X19] :
( ~ is_a_theorem(not(implies(X18,X19)))
| is_a_theorem(X18) )
| ~ spl2_560 ),
inference(avatar_component_clause,[],[f29337]) ).
fof(f66816,plain,
( spl2_921
| ~ spl2_23
| ~ spl2_37
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29061,f29009,f373,f286,f66814]) ).
fof(f29061,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(necessarily(not(X14)),X15),X16)))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_547 ),
inference(forward_demodulation,[],[f29053,f287]) ).
fof(f29053,plain,
( ! [X16,X14,X15] : is_a_theorem(necessarily(implies(possibly(X14),implies(and(necessarily(not(X14)),X15),X16))))
| ~ spl2_37
| ~ spl2_547 ),
inference(superposition,[],[f29010,f374]) ).
fof(f66812,plain,
( spl2_920
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29055,f29009,f19362,f810,f505,f66810]) ).
fof(f66810,plain,
( spl2_920
<=> ! [X6,X4,X5] : is_a_theorem(necessarily(or(X4,not(and(X5,and(X4,possibly(X6))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_920])]) ).
fof(f29055,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(or(X4,not(and(X5,and(X4,possibly(X6)))))))
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_547 ),
inference(forward_demodulation,[],[f29049,f19383]) ).
fof(f29049,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(or(X4,not(and(and(X4,X5),possibly(X6))))))
| ~ spl2_54
| ~ spl2_547 ),
inference(superposition,[],[f29010,f506]) ).
fof(f66733,plain,
( spl2_919
| ~ spl2_34
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29040,f29009,f344,f66731]) ).
fof(f29040,plain,
( ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X94,X95),implies(strict_equiv(X94,X95),X96))))
| ~ spl2_34
| ~ spl2_547 ),
inference(superposition,[],[f29010,f345]) ).
fof(f66729,plain,
( spl2_918
| ~ spl2_517
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29022,f29009,f26955,f66727]) ).
fof(f29022,plain,
( ! [X31,X32,X30,X33] : is_a_theorem(necessarily(or(X30,implies(and(X32,and(X30,X31)),X33))))
| ~ spl2_517
| ~ spl2_547 ),
inference(superposition,[],[f29010,f26956]) ).
fof(f66725,plain,
( spl2_917
| ~ spl2_517
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29021,f29009,f26955,f66723]) ).
fof(f29021,plain,
( ! [X28,X29,X26,X27] : is_a_theorem(necessarily(or(X26,implies(and(X27,and(X28,X26)),X29))))
| ~ spl2_517
| ~ spl2_547 ),
inference(superposition,[],[f29010,f26956]) ).
fof(f66457,plain,
( spl2_916
| ~ spl2_380
| ~ spl2_547 ),
inference(avatar_split_clause,[],[f29012,f29009,f13441,f66455]) ).
fof(f13441,plain,
( spl2_380
<=> ! [X18,X16,X17] :
( is_a_theorem(strict_implies(and(not(X16),X17),X18))
| ~ is_a_theorem(necessarily(or(X16,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_380])]) ).
fof(f29012,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X0,X2),X3)))
| ~ spl2_380
| ~ spl2_547 ),
inference(resolution,[],[f29010,f13442]) ).
fof(f13442,plain,
( ! [X18,X16,X17] :
( ~ is_a_theorem(necessarily(or(X16,X18)))
| is_a_theorem(strict_implies(and(not(X16),X17),X18)) )
| ~ spl2_380 ),
inference(avatar_component_clause,[],[f13441]) ).
fof(f65538,plain,
( spl2_915
| ~ spl2_30
| ~ spl2_612 ),
inference(avatar_split_clause,[],[f37283,f32983,f319,f65536]) ).
fof(f65536,plain,
( spl2_915
<=> ! [X30,X31] :
( ~ is_a_theorem(equiv(not(X31),necessarily(not(X30))))
| is_a_theorem(implies(possibly(X30),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_915])]) ).
fof(f32983,plain,
( spl2_612
<=> ! [X6,X5] : equiv(not(X5),necessarily(not(X6))) = and(implies(possibly(X6),X5),implies(necessarily(not(X6)),not(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_612])]) ).
fof(f37283,plain,
( ! [X31,X30] :
( ~ is_a_theorem(equiv(not(X31),necessarily(not(X30))))
| is_a_theorem(implies(possibly(X30),X31)) )
| ~ spl2_30
| ~ spl2_612 ),
inference(superposition,[],[f320,f32984]) ).
fof(f32984,plain,
( ! [X6,X5] : equiv(not(X5),necessarily(not(X6))) = and(implies(possibly(X6),X5),implies(necessarily(not(X6)),not(X5)))
| ~ spl2_612 ),
inference(avatar_component_clause,[],[f32983]) ).
fof(f65502,plain,
( spl2_914
| ~ spl2_549
| ~ spl2_911 ),
inference(avatar_split_clause,[],[f65389,f65381,f29220,f65500]) ).
fof(f65500,plain,
( spl2_914
<=> ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(not(implies(equiv(X2,not(X2)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_914])]) ).
fof(f65381,plain,
( spl2_911
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(equiv(X0,not(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_911])]) ).
fof(f65389,plain,
( ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(not(implies(equiv(X2,not(X2)),X3))) )
| ~ spl2_549
| ~ spl2_911 ),
inference(resolution,[],[f65382,f29221]) ).
fof(f65382,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(equiv(X0,not(X0)),X1))
| is_a_theorem(X0) )
| ~ spl2_911 ),
inference(avatar_component_clause,[],[f65381]) ).
fof(f65449,plain,
( spl2_913
| ~ spl2_26
| ~ spl2_508 ),
inference(avatar_split_clause,[],[f25192,f24819,f298,f65447]) ).
fof(f65447,plain,
( spl2_913
<=> ! [X36,X37,X35] :
( is_a_theorem(and(X35,strict_equiv(X37,X36)))
| ~ is_a_theorem(strict_equiv(X36,X37))
| ~ is_a_theorem(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_913])]) ).
fof(f25192,plain,
( ! [X36,X37,X35] :
( is_a_theorem(and(X35,strict_equiv(X37,X36)))
| ~ is_a_theorem(strict_equiv(X36,X37))
| ~ is_a_theorem(X35) )
| ~ spl2_26
| ~ spl2_508 ),
inference(superposition,[],[f299,f24820]) ).
fof(f65387,plain,
( spl2_912
| ~ spl2_27
| ~ spl2_909 ),
inference(avatar_split_clause,[],[f65293,f65190,f302,f65385]) ).
fof(f65385,plain,
( spl2_912
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,equiv(X0,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_912])]) ).
fof(f65293,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,equiv(X0,not(X0)))) )
| ~ spl2_27
| ~ spl2_909 ),
inference(resolution,[],[f65191,f303]) ).
fof(f65383,plain,
( spl2_911
| ~ spl2_27
| ~ spl2_908 ),
inference(avatar_split_clause,[],[f65193,f65186,f302,f65381]) ).
fof(f65193,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(equiv(X0,not(X0)),X1)) )
| ~ spl2_27
| ~ spl2_908 ),
inference(resolution,[],[f65187,f303]) ).
fof(f65292,plain,
( spl2_910
| ~ spl2_26
| ~ spl2_506 ),
inference(avatar_split_clause,[],[f24858,f24811,f298,f65290]) ).
fof(f65290,plain,
( spl2_910
<=> ! [X57,X59,X58] :
( is_a_theorem(and(X57,equiv(X59,X58)))
| ~ is_a_theorem(equiv(X58,X59))
| ~ is_a_theorem(X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_910])]) ).
fof(f24858,plain,
( ! [X58,X59,X57] :
( is_a_theorem(and(X57,equiv(X59,X58)))
| ~ is_a_theorem(equiv(X58,X59))
| ~ is_a_theorem(X57) )
| ~ spl2_26
| ~ spl2_506 ),
inference(superposition,[],[f299,f24812]) ).
fof(f65192,plain,
( spl2_909
| ~ spl2_81
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65095,f62814,f911,f65190]) ).
fof(f65095,plain,
( ! [X16,X15] : is_a_theorem(strict_implies(and(X15,equiv(X16,not(X16))),X16))
| ~ spl2_81
| ~ spl2_888 ),
inference(resolution,[],[f62815,f912]) ).
fof(f65188,plain,
( spl2_908
| ~ spl2_19
| ~ spl2_888 ),
inference(avatar_split_clause,[],[f65094,f62814,f269,f65186]) ).
fof(f65094,plain,
( ! [X14,X13] : is_a_theorem(strict_implies(and(equiv(X13,not(X13)),X14),X13))
| ~ spl2_19
| ~ spl2_888 ),
inference(resolution,[],[f62815,f270]) ).
fof(f65184,plain,
( spl2_907
| ~ spl2_31
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f23741,f23256,f330,f65182]) ).
fof(f65182,plain,
( spl2_907
<=> ! [X52,X50,X51] :
( ~ is_a_theorem(and(strict_equiv(X51,X50),X52))
| is_a_theorem(and(X52,strict_equiv(X50,X51))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_907])]) ).
fof(f330,plain,
( spl2_31
<=> ! [X4,X3] :
( is_a_theorem(and(X3,X4))
| ~ is_a_theorem(and(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f23741,plain,
( ! [X50,X51,X52] :
( ~ is_a_theorem(and(strict_equiv(X51,X50),X52))
| is_a_theorem(and(X52,strict_equiv(X50,X51))) )
| ~ spl2_31
| ~ spl2_503 ),
inference(superposition,[],[f331,f23257]) ).
fof(f331,plain,
( ! [X3,X4] :
( ~ is_a_theorem(and(X4,X3))
| is_a_theorem(and(X3,X4)) )
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f64889,plain,
( spl2_906
| ~ spl2_31
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23299,f23252,f330,f64887]) ).
fof(f64887,plain,
( spl2_906
<=> ! [X70,X69,X71] :
( ~ is_a_theorem(and(equiv(X70,X69),X71))
| is_a_theorem(and(X71,equiv(X69,X70))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_906])]) ).
fof(f23299,plain,
( ! [X70,X71,X69] :
( ~ is_a_theorem(and(equiv(X70,X69),X71))
| is_a_theorem(and(X71,equiv(X69,X70))) )
| ~ spl2_31
| ~ spl2_502 ),
inference(superposition,[],[f331,f23253]) ).
fof(f64632,plain,
( spl2_905
| ~ spl2_275
| ~ spl2_490 ),
inference(avatar_split_clause,[],[f23095,f22901,f8172,f64630]) ).
fof(f23095,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(X2,strict_equiv(X1,X0))))
| ~ spl2_275
| ~ spl2_490 ),
inference(resolution,[],[f22902,f8173]) ).
fof(f64411,plain,
( spl2_904
| ~ spl2_275
| ~ spl2_488 ),
inference(avatar_split_clause,[],[f23004,f22735,f8172,f64409]) ).
fof(f23004,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X0,X1),X2),and(X2,equiv(X1,X0))))
| ~ spl2_275
| ~ spl2_488 ),
inference(resolution,[],[f22736,f8173]) ).
fof(f64386,plain,
( spl2_903
| ~ spl2_76
| ~ spl2_301
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21154,f19362,f9399,f810,f64384]) ).
fof(f9399,plain,
( spl2_301
<=> ! [X29,X30,X31] : is_a_theorem(strict_implies(and(and(X29,X30),X31),and(and(X30,X31),X29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_301])]) ).
fof(f21154,plain,
( ! [X31,X29,X30] : is_a_theorem(strict_implies(and(X30,and(X29,X31)),and(X31,and(X30,X29))))
| ~ spl2_76
| ~ spl2_301
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20276,f19383]) ).
fof(f20276,plain,
( ! [X31,X29,X30] : is_a_theorem(strict_implies(and(and(X29,X30),X31),and(X31,and(X30,X29))))
| ~ spl2_76
| ~ spl2_301
| ~ spl2_486 ),
inference(backward_demodulation,[],[f9400,f19383]) ).
fof(f9400,plain,
( ! [X31,X29,X30] : is_a_theorem(strict_implies(and(and(X29,X30),X31),and(and(X30,X31),X29)))
| ~ spl2_301 ),
inference(avatar_component_clause,[],[f9399]) ).
fof(f64332,plain,
( spl2_902
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20160,f19362,f1050,f810,f344,f64330]) ).
fof(f1050,plain,
( spl2_85
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
fof(f20160,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,X3)),and(strict_equiv(X3,X2),X4)))
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1141,f20156]) ).
fof(f20156,plain,
( ! [X48,X49,X47] : and(strict_equiv(X47,X48),X49) = and(strict_implies(X48,X47),and(strict_implies(X47,X48),X49))
| ~ spl2_34
| ~ spl2_76
| ~ spl2_486 ),
inference(forward_demodulation,[],[f19380,f811]) ).
fof(f19380,plain,
( ! [X48,X49,X47] : and(strict_equiv(X47,X48),X49) = and(and(strict_implies(X47,X48),X49),strict_implies(X48,X47))
| ~ spl2_34
| ~ spl2_486 ),
inference(superposition,[],[f19363,f345]) ).
fof(f1141,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,strict_equiv(X2,X3)),and(strict_implies(X2,X3),and(strict_implies(X3,X2),X4))))
| ~ spl2_76
| ~ spl2_85 ),
inference(superposition,[],[f1051,f811]) ).
fof(f1051,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2))))
| ~ spl2_85 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f64150,plain,
( spl2_901
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20025,f19362,f1074,f810,f363,f64148]) ).
fof(f1074,plain,
( spl2_88
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(implies(X3,X4),and(implies(X4,X3),X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).
fof(f20025,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,equiv(X2,X3)),and(equiv(X3,X2),X4)))
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1258,f20021]) ).
fof(f20021,plain,
( ! [X16,X14,X15] : and(equiv(X14,X15),X16) = and(implies(X15,X14),and(implies(X14,X15),X16))
| ~ spl2_36
| ~ spl2_76
| ~ spl2_486 ),
inference(forward_demodulation,[],[f19370,f811]) ).
fof(f19370,plain,
( ! [X16,X14,X15] : and(equiv(X14,X15),X16) = and(and(implies(X14,X15),X16),implies(X15,X14))
| ~ spl2_36
| ~ spl2_486 ),
inference(superposition,[],[f19363,f364]) ).
fof(f1258,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,equiv(X2,X3)),and(implies(X2,X3),and(implies(X3,X2),X4))))
| ~ spl2_76
| ~ spl2_88 ),
inference(superposition,[],[f1075,f811]) ).
fof(f1075,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(implies(X3,X4),and(implies(X4,X3),X5))))
| ~ spl2_88 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f63372,plain,
( spl2_900
| ~ spl2_26
| ~ spl2_846 ),
inference(avatar_split_clause,[],[f60985,f60564,f298,f63370]) ).
fof(f63370,plain,
( spl2_900
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(X7,or(X8,X6)))
| ~ is_a_theorem(not(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_900])]) ).
fof(f60564,plain,
( spl2_846
<=> ! [X6,X7,X8] :
( ~ is_a_theorem(and(not(X6),and(X8,or(X6,X7))))
| is_a_theorem(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_846])]) ).
fof(f60985,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(X7,or(X8,X6)))
| ~ is_a_theorem(not(X8)) )
| ~ spl2_26
| ~ spl2_846 ),
inference(resolution,[],[f60565,f299]) ).
fof(f60565,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(and(not(X6),and(X8,or(X6,X7))))
| is_a_theorem(X7) )
| ~ spl2_846 ),
inference(avatar_component_clause,[],[f60564]) ).
fof(f63368,plain,
( spl2_899
| ~ spl2_550
| ~ spl2_846 ),
inference(avatar_split_clause,[],[f60984,f60564,f29224,f63366]) ).
fof(f63366,plain,
( spl2_899
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(X4,or(X5,X3)),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_899])]) ).
fof(f60984,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(X4,or(X5,X3)),X5))) )
| ~ spl2_550
| ~ spl2_846 ),
inference(resolution,[],[f60565,f29225]) ).
fof(f63364,plain,
( spl2_898
| ~ spl2_75
| ~ spl2_76
| ~ spl2_252
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20603,f19362,f6967,f810,f806,f63362]) ).
fof(f63362,plain,
( spl2_898
<=> ! [X13,X12,X14] : and(not(equiv(and(X13,not(X14)),X12)),implies(and(not(X14),and(X13,not(X12))),not(and(X12,implies(X13,X14))))) = equiv(not(and(X12,implies(X13,X14))),and(not(X14),and(X13,not(X12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_898])]) ).
fof(f6967,plain,
( spl2_252
<=> ! [X4,X5,X3] : equiv(and(X4,not(X5)),X3) = and(not(and(X3,implies(X4,X5))),implies(and(X4,not(X5)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_252])]) ).
fof(f20603,plain,
( ! [X14,X12,X13] : and(not(equiv(and(X13,not(X14)),X12)),implies(and(not(X14),and(X13,not(X12))),not(and(X12,implies(X13,X14))))) = equiv(not(and(X12,implies(X13,X14))),and(not(X14),and(X13,not(X12))))
| ~ spl2_75
| ~ spl2_76
| ~ spl2_252
| ~ spl2_486 ),
inference(backward_demodulation,[],[f7105,f19383]) ).
fof(f7105,plain,
( ! [X14,X12,X13] : and(not(equiv(and(X13,not(X14)),X12)),implies(and(and(X13,not(X14)),not(X12)),not(and(X12,implies(X13,X14))))) = equiv(not(and(X12,implies(X13,X14))),and(and(X13,not(X14)),not(X12)))
| ~ spl2_75
| ~ spl2_252 ),
inference(forward_demodulation,[],[f6992,f807]) ).
fof(f6992,plain,
( ! [X14,X12,X13] : equiv(and(and(X13,not(X14)),not(X12)),not(and(X12,implies(X13,X14)))) = and(not(equiv(and(X13,not(X14)),X12)),implies(and(and(X13,not(X14)),not(X12)),not(and(X12,implies(X13,X14)))))
| ~ spl2_252 ),
inference(superposition,[],[f6968,f6968]) ).
fof(f6968,plain,
( ! [X3,X4,X5] : equiv(and(X4,not(X5)),X3) = and(not(and(X3,implies(X4,X5))),implies(and(X4,not(X5)),X3))
| ~ spl2_252 ),
inference(avatar_component_clause,[],[f6967]) ).
fof(f63360,plain,
( spl2_897
| ~ spl2_517
| ~ spl2_842 ),
inference(avatar_split_clause,[],[f60640,f60078,f26955,f63358]) ).
fof(f63358,plain,
( spl2_897
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(and(X10,and(not(X8),or(X9,X8))))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_897])]) ).
fof(f60078,plain,
( spl2_842
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),and(or(X0,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_842])]) ).
fof(f60640,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(and(X10,and(not(X8),or(X9,X8))))
| is_a_theorem(X9) )
| ~ spl2_517
| ~ spl2_842 ),
inference(superposition,[],[f60079,f26956]) ).
fof(f60079,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),and(or(X0,X1),X2)))
| is_a_theorem(X0) )
| ~ spl2_842 ),
inference(avatar_component_clause,[],[f60078]) ).
fof(f63356,plain,
( spl2_896
| ~ spl2_76
| ~ spl2_842 ),
inference(avatar_split_clause,[],[f60621,f60078,f810,f63354]) ).
fof(f60621,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(and(not(X7),and(X8,or(X6,X7))))
| is_a_theorem(X6) )
| ~ spl2_76
| ~ spl2_842 ),
inference(superposition,[],[f60079,f811]) ).
fof(f63352,plain,
( spl2_895
| ~ spl2_26
| ~ spl2_842 ),
inference(avatar_split_clause,[],[f60577,f60078,f298,f63350]) ).
fof(f63350,plain,
( spl2_895
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(or(X6,X7),X8))
| ~ is_a_theorem(not(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_895])]) ).
fof(f60577,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(or(X6,X7),X8))
| ~ is_a_theorem(not(X7)) )
| ~ spl2_26
| ~ spl2_842 ),
inference(resolution,[],[f60079,f299]) ).
fof(f63348,plain,
( spl2_894
| ~ spl2_550
| ~ spl2_842 ),
inference(avatar_split_clause,[],[f60576,f60078,f29224,f63346]) ).
fof(f60576,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(or(X3,X4),X5),X4))) )
| ~ spl2_550
| ~ spl2_842 ),
inference(resolution,[],[f60079,f29225]) ).
fof(f62836,plain,
( spl2_893
| ~ spl2_550
| ~ spl2_826 ),
inference(avatar_split_clause,[],[f59692,f57334,f29224,f62834]) ).
fof(f62834,plain,
( spl2_893
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(or(X4,X3),X5),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_893])]) ).
fof(f57334,plain,
( spl2_826
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),and(or(X1,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_826])]) ).
fof(f59692,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(or(X4,X3),X5),X4))) )
| ~ spl2_550
| ~ spl2_826 ),
inference(resolution,[],[f57335,f29225]) ).
fof(f57335,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),and(or(X1,X0),X2)))
| is_a_theorem(X0) )
| ~ spl2_826 ),
inference(avatar_component_clause,[],[f57334]) ).
fof(f62832,plain,
( spl2_892
| ~ spl2_20
| ~ spl2_655
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39212,f39162,f37077,f273,f62830]) ).
fof(f39212,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),necessarily(not(X0))))
| ~ spl2_20
| ~ spl2_655
| ~ spl2_672 ),
inference(forward_demodulation,[],[f39196,f37078]) ).
fof(f39196,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(necessarily(not(X0)),possibly(X0)),necessarily(not(X0))))
| ~ spl2_20
| ~ spl2_672 ),
inference(superposition,[],[f39163,f274]) ).
fof(f62828,plain,
( spl2_891
| ~ spl2_136
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39181,f39162,f2344,f62826]) ).
fof(f39181,plain,
( ! [X28,X27] : is_a_theorem(strict_implies(equiv(and(X27,X28),not(and(X27,X28))),X27))
| ~ spl2_136
| ~ spl2_672 ),
inference(resolution,[],[f39163,f2345]) ).
fof(f62824,plain,
( spl2_890
| ~ spl2_75
| ~ spl2_209
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7104,f6967,f4558,f806,f62822]) ).
fof(f62822,plain,
( spl2_890
<=> ! [X11,X10] : and(not(equiv(X10,necessarily(not(X11)))),implies(and(necessarily(not(X11)),not(X10)),not(and(X10,possibly(X11))))) = equiv(not(and(X10,possibly(X11))),and(necessarily(not(X11)),not(X10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_890])]) ).
fof(f7104,plain,
( ! [X10,X11] : and(not(equiv(X10,necessarily(not(X11)))),implies(and(necessarily(not(X11)),not(X10)),not(and(X10,possibly(X11))))) = equiv(not(and(X10,possibly(X11))),and(necessarily(not(X11)),not(X10)))
| ~ spl2_75
| ~ spl2_209
| ~ spl2_252 ),
inference(forward_demodulation,[],[f6991,f807]) ).
fof(f6991,plain,
( ! [X10,X11] : equiv(and(necessarily(not(X11)),not(X10)),not(and(X10,possibly(X11)))) = and(not(equiv(X10,necessarily(not(X11)))),implies(and(necessarily(not(X11)),not(X10)),not(and(X10,possibly(X11)))))
| ~ spl2_209
| ~ spl2_252 ),
inference(superposition,[],[f6968,f4559]) ).
fof(f62820,plain,
( spl2_889
| ~ spl2_152
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39180,f39162,f2665,f62818]) ).
fof(f39180,plain,
( ! [X26,X25] : is_a_theorem(strict_implies(equiv(and(X25,X26),not(and(X25,X26))),X26))
| ~ spl2_152
| ~ spl2_672 ),
inference(resolution,[],[f39163,f2666]) ).
fof(f62816,plain,
( spl2_888
| ~ spl2_122
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39167,f39162,f1831,f62814]) ).
fof(f39167,plain,
( ! [X2,X3] :
( is_a_theorem(strict_implies(X2,X3))
| ~ is_a_theorem(strict_implies(X2,equiv(X3,not(X3)))) )
| ~ spl2_122
| ~ spl2_672 ),
inference(resolution,[],[f39163,f1832]) ).
fof(f62812,plain,
( spl2_887
| ~ spl2_550
| ~ spl2_636 ),
inference(avatar_split_clause,[],[f36179,f34639,f29224,f62810]) ).
fof(f62810,plain,
( spl2_887
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(implies(implies(X0,X1),X2),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_887])]) ).
fof(f34639,plain,
( spl2_636
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X2),implies(implies(X0,X1),X2)))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_636])]) ).
fof(f36179,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(implies(implies(X0,X1),X2),X2))) )
| ~ spl2_550
| ~ spl2_636 ),
inference(resolution,[],[f34640,f29225]) ).
fof(f34640,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X2),implies(implies(X0,X1),X2)))
| is_a_theorem(X0) )
| ~ spl2_636 ),
inference(avatar_component_clause,[],[f34639]) ).
fof(f62808,plain,
( spl2_886
| ~ spl2_550
| ~ spl2_632 ),
inference(avatar_split_clause,[],[f35917,f34623,f29224,f62806]) ).
fof(f62806,plain,
( spl2_886
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(X1,and(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_886])]) ).
fof(f34623,plain,
( spl2_632
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,and(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_632])]) ).
fof(f35917,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(X1,and(X2,X0)),X1))) )
| ~ spl2_550
| ~ spl2_632 ),
inference(resolution,[],[f34624,f29225]) ).
fof(f34624,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X1,and(X2,X0))))
| is_a_theorem(X0) )
| ~ spl2_632 ),
inference(avatar_component_clause,[],[f34623]) ).
fof(f62616,plain,
( spl2_885
| ~ spl2_550
| ~ spl2_631 ),
inference(avatar_split_clause,[],[f35836,f34619,f29224,f62614]) ).
fof(f62614,plain,
( spl2_885
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(and(X1,X0),X2),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_885])]) ).
fof(f34619,plain,
( spl2_631
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(and(X2,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_631])]) ).
fof(f35836,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(and(X1,X0),X2),X2))) )
| ~ spl2_550
| ~ spl2_631 ),
inference(resolution,[],[f34620,f29225]) ).
fof(f34620,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),or(and(X2,X0),X1)))
| is_a_theorem(X0) )
| ~ spl2_631 ),
inference(avatar_component_clause,[],[f34619]) ).
fof(f62612,plain,
( spl2_884
| ~ spl2_550
| ~ spl2_621 ),
inference(avatar_split_clause,[],[f34512,f33188,f29224,f62610]) ).
fof(f33188,plain,
( spl2_621
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,and(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_621])]) ).
fof(f34512,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(X1,and(X0,X2)),X1))) )
| ~ spl2_550
| ~ spl2_621 ),
inference(resolution,[],[f33189,f29225]) ).
fof(f33189,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X1,and(X0,X2))))
| is_a_theorem(X0) )
| ~ spl2_621 ),
inference(avatar_component_clause,[],[f33188]) ).
fof(f62608,plain,
( spl2_883
| ~ spl2_550
| ~ spl2_619 ),
inference(avatar_split_clause,[],[f34356,f33180,f29224,f62606]) ).
fof(f62606,plain,
( spl2_883
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(and(X0,X1),X2),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_883])]) ).
fof(f33180,plain,
( spl2_619
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(and(X0,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_619])]) ).
fof(f34356,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(or(and(X0,X1),X2),X2))) )
| ~ spl2_550
| ~ spl2_619 ),
inference(resolution,[],[f33181,f29225]) ).
fof(f33181,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X1),or(and(X0,X2),X1)))
| is_a_theorem(X0) )
| ~ spl2_619 ),
inference(avatar_component_clause,[],[f33180]) ).
fof(f62356,plain,
( spl2_882
| ~ spl2_194
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29894,f29224,f4132,f62354]) ).
fof(f62354,plain,
( spl2_882
<=> ! [X140,X138,X139,X137] :
( ~ is_a_theorem(not(implies(and(X137,and(X138,X139)),X140)))
| is_a_theorem(X138) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_882])]) ).
fof(f4132,plain,
( spl2_194
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(X11,and(X9,X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_194])]) ).
fof(f29894,plain,
( ! [X140,X138,X139,X137] :
( ~ is_a_theorem(not(implies(and(X137,and(X138,X139)),X140)))
| is_a_theorem(X138) )
| ~ spl2_194
| ~ spl2_550 ),
inference(resolution,[],[f29225,f4133]) ).
fof(f4133,plain,
( ! [X10,X11,X9,X12] :
( ~ is_a_theorem(and(X10,and(X11,and(X9,X12))))
| is_a_theorem(X9) )
| ~ spl2_194 ),
inference(avatar_component_clause,[],[f4132]) ).
fof(f62352,plain,
( spl2_881
| ~ spl2_195
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29893,f29224,f4136,f62350]) ).
fof(f62350,plain,
( spl2_881
<=> ! [X133,X136,X135,X134] :
( ~ is_a_theorem(not(implies(and(X133,and(X134,X135)),X136)))
| is_a_theorem(X135) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_881])]) ).
fof(f4136,plain,
( spl2_195
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(X11,and(X12,X9)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_195])]) ).
fof(f29893,plain,
( ! [X133,X136,X134,X135] :
( ~ is_a_theorem(not(implies(and(X133,and(X134,X135)),X136)))
| is_a_theorem(X135) )
| ~ spl2_195
| ~ spl2_550 ),
inference(resolution,[],[f29225,f4137]) ).
fof(f4137,plain,
( ! [X10,X11,X9,X12] :
( ~ is_a_theorem(and(X10,and(X11,and(X12,X9))))
| is_a_theorem(X9) )
| ~ spl2_195 ),
inference(avatar_component_clause,[],[f4136]) ).
fof(f62348,plain,
( spl2_880
| ~ spl2_289
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29890,f29224,f9060,f62346]) ).
fof(f62346,plain,
( spl2_880
<=> ! [X125,X124,X126] :
( ~ is_a_theorem(not(implies(and(X124,X125),X126)))
| is_a_theorem(and(X125,X124)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_880])]) ).
fof(f9060,plain,
( spl2_289
<=> ! [X22,X24,X23] :
( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(and(X24,and(X23,X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_289])]) ).
fof(f29890,plain,
( ! [X126,X124,X125] :
( ~ is_a_theorem(not(implies(and(X124,X125),X126)))
| is_a_theorem(and(X125,X124)) )
| ~ spl2_289
| ~ spl2_550 ),
inference(resolution,[],[f29225,f9061]) ).
fof(f9061,plain,
( ! [X24,X22,X23] :
( ~ is_a_theorem(and(X24,and(X23,X22)))
| is_a_theorem(and(X22,X23)) )
| ~ spl2_289 ),
inference(avatar_component_clause,[],[f9060]) ).
fof(f62344,plain,
( spl2_879
| ~ spl2_24
| ~ spl2_427
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29326,f29220,f14908,f290,f62342]) ).
fof(f62342,plain,
( spl2_879
<=> ! [X93,X94,X95] :
( ~ is_a_theorem(not(or(not(X93),X94)))
| is_a_theorem(implies(possibly(X95),X93)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_879])]) ).
fof(f14908,plain,
( spl2_427
<=> ! [X18,X17,X19] :
( is_a_theorem(implies(possibly(X17),X18))
| ~ is_a_theorem(and(not(not(X18)),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_427])]) ).
fof(f29326,plain,
( ! [X94,X95,X93] :
( ~ is_a_theorem(not(or(not(X93),X94)))
| is_a_theorem(implies(possibly(X95),X93)) )
| ~ spl2_24
| ~ spl2_427
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29292,f291]) ).
fof(f29292,plain,
( ! [X94,X95,X93] :
( ~ is_a_theorem(not(implies(not(not(X93)),X94)))
| is_a_theorem(implies(possibly(X95),X93)) )
| ~ spl2_427
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14909]) ).
fof(f14909,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(not(not(X18)),X19))
| is_a_theorem(implies(possibly(X17),X18)) )
| ~ spl2_427 ),
inference(avatar_component_clause,[],[f14908]) ).
fof(f62120,plain,
( spl2_878
| ~ spl2_24
| ~ spl2_417
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29324,f29220,f14629,f290,f62118]) ).
fof(f62118,plain,
( spl2_878
<=> ! [X87,X89,X88] :
( ~ is_a_theorem(not(or(X87,X88)))
| is_a_theorem(not(and(X87,possibly(X89)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_878])]) ).
fof(f14629,plain,
( spl2_417
<=> ! [X25,X24,X26] :
( is_a_theorem(not(and(X24,possibly(X25))))
| ~ is_a_theorem(and(not(X24),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_417])]) ).
fof(f29324,plain,
( ! [X88,X89,X87] :
( ~ is_a_theorem(not(or(X87,X88)))
| is_a_theorem(not(and(X87,possibly(X89)))) )
| ~ spl2_24
| ~ spl2_417
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29290,f291]) ).
fof(f29290,plain,
( ! [X88,X89,X87] :
( ~ is_a_theorem(not(implies(not(X87),X88)))
| is_a_theorem(not(and(X87,possibly(X89)))) )
| ~ spl2_417
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14630]) ).
fof(f14630,plain,
( ! [X26,X24,X25] :
( ~ is_a_theorem(and(not(X24),X26))
| is_a_theorem(not(and(X24,possibly(X25)))) )
| ~ spl2_417 ),
inference(avatar_component_clause,[],[f14629]) ).
fof(f62116,plain,
( spl2_877
| ~ spl2_24
| ~ spl2_424
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29323,f29220,f14896,f290,f62114]) ).
fof(f62114,plain,
( spl2_877
<=> ! [X86,X84,X85] :
( ~ is_a_theorem(not(or(X84,X85)))
| is_a_theorem(not(and(possibly(X86),X84))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_877])]) ).
fof(f14896,plain,
( spl2_424
<=> ! [X25,X24,X26] :
( is_a_theorem(not(and(possibly(X24),X25)))
| ~ is_a_theorem(and(not(X25),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_424])]) ).
fof(f29323,plain,
( ! [X86,X84,X85] :
( ~ is_a_theorem(not(or(X84,X85)))
| is_a_theorem(not(and(possibly(X86),X84))) )
| ~ spl2_24
| ~ spl2_424
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29289,f291]) ).
fof(f29289,plain,
( ! [X86,X84,X85] :
( ~ is_a_theorem(not(implies(not(X84),X85)))
| is_a_theorem(not(and(possibly(X86),X84))) )
| ~ spl2_424
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14897]) ).
fof(f14897,plain,
( ! [X26,X24,X25] :
( ~ is_a_theorem(and(not(X25),X26))
| is_a_theorem(not(and(possibly(X24),X25))) )
| ~ spl2_424 ),
inference(avatar_component_clause,[],[f14896]) ).
fof(f62112,plain,
( spl2_876
| ~ spl2_160
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29298,f29220,f2746,f62110]) ).
fof(f62110,plain,
( spl2_876
<=> ! [X112,X113,X111] :
( ~ is_a_theorem(not(implies(strict_equiv(X111,X112),X113)))
| is_a_theorem(strict_implies(X111,X112)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_876])]) ).
fof(f2746,plain,
( spl2_160
<=> ! [X22,X20,X21] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_160])]) ).
fof(f29298,plain,
( ! [X113,X111,X112] :
( ~ is_a_theorem(not(implies(strict_equiv(X111,X112),X113)))
| is_a_theorem(strict_implies(X111,X112)) )
| ~ spl2_160
| ~ spl2_549 ),
inference(resolution,[],[f29221,f2747]) ).
fof(f2747,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X20,X21)) )
| ~ spl2_160 ),
inference(avatar_component_clause,[],[f2746]) ).
fof(f62108,plain,
( spl2_875
| ~ spl2_70
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24679,f23260,f6149,f2474,f681,f62106]) ).
fof(f62106,plain,
( spl2_875
<=> ! [X12,X11,X10] :
( and(X10,strict_equiv(X11,not(X12))) = and(X10,strict_equiv(not(X12),X11))
| ~ is_a_theorem(strict_implies(and(X10,strict_equiv(X11,not(X12))),and(X10,strict_equiv(not(X12),X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_875])]) ).
fof(f24679,plain,
( ! [X10,X11,X12] :
( and(X10,strict_equiv(X11,not(X12))) = and(X10,strict_equiv(not(X12),X11))
| ~ is_a_theorem(strict_implies(and(X10,strict_equiv(X11,not(X12))),and(X10,strict_equiv(not(X12),X11)))) )
| ~ spl2_70
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(forward_demodulation,[],[f24671,f24169]) ).
fof(f24169,plain,
( ! [X54,X52,X53] : and(necessarily(or(X52,X53)),and(X54,strict_implies(X53,not(X52)))) = and(X54,strict_equiv(not(X52),X53))
| ~ spl2_141
| ~ spl2_504 ),
inference(superposition,[],[f23261,f2475]) ).
fof(f24671,plain,
( ! [X10,X11,X12] :
( ~ is_a_theorem(strict_implies(and(X10,strict_equiv(X11,not(X12))),and(X10,strict_equiv(not(X12),X11))))
| and(X10,strict_equiv(X11,not(X12))) = and(necessarily(or(X12,X11)),and(X10,strict_implies(X11,not(X12)))) )
| ~ spl2_70
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(backward_demodulation,[],[f6740,f24169]) ).
fof(f6740,plain,
( ! [X10,X11,X12] :
( ~ is_a_theorem(strict_implies(and(X10,strict_equiv(X11,not(X12))),and(necessarily(or(X12,X11)),and(X10,strict_implies(X11,not(X12))))))
| and(X10,strict_equiv(X11,not(X12))) = and(necessarily(or(X12,X11)),and(X10,strict_implies(X11,not(X12)))) )
| ~ spl2_70
| ~ spl2_241 ),
inference(resolution,[],[f6150,f682]) ).
fof(f62104,plain,
( spl2_874
| ~ spl2_178
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29297,f29220,f3402,f62102]) ).
fof(f62102,plain,
( spl2_874
<=> ! [X109,X108,X110] :
( ~ is_a_theorem(not(implies(strict_equiv(X108,X109),X110)))
| is_a_theorem(strict_implies(X109,X108)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_874])]) ).
fof(f3402,plain,
( spl2_178
<=> ! [X22,X20,X21] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X21,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_178])]) ).
fof(f29297,plain,
( ! [X108,X109,X110] :
( ~ is_a_theorem(not(implies(strict_equiv(X108,X109),X110)))
| is_a_theorem(strict_implies(X109,X108)) )
| ~ spl2_178
| ~ spl2_549 ),
inference(resolution,[],[f29221,f3403]) ).
fof(f3403,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X21,X20)) )
| ~ spl2_178 ),
inference(avatar_component_clause,[],[f3402]) ).
fof(f62100,plain,
( spl2_873
| ~ spl2_213
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29296,f29220,f4847,f62098]) ).
fof(f62098,plain,
( spl2_873
<=> ! [X105,X107,X106] :
( ~ is_a_theorem(not(implies(strict_equiv(X105,X106),X107)))
| is_a_theorem(strict_equiv(X106,X105)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_873])]) ).
fof(f4847,plain,
( spl2_213
<=> ! [X2,X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(and(strict_equiv(X1,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_213])]) ).
fof(f29296,plain,
( ! [X106,X107,X105] :
( ~ is_a_theorem(not(implies(strict_equiv(X105,X106),X107)))
| is_a_theorem(strict_equiv(X106,X105)) )
| ~ spl2_213
| ~ spl2_549 ),
inference(resolution,[],[f29221,f4848]) ).
fof(f4848,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_equiv(X1,X0),X2))
| is_a_theorem(strict_equiv(X0,X1)) )
| ~ spl2_213 ),
inference(avatar_component_clause,[],[f4847]) ).
fof(f62096,plain,
( spl2_872
| ~ spl2_159
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29282,f29220,f2742,f62094]) ).
fof(f62094,plain,
( spl2_872
<=> ! [X66,X67,X68] :
( ~ is_a_theorem(not(implies(equiv(X66,X67),X68)))
| is_a_theorem(implies(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_872])]) ).
fof(f2742,plain,
( spl2_159
<=> ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_159])]) ).
fof(f29282,plain,
( ! [X68,X66,X67] :
( ~ is_a_theorem(not(implies(equiv(X66,X67),X68)))
| is_a_theorem(implies(X66,X67)) )
| ~ spl2_159
| ~ spl2_549 ),
inference(resolution,[],[f29221,f2743]) ).
fof(f2743,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X14,X15)) )
| ~ spl2_159 ),
inference(avatar_component_clause,[],[f2742]) ).
fof(f62092,plain,
( spl2_871
| ~ spl2_177
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29281,f29220,f3398,f62090]) ).
fof(f62090,plain,
( spl2_871
<=> ! [X64,X65,X63] :
( ~ is_a_theorem(not(implies(equiv(X63,X64),X65)))
| is_a_theorem(implies(X64,X63)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_871])]) ).
fof(f3398,plain,
( spl2_177
<=> ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X15,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_177])]) ).
fof(f29281,plain,
( ! [X65,X63,X64] :
( ~ is_a_theorem(not(implies(equiv(X63,X64),X65)))
| is_a_theorem(implies(X64,X63)) )
| ~ spl2_177
| ~ spl2_549 ),
inference(resolution,[],[f29221,f3399]) ).
fof(f3399,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X15,X14)) )
| ~ spl2_177 ),
inference(avatar_component_clause,[],[f3398]) ).
fof(f62088,plain,
( spl2_870
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20153,f19362,f6129,f2474,f810,f681,f62086]) ).
fof(f62086,plain,
( spl2_870
<=> ! [X11,X12,X10] :
( and(strict_equiv(X10,not(X11)),X12) = and(strict_equiv(not(X11),X10),X12)
| ~ is_a_theorem(strict_implies(and(strict_equiv(not(X11),X10),X12),and(strict_equiv(X10,not(X11)),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_870])]) ).
fof(f20153,plain,
( ! [X10,X11,X12] :
( and(strict_equiv(X10,not(X11)),X12) = and(strict_equiv(not(X11),X10),X12)
| ~ is_a_theorem(strict_implies(and(strict_equiv(not(X11),X10),X12),and(strict_equiv(X10,not(X11)),X12))) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20141,f20136]) ).
fof(f20141,plain,
( ! [X10,X11,X12] :
( ~ is_a_theorem(strict_implies(and(strict_equiv(not(X11),X10),X12),and(strict_equiv(X10,not(X11)),X12)))
| and(strict_implies(X10,not(X11)),and(necessarily(or(X11,X10)),X12)) = and(strict_equiv(X10,not(X11)),X12) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(backward_demodulation,[],[f6550,f20136]) ).
fof(f6550,plain,
( ! [X10,X11,X12] :
( ~ is_a_theorem(strict_implies(and(strict_implies(X10,not(X11)),and(necessarily(or(X11,X10)),X12)),and(strict_equiv(X10,not(X11)),X12)))
| and(strict_implies(X10,not(X11)),and(necessarily(or(X11,X10)),X12)) = and(strict_equiv(X10,not(X11)),X12) )
| ~ spl2_70
| ~ spl2_236 ),
inference(resolution,[],[f6130,f682]) ).
fof(f62084,plain,
( spl2_869
| ~ spl2_214
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29280,f29220,f4851,f62082]) ).
fof(f62082,plain,
( spl2_869
<=> ! [X61,X60,X62] :
( ~ is_a_theorem(not(implies(equiv(X60,X61),X62)))
| is_a_theorem(equiv(X61,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_869])]) ).
fof(f4851,plain,
( spl2_214
<=> ! [X4,X5,X3] :
( is_a_theorem(equiv(X3,X4))
| ~ is_a_theorem(and(equiv(X4,X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_214])]) ).
fof(f29280,plain,
( ! [X62,X60,X61] :
( ~ is_a_theorem(not(implies(equiv(X60,X61),X62)))
| is_a_theorem(equiv(X61,X60)) )
| ~ spl2_214
| ~ spl2_549 ),
inference(resolution,[],[f29221,f4852]) ).
fof(f4852,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(equiv(X4,X3),X5))
| is_a_theorem(equiv(X3,X4)) )
| ~ spl2_214 ),
inference(avatar_component_clause,[],[f4851]) ).
fof(f62080,plain,
( spl2_868
| ~ spl2_456
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29277,f29220,f17087,f62078]) ).
fof(f62078,plain,
( spl2_868
<=> ! [X52,X53,X51] :
( ~ is_a_theorem(not(implies(X51,X52)))
| is_a_theorem(and(strict_implies(X53,X53),X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_868])]) ).
fof(f17087,plain,
( spl2_456
<=> ! [X70,X69,X71] :
( ~ is_a_theorem(and(X69,X70))
| is_a_theorem(and(strict_implies(X71,X71),X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_456])]) ).
fof(f29277,plain,
( ! [X51,X52,X53] :
( ~ is_a_theorem(not(implies(X51,X52)))
| is_a_theorem(and(strict_implies(X53,X53),X51)) )
| ~ spl2_456
| ~ spl2_549 ),
inference(resolution,[],[f29221,f17088]) ).
fof(f17088,plain,
( ! [X70,X71,X69] :
( ~ is_a_theorem(and(X69,X70))
| is_a_theorem(and(strict_implies(X71,X71),X69)) )
| ~ spl2_456 ),
inference(avatar_component_clause,[],[f17087]) ).
fof(f62076,plain,
( spl2_867
| ~ spl2_453
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29275,f29220,f16869,f62074]) ).
fof(f62074,plain,
( spl2_867
<=> ! [X45,X46,X47] :
( ~ is_a_theorem(not(implies(X45,X46)))
| is_a_theorem(and(X45,strict_implies(X47,X47))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_867])]) ).
fof(f16869,plain,
( spl2_453
<=> ! [X64,X65,X63] :
( ~ is_a_theorem(and(X63,X64))
| is_a_theorem(and(X63,strict_implies(X65,X65))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_453])]) ).
fof(f29275,plain,
( ! [X46,X47,X45] :
( ~ is_a_theorem(not(implies(X45,X46)))
| is_a_theorem(and(X45,strict_implies(X47,X47))) )
| ~ spl2_453
| ~ spl2_549 ),
inference(resolution,[],[f29221,f16870]) ).
fof(f16870,plain,
( ! [X65,X63,X64] :
( ~ is_a_theorem(and(X63,X64))
| is_a_theorem(and(X63,strict_implies(X65,X65))) )
| ~ spl2_453 ),
inference(avatar_component_clause,[],[f16869]) ).
fof(f62072,plain,
( spl2_866
| ~ spl2_33
| ~ spl2_70
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3478,f2734,f681,f340,f62070]) ).
fof(f62070,plain,
( spl2_866
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(necessarily(or(and(X4,implies(X5,X6)),equiv(X4,and(X5,not(X6))))))
| not(and(X4,implies(X5,X6))) = equiv(X4,and(X5,not(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_866])]) ).
fof(f3478,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(necessarily(or(and(X4,implies(X5,X6)),equiv(X4,and(X5,not(X6))))))
| not(and(X4,implies(X5,X6))) = equiv(X4,and(X5,not(X6))) )
| ~ spl2_33
| ~ spl2_70
| ~ spl2_157 ),
inference(forward_demodulation,[],[f3454,f341]) ).
fof(f3454,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(strict_implies(not(and(X4,implies(X5,X6))),equiv(X4,and(X5,not(X6)))))
| not(and(X4,implies(X5,X6))) = equiv(X4,and(X5,not(X6))) )
| ~ spl2_70
| ~ spl2_157 ),
inference(resolution,[],[f2735,f682]) ).
fof(f62068,plain,
( spl2_865
| ~ spl2_217
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29272,f29220,f4863,f62066]) ).
fof(f62066,plain,
( spl2_865
<=> ! [X38,X36,X37] :
( ~ is_a_theorem(not(implies(X36,X37)))
| ~ is_a_theorem(X38)
| is_a_theorem(and(X38,X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_865])]) ).
fof(f4863,plain,
( spl2_217
<=> ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(and(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_217])]) ).
fof(f29272,plain,
( ! [X38,X36,X37] :
( ~ is_a_theorem(not(implies(X36,X37)))
| ~ is_a_theorem(X38)
| is_a_theorem(and(X38,X36)) )
| ~ spl2_217
| ~ spl2_549 ),
inference(resolution,[],[f29221,f4864]) ).
fof(f4864,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X0)
| is_a_theorem(and(X0,X1)) )
| ~ spl2_217 ),
inference(avatar_component_clause,[],[f4863]) ).
fof(f62064,plain,
( spl2_864
| ~ spl2_205
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29270,f29220,f4542,f62062]) ).
fof(f62062,plain,
( spl2_864
<=> ! [X32,X30,X31] :
( ~ is_a_theorem(not(implies(X30,X31)))
| ~ is_a_theorem(X32)
| is_a_theorem(and(X30,X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_864])]) ).
fof(f4542,plain,
( spl2_205
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_205])]) ).
fof(f29270,plain,
( ! [X31,X32,X30] :
( ~ is_a_theorem(not(implies(X30,X31)))
| ~ is_a_theorem(X32)
| is_a_theorem(and(X30,X32)) )
| ~ spl2_205
| ~ spl2_549 ),
inference(resolution,[],[f29221,f4543]) ).
fof(f4543,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X3,X4)) )
| ~ spl2_205 ),
inference(avatar_component_clause,[],[f4542]) ).
fof(f62060,plain,
( spl2_863
| ~ spl2_435
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29262,f29220,f15127,f62058]) ).
fof(f62058,plain,
( spl2_863
<=> ! [X9,X11,X10] :
( ~ is_a_theorem(not(implies(X9,not(X10))))
| is_a_theorem(implies(possibly(X11),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_863])]) ).
fof(f15127,plain,
( spl2_435
<=> ! [X18,X17,X19] :
( is_a_theorem(implies(possibly(X17),X18))
| ~ is_a_theorem(and(X19,not(not(X18)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_435])]) ).
fof(f29262,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(not(implies(X9,not(X10))))
| is_a_theorem(implies(possibly(X11),X10)) )
| ~ spl2_435
| ~ spl2_549 ),
inference(resolution,[],[f29221,f15128]) ).
fof(f15128,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(X19,not(not(X18))))
| is_a_theorem(implies(possibly(X17),X18)) )
| ~ spl2_435 ),
inference(avatar_component_clause,[],[f15127]) ).
fof(f62056,plain,
( spl2_862
| ~ spl2_428
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29260,f29220,f14912,f62054]) ).
fof(f62054,plain,
( spl2_862
<=> ! [X4,X5,X3] :
( ~ is_a_theorem(not(implies(X3,X4)))
| is_a_theorem(not(and(X4,possibly(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_862])]) ).
fof(f14912,plain,
( spl2_428
<=> ! [X25,X24,X26] :
( is_a_theorem(not(and(X24,possibly(X25))))
| ~ is_a_theorem(and(X26,not(X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_428])]) ).
fof(f29260,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(not(implies(X3,X4)))
| is_a_theorem(not(and(X4,possibly(X5)))) )
| ~ spl2_428
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14913]) ).
fof(f14913,plain,
( ! [X26,X24,X25] :
( ~ is_a_theorem(and(X26,not(X24)))
| is_a_theorem(not(and(X24,possibly(X25)))) )
| ~ spl2_428 ),
inference(avatar_component_clause,[],[f14912]) ).
fof(f62052,plain,
( spl2_861
| ~ spl2_70
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3115,f2558,f681,f62050]) ).
fof(f62050,plain,
( spl2_861
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(strict_implies(necessarily(or(X4,X5)),and(necessarily(or(X4,X6)),strict_implies(X6,X5))))
| necessarily(or(X4,X5)) = and(necessarily(or(X4,X6)),strict_implies(X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_861])]) ).
fof(f3115,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(strict_implies(necessarily(or(X4,X5)),and(necessarily(or(X4,X6)),strict_implies(X6,X5))))
| necessarily(or(X4,X5)) = and(necessarily(or(X4,X6)),strict_implies(X6,X5)) )
| ~ spl2_70
| ~ spl2_146 ),
inference(resolution,[],[f2559,f682]) ).
fof(f62048,plain,
( spl2_860
| ~ spl2_436
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29259,f29220,f15132,f62046]) ).
fof(f62046,plain,
( spl2_860
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(not(and(possibly(X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_860])]) ).
fof(f15132,plain,
( spl2_436
<=> ! [X9,X11,X10] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(possibly(X11),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_436])]) ).
fof(f29259,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(not(and(possibly(X2),X1))) )
| ~ spl2_436
| ~ spl2_549 ),
inference(resolution,[],[f29221,f15133]) ).
fof(f15133,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(possibly(X11),X9))) )
| ~ spl2_436 ),
inference(avatar_component_clause,[],[f15132]) ).
fof(f62044,plain,
( spl2_859
| ~ spl2_23
| ~ spl2_37
| ~ spl2_546 ),
inference(avatar_split_clause,[],[f29006,f28951,f373,f286,f62042]) ).
fof(f29006,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(possibly(X14),implies(and(X15,necessarily(not(X14))),X16)))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_546 ),
inference(forward_demodulation,[],[f29000,f287]) ).
fof(f29000,plain,
( ! [X16,X14,X15] : is_a_theorem(necessarily(implies(possibly(X14),implies(and(X15,necessarily(not(X14))),X16))))
| ~ spl2_37
| ~ spl2_546 ),
inference(superposition,[],[f28952,f374]) ).
fof(f62040,plain,
( spl2_858
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_546 ),
inference(avatar_split_clause,[],[f29002,f28951,f19362,f810,f505,f62038]) ).
fof(f62038,plain,
( spl2_858
<=> ! [X6,X4,X5] : is_a_theorem(necessarily(or(X5,not(and(X5,and(X4,possibly(X6))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_858])]) ).
fof(f29002,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(or(X5,not(and(X5,and(X4,possibly(X6)))))))
| ~ spl2_54
| ~ spl2_76
| ~ spl2_486
| ~ spl2_546 ),
inference(forward_demodulation,[],[f28996,f19383]) ).
fof(f28996,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(or(X5,not(and(and(X4,X5),possibly(X6))))))
| ~ spl2_54
| ~ spl2_546 ),
inference(superposition,[],[f28952,f506]) ).
fof(f62036,plain,
( spl2_857
| ~ spl2_70
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f2978,f2528,f681,f62034]) ).
fof(f62034,plain,
( spl2_857
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(strict_implies(strict_implies(X4,X5),and(strict_implies(X4,not(X6)),necessarily(or(X6,X5)))))
| strict_implies(X4,X5) = and(strict_implies(X4,not(X6)),necessarily(or(X6,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_857])]) ).
fof(f2978,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(strict_implies(strict_implies(X4,X5),and(strict_implies(X4,not(X6)),necessarily(or(X6,X5)))))
| strict_implies(X4,X5) = and(strict_implies(X4,not(X6)),necessarily(or(X6,X5))) )
| ~ spl2_70
| ~ spl2_142 ),
inference(resolution,[],[f2529,f682]) ).
fof(f62032,plain,
( spl2_856
| ~ spl2_34
| ~ spl2_546 ),
inference(avatar_split_clause,[],[f28987,f28951,f344,f62030]) ).
fof(f28987,plain,
( ! [X96,X94,X95] : is_a_theorem(necessarily(or(strict_implies(X95,X94),implies(strict_equiv(X94,X95),X96))))
| ~ spl2_34
| ~ spl2_546 ),
inference(superposition,[],[f28952,f345]) ).
fof(f62028,plain,
( spl2_855
| ~ spl2_380
| ~ spl2_546 ),
inference(avatar_split_clause,[],[f28959,f28951,f13441,f62026]) ).
fof(f28959,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),implies(and(X2,X0),X3)))
| ~ spl2_380
| ~ spl2_546 ),
inference(resolution,[],[f28952,f13442]) ).
fof(f62024,plain,
( spl2_854
| ~ spl2_406
| ~ spl2_529 ),
inference(avatar_split_clause,[],[f28236,f28204,f14472,f62022]) ).
fof(f62022,plain,
( spl2_854
<=> ! [X7,X8] :
( ~ is_a_theorem(not(possibly(possibly(X7))))
| is_a_theorem(strict_implies(X8,necessarily(not(X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_854])]) ).
fof(f14472,plain,
( spl2_406
<=> ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(possibly(X0))))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_406])]) ).
fof(f28204,plain,
( spl2_529
<=> ! [X0] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_529])]) ).
fof(f28236,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(possibly(possibly(X7))))
| is_a_theorem(strict_implies(X8,necessarily(not(X7)))) )
| ~ spl2_406
| ~ spl2_529 ),
inference(resolution,[],[f28205,f14473]) ).
fof(f14473,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(possibly(X0))))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) )
| ~ spl2_406 ),
inference(avatar_component_clause,[],[f14472]) ).
fof(f28205,plain,
( ! [X0] :
( is_a_theorem(necessarily(not(X0)))
| ~ is_a_theorem(not(possibly(X0))) )
| ~ spl2_529 ),
inference(avatar_component_clause,[],[f28204]) ).
fof(f62020,plain,
( spl2_853
| ~ spl2_439
| ~ spl2_529 ),
inference(avatar_split_clause,[],[f28234,f28204,f15221,f62018]) ).
fof(f62018,plain,
( spl2_853
<=> ! [X4,X3] :
( ~ is_a_theorem(not(possibly(equiv(X3,X4))))
| is_a_theorem(necessarily(or(X4,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_853])]) ).
fof(f15221,plain,
( spl2_439
<=> ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X0,X1))))
| is_a_theorem(necessarily(or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_439])]) ).
fof(f28234,plain,
( ! [X3,X4] :
( ~ is_a_theorem(not(possibly(equiv(X3,X4))))
| is_a_theorem(necessarily(or(X4,X3))) )
| ~ spl2_439
| ~ spl2_529 ),
inference(resolution,[],[f28205,f15222]) ).
fof(f15222,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X0,X1))))
| is_a_theorem(necessarily(or(X1,X0))) )
| ~ spl2_439 ),
inference(avatar_component_clause,[],[f15221]) ).
fof(f61562,plain,
( spl2_852
| ~ spl2_440
| ~ spl2_529 ),
inference(avatar_split_clause,[],[f28233,f28204,f15229,f61560]) ).
fof(f61560,plain,
( spl2_852
<=> ! [X2,X1] :
( ~ is_a_theorem(not(possibly(equiv(X1,X2))))
| is_a_theorem(necessarily(or(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_852])]) ).
fof(f15229,plain,
( spl2_440
<=> ! [X2,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X2,X1))))
| is_a_theorem(necessarily(or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_440])]) ).
fof(f28233,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(possibly(equiv(X1,X2))))
| is_a_theorem(necessarily(or(X1,X2))) )
| ~ spl2_440
| ~ spl2_529 ),
inference(resolution,[],[f28205,f15230]) ).
fof(f15230,plain,
( ! [X2,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X2,X1))))
| is_a_theorem(necessarily(or(X2,X1))) )
| ~ spl2_440 ),
inference(avatar_component_clause,[],[f15229]) ).
fof(f61558,plain,
( spl2_851
| ~ spl2_441
| ~ spl2_529 ),
inference(avatar_split_clause,[],[f28232,f28204,f15691,f61556]) ).
fof(f61556,plain,
( spl2_851
<=> ! [X0] :
( ~ is_a_theorem(not(possibly(implies(X0,X0))))
| is_a_theorem(necessarily(not(not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_851])]) ).
fof(f15691,plain,
( spl2_441
<=> ! [X0] :
( is_a_theorem(necessarily(not(not(X0))))
| ~ is_a_theorem(necessarily(not(implies(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_441])]) ).
fof(f28232,plain,
( ! [X0] :
( ~ is_a_theorem(not(possibly(implies(X0,X0))))
| is_a_theorem(necessarily(not(not(X0)))) )
| ~ spl2_441
| ~ spl2_529 ),
inference(resolution,[],[f28205,f15692]) ).
fof(f15692,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(not(implies(X0,X0))))
| is_a_theorem(necessarily(not(not(X0)))) )
| ~ spl2_441 ),
inference(avatar_component_clause,[],[f15691]) ).
fof(f61554,plain,
( spl2_850
| ~ spl2_96
| ~ spl2_431
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24759,f23260,f15004,f1122,f61552]) ).
fof(f61552,plain,
( spl2_850
<=> ! [X18,X17,X19] :
( is_a_theorem(implies(and(possibly(X19),X18),X17))
| ~ is_a_theorem(implies(X18,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_850])]) ).
fof(f15004,plain,
( spl2_431
<=> ! [X7,X8] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(possibly(X8),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_431])]) ).
fof(f24759,plain,
( ! [X18,X19,X17] :
( is_a_theorem(implies(and(possibly(X19),X18),X17))
| ~ is_a_theorem(implies(X18,X17)) )
| ~ spl2_96
| ~ spl2_431
| ~ spl2_504 ),
inference(backward_demodulation,[],[f15013,f24324]) ).
fof(f24324,plain,
( ! [X411,X410,X409] : implies(and(X410,X411),X409) = not(and(X410,and(not(X409),X411)))
| ~ spl2_96
| ~ spl2_504 ),
inference(superposition,[],[f1123,f23261]) ).
fof(f15013,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(implies(X18,X17))
| is_a_theorem(not(and(possibly(X19),and(not(X17),X18)))) )
| ~ spl2_96
| ~ spl2_431 ),
inference(superposition,[],[f15005,f1123]) ).
fof(f15005,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(possibly(X8),X7))) )
| ~ spl2_431 ),
inference(avatar_component_clause,[],[f15004]) ).
fof(f60805,plain,
( spl2_849
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_252
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21618,f19362,f6967,f1122,f814,f810,f60803]) ).
fof(f60803,plain,
( spl2_849
<=> ! [X10,X7,X9,X8] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(implies(and(X7,implies(X9,X10)),X8),implies(and(X9,implies(X7,X8)),X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_849])]) ).
fof(f21618,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(implies(and(X7,implies(X9,X10)),X8),implies(and(X9,implies(X7,X8)),X10))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_252
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21617,f1123]) ).
fof(f21617,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(implies(and(X7,implies(X9,X10)),X8),not(and(not(X10),and(X9,implies(X7,X8)))))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_252
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21616,f19383]) ).
fof(f21616,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(implies(and(X7,implies(X9,X10)),X8),not(and(and(X9,not(X10)),implies(X7,X8))))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_252
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21615,f811]) ).
fof(f21615,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(not(and(and(X9,not(X10)),implies(X7,X8))),implies(and(X7,implies(X9,X10)),X8))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_252
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20596,f1123]) ).
fof(f20596,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(not(and(and(X9,not(X10)),implies(X7,X8))),not(and(not(X8),and(X7,implies(X9,X10)))))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_252
| ~ spl2_486 ),
inference(backward_demodulation,[],[f7011,f19383]) ).
fof(f7011,plain,
( ! [X10,X8,X9,X7] : equiv(and(X7,not(X8)),and(X9,not(X10))) = and(not(and(and(X9,not(X10)),implies(X7,X8))),not(and(and(X7,not(X8)),implies(X9,X10))))
| ~ spl2_77
| ~ spl2_252 ),
inference(superposition,[],[f6968,f815]) ).
fof(f60574,plain,
( spl2_848
| ~ spl2_517
| ~ spl2_826 ),
inference(avatar_split_clause,[],[f59756,f57334,f26955,f60572]) ).
fof(f60572,plain,
( spl2_848
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(and(X10,and(not(X8),or(X8,X9))))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_848])]) ).
fof(f59756,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(and(X10,and(not(X8),or(X8,X9))))
| is_a_theorem(X9) )
| ~ spl2_517
| ~ spl2_826 ),
inference(superposition,[],[f57335,f26956]) ).
fof(f60570,plain,
( spl2_847
| ~ spl2_75
| ~ spl2_80
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7106,f6967,f856,f806,f60568]) ).
fof(f60568,plain,
( spl2_847
<=> ! [X16,X15] : and(not(equiv(not(X15),X16)),implies(and(X16,not(not(X15))),or(X15,X16))) = equiv(or(X15,X16),and(X16,not(not(X15)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_847])]) ).
fof(f7106,plain,
( ! [X16,X15] : and(not(equiv(not(X15),X16)),implies(and(X16,not(not(X15))),or(X15,X16))) = equiv(or(X15,X16),and(X16,not(not(X15))))
| ~ spl2_75
| ~ spl2_80
| ~ spl2_252 ),
inference(forward_demodulation,[],[f6993,f807]) ).
fof(f6993,plain,
( ! [X16,X15] : equiv(and(X16,not(not(X15))),or(X15,X16)) = and(not(equiv(not(X15),X16)),implies(and(X16,not(not(X15))),or(X15,X16)))
| ~ spl2_80
| ~ spl2_252 ),
inference(superposition,[],[f6968,f857]) ).
fof(f60566,plain,
( spl2_846
| ~ spl2_76
| ~ spl2_826 ),
inference(avatar_split_clause,[],[f59737,f57334,f810,f60564]) ).
fof(f59737,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(and(not(X6),and(X8,or(X6,X7))))
| is_a_theorem(X7) )
| ~ spl2_76
| ~ spl2_826 ),
inference(superposition,[],[f57335,f811]) ).
fof(f60562,plain,
( spl2_845
| ~ spl2_26
| ~ spl2_826 ),
inference(avatar_split_clause,[],[f59693,f57334,f298,f60560]) ).
fof(f60560,plain,
( spl2_845
<=> ! [X6,X8,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(or(X7,X6),X8))
| ~ is_a_theorem(not(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_845])]) ).
fof(f59693,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(and(or(X7,X6),X8))
| ~ is_a_theorem(not(X7)) )
| ~ spl2_26
| ~ spl2_826 ),
inference(resolution,[],[f57335,f299]) ).
fof(f60558,plain,
( spl2_844
| ~ spl2_517
| ~ spl2_822 ),
inference(avatar_split_clause,[],[f57443,f57318,f26955,f60556]) ).
fof(f57443,plain,
( ! [X10,X8,X9] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X9,X8))),X9))
| ~ spl2_517
| ~ spl2_822 ),
inference(superposition,[],[f57319,f26956]) ).
fof(f60554,plain,
( spl2_843
| ~ spl2_76
| ~ spl2_822 ),
inference(avatar_split_clause,[],[f57424,f57318,f810,f60552]) ).
fof(f57424,plain,
( ! [X8,X6,X7] : is_a_theorem(strict_implies(and(not(X7),and(X8,or(X6,X7))),X6))
| ~ spl2_76
| ~ spl2_822 ),
inference(superposition,[],[f57319,f811]) ).
fof(f60080,plain,
( spl2_842
| ~ spl2_27
| ~ spl2_822 ),
inference(avatar_split_clause,[],[f57349,f57318,f302,f60078]) ).
fof(f57349,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),and(or(X0,X1),X2))) )
| ~ spl2_27
| ~ spl2_822 ),
inference(resolution,[],[f57319,f303]) ).
fof(f60076,plain,
( spl2_841
| ~ spl2_262
| ~ spl2_616
| ~ spl2_625
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37527,f37227,f34595,f33168,f7538,f60074]) ).
fof(f60074,plain,
( spl2_841
<=> ! [X9,X10] :
( ~ is_a_theorem(and(X10,and(not(X9),not(not(X9)))))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_841])]) ).
fof(f7538,plain,
( spl2_262
<=> ! [X2,X3] :
( ~ is_a_theorem(strict_implies(X2,X3))
| is_a_theorem(X3)
| ~ is_a_theorem(and(X2,not(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_262])]) ).
fof(f37527,plain,
( ! [X10,X9] :
( ~ is_a_theorem(and(X10,and(not(X9),not(not(X9)))))
| is_a_theorem(X9) )
| ~ spl2_262
| ~ spl2_616
| ~ spl2_625
| ~ spl2_663 ),
inference(forward_demodulation,[],[f37526,f33169]) ).
fof(f37526,plain,
( ! [X10,X9] :
( ~ is_a_theorem(and(X10,and(not(not(X9)),not(X9))))
| is_a_theorem(X9) )
| ~ spl2_262
| ~ spl2_625
| ~ spl2_663 ),
inference(forward_demodulation,[],[f37465,f34596]) ).
fof(f37465,plain,
( ! [X10,X9] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(not(not(X9)),X10),not(X9))) )
| ~ spl2_262
| ~ spl2_663 ),
inference(resolution,[],[f37228,f7539]) ).
fof(f7539,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_implies(X2,X3))
| is_a_theorem(X3)
| ~ is_a_theorem(and(X2,not(X3))) )
| ~ spl2_262 ),
inference(avatar_component_clause,[],[f7538]) ).
fof(f60072,plain,
( spl2_840
| ~ spl2_249
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37464,f37227,f6955,f60070]) ).
fof(f60070,plain,
( spl2_840
<=> ! [X7,X8] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),and(not(not(X7)),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_840])]) ).
fof(f37464,plain,
( ! [X8,X7] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),and(not(not(X7)),X8))) )
| ~ spl2_249
| ~ spl2_663 ),
inference(resolution,[],[f37228,f6956]) ).
fof(f60068,plain,
( spl2_839
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_209
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21640,f19362,f4558,f1122,f814,f810,f60066]) ).
fof(f60066,plain,
( spl2_839
<=> ! [X4,X2,X3] : equiv(and(X3,not(X4)),necessarily(not(X2))) = and(implies(and(X3,possibly(X2)),X4),not(and(necessarily(not(X2)),implies(X3,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_839])]) ).
fof(f21640,plain,
( ! [X2,X3,X4] : equiv(and(X3,not(X4)),necessarily(not(X2))) = and(implies(and(X3,possibly(X2)),X4),not(and(necessarily(not(X2)),implies(X3,X4))))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_96
| ~ spl2_209
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20619,f1123]) ).
fof(f20619,plain,
( ! [X2,X3,X4] : equiv(and(X3,not(X4)),necessarily(not(X2))) = and(not(and(not(X4),and(X3,possibly(X2)))),not(and(necessarily(not(X2)),implies(X3,X4))))
| ~ spl2_76
| ~ spl2_77
| ~ spl2_209
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4597,f19383]) ).
fof(f4597,plain,
( ! [X2,X3,X4] : equiv(and(X3,not(X4)),necessarily(not(X2))) = and(not(and(and(X3,not(X4)),possibly(X2))),not(and(necessarily(not(X2)),implies(X3,X4))))
| ~ spl2_77
| ~ spl2_209 ),
inference(superposition,[],[f4559,f815]) ).
fof(f60064,plain,
( spl2_838
| ~ spl2_29
| ~ spl2_76
| ~ spl2_96
| ~ spl2_420
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21654,f19362,f14870,f1122,f810,f315,f60062]) ).
fof(f60062,plain,
( spl2_838
<=> ! [X13,X12,X11] :
( is_a_theorem(implies(and(X11,possibly(X13)),X12))
| ~ is_a_theorem(implies(X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_838])]) ).
fof(f14870,plain,
( spl2_420
<=> ! [X7,X8] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(X7,possibly(X8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_420])]) ).
fof(f21654,plain,
( ! [X11,X12,X13] :
( is_a_theorem(implies(and(X11,possibly(X13)),X12))
| ~ is_a_theorem(implies(X11,X12)) )
| ~ spl2_29
| ~ spl2_76
| ~ spl2_96
| ~ spl2_420
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20631,f1123]) ).
fof(f20631,plain,
( ! [X11,X12,X13] :
( is_a_theorem(not(and(not(X12),and(X11,possibly(X13)))))
| ~ is_a_theorem(implies(X11,X12)) )
| ~ spl2_29
| ~ spl2_76
| ~ spl2_420
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14881,f19383]) ).
fof(f14881,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(implies(X11,X12))
| is_a_theorem(not(and(and(X11,not(X12)),possibly(X13)))) )
| ~ spl2_29
| ~ spl2_420 ),
inference(superposition,[],[f14871,f316]) ).
fof(f14871,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(X7,possibly(X8)))) )
| ~ spl2_420 ),
inference(avatar_component_clause,[],[f14870]) ).
fof(f59393,plain,
( spl2_837
| ~ spl2_26
| ~ spl2_835 ),
inference(avatar_split_clause,[],[f58554,f58055,f298,f59391]) ).
fof(f59391,plain,
( spl2_837
<=> ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(X3,not(X2)))
| ~ is_a_theorem(not(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_837])]) ).
fof(f58055,plain,
( spl2_835
<=> ! [X2,X1] :
( ~ is_a_theorem(and(not(X2),equiv(X2,not(X1))))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_835])]) ).
fof(f58554,plain,
( ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(X3,not(X2)))
| ~ is_a_theorem(not(X3)) )
| ~ spl2_26
| ~ spl2_835 ),
inference(resolution,[],[f58056,f299]) ).
fof(f58056,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(not(X2),equiv(X2,not(X1))))
| is_a_theorem(X1) )
| ~ spl2_835 ),
inference(avatar_component_clause,[],[f58055]) ).
fof(f58601,plain,
( spl2_836
| ~ spl2_75
| ~ spl2_833 ),
inference(avatar_split_clause,[],[f58526,f58047,f806,f58599]) ).
fof(f58599,plain,
( spl2_836
<=> ! [X2,X1] :
( ~ is_a_theorem(not(implies(equiv(X2,not(X1)),X2)))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_836])]) ).
fof(f58047,plain,
( spl2_833
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(equiv(not(X0),X1),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_833])]) ).
fof(f58526,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(implies(equiv(X2,not(X1)),X2)))
| is_a_theorem(X1) )
| ~ spl2_75
| ~ spl2_833 ),
inference(superposition,[],[f58048,f807]) ).
fof(f58048,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(implies(equiv(not(X0),X1),X1)))
| is_a_theorem(X0) )
| ~ spl2_833 ),
inference(avatar_component_clause,[],[f58047]) ).
fof(f58057,plain,
( spl2_835
| ~ spl2_75
| ~ spl2_831 ),
inference(avatar_split_clause,[],[f57726,f57678,f806,f58055]) ).
fof(f57678,plain,
( spl2_831
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),equiv(not(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_831])]) ).
fof(f57726,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(not(X2),equiv(X2,not(X1))))
| is_a_theorem(X1) )
| ~ spl2_75
| ~ spl2_831 ),
inference(superposition,[],[f57679,f807]) ).
fof(f57679,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(X1),equiv(not(X0),X1)))
| is_a_theorem(X0) )
| ~ spl2_831 ),
inference(avatar_component_clause,[],[f57678]) ).
fof(f58053,plain,
( spl2_834
| ~ spl2_26
| ~ spl2_831 ),
inference(avatar_split_clause,[],[f57686,f57678,f298,f58051]) ).
fof(f58051,plain,
( spl2_834
<=> ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(not(X2),X3))
| ~ is_a_theorem(not(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_834])]) ).
fof(f57686,plain,
( ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(not(X2),X3))
| ~ is_a_theorem(not(X3)) )
| ~ spl2_26
| ~ spl2_831 ),
inference(resolution,[],[f57679,f299]) ).
fof(f58049,plain,
( spl2_833
| ~ spl2_550
| ~ spl2_831 ),
inference(avatar_split_clause,[],[f57685,f57678,f29224,f58047]) ).
fof(f57685,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(equiv(not(X0),X1),X1))) )
| ~ spl2_550
| ~ spl2_831 ),
inference(resolution,[],[f57679,f29225]) ).
fof(f57684,plain,
( spl2_832
| ~ spl2_75
| ~ spl2_830 ),
inference(avatar_split_clause,[],[f57565,f57491,f806,f57682]) ).
fof(f57565,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(not(X2),equiv(X2,not(X1))),X1))
| ~ spl2_75
| ~ spl2_830 ),
inference(superposition,[],[f57492,f807]) ).
fof(f57680,plain,
( spl2_831
| ~ spl2_27
| ~ spl2_830 ),
inference(avatar_split_clause,[],[f57494,f57491,f302,f57678]) ).
fof(f57494,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),equiv(not(X0),X1))) )
| ~ spl2_27
| ~ spl2_830 ),
inference(resolution,[],[f57492,f303]) ).
fof(f57493,plain,
( spl2_830
| ~ spl2_80
| ~ spl2_822 ),
inference(avatar_split_clause,[],[f57421,f57318,f856,f57491]) ).
fof(f57421,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(not(X0),X1)),X0))
| ~ spl2_80
| ~ spl2_822 ),
inference(superposition,[],[f57319,f857]) ).
fof(f57348,plain,
( spl2_829
| ~ spl2_76
| ~ spl2_157
| ~ spl2_252
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20602,f19362,f6967,f2734,f810,f57346]) ).
fof(f20602,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(equiv(not(and(X21,implies(X22,X23))),and(not(X23),and(X22,not(X21)))),not(equiv(and(X22,not(X23)),X21))))
| ~ spl2_76
| ~ spl2_157
| ~ spl2_252
| ~ spl2_486 ),
inference(backward_demodulation,[],[f7019,f19383]) ).
fof(f7019,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(equiv(not(and(X21,implies(X22,X23))),and(and(X22,not(X23)),not(X21))),not(equiv(and(X22,not(X23)),X21))))
| ~ spl2_157
| ~ spl2_252 ),
inference(superposition,[],[f2735,f6968]) ).
fof(f57344,plain,
( spl2_828
| ~ spl2_517
| ~ spl2_654 ),
inference(avatar_split_clause,[],[f37187,f37073,f26955,f57342]) ).
fof(f37187,plain,
( ! [X10,X8,X9] : is_a_theorem(strict_implies(and(X10,and(not(X8),or(X8,X9))),X9))
| ~ spl2_517
| ~ spl2_654 ),
inference(superposition,[],[f37074,f26956]) ).
fof(f57340,plain,
( spl2_827
| ~ spl2_76
| ~ spl2_654 ),
inference(avatar_split_clause,[],[f37168,f37073,f810,f57338]) ).
fof(f37168,plain,
( ! [X8,X6,X7] : is_a_theorem(strict_implies(and(not(X6),and(X8,or(X6,X7))),X7))
| ~ spl2_76
| ~ spl2_654 ),
inference(superposition,[],[f37074,f811]) ).
fof(f57336,plain,
( spl2_826
| ~ spl2_27
| ~ spl2_654 ),
inference(avatar_split_clause,[],[f37108,f37073,f302,f57334]) ).
fof(f37108,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),and(or(X1,X0),X2))) )
| ~ spl2_27
| ~ spl2_654 ),
inference(resolution,[],[f37074,f303]) ).
fof(f57332,plain,
( spl2_825
| ~ spl2_249
| ~ spl2_524 ),
inference(avatar_split_clause,[],[f27992,f27818,f6955,f57330]) ).
fof(f57330,plain,
( spl2_825
<=> ! [X9,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(not(X9),implies(implies(X9,X10),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_825])]) ).
fof(f27992,plain,
( ! [X10,X9] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(not(X9),implies(implies(X9,X10),X9))) )
| ~ spl2_249
| ~ spl2_524 ),
inference(resolution,[],[f27819,f6956]) ).
fof(f57328,plain,
( spl2_824
| ~ spl2_54
| ~ spl2_209 ),
inference(avatar_split_clause,[],[f4596,f4558,f505,f57326]) ).
fof(f57326,plain,
( spl2_824
<=> ! [X0,X1] : equiv(necessarily(not(X1)),necessarily(not(X0))) = and(not(and(necessarily(not(X1)),possibly(X0))),not(and(necessarily(not(X0)),possibly(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_824])]) ).
fof(f4596,plain,
( ! [X0,X1] : equiv(necessarily(not(X1)),necessarily(not(X0))) = and(not(and(necessarily(not(X1)),possibly(X0))),not(and(necessarily(not(X0)),possibly(X1))))
| ~ spl2_54
| ~ spl2_209 ),
inference(superposition,[],[f4559,f506]) ).
fof(f57324,plain,
( spl2_823
| ~ spl2_249
| ~ spl2_522 ),
inference(avatar_split_clause,[],[f27889,f27810,f6955,f57322]) ).
fof(f57322,plain,
( spl2_823
<=> ! [X7,X8] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),or(X7,and(X8,X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_823])]) ).
fof(f27889,plain,
( ! [X8,X7] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),or(X7,and(X8,X7)))) )
| ~ spl2_249
| ~ spl2_522 ),
inference(resolution,[],[f27811,f6956]) ).
fof(f57320,plain,
( spl2_822
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21019,f19362,f18075,f12444,f4550,f1856,f1499,f1122,f810,f681,f436,f315,f290,f286,f57318]) ).
fof(f1499,plain,
( spl2_111
<=> ! [X0,X1] : and(X0,X1) = and(X0,and(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_111])]) ).
fof(f21019,plain,
( ! [X222,X220,X221] : is_a_theorem(strict_implies(and(not(X221),and(or(X220,X221),X222)),X220))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21018,f20741]) ).
fof(f21018,plain,
( ! [X222,X220,X221] : is_a_theorem(strict_implies(and(or(X220,X221),and(not(X221),X222)),X220))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21017,f287]) ).
fof(f21017,plain,
( ! [X222,X220,X221] : is_a_theorem(necessarily(implies(and(or(X220,X221),and(not(X221),X222)),X220)))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20821,f1123]) ).
fof(f20821,plain,
( ! [X222,X220,X221] : is_a_theorem(necessarily(not(and(not(X220),and(or(X220,X221),and(not(X221),X222))))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14011,f20741]) ).
fof(f14011,plain,
( ! [X222,X220,X221] : is_a_theorem(necessarily(not(and(or(X220,X221),and(not(X220),and(not(X221),X222))))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_207
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13876,f13940]) ).
fof(f13940,plain,
( ! [X10,X8,X9] : necessarily(not(and(or(X8,X9),X10))) = necessarily(not(and(X10,or(X8,X9))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13939,f12445]) ).
fof(f13939,plain,
( ! [X10,X8,X9] : strict_implies(X10,and(not(X8),not(X9))) = necessarily(not(and(or(X8,X9),X10)))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13938,f1500]) ).
fof(f1500,plain,
( ! [X0,X1] : and(X0,X1) = and(X0,and(X0,X1))
| ~ spl2_111 ),
inference(avatar_component_clause,[],[f1499]) ).
fof(f13938,plain,
( ! [X10,X8,X9] : strict_implies(X10,and(not(X8),not(X9))) = necessarily(not(and(or(X8,X9),and(or(X8,X9),X10))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13937,f291]) ).
fof(f13937,plain,
( ! [X10,X8,X9] : strict_implies(X10,and(not(X8),not(X9))) = necessarily(not(and(or(X8,X9),and(implies(not(X8),X9),X10))))
| ~ spl2_29
| ~ spl2_76
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13936,f316]) ).
fof(f13936,plain,
( ! [X10,X8,X9] : strict_implies(X10,and(not(X8),not(X9))) = necessarily(not(and(or(X8,X9),and(not(and(not(X8),not(X9))),X10))))
| ~ spl2_76
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13808,f811]) ).
fof(f13808,plain,
( ! [X10,X8,X9] : strict_implies(X10,and(not(X8),not(X9))) = necessarily(not(and(and(not(and(not(X8),not(X9))),X10),or(X8,X9))))
| ~ spl2_126
| ~ spl2_371 ),
inference(superposition,[],[f12445,f1857]) ).
fof(f13876,plain,
( ! [X222,X220,X221] : is_a_theorem(necessarily(not(and(and(not(X220),and(not(X221),X222)),or(X220,X221)))))
| ~ spl2_207
| ~ spl2_371 ),
inference(superposition,[],[f4551,f12445]) ).
fof(f57258,plain,
( spl2_821
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3238,f2598,f57256]) ).
fof(f57256,plain,
( spl2_821
<=> ! [X15,X17,X18,X16,X19] : possibly(and(X18,implies(X19,strict_implies(X15,and(X16,not(X17)))))) = not(strict_implies(X18,and(X19,possibly(and(X15,implies(X16,X17)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_821])]) ).
fof(f2598,plain,
( spl2_148
<=> ! [X2,X4,X3] : not(strict_implies(X4,and(X2,not(X3)))) = possibly(and(X4,implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_148])]) ).
fof(f3238,plain,
( ! [X18,X19,X16,X17,X15] : possibly(and(X18,implies(X19,strict_implies(X15,and(X16,not(X17)))))) = not(strict_implies(X18,and(X19,possibly(and(X15,implies(X16,X17))))))
| ~ spl2_148 ),
inference(superposition,[],[f2599,f2599]) ).
fof(f2599,plain,
( ! [X2,X3,X4] : not(strict_implies(X4,and(X2,not(X3)))) = possibly(and(X4,implies(X2,X3)))
| ~ spl2_148 ),
inference(avatar_component_clause,[],[f2598]) ).
fof(f56555,plain,
( spl2_820
| ~ spl2_33
| ~ spl2_70
| ~ spl2_114 ),
inference(avatar_split_clause,[],[f2081,f1640,f681,f340,f56553]) ).
fof(f56553,plain,
( spl2_820
<=> ! [X0,X1] :
( ~ is_a_theorem(necessarily(or(and(X0,possibly(X1)),equiv(X0,necessarily(not(X1))))))
| not(and(X0,possibly(X1))) = equiv(X0,necessarily(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_820])]) ).
fof(f2081,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(or(and(X0,possibly(X1)),equiv(X0,necessarily(not(X1))))))
| not(and(X0,possibly(X1))) = equiv(X0,necessarily(not(X1))) )
| ~ spl2_33
| ~ spl2_70
| ~ spl2_114 ),
inference(forward_demodulation,[],[f2065,f341]) ).
fof(f2065,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(and(X0,possibly(X1))),equiv(X0,necessarily(not(X1)))))
| not(and(X0,possibly(X1))) = equiv(X0,necessarily(not(X1))) )
| ~ spl2_70
| ~ spl2_114 ),
inference(resolution,[],[f1641,f682]) ).
fof(f56485,plain,
( spl2_819
| ~ spl2_83
| ~ spl2_812 ),
inference(avatar_split_clause,[],[f56202,f55130,f1024,f56483]) ).
fof(f56483,plain,
( spl2_819
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(not(and(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_819])]) ).
fof(f55130,plain,
( spl2_812
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(X6,X8)))
| is_a_theorem(not(and(X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_812])]) ).
fof(f56202,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(not(and(X0,X1))) )
| ~ spl2_83
| ~ spl2_812 ),
inference(superposition,[],[f55131,f1025]) ).
fof(f55131,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(X6,X8)))
| is_a_theorem(not(and(X6,X7))) )
| ~ spl2_812 ),
inference(avatar_component_clause,[],[f55130]) ).
fof(f56481,plain,
( spl2_818
| ~ spl2_46
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f697,f681,f450,f56479]) ).
fof(f56479,plain,
( spl2_818
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(strict_implies(strict_implies(X15,X16),and(strict_implies(X15,X17),strict_implies(X17,X16))))
| strict_implies(X15,X16) = and(strict_implies(X15,X17),strict_implies(X17,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_818])]) ).
fof(f697,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(strict_implies(strict_implies(X15,X16),and(strict_implies(X15,X17),strict_implies(X17,X16))))
| strict_implies(X15,X16) = and(strict_implies(X15,X17),strict_implies(X17,X16)) )
| ~ spl2_46
| ~ spl2_70 ),
inference(resolution,[],[f682,f451]) ).
fof(f56477,plain,
( spl2_817
| ~ spl2_24
| ~ spl2_810 ),
inference(avatar_split_clause,[],[f55797,f55121,f290,f56475]) ).
fof(f56475,plain,
( spl2_817
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(not(and(X16,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_817])]) ).
fof(f55121,plain,
( spl2_810
<=> ! [X2,X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(implies(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_810])]) ).
fof(f55797,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(not(and(X16,X17))) )
| ~ spl2_24
| ~ spl2_810 ),
inference(superposition,[],[f55122,f291]) ).
fof(f55122,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,X0)))
| is_a_theorem(not(and(X0,X1))) )
| ~ spl2_810 ),
inference(avatar_component_clause,[],[f55121]) ).
fof(f55720,plain,
( spl2_816
| ~ spl2_83
| ~ spl2_799 ),
inference(avatar_split_clause,[],[f54163,f53238,f1024,f55718]) ).
fof(f55718,plain,
( spl2_816
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(or(X0,X1)))))
| is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_816])]) ).
fof(f53238,plain,
( spl2_799
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(or(X7,X6),X8)))
| is_a_theorem(not(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_799])]) ).
fof(f54163,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(or(X0,X1)))))
| is_a_theorem(not(X1)) )
| ~ spl2_83
| ~ spl2_799 ),
inference(superposition,[],[f53239,f1025]) ).
fof(f53239,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(or(X7,X6),X8)))
| is_a_theorem(not(X6)) )
| ~ spl2_799 ),
inference(avatar_component_clause,[],[f53238]) ).
fof(f55275,plain,
( spl2_815
| ~ spl2_24
| ~ spl2_797 ),
inference(avatar_split_clause,[],[f54097,f53230,f290,f55273]) ).
fof(f55273,plain,
( spl2_815
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,or(X9,X10))))
| is_a_theorem(not(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_815])]) ).
fof(f53230,plain,
( spl2_797
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X17,or(X15,X16))))
| is_a_theorem(not(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_797])]) ).
fof(f54097,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,or(X9,X10))))
| is_a_theorem(not(X10)) )
| ~ spl2_24
| ~ spl2_797 ),
inference(superposition,[],[f53231,f291]) ).
fof(f53231,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X17,or(X15,X16))))
| is_a_theorem(not(X16)) )
| ~ spl2_797 ),
inference(avatar_component_clause,[],[f53230]) ).
fof(f55271,plain,
( spl2_814
| ~ spl2_83
| ~ spl2_795 ),
inference(avatar_split_clause,[],[f53999,f53118,f1024,f55269]) ).
fof(f55269,plain,
( spl2_814
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(not(and(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_814])]) ).
fof(f53118,plain,
( spl2_795
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(X7,X8)))
| is_a_theorem(not(and(X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_795])]) ).
fof(f53999,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(not(and(X1,X0))) )
| ~ spl2_83
| ~ spl2_795 ),
inference(superposition,[],[f53119,f1025]) ).
fof(f53119,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(X7,X8)))
| is_a_theorem(not(and(X6,X7))) )
| ~ spl2_795 ),
inference(avatar_component_clause,[],[f53118]) ).
fof(f55267,plain,
( spl2_813
| ~ spl2_24
| ~ spl2_793 ),
inference(avatar_split_clause,[],[f53948,f52776,f290,f55265]) ).
fof(f55265,plain,
( spl2_813
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(not(and(X17,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_813])]) ).
fof(f52776,plain,
( spl2_793
<=> ! [X2,X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(implies(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_793])]) ).
fof(f53948,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(not(and(X17,X16))) )
| ~ spl2_24
| ~ spl2_793 ),
inference(superposition,[],[f52777,f291]) ).
fof(f52777,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,X1)))
| is_a_theorem(not(and(X0,X1))) )
| ~ spl2_793 ),
inference(avatar_component_clause,[],[f52776]) ).
fof(f55132,plain,
( spl2_812
| ~ spl2_24
| ~ spl2_549
| ~ spl2_789 ),
inference(avatar_split_clause,[],[f53706,f52381,f29220,f290,f55130]) ).
fof(f52381,plain,
( spl2_789
<=> ! [X9,X8,X7] :
( is_a_theorem(not(and(X7,X8)))
| ~ is_a_theorem(and(not(X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_789])]) ).
fof(f53706,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(X6,X8)))
| is_a_theorem(not(and(X6,X7))) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_789 ),
inference(forward_demodulation,[],[f53663,f291]) ).
fof(f53663,plain,
( ! [X8,X6,X7] :
( is_a_theorem(not(and(X6,X7)))
| ~ is_a_theorem(not(implies(not(X6),X8))) )
| ~ spl2_549
| ~ spl2_789 ),
inference(resolution,[],[f52382,f29221]) ).
fof(f52382,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(not(X7),X9))
| is_a_theorem(not(and(X7,X8))) )
| ~ spl2_789 ),
inference(avatar_component_clause,[],[f52381]) ).
fof(f55128,plain,
( spl2_811
| ~ spl2_76
| ~ spl2_789 ),
inference(avatar_split_clause,[],[f53688,f52381,f810,f55126]) ).
fof(f55126,plain,
( spl2_811
<=> ! [X9,X11,X10] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(X9,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_811])]) ).
fof(f53688,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(X9,X11))) )
| ~ spl2_76
| ~ spl2_789 ),
inference(superposition,[],[f52382,f811]) ).
fof(f55124,plain,
( spl2_387
| spl2_803
| ~ spl2_26
| ~ spl2_789 ),
inference(avatar_split_clause,[],[f53662,f52381,f298,f53726,f14075]) ).
fof(f53726,plain,
( spl2_803
<=> ! [X13,X14] :
( is_a_theorem(not(and(X13,X14)))
| ~ is_a_theorem(not(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_803])]) ).
fof(f53662,plain,
( ! [X3,X4,X5] :
( is_a_theorem(not(and(X3,X4)))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(not(X3)) )
| ~ spl2_26
| ~ spl2_789 ),
inference(resolution,[],[f52382,f299]) ).
fof(f55123,plain,
( spl2_810
| ~ spl2_550
| ~ spl2_789 ),
inference(avatar_split_clause,[],[f53661,f52381,f29224,f55121]) ).
fof(f53661,plain,
( ! [X2,X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(implies(X2,X0))) )
| ~ spl2_550
| ~ spl2_789 ),
inference(resolution,[],[f52382,f29225]) ).
fof(f54210,plain,
( spl2_809
| ~ spl2_24
| ~ spl2_691 ),
inference(avatar_split_clause,[],[f41871,f41678,f290,f54208]) ).
fof(f54208,plain,
( spl2_809
<=> ! [X11,X12] :
( ~ is_a_theorem(not(not(not(or(X11,X12)))))
| is_a_theorem(not(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_809])]) ).
fof(f41678,plain,
( spl2_691
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(implies(X0,X1)))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_691])]) ).
fof(f41871,plain,
( ! [X11,X12] :
( ~ is_a_theorem(not(not(not(or(X11,X12)))))
| is_a_theorem(not(X11)) )
| ~ spl2_24
| ~ spl2_691 ),
inference(superposition,[],[f41679,f291]) ).
fof(f41679,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(implies(X0,X1)))))
| is_a_theorem(X0) )
| ~ spl2_691 ),
inference(avatar_component_clause,[],[f41678]) ).
fof(f54206,plain,
( spl2_808
| ~ spl2_24
| ~ spl2_690 ),
inference(avatar_split_clause,[],[f41685,f41674,f290,f54204]) ).
fof(f54204,plain,
( spl2_808
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X17,or(X15,X16))))
| is_a_theorem(not(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_808])]) ).
fof(f41674,plain,
( spl2_690
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,implies(X9,X10))))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_690])]) ).
fof(f41685,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X17,or(X15,X16))))
| is_a_theorem(not(X15)) )
| ~ spl2_24
| ~ spl2_690 ),
inference(superposition,[],[f41675,f291]) ).
fof(f41675,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,implies(X9,X10))))
| is_a_theorem(X9) )
| ~ spl2_690 ),
inference(avatar_component_clause,[],[f41674]) ).
fof(f54187,plain,
( spl2_807
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_122
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21300,f19362,f18075,f9399,f9376,f8431,f6967,f1831,f810,f681,f436,f54185]) ).
fof(f54185,plain,
( spl2_807
<=> ! [X24,X20,X21,X23,X22] :
( ~ is_a_theorem(strict_implies(X20,and(equiv(and(X23,not(X24)),X22),X21)))
| is_a_theorem(strict_implies(X20,and(X21,equiv(X22,and(X23,not(X24)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_807])]) ).
fof(f8431,plain,
( spl2_283
<=> ! [X9,X7,X6,X8] : is_a_theorem(strict_implies(and(implies(and(X7,not(X8)),X6),and(X9,not(and(X6,implies(X7,X8))))),and(X9,equiv(X6,and(X7,not(X8)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_283])]) ).
fof(f9376,plain,
( spl2_298
<=> ! [X18,X16,X17] : is_a_theorem(strict_implies(and(and(X18,X16),X17),and(X18,and(X17,X16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_298])]) ).
fof(f21300,plain,
( ! [X21,X24,X22,X23,X20] :
( ~ is_a_theorem(strict_implies(X20,and(equiv(and(X23,not(X24)),X22),X21)))
| is_a_theorem(strict_implies(X20,and(X21,equiv(X22,and(X23,not(X24)))))) )
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_122
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21185,f20754]) ).
fof(f20754,plain,
( ! [X28,X29,X26,X27] : and(equiv(and(X27,not(X28)),X26),X29) = and(not(and(X26,implies(X27,X28))),and(implies(and(X27,not(X28)),X26),X29))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_252
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f20080,f20741]) ).
fof(f20080,plain,
( ! [X28,X29,X26,X27] : and(equiv(and(X27,not(X28)),X26),X29) = and(implies(and(X27,not(X28)),X26),and(not(and(X26,implies(X27,X28))),X29))
| ~ spl2_76
| ~ spl2_252
| ~ spl2_486 ),
inference(forward_demodulation,[],[f19374,f811]) ).
fof(f19374,plain,
( ! [X28,X29,X26,X27] : and(equiv(and(X27,not(X28)),X26),X29) = and(and(not(and(X26,implies(X27,X28))),X29),implies(and(X27,not(X28)),X26))
| ~ spl2_252
| ~ spl2_486 ),
inference(superposition,[],[f19363,f6968]) ).
fof(f21185,plain,
( ! [X21,X24,X22,X23,X20] :
( ~ is_a_theorem(strict_implies(X20,and(not(and(X22,implies(X23,X24))),and(implies(and(X23,not(X24)),X22),X21))))
| is_a_theorem(strict_implies(X20,and(X21,equiv(X22,and(X23,not(X24)))))) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_122
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(backward_demodulation,[],[f9121,f21159]) ).
fof(f21159,plain,
( ! [X21,X19,X20] : and(X19,and(X20,X21)) = and(X21,and(X19,X20))
| ~ spl2_70
| ~ spl2_76
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21158,f19383]) ).
fof(f21158,plain,
( ! [X21,X19,X20] : and(X19,and(X20,X21)) = and(and(X19,X21),X20)
| ~ spl2_70
| ~ spl2_76
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(subsumption_resolution,[],[f20285,f21154]) ).
fof(f20285,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(strict_implies(and(X19,and(X20,X21)),and(X21,and(X19,X20))))
| and(X19,and(X20,X21)) = and(and(X19,X21),X20) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_298
| ~ spl2_486 ),
inference(backward_demodulation,[],[f9569,f19383]) ).
fof(f9569,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(strict_implies(and(X19,and(X20,X21)),and(and(X19,X21),X20)))
| and(X19,and(X20,X21)) = and(and(X19,X21),X20) )
| ~ spl2_70
| ~ spl2_298 ),
inference(resolution,[],[f9377,f682]) ).
fof(f9377,plain,
( ! [X18,X16,X17] : is_a_theorem(strict_implies(and(and(X18,X16),X17),and(X18,and(X17,X16))))
| ~ spl2_298 ),
inference(avatar_component_clause,[],[f9376]) ).
fof(f9121,plain,
( ! [X21,X24,X22,X23,X20] :
( is_a_theorem(strict_implies(X20,and(X21,equiv(X22,and(X23,not(X24))))))
| ~ is_a_theorem(strict_implies(X20,and(implies(and(X23,not(X24)),X22),and(X21,not(and(X22,implies(X23,X24))))))) )
| ~ spl2_122
| ~ spl2_283 ),
inference(resolution,[],[f8432,f1832]) ).
fof(f8432,plain,
( ! [X8,X6,X9,X7] : is_a_theorem(strict_implies(and(implies(and(X7,not(X8)),X6),and(X9,not(and(X6,implies(X7,X8))))),and(X9,equiv(X6,and(X7,not(X8))))))
| ~ spl2_283 ),
inference(avatar_component_clause,[],[f8431]) ).
fof(f54027,plain,
( spl2_806
| ~ spl2_76
| ~ spl2_120
| ~ spl2_215
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20453,f19362,f4855,f1712,f810,f54025]) ).
fof(f54025,plain,
( spl2_806
<=> ! [X38,X36,X35,X37] :
( is_a_theorem(and(or(X35,X36),and(X37,and(implies(X36,not(X35)),X38))))
| ~ is_a_theorem(and(equiv(not(X35),X36),X37))
| ~ is_a_theorem(X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_806])]) ).
fof(f1712,plain,
( spl2_120
<=> ! [X2,X0,X1] :
( is_a_theorem(and(X0,and(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(and(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_120])]) ).
fof(f4855,plain,
( spl2_215
<=> ! [X20,X18,X19] :
( ~ is_a_theorem(and(equiv(not(X18),X19),X20))
| is_a_theorem(and(or(X18,X19),and(implies(X19,not(X18)),X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_215])]) ).
fof(f20453,plain,
( ! [X38,X36,X37,X35] :
( is_a_theorem(and(or(X35,X36),and(X37,and(implies(X36,not(X35)),X38))))
| ~ is_a_theorem(and(equiv(not(X35),X36),X37))
| ~ is_a_theorem(X38) )
| ~ spl2_76
| ~ spl2_120
| ~ spl2_215
| ~ spl2_486 ),
inference(backward_demodulation,[],[f5480,f19383]) ).
fof(f5480,plain,
( ! [X38,X36,X37,X35] :
( ~ is_a_theorem(and(equiv(not(X35),X36),X37))
| ~ is_a_theorem(X38)
| is_a_theorem(and(or(X35,X36),and(and(implies(X36,not(X35)),X37),X38))) )
| ~ spl2_120
| ~ spl2_215 ),
inference(resolution,[],[f4856,f1713]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X2)
| is_a_theorem(and(X0,and(X1,X2))) )
| ~ spl2_120 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f4856,plain,
( ! [X18,X19,X20] :
( is_a_theorem(and(or(X18,X19),and(implies(X19,not(X18)),X20)))
| ~ is_a_theorem(and(equiv(not(X18),X19),X20)) )
| ~ spl2_215 ),
inference(avatar_component_clause,[],[f4855]) ).
fof(f53943,plain,
( spl2_805
| ~ spl2_36
| ~ spl2_75
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7103,f6967,f806,f363,f53941]) ).
fof(f53941,plain,
( spl2_805
<=> ! [X9,X8] : equiv(implies(X8,X9),and(X9,not(X8))) = and(not(equiv(X8,X9)),implies(and(X9,not(X8)),implies(X8,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_805])]) ).
fof(f7103,plain,
( ! [X8,X9] : equiv(implies(X8,X9),and(X9,not(X8))) = and(not(equiv(X8,X9)),implies(and(X9,not(X8)),implies(X8,X9)))
| ~ spl2_36
| ~ spl2_75
| ~ spl2_252 ),
inference(forward_demodulation,[],[f6990,f807]) ).
fof(f6990,plain,
( ! [X8,X9] : equiv(and(X9,not(X8)),implies(X8,X9)) = and(not(equiv(X8,X9)),implies(and(X9,not(X8)),implies(X8,X9)))
| ~ spl2_36
| ~ spl2_252 ),
inference(superposition,[],[f6968,f364]) ).
fof(f53732,plain,
( spl2_804
| ~ spl2_24
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f6982,f6967,f290,f53730]) ).
fof(f6982,plain,
( ! [X2,X0,X1] : equiv(and(not(X0),not(X1)),X2) = and(not(and(X2,or(X0,X1))),implies(and(not(X0),not(X1)),X2))
| ~ spl2_24
| ~ spl2_252 ),
inference(superposition,[],[f6968,f291]) ).
fof(f53728,plain,
( spl2_803
| ~ spl2_451
| ~ spl2_789 ),
inference(avatar_split_clause,[],[f53665,f52381,f16617,f53726]) ).
fof(f53665,plain,
( ! [X14,X13] :
( is_a_theorem(not(and(X13,X14)))
| ~ is_a_theorem(not(X13)) )
| ~ spl2_451
| ~ spl2_789 ),
inference(resolution,[],[f52382,f16618]) ).
fof(f53657,plain,
( spl2_802
| ~ spl2_125
| ~ spl2_170 ),
inference(avatar_split_clause,[],[f3672,f2786,f1852,f53655]) ).
fof(f53655,plain,
( spl2_802
<=> ! [X11,X12,X10] : is_a_theorem(strict_implies(equiv(not(X10),and(X11,not(X12))),and(implies(implies(X11,X12),X10),equiv(and(X11,not(X12)),not(X10))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_802])]) ).
fof(f2786,plain,
( spl2_170
<=> ! [X11,X10] : is_a_theorem(strict_implies(equiv(not(X10),X11),and(or(X10,X11),equiv(X11,not(X10))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_170])]) ).
fof(f3672,plain,
( ! [X10,X11,X12] : is_a_theorem(strict_implies(equiv(not(X10),and(X11,not(X12))),and(implies(implies(X11,X12),X10),equiv(and(X11,not(X12)),not(X10)))))
| ~ spl2_125
| ~ spl2_170 ),
inference(superposition,[],[f2787,f1853]) ).
fof(f2787,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(equiv(not(X10),X11),and(or(X10,X11),equiv(X11,not(X10)))))
| ~ spl2_170 ),
inference(avatar_component_clause,[],[f2786]) ).
fof(f53534,plain,
( spl2_801
| ~ spl2_77
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3262,f2598,f814,f53532]) ).
fof(f53532,plain,
( spl2_801
<=> ! [X69,X68,X70,X67,X66] : not(and(X69,implies(X70,strict_implies(X66,and(X67,not(X68)))))) = implies(X69,and(X70,possibly(and(X66,implies(X67,X68))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_801])]) ).
fof(f3262,plain,
( ! [X70,X68,X69,X66,X67] : not(and(X69,implies(X70,strict_implies(X66,and(X67,not(X68)))))) = implies(X69,and(X70,possibly(and(X66,implies(X67,X68)))))
| ~ spl2_77
| ~ spl2_148 ),
inference(superposition,[],[f815,f2599]) ).
fof(f53443,plain,
( spl2_800
| ~ spl2_83
| ~ spl2_770 ),
inference(avatar_split_clause,[],[f50991,f49240,f1024,f53441]) ).
fof(f53441,plain,
( spl2_800
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(implies(X0,X1)))))
| is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_800])]) ).
fof(f49240,plain,
( spl2_770
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(implies(X7,X6),X8)))
| is_a_theorem(not(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_770])]) ).
fof(f50991,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(implies(X0,X1)))))
| is_a_theorem(not(X1)) )
| ~ spl2_83
| ~ spl2_770 ),
inference(superposition,[],[f49241,f1025]) ).
fof(f49241,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(implies(X7,X6),X8)))
| is_a_theorem(not(X6)) )
| ~ spl2_770 ),
inference(avatar_component_clause,[],[f49240]) ).
fof(f53240,plain,
( spl2_799
| ~ spl2_24
| ~ spl2_549
| ~ spl2_768 ),
inference(avatar_split_clause,[],[f50969,f49232,f29220,f290,f53238]) ).
fof(f49232,plain,
( spl2_768
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(and(not(or(X15,X16)),X17))
| is_a_theorem(not(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_768])]) ).
fof(f50969,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(or(X7,X6),X8)))
| is_a_theorem(not(X6)) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_768 ),
inference(forward_demodulation,[],[f50927,f291]) ).
fof(f50927,plain,
( ! [X8,X6,X7] :
( is_a_theorem(not(X6))
| ~ is_a_theorem(not(implies(not(or(X7,X6)),X8))) )
| ~ spl2_549
| ~ spl2_768 ),
inference(resolution,[],[f49233,f29221]) ).
fof(f49233,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(and(not(or(X15,X16)),X17))
| is_a_theorem(not(X16)) )
| ~ spl2_768 ),
inference(avatar_component_clause,[],[f49232]) ).
fof(f53236,plain,
( spl2_798
| ~ spl2_24
| ~ spl2_766 ),
inference(avatar_split_clause,[],[f50547,f49224,f290,f53234]) ).
fof(f53234,plain,
( spl2_798
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,implies(X9,X10))))
| is_a_theorem(not(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_798])]) ).
fof(f49224,plain,
( spl2_766
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,implies(X0,X1))))
| is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_766])]) ).
fof(f50547,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,implies(X9,X10))))
| is_a_theorem(not(X10)) )
| ~ spl2_24
| ~ spl2_766 ),
inference(superposition,[],[f49225,f291]) ).
fof(f49225,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,implies(X0,X1))))
| is_a_theorem(not(X1)) )
| ~ spl2_766 ),
inference(avatar_component_clause,[],[f49224]) ).
fof(f53232,plain,
( spl2_797
| ~ spl2_24
| ~ spl2_766 ),
inference(avatar_split_clause,[],[f50536,f49224,f290,f53230]) ).
fof(f50536,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X17,or(X15,X16))))
| is_a_theorem(not(X16)) )
| ~ spl2_24
| ~ spl2_766 ),
inference(superposition,[],[f49225,f291]) ).
fof(f53228,plain,
( spl2_796
| ~ spl2_24
| ~ spl2_763 ),
inference(avatar_split_clause,[],[f50287,f49212,f290,f53226]) ).
fof(f53226,plain,
( spl2_796
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(and(X17,not(or(X15,X16))))
| is_a_theorem(not(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_796])]) ).
fof(f49212,plain,
( spl2_763
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,not(implies(X0,X1))))
| is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_763])]) ).
fof(f50287,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(and(X17,not(or(X15,X16))))
| is_a_theorem(not(X16)) )
| ~ spl2_24
| ~ spl2_763 ),
inference(superposition,[],[f49213,f291]) ).
fof(f49213,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,not(implies(X0,X1))))
| is_a_theorem(not(X1)) )
| ~ spl2_763 ),
inference(avatar_component_clause,[],[f49212]) ).
fof(f53120,plain,
( spl2_795
| ~ spl2_24
| ~ spl2_549
| ~ spl2_758 ),
inference(avatar_split_clause,[],[f50084,f49192,f29220,f290,f53118]) ).
fof(f49192,plain,
( spl2_758
<=> ! [X9,X8,X7] :
( is_a_theorem(not(and(X7,X8)))
| ~ is_a_theorem(and(not(X8),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_758])]) ).
fof(f50084,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(X7,X8)))
| is_a_theorem(not(and(X6,X7))) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_758 ),
inference(forward_demodulation,[],[f50041,f291]) ).
fof(f50041,plain,
( ! [X8,X6,X7] :
( is_a_theorem(not(and(X6,X7)))
| ~ is_a_theorem(not(implies(not(X7),X8))) )
| ~ spl2_549
| ~ spl2_758 ),
inference(resolution,[],[f49193,f29221]) ).
fof(f49193,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(not(X8),X9))
| is_a_theorem(not(and(X7,X8))) )
| ~ spl2_758 ),
inference(avatar_component_clause,[],[f49192]) ).
fof(f53116,plain,
( spl2_794
| ~ spl2_76
| ~ spl2_758 ),
inference(avatar_split_clause,[],[f50066,f49192,f810,f53114]) ).
fof(f53114,plain,
( spl2_794
<=> ! [X9,X11,X10] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(X11,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_794])]) ).
fof(f50066,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(X11,X9))) )
| ~ spl2_76
| ~ spl2_758 ),
inference(superposition,[],[f49193,f811]) ).
fof(f53112,plain,
( spl2_387
| spl2_780
| ~ spl2_26
| ~ spl2_758 ),
inference(avatar_split_clause,[],[f50040,f49192,f298,f50093,f14075]) ).
fof(f50093,plain,
( spl2_780
<=> ! [X13,X14] :
( is_a_theorem(not(and(X13,X14)))
| ~ is_a_theorem(not(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_780])]) ).
fof(f50040,plain,
( ! [X3,X4,X5] :
( is_a_theorem(not(and(X3,X4)))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(not(X4)) )
| ~ spl2_26
| ~ spl2_758 ),
inference(resolution,[],[f49193,f299]) ).
fof(f52778,plain,
( spl2_793
| ~ spl2_550
| ~ spl2_758 ),
inference(avatar_split_clause,[],[f50039,f49192,f29224,f52776]) ).
fof(f50039,plain,
( ! [X2,X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(implies(X2,X1))) )
| ~ spl2_550
| ~ spl2_758 ),
inference(resolution,[],[f49193,f29225]) ).
fof(f52774,plain,
( spl2_792
| ~ spl2_27
| ~ spl2_753 ),
inference(avatar_split_clause,[],[f49694,f49121,f302,f52772]) ).
fof(f52772,plain,
( spl2_792
<=> ! [X6,X5] :
( is_a_theorem(not(and(necessarily(not(X5)),X6)))
| ~ is_a_theorem(possibly(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_792])]) ).
fof(f49694,plain,
( ! [X6,X5] :
( is_a_theorem(not(and(necessarily(not(X5)),X6)))
| ~ is_a_theorem(possibly(X5)) )
| ~ spl2_27
| ~ spl2_753 ),
inference(resolution,[],[f49122,f303]) ).
fof(f52770,plain,
( spl2_791
| ~ spl2_27
| ~ spl2_752 ),
inference(avatar_split_clause,[],[f49600,f49066,f302,f52768]) ).
fof(f49600,plain,
( ! [X3,X4,X5] :
( is_a_theorem(implies(and(X3,X4),X5))
| ~ is_a_theorem(implies(X3,X5)) )
| ~ spl2_27
| ~ spl2_752 ),
inference(resolution,[],[f49067,f303]) ).
fof(f52766,plain,
( spl2_790
| ~ spl2_76
| ~ spl2_747 ),
inference(avatar_split_clause,[],[f49354,f48847,f810,f52764]) ).
fof(f49354,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X9,X11))))
| ~ spl2_76
| ~ spl2_747 ),
inference(superposition,[],[f48848,f811]) ).
fof(f52383,plain,
( spl2_789
| ~ spl2_27
| ~ spl2_747 ),
inference(avatar_split_clause,[],[f49326,f48847,f302,f52381]) ).
fof(f49326,plain,
( ! [X8,X9,X7] :
( is_a_theorem(not(and(X7,X8)))
| ~ is_a_theorem(and(not(X7),X9)) )
| ~ spl2_27
| ~ spl2_747 ),
inference(resolution,[],[f48848,f303]) ).
fof(f52379,plain,
( spl2_788
| ~ spl2_513
| ~ spl2_716 ),
inference(avatar_split_clause,[],[f43310,f43266,f25507,f52377]) ).
fof(f52377,plain,
( spl2_788
<=> ! [X104,X103] :
( ~ is_a_theorem(not(not(strict_equiv(X104,X103))))
| is_a_theorem(strict_equiv(X103,X104)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_788])]) ).
fof(f25507,plain,
( spl2_513
<=> ! [X6,X7] : strict_equiv(X6,X7) = and(strict_equiv(X7,X6),strict_equiv(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_513])]) ).
fof(f43266,plain,
( spl2_716
<=> ! [X2,X1] :
( ~ is_a_theorem(not(not(and(X2,X1))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_716])]) ).
fof(f43310,plain,
( ! [X104,X103] :
( ~ is_a_theorem(not(not(strict_equiv(X104,X103))))
| is_a_theorem(strict_equiv(X103,X104)) )
| ~ spl2_513
| ~ spl2_716 ),
inference(superposition,[],[f43267,f25508]) ).
fof(f25508,plain,
( ! [X6,X7] : strict_equiv(X6,X7) = and(strict_equiv(X7,X6),strict_equiv(X6,X7))
| ~ spl2_513 ),
inference(avatar_component_clause,[],[f25507]) ).
fof(f43267,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(not(and(X2,X1))))
| is_a_theorem(X2) )
| ~ spl2_716 ),
inference(avatar_component_clause,[],[f43266]) ).
fof(f52375,plain,
( spl2_787
| ~ spl2_34
| ~ spl2_716 ),
inference(avatar_split_clause,[],[f43303,f43266,f344,f52373]) ).
fof(f52373,plain,
( spl2_787
<=> ! [X86,X87] :
( ~ is_a_theorem(not(not(strict_equiv(X86,X87))))
| is_a_theorem(strict_implies(X86,X87)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_787])]) ).
fof(f43303,plain,
( ! [X86,X87] :
( ~ is_a_theorem(not(not(strict_equiv(X86,X87))))
| is_a_theorem(strict_implies(X86,X87)) )
| ~ spl2_34
| ~ spl2_716 ),
inference(superposition,[],[f43267,f345]) ).
fof(f51903,plain,
( spl2_786
| ~ spl2_510
| ~ spl2_716 ),
inference(avatar_split_clause,[],[f43295,f43266,f25495,f51901]) ).
fof(f51901,plain,
( spl2_786
<=> ! [X69,X68] :
( ~ is_a_theorem(not(not(equiv(X69,X68))))
| is_a_theorem(equiv(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_786])]) ).
fof(f25495,plain,
( spl2_510
<=> ! [X6,X7] : equiv(X6,X7) = and(equiv(X7,X6),equiv(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_510])]) ).
fof(f43295,plain,
( ! [X68,X69] :
( ~ is_a_theorem(not(not(equiv(X69,X68))))
| is_a_theorem(equiv(X68,X69)) )
| ~ spl2_510
| ~ spl2_716 ),
inference(superposition,[],[f43267,f25496]) ).
fof(f25496,plain,
( ! [X6,X7] : equiv(X6,X7) = and(equiv(X7,X6),equiv(X6,X7))
| ~ spl2_510 ),
inference(avatar_component_clause,[],[f25495]) ).
fof(f51899,plain,
( spl2_785
| ~ spl2_504
| ~ spl2_716 ),
inference(avatar_split_clause,[],[f43277,f43266,f23260,f51897]) ).
fof(f51897,plain,
( spl2_785
<=> ! [X20,X19,X18] :
( ~ is_a_theorem(not(not(and(X19,and(X18,X20)))))
| is_a_theorem(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_785])]) ).
fof(f43277,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(not(not(and(X19,and(X18,X20)))))
| is_a_theorem(X18) )
| ~ spl2_504
| ~ spl2_716 ),
inference(superposition,[],[f43267,f23261]) ).
fof(f51895,plain,
( spl2_784
| ~ spl2_24
| ~ spl2_689 ),
inference(avatar_split_clause,[],[f41655,f41517,f290,f51893]) ).
fof(f51893,plain,
( spl2_784
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(or(X15,X16),X17)))
| is_a_theorem(not(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_784])]) ).
fof(f41517,plain,
( spl2_689
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(implies(X6,X7),X8)))
| is_a_theorem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_689])]) ).
fof(f41655,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(or(X15,X16),X17)))
| is_a_theorem(not(X15)) )
| ~ spl2_24
| ~ spl2_689 ),
inference(superposition,[],[f41518,f291]) ).
fof(f41518,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(implies(X6,X7),X8)))
| is_a_theorem(X6) )
| ~ spl2_689 ),
inference(avatar_component_clause,[],[f41517]) ).
fof(f51891,plain,
( spl2_783
| ~ spl2_24
| ~ spl2_688 ),
inference(avatar_split_clause,[],[f41553,f41423,f290,f51889]) ).
fof(f51889,plain,
( spl2_783
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(and(X17,not(or(X15,X16))))
| is_a_theorem(not(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_783])]) ).
fof(f41423,plain,
( spl2_688
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,not(implies(X2,X3))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_688])]) ).
fof(f41553,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(and(X17,not(or(X15,X16))))
| is_a_theorem(not(X15)) )
| ~ spl2_24
| ~ spl2_688 ),
inference(superposition,[],[f41424,f291]) ).
fof(f41424,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,not(implies(X2,X3))))
| is_a_theorem(X2) )
| ~ spl2_688 ),
inference(avatar_component_clause,[],[f41423]) ).
fof(f51471,plain,
( spl2_782
| ~ spl2_24
| ~ spl2_687 ),
inference(avatar_split_clause,[],[f41524,f41419,f290,f51469]) ).
fof(f51469,plain,
( spl2_782
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X17,or(X15,X16))))
| is_a_theorem(not(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_782])]) ).
fof(f41419,plain,
( spl2_687
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,implies(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_687])]) ).
fof(f41524,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X17,or(X15,X16))))
| is_a_theorem(not(X15)) )
| ~ spl2_24
| ~ spl2_687 ),
inference(superposition,[],[f41420,f291]) ).
fof(f41420,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X1,implies(X0,X2))))
| is_a_theorem(X0) )
| ~ spl2_687 ),
inference(avatar_component_clause,[],[f41419]) ).
fof(f50124,plain,
( spl2_781
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7138,f6967,f2750,f1852,f340,f286,f50122]) ).
fof(f50122,plain,
( spl2_781
<=> ! [X20,X18,X19] : necessarily(not(equiv(and(X19,not(X20)),X18))) = strict_implies(implies(and(X19,not(X20)),X18),and(X18,implies(X19,X20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_781])]) ).
fof(f7138,plain,
( ! [X18,X19,X20] : necessarily(not(equiv(and(X19,not(X20)),X18))) = strict_implies(implies(and(X19,not(X20)),X18),and(X18,implies(X19,X20)))
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_252 ),
inference(forward_demodulation,[],[f7137,f287]) ).
fof(f7137,plain,
( ! [X18,X19,X20] : necessarily(not(equiv(and(X19,not(X20)),X18))) = necessarily(implies(implies(and(X19,not(X20)),X18),and(X18,implies(X19,X20))))
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_252 ),
inference(forward_demodulation,[],[f7136,f1853]) ).
fof(f7136,plain,
( ! [X18,X19,X20] : necessarily(not(equiv(and(X19,not(X20)),X18))) = necessarily(or(and(X18,implies(X19,X20)),and(and(X19,not(X20)),not(X18))))
| ~ spl2_33
| ~ spl2_161
| ~ spl2_252 ),
inference(forward_demodulation,[],[f7018,f341]) ).
fof(f7018,plain,
( ! [X18,X19,X20] : strict_implies(not(and(X18,implies(X19,X20))),and(and(X19,not(X20)),not(X18))) = necessarily(not(equiv(and(X19,not(X20)),X18)))
| ~ spl2_161
| ~ spl2_252 ),
inference(superposition,[],[f2751,f6968]) ).
fof(f50095,plain,
( spl2_780
| ~ spl2_451
| ~ spl2_758 ),
inference(avatar_split_clause,[],[f50043,f49192,f16617,f50093]) ).
fof(f50043,plain,
( ! [X14,X13] :
( is_a_theorem(not(and(X13,X14)))
| ~ is_a_theorem(not(X14)) )
| ~ spl2_451
| ~ spl2_758 ),
inference(resolution,[],[f49193,f16618]) ).
fof(f50038,plain,
( spl2_779
| ~ spl2_26
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7025,f6967,f298,f50036]) ).
fof(f50036,plain,
( spl2_779
<=> ! [X41,X40,X39] :
( is_a_theorem(equiv(and(X40,not(X41)),X39))
| ~ is_a_theorem(implies(and(X40,not(X41)),X39))
| ~ is_a_theorem(not(and(X39,implies(X40,X41)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_779])]) ).
fof(f7025,plain,
( ! [X40,X41,X39] :
( is_a_theorem(equiv(and(X40,not(X41)),X39))
| ~ is_a_theorem(implies(and(X40,not(X41)),X39))
| ~ is_a_theorem(not(and(X39,implies(X40,X41)))) )
| ~ spl2_26
| ~ spl2_252 ),
inference(superposition,[],[f299,f6968]) ).
fof(f49813,plain,
( spl2_778
| ~ spl2_125
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3286,f2598,f1852,f49811]) ).
fof(f49811,plain,
( spl2_778
<=> ! [X160,X163,X161,X159,X162] : implies(implies(X163,strict_implies(X159,and(X160,not(X161)))),X162) = or(X162,and(X163,possibly(and(X159,implies(X160,X161))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_778])]) ).
fof(f3286,plain,
( ! [X162,X163,X160,X161,X159] : implies(implies(X163,strict_implies(X159,and(X160,not(X161)))),X162) = or(X162,and(X163,possibly(and(X159,implies(X160,X161)))))
| ~ spl2_125
| ~ spl2_148 ),
inference(superposition,[],[f1853,f2599]) ).
fof(f49591,plain,
( spl2_777
| ~ spl2_112
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3277,f2598,f1558,f49589]) ).
fof(f49589,plain,
( spl2_777
<=> ! [X125,X128,X127,X126] : possibly(and(X128,possibly(strict_implies(X125,and(X126,not(X127)))))) = not(strict_implies(X128,necessarily(possibly(and(X125,implies(X126,X127)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_777])]) ).
fof(f3277,plain,
( ! [X126,X127,X125,X128] : possibly(and(X128,possibly(strict_implies(X125,and(X126,not(X127)))))) = not(strict_implies(X128,necessarily(possibly(and(X125,implies(X126,X127))))))
| ~ spl2_112
| ~ spl2_148 ),
inference(superposition,[],[f1559,f2599]) ).
fof(f49323,plain,
( spl2_776
| ~ spl2_58
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3255,f2598,f544,f49321]) ).
fof(f49321,plain,
( spl2_776
<=> ! [X38,X41,X40,X42,X39] : implies(implies(X41,strict_implies(X38,and(X39,not(X40)))),X42) = or(and(X41,possibly(and(X38,implies(X39,X40)))),X42) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_776])]) ).
fof(f3255,plain,
( ! [X40,X38,X41,X39,X42] : implies(implies(X41,strict_implies(X38,and(X39,not(X40)))),X42) = or(and(X41,possibly(and(X38,implies(X39,X40)))),X42)
| ~ spl2_58
| ~ spl2_148 ),
inference(superposition,[],[f545,f2599]) ).
fof(f49262,plain,
( spl2_775
| ~ spl2_26
| ~ spl2_738 ),
inference(avatar_split_clause,[],[f47997,f45835,f298,f49260]) ).
fof(f49260,plain,
( spl2_775
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,possibly(X1)))
| ~ is_a_theorem(possibly(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_775])]) ).
fof(f45835,plain,
( spl2_738
<=> ! [X2,X1] :
( ~ is_a_theorem(and(possibly(X1),equiv(X2,possibly(X1))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_738])]) ).
fof(f47997,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,possibly(X1)))
| ~ is_a_theorem(possibly(X1)) )
| ~ spl2_26
| ~ spl2_738 ),
inference(resolution,[],[f45836,f299]) ).
fof(f45836,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(possibly(X1),equiv(X2,possibly(X1))))
| is_a_theorem(X2) )
| ~ spl2_738 ),
inference(avatar_component_clause,[],[f45835]) ).
fof(f49258,plain,
( spl2_774
| ~ spl2_112
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3237,f2598,f1558,f49256]) ).
fof(f49256,plain,
( spl2_774
<=> ! [X11,X14,X13,X12] : possibly(and(X13,implies(X14,strict_implies(X11,necessarily(not(X12)))))) = not(strict_implies(X13,and(X14,possibly(and(X11,possibly(X12)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_774])]) ).
fof(f3237,plain,
( ! [X11,X14,X12,X13] : possibly(and(X13,implies(X14,strict_implies(X11,necessarily(not(X12)))))) = not(strict_implies(X13,and(X14,possibly(and(X11,possibly(X12))))))
| ~ spl2_112
| ~ spl2_148 ),
inference(superposition,[],[f2599,f1559]) ).
fof(f49254,plain,
( spl2_773
| ~ spl2_83
| ~ spl2_735 ),
inference(avatar_split_clause,[],[f47113,f45823,f1024,f49252]) ).
fof(f49252,plain,
( spl2_773
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(and(X0,X1))))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_773])]) ).
fof(f45823,plain,
( spl2_735
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(not(and(X6,X7)),X8)))
| is_a_theorem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_735])]) ).
fof(f47113,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(and(X0,X1))))))
| is_a_theorem(X0) )
| ~ spl2_83
| ~ spl2_735 ),
inference(superposition,[],[f45824,f1025]) ).
fof(f45824,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(and(X6,X7)),X8)))
| is_a_theorem(X6) )
| ~ spl2_735 ),
inference(avatar_component_clause,[],[f45823]) ).
fof(f49250,plain,
( spl2_772
| ~ spl2_24
| ~ spl2_733 ),
inference(avatar_split_clause,[],[f47055,f45815,f290,f49248]) ).
fof(f49248,plain,
( spl2_772
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,not(and(X9,X10)))))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_772])]) ).
fof(f45815,plain,
( spl2_733
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(and(X0,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_733])]) ).
fof(f47055,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,not(and(X9,X10)))))
| is_a_theorem(X9) )
| ~ spl2_24
| ~ spl2_733 ),
inference(superposition,[],[f45816,f291]) ).
fof(f45816,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X1,not(and(X0,X2)))))
| is_a_theorem(X0) )
| ~ spl2_733 ),
inference(avatar_component_clause,[],[f45815]) ).
fof(f49246,plain,
( spl2_771
| ~ spl2_83
| ~ spl2_731 ),
inference(avatar_split_clause,[],[f46841,f45807,f1024,f49244]) ).
fof(f49244,plain,
( spl2_771
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(and(X0,X1))))))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_771])]) ).
fof(f45807,plain,
( spl2_731
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(not(and(X7,X6)),X8)))
| is_a_theorem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_731])]) ).
fof(f46841,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(and(X0,X1))))))
| is_a_theorem(X1) )
| ~ spl2_83
| ~ spl2_731 ),
inference(superposition,[],[f45808,f1025]) ).
fof(f45808,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(and(X7,X6)),X8)))
| is_a_theorem(X6) )
| ~ spl2_731 ),
inference(avatar_component_clause,[],[f45807]) ).
fof(f49242,plain,
( spl2_770
| ~ spl2_24
| ~ spl2_549
| ~ spl2_730 ),
inference(avatar_split_clause,[],[f46789,f45672,f29220,f290,f49240]) ).
fof(f45672,plain,
( spl2_730
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(implies(X0,X1)),X2))
| is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_730])]) ).
fof(f46789,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(implies(X7,X6),X8)))
| is_a_theorem(not(X6)) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_730 ),
inference(forward_demodulation,[],[f46753,f291]) ).
fof(f46753,plain,
( ! [X8,X6,X7] :
( is_a_theorem(not(X6))
| ~ is_a_theorem(not(implies(not(implies(X7,X6)),X8))) )
| ~ spl2_549
| ~ spl2_730 ),
inference(resolution,[],[f45673,f29221]) ).
fof(f45673,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(implies(X0,X1)),X2))
| is_a_theorem(not(X1)) )
| ~ spl2_730 ),
inference(avatar_component_clause,[],[f45672]) ).
fof(f49238,plain,
( spl2_769
| ~ spl2_23
| ~ spl2_125
| ~ spl2_141 ),
inference(avatar_split_clause,[],[f2901,f2474,f1852,f286,f49236]) ).
fof(f2901,plain,
( ! [X10,X11,X12] : strict_equiv(not(X10),and(X11,not(X12))) = and(strict_implies(implies(X11,X12),X10),strict_implies(and(X11,not(X12)),not(X10)))
| ~ spl2_23
| ~ spl2_125
| ~ spl2_141 ),
inference(forward_demodulation,[],[f2855,f287]) ).
fof(f2855,plain,
( ! [X10,X11,X12] : strict_equiv(not(X10),and(X11,not(X12))) = and(necessarily(implies(implies(X11,X12),X10)),strict_implies(and(X11,not(X12)),not(X10)))
| ~ spl2_125
| ~ spl2_141 ),
inference(superposition,[],[f2475,f1853]) ).
fof(f49234,plain,
( spl2_768
| ~ spl2_24
| ~ spl2_730 ),
inference(avatar_split_clause,[],[f46761,f45672,f290,f49232]) ).
fof(f46761,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(and(not(or(X15,X16)),X17))
| is_a_theorem(not(X16)) )
| ~ spl2_24
| ~ spl2_730 ),
inference(superposition,[],[f45673,f291]) ).
fof(f49230,plain,
( spl2_767
| ~ spl2_24
| ~ spl2_729 ),
inference(avatar_split_clause,[],[f46738,f45667,f290,f49228]) ).
fof(f49228,plain,
( spl2_767
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,not(and(X9,X10)))))
| is_a_theorem(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_767])]) ).
fof(f45667,plain,
( spl2_729
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(and(X2,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_729])]) ).
fof(f46738,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,not(and(X9,X10)))))
| is_a_theorem(X10) )
| ~ spl2_24
| ~ spl2_729 ),
inference(superposition,[],[f45668,f291]) ).
fof(f45668,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X1,not(and(X2,X0)))))
| is_a_theorem(X0) )
| ~ spl2_729 ),
inference(avatar_component_clause,[],[f45667]) ).
fof(f49226,plain,
( spl2_766
| ~ spl2_29
| ~ spl2_729 ),
inference(avatar_split_clause,[],[f46729,f45667,f315,f49224]) ).
fof(f46729,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,implies(X0,X1))))
| is_a_theorem(not(X1)) )
| ~ spl2_29
| ~ spl2_729 ),
inference(superposition,[],[f45668,f316]) ).
fof(f49222,plain,
( spl2_765
| ~ spl2_80
| ~ spl2_125 ),
inference(avatar_split_clause,[],[f2387,f1852,f856,f49220]) ).
fof(f2387,plain,
( ! [X10,X8,X9] : equiv(not(X8),and(X9,not(X10))) = and(implies(implies(X9,X10),X8),implies(and(X9,not(X10)),not(X8)))
| ~ spl2_80
| ~ spl2_125 ),
inference(superposition,[],[f857,f1853]) ).
fof(f49218,plain,
( spl2_764
| ~ spl2_24
| ~ spl2_727 ),
inference(avatar_split_clause,[],[f46564,f45382,f290,f49216]) ).
fof(f46564,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X16)))
| ~ spl2_24
| ~ spl2_727 ),
inference(superposition,[],[f45383,f291]) ).
fof(f49214,plain,
( spl2_763
| ~ spl2_29
| ~ spl2_726 ),
inference(avatar_split_clause,[],[f46533,f45378,f315,f49212]) ).
fof(f45378,plain,
( spl2_726
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,not(not(and(X2,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_726])]) ).
fof(f46533,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,not(implies(X0,X1))))
| is_a_theorem(not(X1)) )
| ~ spl2_29
| ~ spl2_726 ),
inference(superposition,[],[f45379,f316]) ).
fof(f45379,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,not(not(and(X2,X0)))))
| is_a_theorem(X0) )
| ~ spl2_726 ),
inference(avatar_component_clause,[],[f45378]) ).
fof(f49210,plain,
( spl2_762
| ~ spl2_27
| ~ spl2_724 ),
inference(avatar_split_clause,[],[f46286,f45049,f302,f49208]) ).
fof(f49208,plain,
( spl2_762
<=> ! [X6,X5] :
( is_a_theorem(not(and(X5,necessarily(not(X6)))))
| ~ is_a_theorem(possibly(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_762])]) ).
fof(f46286,plain,
( ! [X6,X5] :
( is_a_theorem(not(and(X5,necessarily(not(X6)))))
| ~ is_a_theorem(possibly(X6)) )
| ~ spl2_27
| ~ spl2_724 ),
inference(resolution,[],[f45050,f303]) ).
fof(f49206,plain,
( spl2_761
| ~ spl2_27
| ~ spl2_723 ),
inference(avatar_split_clause,[],[f46198,f45045,f302,f49204]) ).
fof(f46198,plain,
( ! [X3,X4,X5] :
( is_a_theorem(implies(and(X3,X4),X5))
| ~ is_a_theorem(implies(X4,X5)) )
| ~ spl2_27
| ~ spl2_723 ),
inference(resolution,[],[f45046,f303]) ).
fof(f49202,plain,
( spl2_760
| ~ spl2_65
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f704,f681,f602,f49200]) ).
fof(f49200,plain,
( spl2_760
<=> ! [X29,X28] :
( ~ is_a_theorem(strict_implies(necessarily(or(X28,not(X28))),strict_equiv(not(X28),X29)))
| necessarily(or(X28,not(X28))) = strict_equiv(not(X28),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_760])]) ).
fof(f704,plain,
( ! [X28,X29] :
( ~ is_a_theorem(strict_implies(necessarily(or(X28,not(X28))),strict_equiv(not(X28),X29)))
| necessarily(or(X28,not(X28))) = strict_equiv(not(X28),X29) )
| ~ spl2_65
| ~ spl2_70 ),
inference(resolution,[],[f682,f603]) ).
fof(f49198,plain,
( spl2_759
| ~ spl2_76
| ~ spl2_720 ),
inference(avatar_split_clause,[],[f45985,f44643,f810,f49196]) ).
fof(f45985,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(X11,X9))))
| ~ spl2_76
| ~ spl2_720 ),
inference(superposition,[],[f44644,f811]) ).
fof(f49194,plain,
( spl2_758
| ~ spl2_27
| ~ spl2_720 ),
inference(avatar_split_clause,[],[f45959,f44643,f302,f49192]) ).
fof(f45959,plain,
( ! [X8,X9,X7] :
( is_a_theorem(not(and(X7,X8)))
| ~ is_a_theorem(and(not(X8),X9)) )
| ~ spl2_27
| ~ spl2_720 ),
inference(resolution,[],[f44644,f303]) ).
fof(f49190,plain,
( spl2_757
| ~ spl2_34
| ~ spl2_715 ),
inference(avatar_split_clause,[],[f43250,f43093,f344,f49188]) ).
fof(f49188,plain,
( spl2_757
<=> ! [X86,X87] :
( ~ is_a_theorem(not(not(strict_equiv(X86,X87))))
| is_a_theorem(strict_implies(X87,X86)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_757])]) ).
fof(f43093,plain,
( spl2_715
<=> ! [X13,X14] :
( is_a_theorem(X13)
| ~ is_a_theorem(not(not(and(X14,X13)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_715])]) ).
fof(f43250,plain,
( ! [X86,X87] :
( ~ is_a_theorem(not(not(strict_equiv(X86,X87))))
| is_a_theorem(strict_implies(X87,X86)) )
| ~ spl2_34
| ~ spl2_715 ),
inference(superposition,[],[f43094,f345]) ).
fof(f43094,plain,
( ! [X14,X13] :
( ~ is_a_theorem(not(not(and(X14,X13))))
| is_a_theorem(X13) )
| ~ spl2_715 ),
inference(avatar_component_clause,[],[f43093]) ).
fof(f49135,plain,
( spl2_756
| ~ spl2_625
| ~ spl2_715 ),
inference(avatar_split_clause,[],[f43245,f43093,f34595,f49133]) ).
fof(f49133,plain,
( spl2_756
<=> ! [X77,X76,X75] :
( ~ is_a_theorem(not(not(and(X76,and(X75,X77)))))
| is_a_theorem(X77) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_756])]) ).
fof(f43245,plain,
( ! [X76,X77,X75] :
( ~ is_a_theorem(not(not(and(X76,and(X75,X77)))))
| is_a_theorem(X77) )
| ~ spl2_625
| ~ spl2_715 ),
inference(superposition,[],[f43094,f34596]) ).
fof(f49131,plain,
( spl2_755
| ~ spl2_24
| ~ spl2_686 ),
inference(avatar_split_clause,[],[f41380,f41208,f290,f49129]) ).
fof(f41380,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(X17,not(or(X15,X16))),not(X15)))
| ~ spl2_24
| ~ spl2_686 ),
inference(superposition,[],[f41209,f291]) ).
fof(f49127,plain,
( spl2_754
| ~ spl2_24
| ~ spl2_685 ),
inference(avatar_split_clause,[],[f41316,f41204,f290,f49125]) ).
fof(f49125,plain,
( spl2_754
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(and(not(or(X15,X16)),X17))
| is_a_theorem(not(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_754])]) ).
fof(f41204,plain,
( spl2_685
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(implies(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_685])]) ).
fof(f41316,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(and(not(or(X15,X16)),X17))
| is_a_theorem(not(X15)) )
| ~ spl2_24
| ~ spl2_685 ),
inference(superposition,[],[f41205,f291]) ).
fof(f41205,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(implies(X0,X1)),X2))
| is_a_theorem(X0) )
| ~ spl2_685 ),
inference(avatar_component_clause,[],[f41204]) ).
fof(f49123,plain,
( spl2_753
| ~ spl2_23
| ~ spl2_37
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f41043,f40978,f373,f286,f49121]) ).
fof(f41043,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(possibly(X10),not(and(necessarily(not(X10)),X11))))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_683 ),
inference(forward_demodulation,[],[f41033,f287]) ).
fof(f41033,plain,
( ! [X10,X11] : is_a_theorem(necessarily(implies(possibly(X10),not(and(necessarily(not(X10)),X11)))))
| ~ spl2_37
| ~ spl2_683 ),
inference(superposition,[],[f40979,f374]) ).
fof(f49068,plain,
( spl2_752
| ~ spl2_23
| ~ spl2_58
| ~ spl2_96
| ~ spl2_625
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f41039,f40978,f34595,f1122,f544,f286,f49066]) ).
fof(f41039,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X4,X6),X5)))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_96
| ~ spl2_625
| ~ spl2_683 ),
inference(forward_demodulation,[],[f41038,f1123]) ).
fof(f41038,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),not(and(not(X5),and(X4,X6)))))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_625
| ~ spl2_683 ),
inference(forward_demodulation,[],[f41037,f34596]) ).
fof(f41037,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),not(and(and(X4,not(X5)),X6))))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_683 ),
inference(forward_demodulation,[],[f41031,f287]) ).
fof(f41031,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(implies(implies(X4,X5),not(and(and(X4,not(X5)),X6)))))
| ~ spl2_58
| ~ spl2_683 ),
inference(superposition,[],[f40979,f545]) ).
fof(f49064,plain,
( spl2_751
| ~ spl2_513
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f41023,f40978,f25507,f49062]) ).
fof(f41023,plain,
( ! [X104,X103] : is_a_theorem(necessarily(or(strict_equiv(X103,X104),not(strict_equiv(X104,X103)))))
| ~ spl2_513
| ~ spl2_683 ),
inference(superposition,[],[f40979,f25508]) ).
fof(f49060,plain,
( spl2_750
| ~ spl2_34
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f41016,f40978,f344,f49058]) ).
fof(f41016,plain,
( ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X86,X87),not(strict_equiv(X86,X87)))))
| ~ spl2_34
| ~ spl2_683 ),
inference(superposition,[],[f40979,f345]) ).
fof(f48857,plain,
( spl2_749
| ~ spl2_510
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f41008,f40978,f25495,f48855]) ).
fof(f41008,plain,
( ! [X68,X69] : is_a_theorem(necessarily(or(equiv(X68,X69),not(equiv(X69,X68)))))
| ~ spl2_510
| ~ spl2_683 ),
inference(superposition,[],[f40979,f25496]) ).
fof(f48853,plain,
( spl2_748
| ~ spl2_504
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f40990,f40978,f23260,f48851]) ).
fof(f40990,plain,
( ! [X18,X19,X20] : is_a_theorem(necessarily(or(X18,not(and(X19,and(X18,X20))))))
| ~ spl2_504
| ~ spl2_683 ),
inference(superposition,[],[f40979,f23261]) ).
fof(f48849,plain,
( spl2_747
| ~ spl2_380
| ~ spl2_683 ),
inference(avatar_split_clause,[],[f40981,f40978,f13441,f48847]) ).
fof(f40981,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X0,X2))))
| ~ spl2_380
| ~ spl2_683 ),
inference(resolution,[],[f40979,f13442]) ).
fof(f48845,plain,
( spl2_746
| ~ spl2_20
| ~ spl2_670 ),
inference(avatar_split_clause,[],[f38961,f38812,f273,f48843]) ).
fof(f48843,plain,
( spl2_746
<=> ! [X0] :
( ~ is_a_theorem(not(not(not(possibly(X0)))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_746])]) ).
fof(f38812,plain,
( spl2_670
<=> ! [X0] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_670])]) ).
fof(f38961,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(not(possibly(X0)))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_670 ),
inference(superposition,[],[f38813,f274]) ).
fof(f38813,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(X0) )
| ~ spl2_670 ),
inference(avatar_component_clause,[],[f38812]) ).
fof(f48033,plain,
( spl2_745
| ~ spl2_20
| ~ spl2_669 ),
inference(avatar_split_clause,[],[f38815,f38808,f273,f48031]) ).
fof(f48031,plain,
( spl2_745
<=> ! [X0,X1] :
( ~ is_a_theorem(not(or(X1,possibly(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_745])]) ).
fof(f38808,plain,
( spl2_669
<=> ! [X6,X7] :
( ~ is_a_theorem(not(or(X6,not(X7))))
| is_a_theorem(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_669])]) ).
fof(f38815,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(or(X1,possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_669 ),
inference(superposition,[],[f38809,f274]) ).
fof(f38809,plain,
( ! [X6,X7] :
( ~ is_a_theorem(not(or(X6,not(X7))))
| is_a_theorem(X7) )
| ~ spl2_669 ),
inference(avatar_component_clause,[],[f38808]) ).
fof(f46750,plain,
( spl2_744
| ~ spl2_76
| ~ spl2_120
| ~ spl2_190
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20490,f19362,f4074,f1712,f810,f46748]) ).
fof(f46748,plain,
( spl2_744
<=> ! [X9,X7,X6,X8] :
( is_a_theorem(and(strict_implies(X6,X7),and(X8,and(strict_implies(X7,X6),X9))))
| ~ is_a_theorem(and(strict_equiv(X6,X7),X8))
| ~ is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_744])]) ).
fof(f4074,plain,
( spl2_190
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_equiv(X0,X1),X2))
| is_a_theorem(and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_190])]) ).
fof(f20490,plain,
( ! [X8,X6,X9,X7] :
( is_a_theorem(and(strict_implies(X6,X7),and(X8,and(strict_implies(X7,X6),X9))))
| ~ is_a_theorem(and(strict_equiv(X6,X7),X8))
| ~ is_a_theorem(X9) )
| ~ spl2_76
| ~ spl2_120
| ~ spl2_190
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4184,f19383]) ).
fof(f4184,plain,
( ! [X8,X6,X9,X7] :
( ~ is_a_theorem(and(strict_equiv(X6,X7),X8))
| ~ is_a_theorem(X9)
| is_a_theorem(and(strict_implies(X6,X7),and(and(strict_implies(X7,X6),X8),X9))) )
| ~ spl2_120
| ~ spl2_190 ),
inference(resolution,[],[f4075,f1713]) ).
fof(f4075,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)))
| ~ is_a_theorem(and(strict_equiv(X0,X1),X2)) )
| ~ spl2_190 ),
inference(avatar_component_clause,[],[f4074]) ).
fof(f46485,plain,
( spl2_743
| ~ spl2_76
| ~ spl2_120
| ~ spl2_192
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20452,f19362,f4124,f1712,f810,f46483]) ).
fof(f46483,plain,
( spl2_743
<=> ! [X17,X14,X16,X15] :
( is_a_theorem(and(implies(X14,X15),and(X16,and(implies(X15,X14),X17))))
| ~ is_a_theorem(and(equiv(X14,X15),X16))
| ~ is_a_theorem(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_743])]) ).
fof(f4124,plain,
( spl2_192
<=> ! [X4,X5,X3] :
( ~ is_a_theorem(and(equiv(X3,X4),X5))
| is_a_theorem(and(implies(X3,X4),and(implies(X4,X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_192])]) ).
fof(f20452,plain,
( ! [X16,X14,X17,X15] :
( is_a_theorem(and(implies(X14,X15),and(X16,and(implies(X15,X14),X17))))
| ~ is_a_theorem(and(equiv(X14,X15),X16))
| ~ is_a_theorem(X17) )
| ~ spl2_76
| ~ spl2_120
| ~ spl2_192
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4267,f19383]) ).
fof(f4267,plain,
( ! [X16,X14,X17,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| ~ is_a_theorem(X17)
| is_a_theorem(and(implies(X14,X15),and(and(implies(X15,X14),X16),X17))) )
| ~ spl2_120
| ~ spl2_192 ),
inference(resolution,[],[f4125,f1713]) ).
fof(f4125,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(implies(X3,X4),and(implies(X4,X3),X5)))
| ~ is_a_theorem(and(equiv(X3,X4),X5)) )
| ~ spl2_192 ),
inference(avatar_component_clause,[],[f4124]) ).
fof(f46196,plain,
( spl2_742
| ~ spl2_157
| ~ spl2_209 ),
inference(avatar_split_clause,[],[f4604,f4558,f2734,f46194]) ).
fof(f4604,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(equiv(not(and(X12,possibly(X13))),and(necessarily(not(X13)),not(X12))),not(equiv(X12,necessarily(not(X13))))))
| ~ spl2_157
| ~ spl2_209 ),
inference(superposition,[],[f2735,f4559]) ).
fof(f45922,plain,
( spl2_741
| ~ spl2_54
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3252,f2598,f505,f45920]) ).
fof(f45920,plain,
( spl2_741
<=> ! [X29,X27,X28,X26] : not(and(X29,possibly(strict_implies(X26,and(X27,not(X28)))))) = implies(X29,necessarily(possibly(and(X26,implies(X27,X28))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_741])]) ).
fof(f3252,plain,
( ! [X28,X29,X26,X27] : not(and(X29,possibly(strict_implies(X26,and(X27,not(X28)))))) = implies(X29,necessarily(possibly(and(X26,implies(X27,X28)))))
| ~ spl2_54
| ~ spl2_148 ),
inference(superposition,[],[f506,f2599]) ).
fof(f45845,plain,
( spl2_740
| ~ spl2_26
| ~ spl2_711 ),
inference(avatar_split_clause,[],[f44276,f42525,f298,f45843]) ).
fof(f45843,plain,
( spl2_740
<=> ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(X2,not(X3)))
| ~ is_a_theorem(not(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_740])]) ).
fof(f42525,plain,
( spl2_711
<=> ! [X2,X1] :
( ~ is_a_theorem(and(not(X1),equiv(X2,not(X1))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_711])]) ).
fof(f44276,plain,
( ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(X2,not(X3)))
| ~ is_a_theorem(not(X3)) )
| ~ spl2_26
| ~ spl2_711 ),
inference(resolution,[],[f42526,f299]) ).
fof(f42526,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(not(X1),equiv(X2,not(X1))))
| is_a_theorem(X2) )
| ~ spl2_711 ),
inference(avatar_component_clause,[],[f42525]) ).
fof(f45841,plain,
( spl2_739
| ~ spl2_77
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1957,f1558,f814,f45839]) ).
fof(f45839,plain,
( spl2_739
<=> ! [X51,X50,X49,X52] : not(and(X51,implies(X52,strict_implies(X49,necessarily(not(X50)))))) = implies(X51,and(X52,possibly(and(X49,possibly(X50))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_739])]) ).
fof(f1957,plain,
( ! [X50,X51,X49,X52] : not(and(X51,implies(X52,strict_implies(X49,necessarily(not(X50)))))) = implies(X51,and(X52,possibly(and(X49,possibly(X50)))))
| ~ spl2_77
| ~ spl2_112 ),
inference(superposition,[],[f815,f1559]) ).
fof(f45837,plain,
( spl2_738
| ~ spl2_75
| ~ spl2_709 ),
inference(avatar_split_clause,[],[f44271,f42517,f806,f45835]) ).
fof(f42517,plain,
( spl2_709
<=> ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),equiv(possibly(X0),X1)))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_709])]) ).
fof(f44271,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(possibly(X1),equiv(X2,possibly(X1))))
| is_a_theorem(X2) )
| ~ spl2_75
| ~ spl2_709 ),
inference(superposition,[],[f42518,f807]) ).
fof(f42518,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),equiv(possibly(X0),X1)))
| is_a_theorem(X1) )
| ~ spl2_709 ),
inference(avatar_component_clause,[],[f42517]) ).
fof(f45833,plain,
( spl2_737
| ~ spl2_20
| ~ spl2_708 ),
inference(avatar_split_clause,[],[f43831,f42513,f273,f45831]) ).
fof(f45831,plain,
( spl2_737
<=> ! [X0,X1] :
( ~ is_a_theorem(possibly(X0))
| ~ is_a_theorem(equiv(possibly(X0),X1))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_737])]) ).
fof(f42513,plain,
( spl2_708
<=> ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(not(X3),X2))
| ~ is_a_theorem(not(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_708])]) ).
fof(f43831,plain,
( ! [X0,X1] :
( ~ is_a_theorem(possibly(X0))
| ~ is_a_theorem(equiv(possibly(X0),X1))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_708 ),
inference(superposition,[],[f42514,f274]) ).
fof(f42514,plain,
( ! [X2,X3] :
( ~ is_a_theorem(not(X3))
| ~ is_a_theorem(equiv(not(X3),X2))
| is_a_theorem(X2) )
| ~ spl2_708 ),
inference(avatar_component_clause,[],[f42513]) ).
fof(f45829,plain,
( spl2_736
| ~ spl2_75
| ~ spl2_707 ),
inference(avatar_split_clause,[],[f43815,f42509,f806,f45827]) ).
fof(f45827,plain,
( spl2_736
<=> ! [X2,X1] :
( ~ is_a_theorem(not(implies(equiv(X2,not(X1)),X1)))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_736])]) ).
fof(f42509,plain,
( spl2_707
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(equiv(not(X1),X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_707])]) ).
fof(f43815,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(implies(equiv(X2,not(X1)),X1)))
| is_a_theorem(X2) )
| ~ spl2_75
| ~ spl2_707 ),
inference(superposition,[],[f42510,f807]) ).
fof(f42510,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(implies(equiv(not(X1),X0),X1)))
| is_a_theorem(X0) )
| ~ spl2_707 ),
inference(avatar_component_clause,[],[f42509]) ).
fof(f45825,plain,
( spl2_735
| ~ spl2_24
| ~ spl2_549
| ~ spl2_706 ),
inference(avatar_split_clause,[],[f43797,f42505,f29220,f290,f45823]) ).
fof(f42505,plain,
( spl2_706
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(and(X0,X1))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_706])]) ).
fof(f43797,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(and(X6,X7)),X8)))
| is_a_theorem(X6) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_706 ),
inference(forward_demodulation,[],[f43725,f291]) ).
fof(f43725,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(not(not(and(X6,X7))),X8))) )
| ~ spl2_549
| ~ spl2_706 ),
inference(resolution,[],[f42506,f29221]) ).
fof(f42506,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(not(and(X0,X1))),X2))
| is_a_theorem(X0) )
| ~ spl2_706 ),
inference(avatar_component_clause,[],[f42505]) ).
fof(f45821,plain,
( spl2_734
| ~ spl2_77
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1479,f1462,f814,f45819]) ).
fof(f45819,plain,
( spl2_734
<=> ! [X6,X4,X5] :
( ~ is_a_theorem(not(and(X4,implies(X5,X6))))
| ~ is_a_theorem(implies(and(X5,not(X6)),X4))
| and(X5,not(X6)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_734])]) ).
fof(f1462,plain,
( spl2_106
<=> ! [X4,X5] :
( ~ is_a_theorem(implies(X4,X5))
| ~ is_a_theorem(implies(X5,X4))
| X4 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_106])]) ).
fof(f1479,plain,
( ! [X6,X4,X5] :
( ~ is_a_theorem(not(and(X4,implies(X5,X6))))
| ~ is_a_theorem(implies(and(X5,not(X6)),X4))
| and(X5,not(X6)) = X4 )
| ~ spl2_77
| ~ spl2_106 ),
inference(superposition,[],[f1463,f815]) ).
fof(f1463,plain,
( ! [X4,X5] :
( ~ is_a_theorem(implies(X5,X4))
| ~ is_a_theorem(implies(X4,X5))
| X4 = X5 )
| ~ spl2_106 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f45817,plain,
( spl2_733
| ~ spl2_550
| ~ spl2_706 ),
inference(avatar_split_clause,[],[f43723,f42505,f29224,f45815]) ).
fof(f43723,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(and(X0,X2))))) )
| ~ spl2_550
| ~ spl2_706 ),
inference(resolution,[],[f42506,f29225]) ).
fof(f45813,plain,
( spl2_732
| ~ spl2_24
| ~ spl2_704 ),
inference(avatar_split_clause,[],[f43331,f42497,f290,f45811]) ).
fof(f43331,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X16)))
| ~ spl2_24
| ~ spl2_704 ),
inference(superposition,[],[f42498,f291]) ).
fof(f45809,plain,
( spl2_731
| ~ spl2_24
| ~ spl2_549
| ~ spl2_703 ),
inference(avatar_split_clause,[],[f43091,f42493,f29220,f290,f45807]) ).
fof(f42493,plain,
( spl2_703
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(and(X1,X0))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_703])]) ).
fof(f43091,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(and(X7,X6)),X8)))
| is_a_theorem(X6) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_703 ),
inference(forward_demodulation,[],[f43019,f291]) ).
fof(f43019,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(not(not(and(X7,X6))),X8))) )
| ~ spl2_549
| ~ spl2_703 ),
inference(resolution,[],[f42494,f29221]) ).
fof(f42494,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(not(and(X1,X0))),X2))
| is_a_theorem(X0) )
| ~ spl2_703 ),
inference(avatar_component_clause,[],[f42493]) ).
fof(f45674,plain,
( spl2_730
| ~ spl2_29
| ~ spl2_703 ),
inference(avatar_split_clause,[],[f43065,f42493,f315,f45672]) ).
fof(f43065,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(implies(X0,X1)),X2))
| is_a_theorem(not(X1)) )
| ~ spl2_29
| ~ spl2_703 ),
inference(superposition,[],[f42494,f316]) ).
fof(f45670,plain,
( spl2_387
| spl2_715
| ~ spl2_26
| ~ spl2_703 ),
inference(avatar_split_clause,[],[f43018,f42493,f298,f43093,f14075]) ).
fof(f43018,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(X4)
| ~ is_a_theorem(not(not(and(X5,X3)))) )
| ~ spl2_26
| ~ spl2_703 ),
inference(resolution,[],[f42494,f299]) ).
fof(f45669,plain,
( spl2_729
| ~ spl2_550
| ~ spl2_703 ),
inference(avatar_split_clause,[],[f43017,f42493,f29224,f45667]) ).
fof(f43017,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(and(X2,X0))))) )
| ~ spl2_550
| ~ spl2_703 ),
inference(resolution,[],[f42494,f29225]) ).
fof(f45665,plain,
( spl2_728
| ~ spl2_27
| ~ spl2_699 ),
inference(avatar_split_clause,[],[f42809,f42477,f302,f45663]) ).
fof(f45663,plain,
( spl2_728
<=> ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,not(not(and(X0,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_728])]) ).
fof(f42809,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,not(not(and(X0,X2))))) )
| ~ spl2_27
| ~ spl2_699 ),
inference(resolution,[],[f42478,f303]) ).
fof(f45384,plain,
( spl2_727
| ~ spl2_29
| ~ spl2_698 ),
inference(avatar_split_clause,[],[f42772,f42473,f315,f45382]) ).
fof(f42772,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(implies(X0,X1))),not(X1)))
| ~ spl2_29
| ~ spl2_698 ),
inference(superposition,[],[f42474,f316]) ).
fof(f45380,plain,
( spl2_726
| ~ spl2_27
| ~ spl2_698 ),
inference(avatar_split_clause,[],[f42698,f42473,f302,f45378]) ).
fof(f42698,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,not(not(and(X2,X0))))) )
| ~ spl2_27
| ~ spl2_698 ),
inference(resolution,[],[f42474,f303]) ).
fof(f45376,plain,
( spl2_725
| ~ spl2_24
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41155,f41048,f290,f45374]) ).
fof(f41155,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(not(or(X15,X16)),X17),not(X15)))
| ~ spl2_24
| ~ spl2_684 ),
inference(superposition,[],[f41049,f291]) ).
fof(f45051,plain,
( spl2_724
| ~ spl2_23
| ~ spl2_37
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40973,f40362,f373,f286,f45049]) ).
fof(f40973,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(possibly(X10),not(and(X11,necessarily(not(X10))))))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_682 ),
inference(forward_demodulation,[],[f40965,f287]) ).
fof(f40965,plain,
( ! [X10,X11] : is_a_theorem(necessarily(implies(possibly(X10),not(and(X11,necessarily(not(X10)))))))
| ~ spl2_37
| ~ spl2_682 ),
inference(superposition,[],[f40363,f374]) ).
fof(f45047,plain,
( spl2_723
| ~ spl2_23
| ~ spl2_58
| ~ spl2_96
| ~ spl2_517
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40970,f40362,f26955,f1122,f544,f286,f45045]) ).
fof(f40970,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),implies(and(X6,X4),X5)))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_96
| ~ spl2_517
| ~ spl2_682 ),
inference(forward_demodulation,[],[f40969,f27370]) ).
fof(f40969,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(implies(X4,X5),not(and(X6,and(X4,not(X5))))))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_682 ),
inference(forward_demodulation,[],[f40963,f287]) ).
fof(f40963,plain,
( ! [X6,X4,X5] : is_a_theorem(necessarily(implies(implies(X4,X5),not(and(X6,and(X4,not(X5)))))))
| ~ spl2_58
| ~ spl2_682 ),
inference(superposition,[],[f40363,f545]) ).
fof(f45043,plain,
( spl2_722
| ~ spl2_34
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40948,f40362,f344,f45041]) ).
fof(f40948,plain,
( ! [X86,X87] : is_a_theorem(necessarily(or(strict_implies(X87,X86),not(strict_equiv(X86,X87)))))
| ~ spl2_34
| ~ spl2_682 ),
inference(superposition,[],[f40363,f345]) ).
fof(f45039,plain,
( spl2_721
| ~ spl2_625
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40943,f40362,f34595,f45037]) ).
fof(f40943,plain,
( ! [X76,X77,X75] : is_a_theorem(necessarily(or(X77,not(and(X76,and(X75,X77))))))
| ~ spl2_625
| ~ spl2_682 ),
inference(superposition,[],[f40363,f34596]) ).
fof(f44645,plain,
( spl2_720
| ~ spl2_380
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40913,f40362,f13441,f44643]) ).
fof(f40913,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X0),X1),not(and(X2,X0))))
| ~ spl2_380
| ~ spl2_682 ),
inference(resolution,[],[f40363,f13442]) ).
fof(f44641,plain,
( spl2_719
| ~ spl2_20
| ~ spl2_668 ),
inference(avatar_split_clause,[],[f38784,f38600,f273,f44639]) ).
fof(f44639,plain,
( spl2_719
<=> ! [X0,X1] :
( ~ is_a_theorem(not(or(possibly(X0),X1)))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_719])]) ).
fof(f38600,plain,
( spl2_668
<=> ! [X4,X5] :
( ~ is_a_theorem(not(or(not(X4),X5)))
| is_a_theorem(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_668])]) ).
fof(f38784,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(or(possibly(X0),X1)))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_668 ),
inference(superposition,[],[f38601,f274]) ).
fof(f38601,plain,
( ! [X4,X5] :
( ~ is_a_theorem(not(or(not(X4),X5)))
| is_a_theorem(X4) )
| ~ spl2_668 ),
inference(avatar_component_clause,[],[f38600]) ).
fof(f44637,plain,
( spl2_718
| ~ spl2_20
| ~ spl2_667 ),
inference(avatar_split_clause,[],[f38633,f38354,f273,f44635]) ).
fof(f44635,plain,
( spl2_718
<=> ! [X0,X1] :
( ~ is_a_theorem(and(X1,not(possibly(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_718])]) ).
fof(f38354,plain,
( spl2_667
<=> ! [X2,X1] :
( ~ is_a_theorem(and(X2,not(not(X1))))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_667])]) ).
fof(f38633,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X1,not(possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_667 ),
inference(superposition,[],[f38355,f274]) ).
fof(f38355,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(X2,not(not(X1))))
| is_a_theorem(X1) )
| ~ spl2_667 ),
inference(avatar_component_clause,[],[f38354]) ).
fof(f44353,plain,
( spl2_717
| ~ spl2_20
| ~ spl2_666 ),
inference(avatar_split_clause,[],[f38603,f38350,f273,f44351]) ).
fof(f44351,plain,
( spl2_717
<=> ! [X0,X1] :
( ~ is_a_theorem(not(implies(X1,possibly(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_717])]) ).
fof(f38350,plain,
( spl2_666
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_666])]) ).
fof(f38603,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(implies(X1,possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_666 ),
inference(superposition,[],[f38351,f274]) ).
fof(f38351,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(implies(X1,not(X0))))
| is_a_theorem(X0) )
| ~ spl2_666 ),
inference(avatar_component_clause,[],[f38350]) ).
fof(f43268,plain,
( spl2_716
| ~ spl2_76
| ~ spl2_715 ),
inference(avatar_split_clause,[],[f43217,f43093,f810,f43266]) ).
fof(f43217,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(not(and(X2,X1))))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_715 ),
inference(superposition,[],[f43094,f811]) ).
fof(f43095,plain,
( spl2_715
| ~ spl2_451
| ~ spl2_703 ),
inference(avatar_split_clause,[],[f43021,f42493,f16617,f43093]) ).
fof(f43021,plain,
( ! [X14,X13] :
( is_a_theorem(X13)
| ~ is_a_theorem(not(not(and(X14,X13)))) )
| ~ spl2_451
| ~ spl2_703 ),
inference(resolution,[],[f42494,f16618]) ).
fof(f42936,plain,
( spl2_714
| ~ spl2_104
| ~ spl2_170 ),
inference(avatar_split_clause,[],[f3673,f2786,f1388,f42934]) ).
fof(f42934,plain,
( spl2_714
<=> ! [X13,X14] : is_a_theorem(strict_implies(equiv(not(X13),necessarily(not(X14))),and(implies(possibly(X14),X13),equiv(necessarily(not(X14)),not(X13))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_714])]) ).
fof(f3673,plain,
( ! [X14,X13] : is_a_theorem(strict_implies(equiv(not(X13),necessarily(not(X14))),and(implies(possibly(X14),X13),equiv(necessarily(not(X14)),not(X13)))))
| ~ spl2_104
| ~ spl2_170 ),
inference(superposition,[],[f2787,f1389]) ).
fof(f42578,plain,
( spl2_713
| ~ spl2_104
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3273,f2598,f1388,f42576]) ).
fof(f42576,plain,
( spl2_713
<=> ! [X112,X110,X111,X109] : implies(possibly(strict_implies(X109,and(X110,not(X111)))),X112) = or(X112,necessarily(possibly(and(X109,implies(X110,X111))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_713])]) ).
fof(f3273,plain,
( ! [X111,X109,X112,X110] : implies(possibly(strict_implies(X109,and(X110,not(X111)))),X112) = or(X112,necessarily(possibly(and(X109,implies(X110,X111)))))
| ~ spl2_104
| ~ spl2_148 ),
inference(superposition,[],[f1389,f2599]) ).
fof(f42531,plain,
( spl2_712
| ~ spl2_75
| ~ spl2_680 ),
inference(avatar_split_clause,[],[f42377,f39536,f806,f42529]) ).
fof(f42377,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(possibly(X1),equiv(X2,possibly(X1))),X2))
| ~ spl2_75
| ~ spl2_680 ),
inference(superposition,[],[f39537,f807]) ).
fof(f42527,plain,
( spl2_711
| ~ spl2_75
| ~ spl2_679 ),
inference(avatar_split_clause,[],[f42332,f39532,f806,f42525]) ).
fof(f39532,plain,
( spl2_679
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),equiv(not(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_679])]) ).
fof(f42332,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(not(X1),equiv(X2,not(X1))))
| is_a_theorem(X2) )
| ~ spl2_75
| ~ spl2_679 ),
inference(superposition,[],[f39533,f807]) ).
fof(f39533,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(X1),equiv(not(X1),X0)))
| is_a_theorem(X0) )
| ~ spl2_679 ),
inference(avatar_component_clause,[],[f39532]) ).
fof(f42523,plain,
( spl2_710
| ~ spl2_38
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3251,f2598,f377,f42521]) ).
fof(f42521,plain,
( spl2_710
<=> ! [X24,X23,X25,X22] : not(strict_implies(X25,strict_implies(X22,and(X23,not(X24))))) = possibly(and(X25,possibly(and(X22,implies(X23,X24))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_710])]) ).
fof(f3251,plain,
( ! [X24,X22,X25,X23] : not(strict_implies(X25,strict_implies(X22,and(X23,not(X24))))) = possibly(and(X25,possibly(and(X22,implies(X23,X24)))))
| ~ spl2_38
| ~ spl2_148 ),
inference(superposition,[],[f378,f2599]) ).
fof(f42519,plain,
( spl2_709
| ~ spl2_20
| ~ spl2_679 ),
inference(avatar_split_clause,[],[f42315,f39532,f273,f42517]) ).
fof(f42315,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),equiv(possibly(X0),X1)))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_679 ),
inference(superposition,[],[f39533,f274]) ).
fof(f42515,plain,
( spl2_708
| ~ spl2_26
| ~ spl2_679 ),
inference(avatar_split_clause,[],[f42314,f39532,f298,f42513]) ).
fof(f42314,plain,
( ! [X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equiv(not(X3),X2))
| ~ is_a_theorem(not(X3)) )
| ~ spl2_26
| ~ spl2_679 ),
inference(resolution,[],[f39533,f299]) ).
fof(f42511,plain,
( spl2_707
| ~ spl2_550
| ~ spl2_679 ),
inference(avatar_split_clause,[],[f42313,f39532,f29224,f42509]) ).
fof(f42313,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(equiv(not(X1),X0),X1))) )
| ~ spl2_550
| ~ spl2_679 ),
inference(resolution,[],[f39533,f29225]) ).
fof(f42507,plain,
( spl2_706
| ~ spl2_27
| ~ spl2_675 ),
inference(avatar_split_clause,[],[f41880,f39385,f302,f42505]) ).
fof(f41880,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(and(X0,X1))),X2)) )
| ~ spl2_27
| ~ spl2_675 ),
inference(resolution,[],[f39386,f303]) ).
fof(f42503,plain,
( spl2_705
| ~ spl2_37
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3250,f2598,f373,f42501]) ).
fof(f42501,plain,
( spl2_705
<=> ! [X18,X19,X20,X21] : implies(possibly(strict_implies(X18,and(X19,not(X20)))),X21) = or(necessarily(possibly(and(X18,implies(X19,X20)))),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_705])]) ).
fof(f3250,plain,
( ! [X21,X18,X19,X20] : implies(possibly(strict_implies(X18,and(X19,not(X20)))),X21) = or(necessarily(possibly(and(X18,implies(X19,X20)))),X21)
| ~ spl2_37
| ~ spl2_148 ),
inference(superposition,[],[f374,f2599]) ).
fof(f42499,plain,
( spl2_704
| ~ spl2_29
| ~ spl2_674 ),
inference(avatar_split_clause,[],[f40314,f39381,f315,f42497]) ).
fof(f40314,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(implies(X0,X1)),X2),not(X1)))
| ~ spl2_29
| ~ spl2_674 ),
inference(superposition,[],[f39382,f316]) ).
fof(f42495,plain,
( spl2_703
| ~ spl2_27
| ~ spl2_674 ),
inference(avatar_split_clause,[],[f40241,f39381,f302,f42493]) ).
fof(f40241,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(and(X1,X0))),X2)) )
| ~ spl2_27
| ~ spl2_674 ),
inference(resolution,[],[f39382,f303]) ).
fof(f42491,plain,
( spl2_702
| ~ spl2_249
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39168,f39162,f6955,f42489]) ).
fof(f42489,plain,
( spl2_702
<=> ! [X4] :
( is_a_theorem(X4)
| ~ is_a_theorem(and(not(X4),equiv(X4,not(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_702])]) ).
fof(f39168,plain,
( ! [X4] :
( is_a_theorem(X4)
| ~ is_a_theorem(and(not(X4),equiv(X4,not(X4)))) )
| ~ spl2_249
| ~ spl2_672 ),
inference(resolution,[],[f39163,f6956]) ).
fof(f42487,plain,
( spl2_701
| ~ spl2_112
| ~ spl2_125 ),
inference(avatar_split_clause,[],[f2375,f1852,f1558,f42485]) ).
fof(f42485,plain,
( spl2_701
<=> ! [X11,X14,X13,X12] : implies(implies(X14,strict_implies(X11,necessarily(not(X12)))),X13) = or(X13,and(X14,possibly(and(X11,possibly(X12))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_701])]) ).
fof(f2375,plain,
( ! [X11,X14,X12,X13] : implies(implies(X14,strict_implies(X11,necessarily(not(X12)))),X13) = or(X13,and(X14,possibly(and(X11,possibly(X12)))))
| ~ spl2_112
| ~ spl2_125 ),
inference(superposition,[],[f1853,f1559]) ).
fof(f42483,plain,
( spl2_700
| ~ spl2_20
| ~ spl2_665 ),
inference(avatar_split_clause,[],[f38307,f37546,f273,f42481]) ).
fof(f38307,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X1,not(possibly(X0))),necessarily(not(X0))))
| ~ spl2_20
| ~ spl2_665 ),
inference(superposition,[],[f37547,f274]) ).
fof(f42479,plain,
( spl2_699
| ~ spl2_136
| ~ spl2_665 ),
inference(avatar_split_clause,[],[f38294,f37546,f2344,f42477]) ).
fof(f38294,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(X43,not(not(and(X44,X45)))),X44))
| ~ spl2_136
| ~ spl2_665 ),
inference(resolution,[],[f37547,f2345]) ).
fof(f42475,plain,
( spl2_698
| ~ spl2_152
| ~ spl2_665 ),
inference(avatar_split_clause,[],[f38293,f37546,f2665,f42473]) ).
fof(f38293,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(X40,not(not(and(X41,X42)))),X42))
| ~ spl2_152
| ~ spl2_665 ),
inference(resolution,[],[f37547,f2666]) ).
fof(f42471,plain,
( spl2_697
| ~ spl2_517
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38269,f37542,f26955,f42469]) ).
fof(f37542,plain,
( spl2_664
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_664])]) ).
fof(f38269,plain,
( ! [X28,X29,X27] :
( ~ is_a_theorem(and(X28,and(X29,not(not(X27)))))
| is_a_theorem(X27) )
| ~ spl2_517
| ~ spl2_664 ),
inference(superposition,[],[f37543,f26956]) ).
fof(f37543,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(not(X0)),X1))
| is_a_theorem(X0) )
| ~ spl2_664 ),
inference(avatar_component_clause,[],[f37542]) ).
fof(f42467,plain,
( spl2_696
| ~ spl2_58
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1950,f1558,f544,f42465]) ).
fof(f42465,plain,
( spl2_696
<=> ! [X31,X29,X28,X30] : implies(implies(X30,strict_implies(X28,necessarily(not(X29)))),X31) = or(and(X30,possibly(and(X28,possibly(X29)))),X31) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_696])]) ).
fof(f1950,plain,
( ! [X31,X28,X29,X30] : implies(implies(X30,strict_implies(X28,necessarily(not(X29)))),X31) = or(and(X30,possibly(and(X28,possibly(X29)))),X31)
| ~ spl2_58
| ~ spl2_112 ),
inference(superposition,[],[f545,f1559]) ).
fof(f42463,plain,
( spl2_695
| ~ spl2_504
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38266,f37542,f23260,f42461]) ).
fof(f38266,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(and(X19,and(not(not(X18)),X20)))
| is_a_theorem(X18) )
| ~ spl2_504
| ~ spl2_664 ),
inference(superposition,[],[f37543,f23261]) ).
fof(f42459,plain,
( spl2_694
| ~ spl2_20
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38244,f37542,f273,f42457]) ).
fof(f42457,plain,
( spl2_694
<=> ! [X0,X1] :
( ~ is_a_theorem(and(not(possibly(X0)),X1))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_694])]) ).
fof(f38244,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(possibly(X0)),X1))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_664 ),
inference(superposition,[],[f37543,f274]) ).
fof(f42390,plain,
( spl2_693
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1938,f1558,f42388]) ).
fof(f42388,plain,
( spl2_693
<=> ! [X9,X8,X10] : possibly(and(X10,possibly(strict_implies(X8,necessarily(not(X9)))))) = not(strict_implies(X10,necessarily(possibly(and(X8,possibly(X9)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_693])]) ).
fof(f1938,plain,
( ! [X10,X8,X9] : possibly(and(X10,possibly(strict_implies(X8,necessarily(not(X9)))))) = not(strict_implies(X10,necessarily(possibly(and(X8,possibly(X9))))))
| ~ spl2_112 ),
inference(superposition,[],[f1559,f1559]) ).
fof(f42109,plain,
( spl2_692
| ~ spl2_60
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f703,f681,f558,f42107]) ).
fof(f42107,plain,
( spl2_692
<=> ! [X27,X26] :
( ~ is_a_theorem(strict_implies(necessarily(or(X26,X27)),strict_equiv(not(X26),X27)))
| necessarily(or(X26,X27)) = strict_equiv(not(X26),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_692])]) ).
fof(f703,plain,
( ! [X26,X27] :
( ~ is_a_theorem(strict_implies(necessarily(or(X26,X27)),strict_equiv(not(X26),X27)))
| necessarily(or(X26,X27)) = strict_equiv(not(X26),X27) )
| ~ spl2_60
| ~ spl2_70 ),
inference(resolution,[],[f682,f559]) ).
fof(f41680,plain,
( spl2_691
| ~ spl2_83
| ~ spl2_689 ),
inference(avatar_split_clause,[],[f41664,f41517,f1024,f41678]) ).
fof(f41664,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(implies(X0,X1)))))
| is_a_theorem(X0) )
| ~ spl2_83
| ~ spl2_689 ),
inference(superposition,[],[f41518,f1025]) ).
fof(f41676,plain,
( spl2_690
| ~ spl2_24
| ~ spl2_687 ),
inference(avatar_split_clause,[],[f41535,f41419,f290,f41674]) ).
fof(f41535,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,implies(X9,X10))))
| is_a_theorem(X9) )
| ~ spl2_24
| ~ spl2_687 ),
inference(superposition,[],[f41420,f291]) ).
fof(f41519,plain,
( spl2_689
| ~ spl2_24
| ~ spl2_549
| ~ spl2_685 ),
inference(avatar_split_clause,[],[f41344,f41204,f29220,f290,f41517]) ).
fof(f41344,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(implies(X6,X7),X8)))
| is_a_theorem(X6) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_685 ),
inference(forward_demodulation,[],[f41308,f291]) ).
fof(f41308,plain,
( ! [X8,X6,X7] :
( is_a_theorem(X6)
| ~ is_a_theorem(not(implies(not(implies(X6,X7)),X8))) )
| ~ spl2_549
| ~ spl2_685 ),
inference(resolution,[],[f41205,f29221]) ).
fof(f41425,plain,
( spl2_688
| ~ spl2_76
| ~ spl2_685 ),
inference(avatar_split_clause,[],[f41326,f41204,f810,f41423]) ).
fof(f41326,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,not(implies(X2,X3))))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_685 ),
inference(superposition,[],[f41205,f811]) ).
fof(f41421,plain,
( spl2_687
| ~ spl2_550
| ~ spl2_685 ),
inference(avatar_split_clause,[],[f41306,f41204,f29224,f41419]) ).
fof(f41306,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,implies(X0,X2)))) )
| ~ spl2_550
| ~ spl2_685 ),
inference(resolution,[],[f41205,f29225]) ).
fof(f41210,plain,
( spl2_686
| ~ spl2_76
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41165,f41048,f810,f41208]) ).
fof(f41165,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,not(implies(X2,X3))),X2))
| ~ spl2_76
| ~ spl2_684 ),
inference(superposition,[],[f41049,f811]) ).
fof(f41206,plain,
( spl2_685
| ~ spl2_27
| ~ spl2_684 ),
inference(avatar_split_clause,[],[f41120,f41048,f302,f41204]) ).
fof(f41120,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(implies(X0,X1)),X2)) )
| ~ spl2_27
| ~ spl2_684 ),
inference(resolution,[],[f41049,f303]) ).
fof(f41050,plain,
( spl2_684
| ~ spl2_96
| ~ spl2_674 ),
inference(avatar_split_clause,[],[f40319,f39381,f1122,f41048]) ).
fof(f40319,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(not(implies(X20,X19)),X21),X20))
| ~ spl2_96
| ~ spl2_674 ),
inference(superposition,[],[f39382,f1123]) ).
fof(f40980,plain,
( spl2_683
| ~ spl2_76
| ~ spl2_682 ),
inference(avatar_split_clause,[],[f40915,f40362,f810,f40978]) ).
fof(f40915,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(X2,not(and(X2,X1)))))
| ~ spl2_76
| ~ spl2_682 ),
inference(superposition,[],[f40363,f811]) ).
fof(f40364,plain,
( spl2_682
| ~ spl2_33
| ~ spl2_72
| ~ spl2_97
| ~ spl2_674 ),
inference(avatar_split_clause,[],[f40354,f39381,f1233,f748,f340,f40362]) ).
fof(f40354,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X1,not(and(X0,X1)))))
| ~ spl2_33
| ~ spl2_72
| ~ spl2_97
| ~ spl2_674 ),
inference(forward_demodulation,[],[f40353,f1234]) ).
fof(f40353,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(not(and(X0,X1)),X1)))
| ~ spl2_33
| ~ spl2_72
| ~ spl2_674 ),
inference(forward_demodulation,[],[f40321,f341]) ).
fof(f40321,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(not(not(and(X0,X1))),X1))
| ~ spl2_72
| ~ spl2_674 ),
inference(superposition,[],[f39382,f749]) ).
fof(f40240,plain,
( spl2_681
| ~ spl2_75
| ~ spl2_671 ),
inference(avatar_split_clause,[],[f39024,f38976,f806,f40238]) ).
fof(f39024,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(not(X1),equiv(X2,not(X1))),X2))
| ~ spl2_75
| ~ spl2_671 ),
inference(superposition,[],[f38977,f807]) ).
fof(f39538,plain,
( spl2_680
| ~ spl2_20
| ~ spl2_671 ),
inference(avatar_split_clause,[],[f39009,f38976,f273,f39536]) ).
fof(f39009,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),equiv(possibly(X0),X1)),X1))
| ~ spl2_20
| ~ spl2_671 ),
inference(superposition,[],[f38977,f274]) ).
fof(f39534,plain,
( spl2_679
| ~ spl2_27
| ~ spl2_671 ),
inference(avatar_split_clause,[],[f38979,f38976,f302,f39532]) ).
fof(f38979,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),equiv(not(X1),X0))) )
| ~ spl2_27
| ~ spl2_671 ),
inference(resolution,[],[f38977,f303]) ).
fof(f39530,plain,
( spl2_678
| ~ spl2_517
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37514,f37227,f26955,f39528]) ).
fof(f37514,plain,
( ! [X28,X29,X27] : is_a_theorem(strict_implies(and(X28,and(X29,not(not(X27)))),X27))
| ~ spl2_517
| ~ spl2_663 ),
inference(superposition,[],[f37228,f26956]) ).
fof(f39526,plain,
( spl2_677
| ~ spl2_504
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37511,f37227,f23260,f39524]) ).
fof(f37511,plain,
( ! [X18,X19,X20] : is_a_theorem(strict_implies(and(X19,and(not(not(X18)),X20)),X18))
| ~ spl2_504
| ~ spl2_663 ),
inference(superposition,[],[f37228,f23261]) ).
fof(f39391,plain,
( spl2_676
| ~ spl2_20
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37490,f37227,f273,f39389]) ).
fof(f37490,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(possibly(X0)),X1),necessarily(not(X0))))
| ~ spl2_20
| ~ spl2_663 ),
inference(superposition,[],[f37228,f274]) ).
fof(f39387,plain,
( spl2_675
| ~ spl2_136
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37477,f37227,f2344,f39385]) ).
fof(f37477,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(not(and(X43,X44))),X45),X43))
| ~ spl2_136
| ~ spl2_663 ),
inference(resolution,[],[f37228,f2345]) ).
fof(f39383,plain,
( spl2_674
| ~ spl2_152
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37476,f37227,f2665,f39381]) ).
fof(f37476,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(not(and(X40,X41))),X42),X41))
| ~ spl2_152
| ~ spl2_663 ),
inference(resolution,[],[f37228,f2666]) ).
fof(f39226,plain,
( spl2_673
| ~ spl2_27
| ~ spl2_672 ),
inference(avatar_split_clause,[],[f39165,f39162,f302,f39224]) ).
fof(f39165,plain,
( ! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,not(X0))) )
| ~ spl2_27
| ~ spl2_672 ),
inference(resolution,[],[f39163,f303]) ).
fof(f39164,plain,
( spl2_672
| ~ spl2_126
| ~ spl2_655
| ~ spl2_671 ),
inference(avatar_split_clause,[],[f39037,f38976,f37077,f1856,f39162]) ).
fof(f39037,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(X0,not(X0)),X0))
| ~ spl2_126
| ~ spl2_655
| ~ spl2_671 ),
inference(forward_demodulation,[],[f39028,f37078]) ).
fof(f39028,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(not(X0),X0),X0))
| ~ spl2_126
| ~ spl2_671 ),
inference(superposition,[],[f38977,f1857]) ).
fof(f38978,plain,
( spl2_671
| ~ spl2_80
| ~ spl2_654 ),
inference(avatar_split_clause,[],[f37165,f37073,f856,f38976]) ).
fof(f37165,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),equiv(not(X0),X1)),X1))
| ~ spl2_80
| ~ spl2_654 ),
inference(superposition,[],[f37074,f857]) ).
fof(f38814,plain,
( spl2_670
| ~ spl2_83
| ~ spl2_668 ),
inference(avatar_split_clause,[],[f38798,f38600,f1024,f38812]) ).
fof(f38798,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(X0) )
| ~ spl2_83
| ~ spl2_668 ),
inference(superposition,[],[f38601,f1025]) ).
fof(f38810,plain,
( spl2_669
| ~ spl2_24
| ~ spl2_666 ),
inference(avatar_split_clause,[],[f38619,f38350,f290,f38808]) ).
fof(f38619,plain,
( ! [X6,X7] :
( ~ is_a_theorem(not(or(X6,not(X7))))
| is_a_theorem(X7) )
| ~ spl2_24
| ~ spl2_666 ),
inference(superposition,[],[f38351,f291]) ).
fof(f38602,plain,
( spl2_668
| ~ spl2_24
| ~ spl2_549
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38277,f37542,f29220,f290,f38600]) ).
fof(f38277,plain,
( ! [X4,X5] :
( ~ is_a_theorem(not(or(not(X4),X5)))
| is_a_theorem(X4) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_664 ),
inference(forward_demodulation,[],[f38240,f291]) ).
fof(f38240,plain,
( ! [X4,X5] :
( is_a_theorem(X4)
| ~ is_a_theorem(not(implies(not(not(X4)),X5))) )
| ~ spl2_549
| ~ spl2_664 ),
inference(resolution,[],[f37543,f29221]) ).
fof(f38356,plain,
( spl2_667
| ~ spl2_76
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38259,f37542,f810,f38354]) ).
fof(f38259,plain,
( ! [X2,X1] :
( ~ is_a_theorem(and(X2,not(not(X1))))
| is_a_theorem(X1) )
| ~ spl2_76
| ~ spl2_664 ),
inference(superposition,[],[f37543,f811]) ).
fof(f38352,plain,
( spl2_666
| ~ spl2_550
| ~ spl2_664 ),
inference(avatar_split_clause,[],[f38238,f37542,f29224,f38350]) ).
fof(f38238,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(implies(X1,not(X0)))) )
| ~ spl2_550
| ~ spl2_664 ),
inference(resolution,[],[f37543,f29225]) ).
fof(f37548,plain,
( spl2_665
| ~ spl2_76
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37504,f37227,f810,f37546]) ).
fof(f37504,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X2,not(not(X1))),X1))
| ~ spl2_76
| ~ spl2_663 ),
inference(superposition,[],[f37228,f811]) ).
fof(f37544,plain,
( spl2_664
| ~ spl2_27
| ~ spl2_663 ),
inference(avatar_split_clause,[],[f37461,f37227,f302,f37542]) ).
fof(f37461,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(not(X0)),X1)) )
| ~ spl2_27
| ~ spl2_663 ),
inference(resolution,[],[f37228,f303]) ).
fof(f37229,plain,
( spl2_663
| ~ spl2_83
| ~ spl2_126
| ~ spl2_654 ),
inference(avatar_split_clause,[],[f37210,f37073,f1856,f1024,f37227]) ).
fof(f37210,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))
| ~ spl2_83
| ~ spl2_126
| ~ spl2_654 ),
inference(forward_demodulation,[],[f37150,f1857]) ).
fof(f37150,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),and(not(not(X0)),X1)),X0))
| ~ spl2_83
| ~ spl2_654 ),
inference(superposition,[],[f37074,f1025]) ).
fof(f37107,plain,
( spl2_662
| ~ spl2_249
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27717,f27681,f6955,f37105]) ).
fof(f37105,plain,
( spl2_662
<=> ! [X7,X8] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),or(X7,and(X7,X8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_662])]) ).
fof(f27717,plain,
( ! [X8,X7] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(not(X7),or(X7,and(X7,X8)))) )
| ~ spl2_249
| ~ spl2_520 ),
inference(resolution,[],[f27682,f6956]) ).
fof(f37103,plain,
( spl2_661
| ~ spl2_384
| ~ spl2_517 ),
inference(avatar_split_clause,[],[f27383,f26955,f13659,f37101]) ).
fof(f37101,plain,
( spl2_661
<=> ! [X464,X465,X463,X462] :
( ~ is_a_theorem(and(X463,and(X464,not(X462))))
| is_a_theorem(implies(X462,X465)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_661])]) ).
fof(f13659,plain,
( spl2_384
<=> ! [X18,X17,X19] :
( is_a_theorem(implies(X17,X18))
| ~ is_a_theorem(and(not(X17),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_384])]) ).
fof(f27383,plain,
( ! [X465,X463,X464,X462] :
( ~ is_a_theorem(and(X463,and(X464,not(X462))))
| is_a_theorem(implies(X462,X465)) )
| ~ spl2_384
| ~ spl2_517 ),
inference(superposition,[],[f13660,f26956]) ).
fof(f13660,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(not(X17),X19))
| is_a_theorem(implies(X17,X18)) )
| ~ spl2_384 ),
inference(avatar_component_clause,[],[f13659]) ).
fof(f37099,plain,
( spl2_660
| ~ spl2_122
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24670,f23260,f6149,f2474,f1831,f37097]) ).
fof(f37097,plain,
( spl2_660
<=> ! [X9,X7,X6,X8] :
( ~ is_a_theorem(strict_implies(X6,and(X7,strict_equiv(not(X9),X8))))
| is_a_theorem(strict_implies(X6,and(X7,strict_equiv(X8,not(X9))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_660])]) ).
fof(f24670,plain,
( ! [X8,X6,X9,X7] :
( ~ is_a_theorem(strict_implies(X6,and(X7,strict_equiv(not(X9),X8))))
| is_a_theorem(strict_implies(X6,and(X7,strict_equiv(X8,not(X9))))) )
| ~ spl2_122
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(backward_demodulation,[],[f6739,f24169]) ).
fof(f6739,plain,
( ! [X8,X6,X9,X7] :
( is_a_theorem(strict_implies(X6,and(X7,strict_equiv(X8,not(X9)))))
| ~ is_a_theorem(strict_implies(X6,and(necessarily(or(X9,X8)),and(X7,strict_implies(X8,not(X9)))))) )
| ~ spl2_122
| ~ spl2_241 ),
inference(resolution,[],[f6150,f1832]) ).
fof(f37095,plain,
( spl2_659
| ~ spl2_23
| ~ spl2_96
| ~ spl2_300
| ~ spl2_335
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24762,f23260,f11032,f9395,f1122,f286,f37093]) ).
fof(f24762,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(possibly(X7),X6),X5)))
| ~ spl2_23
| ~ spl2_96
| ~ spl2_300
| ~ spl2_335
| ~ spl2_504 ),
inference(backward_demodulation,[],[f11139,f24324]) ).
fof(f11139,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(implies(X6,X5),not(and(possibly(X7),and(not(X5),X6)))))
| ~ spl2_23
| ~ spl2_300
| ~ spl2_335 ),
inference(forward_demodulation,[],[f11133,f287]) ).
fof(f11133,plain,
( ! [X6,X7,X5] : is_a_theorem(necessarily(implies(implies(X6,X5),not(and(possibly(X7),and(not(X5),X6))))))
| ~ spl2_300
| ~ spl2_335 ),
inference(superposition,[],[f11033,f9396]) ).
fof(f37091,plain,
( spl2_658
| ~ spl2_384
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24337,f23260,f13659,f37089]) ).
fof(f37089,plain,
( spl2_658
<=> ! [X455,X454,X453,X456] :
( ~ is_a_theorem(and(X454,and(not(X453),X455)))
| is_a_theorem(implies(X453,X456)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_658])]) ).
fof(f24337,plain,
( ! [X455,X454,X456,X453] :
( ~ is_a_theorem(and(X454,and(not(X453),X455)))
| is_a_theorem(implies(X453,X456)) )
| ~ spl2_384
| ~ spl2_504 ),
inference(superposition,[],[f13660,f23261]) ).
fof(f37087,plain,
( spl2_657
| ~ spl2_128
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f24133,f23256,f2062,f37085]) ).
fof(f37085,plain,
( spl2_657
<=> ! [X400,X401,X402] : strict_implies(strict_equiv(X400,X401),X402) = strict_implies(strict_equiv(X401,X400),X402) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_657])]) ).
fof(f2062,plain,
( spl2_128
<=> ! [X2,X1] : strict_implies(X1,X2) = strict_implies(and(X1,not(X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_128])]) ).
fof(f24133,plain,
( ! [X402,X401,X400] : strict_implies(strict_equiv(X400,X401),X402) = strict_implies(strict_equiv(X401,X400),X402)
| ~ spl2_128
| ~ spl2_503 ),
inference(forward_demodulation,[],[f23830,f2063]) ).
fof(f2063,plain,
( ! [X2,X1] : strict_implies(X1,X2) = strict_implies(and(X1,not(X2)),X2)
| ~ spl2_128 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f23830,plain,
( ! [X402,X401,X400] : strict_implies(strict_equiv(X400,X401),X402) = strict_implies(and(strict_equiv(X401,X400),not(X402)),X402)
| ~ spl2_128
| ~ spl2_503 ),
inference(superposition,[],[f2063,f23257]) ).
fof(f37083,plain,
( spl2_656
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_77
| ~ spl2_201
| ~ spl2_252
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21293,f19362,f18075,f9399,f9376,f6967,f4160,f814,f810,f681,f436,f37081]) ).
fof(f37081,plain,
( spl2_656
<=> ! [X9,X7,X6,X8] :
( ~ is_a_theorem(and(equiv(and(X7,not(X8)),X6),X9))
| is_a_theorem(and(X9,equiv(X6,and(X7,not(X8))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_656])]) ).
fof(f4160,plain,
( spl2_201
<=> ! [X4,X5,X3] :
( is_a_theorem(and(X3,equiv(X4,X5)))
| ~ is_a_theorem(and(implies(X5,X4),and(X3,implies(X4,X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_201])]) ).
fof(f21293,plain,
( ! [X8,X6,X9,X7] :
( ~ is_a_theorem(and(equiv(and(X7,not(X8)),X6),X9))
| is_a_theorem(and(X9,equiv(X6,and(X7,not(X8))))) )
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_77
| ~ spl2_201
| ~ spl2_252
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21178,f20754]) ).
fof(f21178,plain,
( ! [X8,X6,X9,X7] :
( ~ is_a_theorem(and(not(and(X6,implies(X7,X8))),and(implies(and(X7,not(X8)),X6),X9)))
| is_a_theorem(and(X9,equiv(X6,and(X7,not(X8))))) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_77
| ~ spl2_201
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4514,f21159]) ).
fof(f4514,plain,
( ! [X8,X6,X9,X7] :
( ~ is_a_theorem(and(implies(and(X7,not(X8)),X6),and(X9,not(and(X6,implies(X7,X8))))))
| is_a_theorem(and(X9,equiv(X6,and(X7,not(X8))))) )
| ~ spl2_77
| ~ spl2_201 ),
inference(superposition,[],[f4161,f815]) ).
fof(f4161,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(implies(X5,X4),and(X3,implies(X4,X5))))
| is_a_theorem(and(X3,equiv(X4,X5))) )
| ~ spl2_201 ),
inference(avatar_component_clause,[],[f4160]) ).
fof(f37079,plain,
( spl2_655
| ~ spl2_128
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23694,f23252,f2062,f37077]) ).
fof(f23694,plain,
( ! [X421,X420,X419] : strict_implies(equiv(X419,X420),X421) = strict_implies(equiv(X420,X419),X421)
| ~ spl2_128
| ~ spl2_502 ),
inference(forward_demodulation,[],[f23388,f2063]) ).
fof(f23388,plain,
( ! [X421,X420,X419] : strict_implies(equiv(X419,X420),X421) = strict_implies(and(equiv(X420,X419),not(X421)),X421)
| ~ spl2_128
| ~ spl2_502 ),
inference(superposition,[],[f2063,f23253]) ).
fof(f37075,plain,
( spl2_654
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21016,f19362,f18075,f12444,f4156,f1856,f1499,f1122,f810,f681,f436,f315,f290,f286,f37073]) ).
fof(f21016,plain,
( ! [X218,X219,X217] : is_a_theorem(strict_implies(and(not(X218),and(or(X218,X217),X219)),X217))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21015,f20741]) ).
fof(f21015,plain,
( ! [X218,X219,X217] : is_a_theorem(strict_implies(and(or(X218,X217),and(not(X218),X219)),X217))
| ~ spl2_23
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21014,f287]) ).
fof(f21014,plain,
( ! [X218,X219,X217] : is_a_theorem(necessarily(implies(and(or(X218,X217),and(not(X218),X219)),X217)))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20820,f1123]) ).
fof(f20820,plain,
( ! [X218,X219,X217] : is_a_theorem(necessarily(not(and(not(X217),and(or(X218,X217),and(not(X218),X219))))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14010,f20741]) ).
fof(f14010,plain,
( ! [X218,X219,X217] : is_a_theorem(necessarily(not(and(or(X218,X217),and(not(X217),and(not(X218),X219))))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_200
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13875,f13940]) ).
fof(f13875,plain,
( ! [X218,X219,X217] : is_a_theorem(necessarily(not(and(and(not(X217),and(not(X218),X219)),or(X218,X217)))))
| ~ spl2_200
| ~ spl2_371 ),
inference(superposition,[],[f4157,f12445]) ).
fof(f37033,plain,
( spl2_653
| ~ spl2_76
| ~ spl2_122
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20140,f19362,f6129,f2474,f1831,f810,f37031]) ).
fof(f37031,plain,
( spl2_653
<=> ! [X9,X7,X6,X8] :
( is_a_theorem(strict_implies(X6,and(strict_equiv(not(X8),X7),X9)))
| ~ is_a_theorem(strict_implies(X6,and(strict_equiv(X7,not(X8)),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_653])]) ).
fof(f20140,plain,
( ! [X8,X6,X9,X7] :
( is_a_theorem(strict_implies(X6,and(strict_equiv(not(X8),X7),X9)))
| ~ is_a_theorem(strict_implies(X6,and(strict_equiv(X7,not(X8)),X9))) )
| ~ spl2_76
| ~ spl2_122
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(backward_demodulation,[],[f6549,f20136]) ).
fof(f6549,plain,
( ! [X8,X6,X9,X7] :
( is_a_theorem(strict_implies(X6,and(strict_implies(X7,not(X8)),and(necessarily(or(X8,X7)),X9))))
| ~ is_a_theorem(strict_implies(X6,and(strict_equiv(X7,not(X8)),X9))) )
| ~ spl2_122
| ~ spl2_236 ),
inference(resolution,[],[f6130,f1832]) ).
fof(f36436,plain,
( spl2_652
| ~ spl2_23
| ~ spl2_33
| ~ spl2_125
| ~ spl2_161
| ~ spl2_209 ),
inference(avatar_split_clause,[],[f4711,f4558,f2750,f1852,f340,f286,f36434]) ).
fof(f36281,plain,
( spl2_651
| ~ spl2_26
| ~ spl2_636 ),
inference(avatar_split_clause,[],[f36180,f34639,f298,f36279]) ).
fof(f36279,plain,
( spl2_651
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X3,X4),X5))
| ~ is_a_theorem(not(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_651])]) ).
fof(f36180,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X3,X4),X5))
| ~ is_a_theorem(not(X5)) )
| ~ spl2_26
| ~ spl2_636 ),
inference(resolution,[],[f34640,f299]) ).
fof(f36277,plain,
( spl2_650
| ~ spl2_26
| ~ spl2_632 ),
inference(avatar_split_clause,[],[f35918,f34623,f298,f36275]) ).
fof(f36275,plain,
( spl2_650
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(X4,and(X5,X3)))
| ~ is_a_theorem(not(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_650])]) ).
fof(f35918,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(X4,and(X5,X3)))
| ~ is_a_theorem(not(X4)) )
| ~ spl2_26
| ~ spl2_632 ),
inference(resolution,[],[f34624,f299]) ).
fof(f36273,plain,
( spl2_649
| ~ spl2_26
| ~ spl2_209 ),
inference(avatar_split_clause,[],[f4609,f4558,f298,f36271]) ).
fof(f36271,plain,
( spl2_649
<=> ! [X22,X23] :
( is_a_theorem(equiv(X22,necessarily(not(X23))))
| ~ is_a_theorem(implies(necessarily(not(X23)),X22))
| ~ is_a_theorem(not(and(X22,possibly(X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_649])]) ).
fof(f4609,plain,
( ! [X22,X23] :
( is_a_theorem(equiv(X22,necessarily(not(X23))))
| ~ is_a_theorem(implies(necessarily(not(X23)),X22))
| ~ is_a_theorem(not(and(X22,possibly(X23)))) )
| ~ spl2_26
| ~ spl2_209 ),
inference(superposition,[],[f299,f4559]) ).
fof(f36269,plain,
( spl2_648
| ~ spl2_26
| ~ spl2_631 ),
inference(avatar_split_clause,[],[f35837,f34619,f298,f36267]) ).
fof(f36267,plain,
( spl2_648
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(and(X4,X3),X5))
| ~ is_a_theorem(not(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_648])]) ).
fof(f35837,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(and(X4,X3),X5))
| ~ is_a_theorem(not(X5)) )
| ~ spl2_26
| ~ spl2_631 ),
inference(resolution,[],[f34620,f299]) ).
fof(f36265,plain,
( spl2_647
| ~ spl2_126
| ~ spl2_504
| ~ spl2_517 ),
inference(avatar_split_clause,[],[f27515,f26955,f23260,f1856,f36263]) ).
fof(f36263,plain,
( spl2_647
<=> ! [X427,X429,X428] : strict_implies(and(X428,X429),X427) = strict_implies(and(X429,X428),X427) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_647])]) ).
fof(f27515,plain,
( ! [X429,X428,X427] : strict_implies(and(X428,X429),X427) = strict_implies(and(X429,X428),X427)
| ~ spl2_126
| ~ spl2_504
| ~ spl2_517 ),
inference(forward_demodulation,[],[f27207,f24327]) ).
fof(f24327,plain,
( ! [X420,X419,X418] : strict_implies(and(X419,X420),X418) = strict_implies(and(X419,and(not(X418),X420)),X418)
| ~ spl2_126
| ~ spl2_504 ),
inference(superposition,[],[f1857,f23261]) ).
fof(f27207,plain,
( ! [X429,X428,X427] : strict_implies(and(X428,X429),X427) = strict_implies(and(X429,and(not(X427),X428)),X427)
| ~ spl2_126
| ~ spl2_517 ),
inference(superposition,[],[f1857,f26956]) ).
fof(f36261,plain,
( spl2_646
| ~ spl2_383
| ~ spl2_517 ),
inference(avatar_split_clause,[],[f27382,f26955,f13618,f36259]) ).
fof(f27382,plain,
( ! [X461,X460,X459,X458] : is_a_theorem(strict_implies(and(X459,and(X460,not(X458))),implies(X458,X461)))
| ~ spl2_383
| ~ spl2_517 ),
inference(superposition,[],[f13619,f26956]) ).
fof(f36257,plain,
( spl2_645
| ~ spl2_122
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3453,f2734,f1831,f36255]) ).
fof(f36255,plain,
( spl2_645
<=> ! [X0,X3,X2,X1] :
( is_a_theorem(strict_implies(X0,not(and(X1,implies(X2,X3)))))
| ~ is_a_theorem(strict_implies(X0,equiv(X1,and(X2,not(X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_645])]) ).
fof(f3453,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(X0,not(and(X1,implies(X2,X3)))))
| ~ is_a_theorem(strict_implies(X0,equiv(X1,and(X2,not(X3))))) )
| ~ spl2_122
| ~ spl2_157 ),
inference(resolution,[],[f2735,f1832]) ).
fof(f36253,plain,
( spl2_644
| ~ spl2_383
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24336,f23260,f13618,f36251]) ).
fof(f24336,plain,
( ! [X452,X451,X450,X449] : is_a_theorem(strict_implies(and(X450,and(not(X449),X451)),implies(X449,X452)))
| ~ spl2_383
| ~ spl2_504 ),
inference(superposition,[],[f13619,f23261]) ).
fof(f36249,plain,
( spl2_643
| ~ spl2_20
| ~ spl2_497 ),
inference(avatar_split_clause,[],[f23124,f23092,f273,f36247]) ).
fof(f36247,plain,
( spl2_643
<=> ! [X0] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(necessarily(not(X0)))
| ~ is_a_theorem(possibly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_643])]) ).
fof(f23092,plain,
( spl2_497
<=> ! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(X0)))
| ~ is_a_theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_497])]) ).
fof(f23124,plain,
( ! [X0] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(necessarily(not(X0)))
| ~ is_a_theorem(possibly(X0)) )
| ~ spl2_20
| ~ spl2_497 ),
inference(superposition,[],[f23093,f274]) ).
fof(f23093,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0)
| ~ is_a_theorem(not(X0)) )
| ~ spl2_497 ),
inference(avatar_component_clause,[],[f23092]) ).
fof(f36245,plain,
( spl2_642
| ~ spl2_23
| ~ spl2_58
| ~ spl2_76
| ~ spl2_96
| ~ spl2_332
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21649,f19362,f10702,f1122,f810,f544,f286,f36243]) ).
fof(f21649,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,possibly(X4)),X3)))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_76
| ~ spl2_96
| ~ spl2_332
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20625,f1123]) ).
fof(f20625,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),not(and(not(X3),and(X2,possibly(X4))))))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_76
| ~ spl2_332
| ~ spl2_486 ),
inference(backward_demodulation,[],[f10729,f19383]) ).
fof(f10729,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),not(and(and(X2,not(X3)),possibly(X4)))))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_332 ),
inference(forward_demodulation,[],[f10723,f287]) ).
fof(f10723,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(implies(implies(X2,X3),not(and(and(X2,not(X3)),possibly(X4))))))
| ~ spl2_58
| ~ spl2_332 ),
inference(superposition,[],[f10703,f545]) ).
fof(f36219,plain,
( spl2_641
| ~ spl2_23
| ~ spl2_125
| ~ spl2_154 ),
inference(avatar_split_clause,[],[f3426,f2673,f1852,f286,f36217]) ).
fof(f36217,plain,
( spl2_641
<=> ! [X18,X17,X16,X15] :
( ~ is_a_theorem(and(strict_implies(implies(X16,X17),X15),strict_implies(and(X16,not(X17)),X18)))
| is_a_theorem(necessarily(or(X15,X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_641])]) ).
fof(f3426,plain,
( ! [X18,X16,X17,X15] :
( ~ is_a_theorem(and(strict_implies(implies(X16,X17),X15),strict_implies(and(X16,not(X17)),X18)))
| is_a_theorem(necessarily(or(X15,X18))) )
| ~ spl2_23
| ~ spl2_125
| ~ spl2_154 ),
inference(forward_demodulation,[],[f3411,f287]) ).
fof(f3411,plain,
( ! [X18,X16,X17,X15] :
( ~ is_a_theorem(and(necessarily(implies(implies(X16,X17),X15)),strict_implies(and(X16,not(X17)),X18)))
| is_a_theorem(necessarily(or(X15,X18))) )
| ~ spl2_125
| ~ spl2_154 ),
inference(superposition,[],[f2674,f1853]) ).
fof(f36001,plain,
( spl2_640
| ~ spl2_23
| ~ spl2_125
| ~ spl2_151 ),
inference(avatar_split_clause,[],[f3391,f2643,f1852,f286,f35999]) ).
fof(f35999,plain,
( spl2_640
<=> ! [X18,X17,X16,X15] :
( ~ is_a_theorem(and(strict_implies(X18,not(X15)),strict_implies(implies(X16,X17),X15)))
| is_a_theorem(strict_implies(X18,and(X16,not(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_640])]) ).
fof(f3391,plain,
( ! [X18,X16,X17,X15] :
( ~ is_a_theorem(and(strict_implies(X18,not(X15)),strict_implies(implies(X16,X17),X15)))
| is_a_theorem(strict_implies(X18,and(X16,not(X17)))) )
| ~ spl2_23
| ~ spl2_125
| ~ spl2_151 ),
inference(forward_demodulation,[],[f3371,f287]) ).
fof(f3371,plain,
( ! [X18,X16,X17,X15] :
( ~ is_a_theorem(and(strict_implies(X18,not(X15)),necessarily(implies(implies(X16,X17),X15))))
| is_a_theorem(strict_implies(X18,and(X16,not(X17)))) )
| ~ spl2_125
| ~ spl2_151 ),
inference(superposition,[],[f2644,f1853]) ).
fof(f35813,plain,
( spl2_639
| ~ spl2_32
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3248,f2598,f336,f35811]) ).
fof(f35811,plain,
( spl2_639
<=> ! [X13,X12,X11] : not(necessarily(possibly(strict_implies(X11,and(X12,not(X13)))))) = possibly(necessarily(possibly(and(X11,implies(X12,X13))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_639])]) ).
fof(f3248,plain,
( ! [X11,X12,X13] : not(necessarily(possibly(strict_implies(X11,and(X12,not(X13)))))) = possibly(necessarily(possibly(and(X11,implies(X12,X13)))))
| ~ spl2_32
| ~ spl2_148 ),
inference(superposition,[],[f337,f2599]) ).
fof(f34649,plain,
( spl2_638
| ~ spl2_29
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3247,f2598,f315,f34647]) ).
fof(f34647,plain,
( spl2_638
<=> ! [X10,X7,X9,X8] : implies(X10,strict_implies(X7,and(X8,not(X9)))) = not(and(X10,possibly(and(X7,implies(X8,X9))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_638])]) ).
fof(f3247,plain,
( ! [X10,X8,X9,X7] : implies(X10,strict_implies(X7,and(X8,not(X9)))) = not(and(X10,possibly(and(X7,implies(X8,X9)))))
| ~ spl2_29
| ~ spl2_148 ),
inference(superposition,[],[f316,f2599]) ).
fof(f34645,plain,
( spl2_637
| ~ spl2_26
| ~ spl2_621 ),
inference(avatar_split_clause,[],[f34513,f33188,f298,f34643]) ).
fof(f34643,plain,
( spl2_637
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(X4,and(X3,X5)))
| ~ is_a_theorem(not(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_637])]) ).
fof(f34513,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(X4,and(X3,X5)))
| ~ is_a_theorem(not(X4)) )
| ~ spl2_26
| ~ spl2_621 ),
inference(resolution,[],[f33189,f299]) ).
fof(f34641,plain,
( spl2_636
| ~ spl2_58
| ~ spl2_619 ),
inference(avatar_split_clause,[],[f34408,f33180,f544,f34639]) ).
fof(f34408,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X2),implies(implies(X0,X1),X2)))
| is_a_theorem(X0) )
| ~ spl2_58
| ~ spl2_619 ),
inference(superposition,[],[f33181,f545]) ).
fof(f34637,plain,
( spl2_635
| ~ spl2_26
| ~ spl2_619 ),
inference(avatar_split_clause,[],[f34357,f33180,f298,f34635]) ).
fof(f34635,plain,
( spl2_635
<=> ! [X4,X5,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(and(X3,X4),X5))
| ~ is_a_theorem(not(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_635])]) ).
fof(f34357,plain,
( ! [X3,X4,X5] :
( is_a_theorem(X3)
| ~ is_a_theorem(or(and(X3,X4),X5))
| ~ is_a_theorem(not(X5)) )
| ~ spl2_26
| ~ spl2_619 ),
inference(resolution,[],[f33181,f299]) ).
fof(f34633,plain,
( spl2_634
| ~ spl2_328
| ~ spl2_617 ),
inference(avatar_split_clause,[],[f34158,f33172,f10566,f34631]) ).
fof(f34158,plain,
( ! [X136,X137,X135] : is_a_theorem(necessarily(or(and(X135,X136),implies(and(X136,X135),X137))))
| ~ spl2_328
| ~ spl2_617 ),
inference(superposition,[],[f10567,f33173]) ).
fof(f34629,plain,
( spl2_633
| ~ spl2_23
| ~ spl2_125
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3162,f2558,f1852,f286,f34627]) ).
fof(f3162,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(necessarily(or(X15,X18)),strict_implies(X18,and(X16,not(X17)))),strict_implies(implies(X16,X17),X15)))
| ~ spl2_23
| ~ spl2_125
| ~ spl2_146 ),
inference(forward_demodulation,[],[f3136,f287]) ).
fof(f3136,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(necessarily(or(X15,X18)),strict_implies(X18,and(X16,not(X17)))),necessarily(implies(implies(X16,X17),X15))))
| ~ spl2_125
| ~ spl2_146 ),
inference(superposition,[],[f2559,f1853]) ).
fof(f34625,plain,
( spl2_632
| ~ spl2_27
| ~ spl2_615 ),
inference(avatar_split_clause,[],[f33315,f33164,f302,f34623]) ).
fof(f33315,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,and(X2,X0)))) )
| ~ spl2_27
| ~ spl2_615 ),
inference(resolution,[],[f33165,f303]) ).
fof(f34621,plain,
( spl2_631
| ~ spl2_27
| ~ spl2_614 ),
inference(avatar_split_clause,[],[f33195,f33160,f302,f34619]) ).
fof(f33195,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(and(X2,X0),X1))) )
| ~ spl2_27
| ~ spl2_614 ),
inference(resolution,[],[f33161,f303]) ).
fof(f34617,plain,
( spl2_630
| ~ spl2_328
| ~ spl2_515 ),
inference(avatar_split_clause,[],[f26873,f25559,f10566,f34615]) ).
fof(f26873,plain,
( ! [X72,X70,X71] : is_a_theorem(necessarily(or(strict_equiv(X70,X71),implies(strict_equiv(X71,X70),X72))))
| ~ spl2_328
| ~ spl2_515 ),
inference(superposition,[],[f10567,f25560]) ).
fof(f34613,plain,
( spl2_629
| ~ spl2_23
| ~ spl2_125
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3144,f2558,f1852,f286,f34611]) ).
fof(f3144,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(strict_implies(implies(X16,X17),X15),strict_implies(and(X16,not(X17)),X18)),necessarily(or(X15,X18))))
| ~ spl2_23
| ~ spl2_125
| ~ spl2_146 ),
inference(forward_demodulation,[],[f3122,f287]) ).
fof(f3122,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(necessarily(implies(implies(X16,X17),X15)),strict_implies(and(X16,not(X17)),X18)),necessarily(or(X15,X18))))
| ~ spl2_125
| ~ spl2_146 ),
inference(superposition,[],[f2559,f1853]) ).
fof(f34609,plain,
( spl2_628
| ~ spl2_328
| ~ spl2_512 ),
inference(avatar_split_clause,[],[f26213,f25503,f10566,f34607]) ).
fof(f26213,plain,
( ! [X78,X76,X77] : is_a_theorem(necessarily(or(equiv(X76,X77),implies(equiv(X77,X76),X78))))
| ~ spl2_328
| ~ spl2_512 ),
inference(superposition,[],[f10567,f25504]) ).
fof(f34605,plain,
( spl2_627
| ~ spl2_20
| ~ spl2_495 ),
inference(avatar_split_clause,[],[f23056,f22997,f273,f34603]) ).
fof(f34603,plain,
( spl2_627
<=> ! [X0] :
( ~ is_a_theorem(and(possibly(X0),not(possibly(X0))))
| is_a_theorem(necessarily(not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_627])]) ).
fof(f23056,plain,
( ! [X0] :
( ~ is_a_theorem(and(possibly(X0),not(possibly(X0))))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_495 ),
inference(superposition,[],[f22998,f274]) ).
fof(f34601,plain,
( spl2_626
| ~ spl2_76
| ~ spl2_111
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21491,f19362,f1499,f810,f34599]) ).
fof(f34599,plain,
( spl2_626
<=> ! [X9,X8,X10] : and(X10,and(X8,X9)) = and(X9,and(X8,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_626])]) ).
fof(f21491,plain,
( ! [X10,X8,X9] : and(X10,and(X8,X9)) = and(X9,and(X8,X10))
| ~ spl2_76
| ~ spl2_111
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21490,f1500]) ).
fof(f21490,plain,
( ! [X10,X8,X9] : and(X10,and(X8,and(X8,X9))) = and(X9,and(X8,X10))
| ~ spl2_76
| ~ spl2_111
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20389,f19383]) ).
fof(f20389,plain,
( ! [X10,X8,X9] : and(and(X8,X10),and(X8,X9)) = and(X9,and(X8,X10))
| ~ spl2_76
| ~ spl2_111
| ~ spl2_486 ),
inference(backward_demodulation,[],[f19368,f19383]) ).
fof(f19368,plain,
( ! [X10,X8,X9] : and(and(X8,X9),X10) = and(and(X8,X10),and(X8,X9))
| ~ spl2_111
| ~ spl2_486 ),
inference(superposition,[],[f19363,f1500]) ).
fof(f34597,plain,
( spl2_625
| ~ spl2_76
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f19383,f19362,f810,f34595]) ).
fof(f34593,plain,
( spl2_624
| ~ spl2_122
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3114,f2558,f1831,f34591]) ).
fof(f34591,plain,
( spl2_624
<=> ! [X0,X3,X2,X1] :
( is_a_theorem(strict_implies(X0,necessarily(or(X1,X2))))
| ~ is_a_theorem(strict_implies(X0,and(necessarily(or(X1,X3)),strict_implies(X3,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_624])]) ).
fof(f3114,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(X0,necessarily(or(X1,X2))))
| ~ is_a_theorem(strict_implies(X0,and(necessarily(or(X1,X3)),strict_implies(X3,X2)))) )
| ~ spl2_122
| ~ spl2_146 ),
inference(resolution,[],[f2559,f1832]) ).
fof(f34355,plain,
( spl2_623
| ~ spl2_23
| ~ spl2_125
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f3014,f2528,f1852,f286,f34353]) ).
fof(f3014,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(strict_implies(X18,not(X15)),strict_implies(implies(X16,X17),X15)),strict_implies(X18,and(X16,not(X17)))))
| ~ spl2_23
| ~ spl2_125
| ~ spl2_142 ),
inference(forward_demodulation,[],[f2992,f287]) ).
fof(f2992,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(strict_implies(and(strict_implies(X18,not(X15)),necessarily(implies(implies(X16,X17),X15))),strict_implies(X18,and(X16,not(X17)))))
| ~ spl2_125
| ~ spl2_142 ),
inference(superposition,[],[f2529,f1853]) ).
fof(f33194,plain,
( spl2_622
| ~ spl2_122
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f2977,f2528,f1831,f33192]) ).
fof(f33192,plain,
( spl2_622
<=> ! [X0,X3,X2,X1] :
( is_a_theorem(strict_implies(X0,strict_implies(X1,X2)))
| ~ is_a_theorem(strict_implies(X0,and(strict_implies(X1,not(X3)),necessarily(or(X3,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_622])]) ).
fof(f2977,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(X0,strict_implies(X1,X2)))
| ~ is_a_theorem(strict_implies(X0,and(strict_implies(X1,not(X3)),necessarily(or(X3,X2))))) )
| ~ spl2_122
| ~ spl2_142 ),
inference(resolution,[],[f2529,f1832]) ).
fof(f33190,plain,
( spl2_621
| ~ spl2_27
| ~ spl2_519 ),
inference(avatar_split_clause,[],[f33025,f26991,f302,f33188]) ).
fof(f33025,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,and(X0,X2)))) )
| ~ spl2_27
| ~ spl2_519 ),
inference(resolution,[],[f26992,f303]) ).
fof(f33186,plain,
( spl2_620
| ~ spl2_58
| ~ spl2_518 ),
inference(avatar_split_clause,[],[f27636,f26959,f544,f33184]) ).
fof(f27636,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(X2),implies(implies(X0,X1),X2)),X0))
| ~ spl2_58
| ~ spl2_518 ),
inference(superposition,[],[f26960,f545]) ).
fof(f33182,plain,
( spl2_619
| ~ spl2_27
| ~ spl2_518 ),
inference(avatar_split_clause,[],[f27565,f26959,f302,f33180]) ).
fof(f27565,plain,
( ! [X2,X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(and(X0,X2),X1))) )
| ~ spl2_27
| ~ spl2_518 ),
inference(resolution,[],[f26960,f303]) ).
fof(f33178,plain,
( spl2_618
| ~ spl2_23
| ~ spl2_104
| ~ spl2_141 ),
inference(avatar_split_clause,[],[f2902,f2474,f1388,f286,f33176]) ).
fof(f33176,plain,
( spl2_618
<=> ! [X13,X14] : strict_equiv(not(X13),necessarily(not(X14))) = and(strict_implies(possibly(X14),X13),strict_implies(necessarily(not(X14)),not(X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_618])]) ).
fof(f2902,plain,
( ! [X14,X13] : strict_equiv(not(X13),necessarily(not(X14))) = and(strict_implies(possibly(X14),X13),strict_implies(necessarily(not(X14)),not(X13)))
| ~ spl2_23
| ~ spl2_104
| ~ spl2_141 ),
inference(forward_demodulation,[],[f2856,f287]) ).
fof(f2856,plain,
( ! [X14,X13] : strict_equiv(not(X13),necessarily(not(X14))) = and(necessarily(implies(possibly(X14),X13)),strict_implies(necessarily(not(X14)),not(X13)))
| ~ spl2_104
| ~ spl2_141 ),
inference(superposition,[],[f2475,f1389]) ).
fof(f33174,plain,
( spl2_617
| ~ spl2_96
| ~ spl2_504
| ~ spl2_517 ),
inference(avatar_split_clause,[],[f27512,f26955,f23260,f1122,f33172]) ).
fof(f27512,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = implies(and(X420,X419),X418)
| ~ spl2_96
| ~ spl2_504
| ~ spl2_517 ),
inference(forward_demodulation,[],[f27204,f24324]) ).
fof(f27204,plain,
( ! [X420,X419,X418] : implies(and(X419,X420),X418) = not(and(X420,and(not(X418),X419)))
| ~ spl2_96
| ~ spl2_517 ),
inference(superposition,[],[f1123,f26956]) ).
fof(f33170,plain,
( spl2_616
| ~ spl2_76
| ~ spl2_486
| ~ spl2_517 ),
inference(avatar_split_clause,[],[f27448,f26955,f19362,f810,f33168]) ).
fof(f27448,plain,
( ! [X18,X19,X20] : and(X20,and(X19,X18)) = and(X20,and(X18,X19))
| ~ spl2_76
| ~ spl2_486
| ~ spl2_517 ),
inference(forward_demodulation,[],[f27034,f19383]) ).
fof(f27034,plain,
( ! [X18,X19,X20] : and(X20,and(X18,X19)) = and(and(X19,X20),X18)
| ~ spl2_76
| ~ spl2_517 ),
inference(superposition,[],[f26956,f811]) ).
fof(f33166,plain,
( spl2_615
| ~ spl2_152
| ~ spl2_489 ),
inference(avatar_split_clause,[],[f22836,f22739,f2665,f33164]) ).
fof(f22836,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(X40),or(X40,and(X41,X42))),X42))
| ~ spl2_152
| ~ spl2_489 ),
inference(resolution,[],[f22740,f2666]) ).
fof(f33162,plain,
( spl2_614
| ~ spl2_152
| ~ spl2_487 ),
inference(avatar_split_clause,[],[f22757,f22731,f2665,f33160]) ).
fof(f22757,plain,
( ! [X40,X41,X42] : is_a_theorem(strict_implies(and(not(X40),or(and(X41,X42),X40)),X42))
| ~ spl2_152
| ~ spl2_487 ),
inference(resolution,[],[f22732,f2666]) ).
fof(f33158,plain,
( spl2_613
| ~ spl2_54
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1947,f1558,f505,f33156]) ).
fof(f33156,plain,
( spl2_613
<=> ! [X20,X21,X19] : not(and(X21,possibly(strict_implies(X19,necessarily(not(X20)))))) = implies(X21,necessarily(possibly(and(X19,possibly(X20))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_613])]) ).
fof(f1947,plain,
( ! [X21,X19,X20] : not(and(X21,possibly(strict_implies(X19,necessarily(not(X20)))))) = implies(X21,necessarily(possibly(and(X19,possibly(X20)))))
| ~ spl2_54
| ~ spl2_112 ),
inference(superposition,[],[f506,f1559]) ).
fof(f32985,plain,
( spl2_612
| ~ spl2_80
| ~ spl2_104 ),
inference(avatar_split_clause,[],[f1426,f1388,f856,f32983]) ).
fof(f1426,plain,
( ! [X6,X5] : equiv(not(X5),necessarily(not(X6))) = and(implies(possibly(X6),X5),implies(necessarily(not(X6)),not(X5)))
| ~ spl2_80
| ~ spl2_104 ),
inference(superposition,[],[f857,f1389]) ).
fof(f32981,plain,
( spl2_611
| ~ spl2_36
| ~ spl2_605 ),
inference(avatar_split_clause,[],[f32623,f31945,f363,f32979]) ).
fof(f32979,plain,
( spl2_611
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(equiv(X0,X1))))
| is_a_theorem(implies(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_611])]) ).
fof(f31945,plain,
( spl2_605
<=> ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(implies(X3,X4),X2))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_605])]) ).
fof(f32623,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(equiv(X0,X1))))
| is_a_theorem(implies(X1,X0)) )
| ~ spl2_36
| ~ spl2_605 ),
inference(superposition,[],[f31946,f364]) ).
fof(f31946,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(implies(X3,X4),X2))))
| is_a_theorem(X2) )
| ~ spl2_605 ),
inference(avatar_component_clause,[],[f31945]) ).
fof(f32977,plain,
( spl2_610
| ~ spl2_76
| ~ spl2_604 ),
inference(avatar_split_clause,[],[f32250,f31728,f810,f32975]) ).
fof(f32975,plain,
( spl2_610
<=> ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(or(X3,X4),X2))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_610])]) ).
fof(f31728,plain,
( spl2_604
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(not(and(X17,or(X15,X16)))))
| is_a_theorem(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_604])]) ).
fof(f32250,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(or(X3,X4),X2))))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_604 ),
inference(superposition,[],[f31729,f811]) ).
fof(f31729,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(not(and(X17,or(X15,X16)))))
| is_a_theorem(X17) )
| ~ spl2_604 ),
inference(avatar_component_clause,[],[f31728]) ).
fof(f32223,plain,
( spl2_609
| ~ spl2_83
| ~ spl2_602 ),
inference(avatar_split_clause,[],[f31713,f30895,f1024,f32221]) ).
fof(f32221,plain,
( spl2_609
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(implies(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_609])]) ).
fof(f30895,plain,
( spl2_602
<=> ! [X6,X8,X7] :
( ~ is_a_theorem(not(or(not(X7),X8)))
| is_a_theorem(implies(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_602])]) ).
fof(f31713,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(implies(X1,X0)) )
| ~ spl2_83
| ~ spl2_602 ),
inference(superposition,[],[f30896,f1025]) ).
fof(f30896,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(X7),X8)))
| is_a_theorem(implies(X6,X7)) )
| ~ spl2_602 ),
inference(avatar_component_clause,[],[f30895]) ).
fof(f32219,plain,
( spl2_608
| ~ spl2_24
| ~ spl2_599 ),
inference(avatar_split_clause,[],[f31411,f30882,f290,f32217]) ).
fof(f32217,plain,
( spl2_608
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(implies(X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_608])]) ).
fof(f30882,plain,
( spl2_599
<=> ! [X2,X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(implies(X2,not(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_599])]) ).
fof(f31411,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(implies(X10,X9)) )
| ~ spl2_24
| ~ spl2_599 ),
inference(superposition,[],[f30883,f291]) ).
fof(f30883,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X2,not(X1))))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_599 ),
inference(avatar_component_clause,[],[f30882]) ).
fof(f31955,plain,
( spl2_607
| ~ spl2_76
| ~ spl2_594 ),
inference(avatar_split_clause,[],[f30975,f30804,f810,f31953]) ).
fof(f31953,plain,
( spl2_607
<=> ! [X2,X1] :
( ~ is_a_theorem(not(not(and(possibly(X2),X1))))
| is_a_theorem(possibly(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_607])]) ).
fof(f30804,plain,
( spl2_594
<=> ! [X0,X1] :
( is_a_theorem(possibly(X1))
| ~ is_a_theorem(not(not(and(X0,possibly(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_594])]) ).
fof(f30975,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(not(and(possibly(X2),X1))))
| is_a_theorem(possibly(X2)) )
| ~ spl2_76
| ~ spl2_594 ),
inference(superposition,[],[f30805,f811]) ).
fof(f30805,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(and(X0,possibly(X1)))))
| is_a_theorem(possibly(X1)) )
| ~ spl2_594 ),
inference(avatar_component_clause,[],[f30804]) ).
fof(f31951,plain,
( spl2_606
| ~ spl2_36
| ~ spl2_593 ),
inference(avatar_split_clause,[],[f30953,f30800,f363,f31949]) ).
fof(f31949,plain,
( spl2_606
<=> ! [X9,X8] :
( ~ is_a_theorem(not(not(equiv(X8,X9))))
| is_a_theorem(implies(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_606])]) ).
fof(f30800,plain,
( spl2_593
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(not(not(and(X2,implies(X3,X4)))))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_593])]) ).
fof(f30953,plain,
( ! [X8,X9] :
( ~ is_a_theorem(not(not(equiv(X8,X9))))
| is_a_theorem(implies(X8,X9)) )
| ~ spl2_36
| ~ spl2_593 ),
inference(superposition,[],[f30801,f364]) ).
fof(f30801,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(X2,implies(X3,X4)))))
| is_a_theorem(X2) )
| ~ spl2_593 ),
inference(avatar_component_clause,[],[f30800]) ).
fof(f31947,plain,
( spl2_605
| ~ spl2_76
| ~ spl2_593 ),
inference(avatar_split_clause,[],[f30951,f30800,f810,f31945]) ).
fof(f30951,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(implies(X3,X4),X2))))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_593 ),
inference(superposition,[],[f30801,f811]) ).
fof(f31730,plain,
( spl2_604
| ~ spl2_24
| ~ spl2_593 ),
inference(avatar_split_clause,[],[f30943,f30800,f290,f31728]) ).
fof(f30943,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(not(and(X17,or(X15,X16)))))
| is_a_theorem(X17) )
| ~ spl2_24
| ~ spl2_593 ),
inference(superposition,[],[f30801,f291]) ).
fof(f31726,plain,
( spl2_603
| ~ spl2_20
| ~ spl2_54
| ~ spl2_591 ),
inference(avatar_split_clause,[],[f30711,f30695,f505,f273,f31724]) ).
fof(f31724,plain,
( spl2_603
<=> ! [X0,X1] :
( is_a_theorem(not(and(X1,possibly(X0))))
| ~ is_a_theorem(not(possibly(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_603])]) ).
fof(f30711,plain,
( ! [X0,X1] :
( is_a_theorem(not(and(X1,possibly(X0))))
| ~ is_a_theorem(not(possibly(X0))) )
| ~ spl2_20
| ~ spl2_54
| ~ spl2_591 ),
inference(forward_demodulation,[],[f30698,f506]) ).
fof(f30698,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(implies(X1,necessarily(not(X0)))) )
| ~ spl2_20
| ~ spl2_591 ),
inference(superposition,[],[f30696,f274]) ).
fof(f30897,plain,
( spl2_602
| ~ spl2_24
| ~ spl2_549
| ~ spl2_585 ),
inference(avatar_split_clause,[],[f30686,f30513,f29220,f290,f30895]) ).
fof(f30513,plain,
( spl2_585
<=> ! [X2,X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(and(not(not(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_585])]) ).
fof(f30686,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(or(not(X7),X8)))
| is_a_theorem(implies(X6,X7)) )
| ~ spl2_24
| ~ spl2_549
| ~ spl2_585 ),
inference(forward_demodulation,[],[f30654,f291]) ).
fof(f30654,plain,
( ! [X8,X6,X7] :
( is_a_theorem(implies(X6,X7))
| ~ is_a_theorem(not(implies(not(not(X7)),X8))) )
| ~ spl2_549
| ~ spl2_585 ),
inference(resolution,[],[f30514,f29221]) ).
fof(f30514,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(not(not(X1)),X2))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_585 ),
inference(avatar_component_clause,[],[f30513]) ).
fof(f30893,plain,
( spl2_601
| ~ spl2_76
| ~ spl2_585 ),
inference(avatar_split_clause,[],[f30672,f30513,f810,f30891]) ).
fof(f30891,plain,
( spl2_601
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X3,not(not(X2))))
| is_a_theorem(implies(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_601])]) ).
fof(f30672,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,not(not(X2))))
| is_a_theorem(implies(X4,X2)) )
| ~ spl2_76
| ~ spl2_585 ),
inference(superposition,[],[f30514,f811]) ).
fof(f30889,plain,
( spl2_387
| spl2_591
| ~ spl2_26
| ~ spl2_585 ),
inference(avatar_split_clause,[],[f30653,f30513,f298,f30695,f14075]) ).
fof(f30653,plain,
( ! [X3,X4,X5] :
( is_a_theorem(implies(X3,X4))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(not(not(X4))) )
| ~ spl2_26
| ~ spl2_585 ),
inference(resolution,[],[f30514,f299]) ).
fof(f30888,plain,
( spl2_600
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21304,f19362,f18075,f9399,f9376,f8431,f6967,f1074,f810,f681,f436,f363,f30886]) ).
fof(f30886,plain,
( spl2_600
<=> ! [X28,X27,X25,X26] : and(X25,equiv(X26,and(X27,not(X28)))) = and(equiv(and(X27,not(X28)),X26),X25) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_600])]) ).
fof(f21304,plain,
( ! [X28,X26,X27,X25] : and(X25,equiv(X26,and(X27,not(X28)))) = and(equiv(and(X27,not(X28)),X26),X25)
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21303,f20754]) ).
fof(f21303,plain,
( ! [X28,X26,X27,X25] : and(X25,equiv(X26,and(X27,not(X28)))) = and(not(and(X26,implies(X27,X28))),and(implies(and(X27,not(X28)),X26),X25))
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21302,f21159]) ).
fof(f21302,plain,
( ! [X28,X26,X27,X25] : and(X25,equiv(X26,and(X27,not(X28)))) = and(implies(and(X27,not(X28)),X26),and(X25,not(and(X26,implies(X27,X28)))))
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(subsumption_resolution,[],[f21301,f20025]) ).
fof(f21301,plain,
( ! [X28,X26,X27,X25] :
( ~ is_a_theorem(strict_implies(and(X25,equiv(X26,and(X27,not(X28)))),and(equiv(and(X27,not(X28)),X26),X25)))
| and(X25,equiv(X26,and(X27,not(X28)))) = and(implies(and(X27,not(X28)),X26),and(X25,not(and(X26,implies(X27,X28))))) )
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_252
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21186,f20754]) ).
fof(f21186,plain,
( ! [X28,X26,X27,X25] :
( ~ is_a_theorem(strict_implies(and(X25,equiv(X26,and(X27,not(X28)))),and(not(and(X26,implies(X27,X28))),and(implies(and(X27,not(X28)),X26),X25))))
| and(X25,equiv(X26,and(X27,not(X28)))) = and(implies(and(X27,not(X28)),X26),and(X25,not(and(X26,implies(X27,X28))))) )
| ~ spl2_70
| ~ spl2_76
| ~ spl2_283
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(backward_demodulation,[],[f9122,f21159]) ).
fof(f9122,plain,
( ! [X28,X26,X27,X25] :
( ~ is_a_theorem(strict_implies(and(X25,equiv(X26,and(X27,not(X28)))),and(implies(and(X27,not(X28)),X26),and(X25,not(and(X26,implies(X27,X28)))))))
| and(X25,equiv(X26,and(X27,not(X28)))) = and(implies(and(X27,not(X28)),X26),and(X25,not(and(X26,implies(X27,X28))))) )
| ~ spl2_70
| ~ spl2_283 ),
inference(resolution,[],[f8432,f682]) ).
fof(f30884,plain,
( spl2_599
| ~ spl2_550
| ~ spl2_585 ),
inference(avatar_split_clause,[],[f30652,f30513,f29224,f30882]) ).
fof(f30652,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(implies(X2,not(X1)))) )
| ~ spl2_550
| ~ spl2_585 ),
inference(resolution,[],[f30514,f29225]) ).
fof(f30880,plain,
( spl2_598
| ~ spl2_83
| ~ spl2_584 ),
inference(avatar_split_clause,[],[f30636,f30509,f1024,f30878]) ).
fof(f30878,plain,
( spl2_598
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_598])]) ).
fof(f30509,plain,
( spl2_584
<=> ! [X100,X101,X99] :
( ~ is_a_theorem(not(or(not(X99),X100)))
| is_a_theorem(or(X99,X101)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_584])]) ).
fof(f30636,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(or(X0,X1)) )
| ~ spl2_83
| ~ spl2_584 ),
inference(superposition,[],[f30510,f1025]) ).
fof(f30510,plain,
( ! [X101,X99,X100] :
( ~ is_a_theorem(not(or(not(X99),X100)))
| is_a_theorem(or(X99,X101)) )
| ~ spl2_584 ),
inference(avatar_component_clause,[],[f30509]) ).
fof(f30876,plain,
( spl2_597
| ~ spl2_83
| ~ spl2_583 ),
inference(avatar_split_clause,[],[f30607,f30505,f1024,f30874]) ).
fof(f30874,plain,
( spl2_597
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_597])]) ).
fof(f30505,plain,
( spl2_583
<=> ! [X98,X96,X97] :
( ~ is_a_theorem(not(or(not(X96),X97)))
| is_a_theorem(or(X98,X96)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_583])]) ).
fof(f30607,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(not(X0)))))
| is_a_theorem(or(X1,X0)) )
| ~ spl2_83
| ~ spl2_583 ),
inference(superposition,[],[f30506,f1025]) ).
fof(f30506,plain,
( ! [X98,X96,X97] :
( ~ is_a_theorem(not(or(not(X96),X97)))
| is_a_theorem(or(X98,X96)) )
| ~ spl2_583 ),
inference(avatar_component_clause,[],[f30505]) ).
fof(f30872,plain,
( spl2_596
| ~ spl2_24
| ~ spl2_581 ),
inference(avatar_split_clause,[],[f30574,f30497,f290,f30870]) ).
fof(f30870,plain,
( spl2_596
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(or(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_596])]) ).
fof(f30497,plain,
( spl2_581
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X15,not(X16))))
| is_a_theorem(or(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_581])]) ).
fof(f30574,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(or(X9,X10)) )
| ~ spl2_24
| ~ spl2_581 ),
inference(superposition,[],[f30498,f291]) ).
fof(f30498,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X15,not(X16))))
| is_a_theorem(or(X16,X17)) )
| ~ spl2_581 ),
inference(avatar_component_clause,[],[f30497]) ).
fof(f30810,plain,
( spl2_595
| ~ spl2_24
| ~ spl2_580 ),
inference(avatar_split_clause,[],[f30543,f30493,f290,f30808]) ).
fof(f30808,plain,
( spl2_595
<=> ! [X9,X8,X10] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(or(X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_595])]) ).
fof(f30493,plain,
( spl2_580
<=> ! [X13,X12,X14] :
( ~ is_a_theorem(not(implies(X12,not(X13))))
| is_a_theorem(or(X14,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_580])]) ).
fof(f30543,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(or(X8,not(X9))))
| is_a_theorem(or(X10,X9)) )
| ~ spl2_24
| ~ spl2_580 ),
inference(superposition,[],[f30494,f291]) ).
fof(f30494,plain,
( ! [X14,X12,X13] :
( ~ is_a_theorem(not(implies(X12,not(X13))))
| is_a_theorem(or(X14,X13)) )
| ~ spl2_580 ),
inference(avatar_component_clause,[],[f30493]) ).
fof(f30806,plain,
( spl2_594
| ~ spl2_20
| ~ spl2_54
| ~ spl2_561 ),
inference(avatar_split_clause,[],[f29374,f29352,f505,f273,f30804]) ).
fof(f29352,plain,
( spl2_561
<=> ! [X22,X23] :
( ~ is_a_theorem(not(implies(X22,X23)))
| is_a_theorem(not(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_561])]) ).
fof(f29374,plain,
( ! [X0,X1] :
( is_a_theorem(possibly(X1))
| ~ is_a_theorem(not(not(and(X0,possibly(X1))))) )
| ~ spl2_20
| ~ spl2_54
| ~ spl2_561 ),
inference(forward_demodulation,[],[f29363,f274]) ).
fof(f29363,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(and(X0,possibly(X1)))))
| is_a_theorem(not(necessarily(not(X1)))) )
| ~ spl2_54
| ~ spl2_561 ),
inference(superposition,[],[f29353,f506]) ).
fof(f29353,plain,
( ! [X22,X23] :
( ~ is_a_theorem(not(implies(X22,X23)))
| is_a_theorem(not(X23)) )
| ~ spl2_561 ),
inference(avatar_component_clause,[],[f29352]) ).
fof(f30802,plain,
( spl2_593
| ~ spl2_77
| ~ spl2_560 ),
inference(avatar_split_clause,[],[f29341,f29337,f814,f30800]) ).
fof(f29341,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(not(not(and(X2,implies(X3,X4)))))
| is_a_theorem(X2) )
| ~ spl2_77
| ~ spl2_560 ),
inference(superposition,[],[f29338,f815]) ).
fof(f30798,plain,
( spl2_592
| ~ spl2_104
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3529,f2750,f1388,f30796]) ).
fof(f30796,plain,
( spl2_592
<=> ! [X17,X14,X16,X15] : or(X17,strict_implies(X14,and(X15,not(X16)))) = implies(possibly(and(X14,implies(X15,X16))),X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_592])]) ).
fof(f3529,plain,
( ! [X16,X14,X17,X15] : or(X17,strict_implies(X14,and(X15,not(X16)))) = implies(possibly(and(X14,implies(X15,X16))),X17)
| ~ spl2_104
| ~ spl2_161 ),
inference(superposition,[],[f1389,f2751]) ).
fof(f30697,plain,
( spl2_591
| ~ spl2_451
| ~ spl2_585 ),
inference(avatar_split_clause,[],[f30656,f30513,f16617,f30695]) ).
fof(f30656,plain,
( ! [X14,X13] :
( is_a_theorem(implies(X13,X14))
| ~ is_a_theorem(not(not(X14))) )
| ~ spl2_451
| ~ spl2_585 ),
inference(resolution,[],[f30514,f16618]) ).
fof(f30693,plain,
( spl2_590
| ~ spl2_24
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3246,f2598,f290,f30691]) ).
fof(f30691,plain,
( spl2_590
<=> ! [X5,X4,X6,X3] : or(strict_implies(X3,and(X4,not(X5))),X6) = implies(possibly(and(X3,implies(X4,X5))),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_590])]) ).
fof(f3246,plain,
( ! [X3,X6,X4,X5] : or(strict_implies(X3,and(X4,not(X5))),X6) = implies(possibly(and(X3,implies(X4,X5))),X6)
| ~ spl2_24
| ~ spl2_148 ),
inference(superposition,[],[f291,f2599]) ).
fof(f30593,plain,
( spl2_589
| ~ spl2_33
| ~ spl2_141 ),
inference(avatar_split_clause,[],[f2861,f2474,f340,f30591]) ).
fof(f30591,plain,
( spl2_589
<=> ! [X0,X1] : strict_equiv(not(X1),not(X0)) = and(necessarily(or(X1,not(X0))),necessarily(or(X0,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_589])]) ).
fof(f2861,plain,
( ! [X0,X1] : strict_equiv(not(X1),not(X0)) = and(necessarily(or(X1,not(X0))),necessarily(or(X0,not(X1))))
| ~ spl2_33
| ~ spl2_141 ),
inference(superposition,[],[f2475,f341]) ).
fof(f30527,plain,
( spl2_588
| ~ spl2_76
| ~ spl2_554 ),
inference(avatar_split_clause,[],[f30335,f29240,f810,f30525]) ).
fof(f30335,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(possibly(X2),not(and(possibly(X2),X1)))))
| ~ spl2_76
| ~ spl2_554 ),
inference(superposition,[],[f29241,f811]) ).
fof(f30523,plain,
( spl2_587
| ~ spl2_76
| ~ spl2_553 ),
inference(avatar_split_clause,[],[f30289,f29236,f810,f30521]) ).
fof(f30289,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),implies(X4,X2)))
| ~ spl2_76
| ~ spl2_553 ),
inference(superposition,[],[f29237,f811]) ).
fof(f30519,plain,
( spl2_586
| ~ spl2_104
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1968,f1558,f1388,f30517]) ).
fof(f30517,plain,
( spl2_586
<=> ! [X82,X81,X83] : implies(possibly(strict_implies(X81,necessarily(not(X82)))),X83) = or(X83,necessarily(possibly(and(X81,possibly(X82))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_586])]) ).
fof(f1968,plain,
( ! [X82,X83,X81] : implies(possibly(strict_implies(X81,necessarily(not(X82)))),X83) = or(X83,necessarily(possibly(and(X81,possibly(X82)))))
| ~ spl2_104
| ~ spl2_112 ),
inference(superposition,[],[f1389,f1559]) ).
fof(f30515,plain,
( spl2_585
| ~ spl2_27
| ~ spl2_553 ),
inference(avatar_split_clause,[],[f30268,f29236,f302,f30513]) ).
fof(f30268,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(and(not(not(X1)),X2)) )
| ~ spl2_27
| ~ spl2_553 ),
inference(resolution,[],[f29237,f303]) ).
fof(f30511,plain,
( spl2_584
| ~ spl2_24
| ~ spl2_394
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29328,f29220,f14165,f290,f30509]) ).
fof(f14165,plain,
( spl2_394
<=> ! [X18,X17,X19] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(not(not(X17)),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_394])]) ).
fof(f29328,plain,
( ! [X101,X99,X100] :
( ~ is_a_theorem(not(or(not(X99),X100)))
| is_a_theorem(or(X99,X101)) )
| ~ spl2_24
| ~ spl2_394
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29294,f291]) ).
fof(f29294,plain,
( ! [X101,X99,X100] :
( ~ is_a_theorem(not(implies(not(not(X99)),X100)))
| is_a_theorem(or(X99,X101)) )
| ~ spl2_394
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14166]) ).
fof(f14166,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(not(not(X17)),X19))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_394 ),
inference(avatar_component_clause,[],[f14165]) ).
fof(f30507,plain,
( spl2_583
| ~ spl2_24
| ~ spl2_398
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29327,f29220,f14312,f290,f30505]) ).
fof(f14312,plain,
( spl2_398
<=> ! [X18,X17,X19] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(not(not(X18)),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_398])]) ).
fof(f29327,plain,
( ! [X98,X96,X97] :
( ~ is_a_theorem(not(or(not(X96),X97)))
| is_a_theorem(or(X98,X96)) )
| ~ spl2_24
| ~ spl2_398
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29293,f291]) ).
fof(f29293,plain,
( ! [X98,X96,X97] :
( ~ is_a_theorem(not(implies(not(not(X96)),X97)))
| is_a_theorem(or(X98,X96)) )
| ~ spl2_398
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14313]) ).
fof(f14313,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(not(not(X18)),X19))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_398 ),
inference(avatar_component_clause,[],[f14312]) ).
fof(f30503,plain,
( spl2_582
| ~ spl2_38
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1946,f1558,f377,f30501]) ).
fof(f30501,plain,
( spl2_582
<=> ! [X18,X16,X17] : not(strict_implies(X18,strict_implies(X16,necessarily(not(X17))))) = possibly(and(X18,possibly(and(X16,possibly(X17))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_582])]) ).
fof(f1946,plain,
( ! [X18,X16,X17] : not(strict_implies(X18,strict_implies(X16,necessarily(not(X17))))) = possibly(and(X18,possibly(and(X16,possibly(X17)))))
| ~ spl2_38
| ~ spl2_112 ),
inference(superposition,[],[f378,f1559]) ).
fof(f30499,plain,
( spl2_581
| ~ spl2_400
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29264,f29220,f14320,f30497]) ).
fof(f14320,plain,
( spl2_400
<=> ! [X18,X17,X19] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(X19,not(not(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_400])]) ).
fof(f29264,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(implies(X15,not(X16))))
| is_a_theorem(or(X16,X17)) )
| ~ spl2_400
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14321]) ).
fof(f14321,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(X19,not(not(X17))))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_400 ),
inference(avatar_component_clause,[],[f14320]) ).
fof(f30495,plain,
( spl2_580
| ~ spl2_405
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29263,f29220,f14447,f30493]) ).
fof(f14447,plain,
( spl2_405
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X3,not(not(X2))))
| is_a_theorem(or(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_405])]) ).
fof(f29263,plain,
( ! [X14,X12,X13] :
( ~ is_a_theorem(not(implies(X12,not(X13))))
| is_a_theorem(or(X14,X13)) )
| ~ spl2_405
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14448]) ).
fof(f14448,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,not(not(X2))))
| is_a_theorem(or(X4,X2)) )
| ~ spl2_405 ),
inference(avatar_component_clause,[],[f14447]) ).
fof(f30399,plain,
( spl2_579
| ~ spl2_37
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1945,f1558,f373,f30397]) ).
fof(f30397,plain,
( spl2_579
<=> ! [X13,X14,X15] : implies(possibly(strict_implies(X13,necessarily(not(X14)))),X15) = or(necessarily(possibly(and(X13,possibly(X14)))),X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_579])]) ).
fof(f1945,plain,
( ! [X14,X15,X13] : implies(possibly(strict_implies(X13,necessarily(not(X14)))),X15) = or(necessarily(possibly(and(X13,possibly(X14)))),X15)
| ~ spl2_37
| ~ spl2_112 ),
inference(superposition,[],[f374,f1559]) ).
fof(f30267,plain,
( spl2_578
| ~ spl2_54
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1478,f1462,f505,f30265]) ).
fof(f30265,plain,
( spl2_578
<=> ! [X2,X3] :
( ~ is_a_theorem(not(and(X2,possibly(X3))))
| ~ is_a_theorem(implies(necessarily(not(X3)),X2))
| necessarily(not(X3)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_578])]) ).
fof(f1478,plain,
( ! [X2,X3] :
( ~ is_a_theorem(not(and(X2,possibly(X3))))
| ~ is_a_theorem(implies(necessarily(not(X3)),X2))
| necessarily(not(X3)) = X2 )
| ~ spl2_54
| ~ spl2_106 ),
inference(superposition,[],[f1463,f506]) ).
fof(f30021,plain,
( spl2_577
| ~ spl2_147
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29885,f29224,f2594,f30019]) ).
fof(f2594,plain,
( spl2_147
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,and(X3,X2)))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_147])]) ).
fof(f29885,plain,
( ! [X111,X109,X110] :
( ~ is_a_theorem(not(implies(and(X109,X110),X111)))
| is_a_theorem(X110) )
| ~ spl2_147
| ~ spl2_550 ),
inference(resolution,[],[f29225,f2595]) ).
fof(f2595,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X3,X2)))
| is_a_theorem(X2) )
| ~ spl2_147 ),
inference(avatar_component_clause,[],[f2594]) ).
fof(f30017,plain,
( spl2_576
| ~ spl2_143
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29884,f29224,f2532,f30015]) ).
fof(f2532,plain,
( spl2_143
<=> ! [X9,X7,X8] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(X8,and(X7,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_143])]) ).
fof(f29884,plain,
( ! [X108,X106,X107] :
( ~ is_a_theorem(not(implies(and(X106,X107),X108)))
| is_a_theorem(X106) )
| ~ spl2_143
| ~ spl2_550 ),
inference(resolution,[],[f29225,f2533]) ).
fof(f2533,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(X8,and(X7,X9)))
| is_a_theorem(X7) )
| ~ spl2_143 ),
inference(avatar_component_clause,[],[f2532]) ).
fof(f29950,plain,
( spl2_575
| ~ spl2_492
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29853,f29224,f22909,f29948]) ).
fof(f29948,plain,
( spl2_575
<=> ! [X20,X21] :
( ~ is_a_theorem(not(implies(or(X20,X21),X20)))
| is_a_theorem(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_575])]) ).
fof(f22909,plain,
( spl2_492
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_492])]) ).
fof(f29853,plain,
( ! [X21,X20] :
( ~ is_a_theorem(not(implies(or(X20,X21),X20)))
| is_a_theorem(X21) )
| ~ spl2_492
| ~ spl2_550 ),
inference(resolution,[],[f29225,f22910]) ).
fof(f22910,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X1,X0)))
| is_a_theorem(X0) )
| ~ spl2_492 ),
inference(avatar_component_clause,[],[f22909]) ).
fof(f29946,plain,
( spl2_574
| ~ spl2_491
| ~ spl2_550 ),
inference(avatar_split_clause,[],[f29852,f29224,f22905,f29944]) ).
fof(f29944,plain,
( spl2_574
<=> ! [X18,X19] :
( ~ is_a_theorem(not(implies(or(X18,X19),X19)))
| is_a_theorem(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_574])]) ).
fof(f22905,plain,
( spl2_491
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_491])]) ).
fof(f29852,plain,
( ! [X18,X19] :
( ~ is_a_theorem(not(implies(or(X18,X19),X19)))
| is_a_theorem(X18) )
| ~ spl2_491
| ~ spl2_550 ),
inference(resolution,[],[f29225,f22906]) ).
fof(f22906,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X0,X1)))
| is_a_theorem(X0) )
| ~ spl2_491 ),
inference(avatar_component_clause,[],[f22905]) ).
fof(f29690,plain,
( spl2_573
| ~ spl2_76
| ~ spl2_570 ),
inference(avatar_split_clause,[],[f29576,f29557,f810,f29688]) ).
fof(f29688,plain,
( spl2_573
<=> ! [X2,X1] :
( ~ is_a_theorem(not(not(and(possibly(X2),X1))))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_573])]) ).
fof(f29557,plain,
( spl2_570
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(and(X0,possibly(X1)))))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_570])]) ).
fof(f29576,plain,
( ! [X2,X1] :
( ~ is_a_theorem(not(not(and(possibly(X2),X1))))
| is_a_theorem(X1) )
| ~ spl2_76
| ~ spl2_570 ),
inference(superposition,[],[f29558,f811]) ).
fof(f29558,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(and(X0,possibly(X1)))))
| is_a_theorem(X0) )
| ~ spl2_570 ),
inference(avatar_component_clause,[],[f29557]) ).
fof(f29567,plain,
( spl2_572
| ~ spl2_83
| ~ spl2_569 ),
inference(avatar_split_clause,[],[f29473,f29459,f1024,f29565]) ).
fof(f29565,plain,
( spl2_572
<=> ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_572])]) ).
fof(f29459,plain,
( spl2_569
<=> ! [X91,X92,X90] :
( ~ is_a_theorem(not(or(X90,X91)))
| is_a_theorem(implies(X90,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_569])]) ).
fof(f29473,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(not(X0))))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_83
| ~ spl2_569 ),
inference(superposition,[],[f29460,f1025]) ).
fof(f29460,plain,
( ! [X90,X91,X92] :
( ~ is_a_theorem(not(or(X90,X91)))
| is_a_theorem(implies(X90,X92)) )
| ~ spl2_569 ),
inference(avatar_component_clause,[],[f29459]) ).
fof(f29563,plain,
( spl2_571
| ~ spl2_24
| ~ spl2_567 ),
inference(avatar_split_clause,[],[f29466,f29451,f290,f29561]) ).
fof(f29561,plain,
( spl2_571
<=> ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(implies(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_571])]) ).
fof(f29451,plain,
( spl2_567
<=> ! [X6,X7,X8] :
( ~ is_a_theorem(not(implies(X6,X7)))
| is_a_theorem(implies(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_567])]) ).
fof(f29466,plain,
( ! [X16,X17,X15] :
( ~ is_a_theorem(not(or(X15,X16)))
| is_a_theorem(implies(X16,X17)) )
| ~ spl2_24
| ~ spl2_567 ),
inference(superposition,[],[f29452,f291]) ).
fof(f29452,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(implies(X6,X7)))
| is_a_theorem(implies(X7,X8)) )
| ~ spl2_567 ),
inference(avatar_component_clause,[],[f29451]) ).
fof(f29559,plain,
( spl2_570
| ~ spl2_54
| ~ spl2_560 ),
inference(avatar_split_clause,[],[f29340,f29337,f505,f29557]) ).
fof(f29340,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(and(X0,possibly(X1)))))
| is_a_theorem(X0) )
| ~ spl2_54
| ~ spl2_560 ),
inference(superposition,[],[f29338,f506]) ).
fof(f29461,plain,
( spl2_569
| ~ spl2_24
| ~ spl2_384
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29325,f29220,f13659,f290,f29459]) ).
fof(f29325,plain,
( ! [X90,X91,X92] :
( ~ is_a_theorem(not(or(X90,X91)))
| is_a_theorem(implies(X90,X92)) )
| ~ spl2_24
| ~ spl2_384
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29291,f291]) ).
fof(f29291,plain,
( ! [X90,X91,X92] :
( ~ is_a_theorem(not(implies(not(X90),X91)))
| is_a_theorem(implies(X90,X92)) )
| ~ spl2_384
| ~ spl2_549 ),
inference(resolution,[],[f29221,f13660]) ).
fof(f29457,plain,
( spl2_568
| ~ spl2_34
| ~ spl2_91
| ~ spl2_122
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24686,f23260,f1831,f1092,f344,f29455]) ).
fof(f29455,plain,
( spl2_568
<=> ! [X55,X54,X53,X56] :
( ~ is_a_theorem(strict_implies(X53,and(X54,strict_equiv(X56,X55))))
| is_a_theorem(strict_implies(X53,and(X54,strict_equiv(X55,X56)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_568])]) ).
fof(f1092,plain,
( spl2_91
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X1,X0),and(X2,strict_implies(X0,X1))),and(X2,strict_equiv(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).
fof(f24686,plain,
( ! [X56,X54,X55,X53] :
( ~ is_a_theorem(strict_implies(X53,and(X54,strict_equiv(X56,X55))))
| is_a_theorem(strict_implies(X53,and(X54,strict_equiv(X55,X56)))) )
| ~ spl2_34
| ~ spl2_91
| ~ spl2_122
| ~ spl2_504 ),
inference(backward_demodulation,[],[f2325,f24170]) ).
fof(f2325,plain,
( ! [X56,X54,X55,X53] :
( is_a_theorem(strict_implies(X53,and(X54,strict_equiv(X55,X56))))
| ~ is_a_theorem(strict_implies(X53,and(strict_implies(X56,X55),and(X54,strict_implies(X55,X56))))) )
| ~ spl2_91
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1093]) ).
fof(f1093,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X1,X0),and(X2,strict_implies(X0,X1))),and(X2,strict_equiv(X0,X1))))
| ~ spl2_91 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f29453,plain,
( spl2_567
| ~ spl2_388
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29261,f29220,f14079,f29451]) ).
fof(f29261,plain,
( ! [X8,X6,X7] :
( ~ is_a_theorem(not(implies(X6,X7)))
| is_a_theorem(implies(X7,X8)) )
| ~ spl2_388
| ~ spl2_549 ),
inference(resolution,[],[f29221,f14080]) ).
fof(f29419,plain,
( spl2_566
| ~ spl2_24
| ~ spl2_561 ),
inference(avatar_split_clause,[],[f29367,f29352,f290,f29417]) ).
fof(f29417,plain,
( spl2_566
<=> ! [X11,X12] :
( ~ is_a_theorem(not(or(X11,X12)))
| is_a_theorem(not(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_566])]) ).
fof(f29367,plain,
( ! [X11,X12] :
( ~ is_a_theorem(not(or(X11,X12)))
| is_a_theorem(not(X12)) )
| ~ spl2_24
| ~ spl2_561 ),
inference(superposition,[],[f29353,f291]) ).
fof(f29415,plain,
( spl2_565
| ~ spl2_36
| ~ spl2_94
| ~ spl2_122
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24589,f23260,f1831,f1114,f363,f29413]) ).
fof(f29413,plain,
( spl2_565
<=> ! [X38,X40,X39,X37] :
( ~ is_a_theorem(strict_implies(X37,and(X38,equiv(X40,X39))))
| is_a_theorem(strict_implies(X37,and(X38,equiv(X39,X40)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_565])]) ).
fof(f1114,plain,
( spl2_94
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(implies(X4,X3),and(X5,implies(X3,X4))),and(X5,equiv(X3,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).
fof(f24589,plain,
( ! [X40,X38,X39,X37] :
( ~ is_a_theorem(strict_implies(X37,and(X38,equiv(X40,X39))))
| is_a_theorem(strict_implies(X37,and(X38,equiv(X39,X40)))) )
| ~ spl2_36
| ~ spl2_94
| ~ spl2_122
| ~ spl2_504 ),
inference(backward_demodulation,[],[f2321,f24160]) ).
fof(f2321,plain,
( ! [X40,X38,X39,X37] :
( is_a_theorem(strict_implies(X37,and(X38,equiv(X39,X40))))
| ~ is_a_theorem(strict_implies(X37,and(implies(X40,X39),and(X38,implies(X39,X40))))) )
| ~ spl2_94
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1115]) ).
fof(f1115,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(implies(X4,X3),and(X5,implies(X3,X4))),and(X5,equiv(X3,X4))))
| ~ spl2_94 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f29411,plain,
( spl2_564
| ~ spl2_24
| ~ spl2_560 ),
inference(avatar_split_clause,[],[f29344,f29337,f290,f29409]) ).
fof(f29409,plain,
( spl2_564
<=> ! [X11,X12] :
( ~ is_a_theorem(not(or(X11,X12)))
| is_a_theorem(not(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_564])]) ).
fof(f29344,plain,
( ! [X11,X12] :
( ~ is_a_theorem(not(or(X11,X12)))
| is_a_theorem(not(X11)) )
| ~ spl2_24
| ~ spl2_560 ),
inference(superposition,[],[f29338,f291]) ).
fof(f29362,plain,
( spl2_563
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20312,f19362,f14372,f810,f29360]) ).
fof(f29360,plain,
( spl2_563
<=> ! [X48,X47,X46,X45] :
( ~ is_a_theorem(strict_implies(X45,and(X47,and(X46,X48))))
| is_a_theorem(strict_implies(X45,and(X46,and(X47,X48)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_563])]) ).
fof(f20312,plain,
( ! [X48,X46,X47,X45] :
( ~ is_a_theorem(strict_implies(X45,and(X47,and(X46,X48))))
| is_a_theorem(strict_implies(X45,and(X46,and(X47,X48)))) )
| ~ spl2_76
| ~ spl2_403
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14373,f19383]) ).
fof(f29358,plain,
( spl2_562
| ~ spl2_24
| ~ spl2_495
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29322,f29220,f22997,f290,f29356]) ).
fof(f29322,plain,
( ! [X83] :
( ~ is_a_theorem(not(or(X83,not(X83))))
| is_a_theorem(X83) )
| ~ spl2_24
| ~ spl2_495
| ~ spl2_549 ),
inference(forward_demodulation,[],[f29288,f291]) ).
fof(f29288,plain,
( ! [X83] :
( ~ is_a_theorem(not(implies(not(X83),not(X83))))
| is_a_theorem(X83) )
| ~ spl2_495
| ~ spl2_549 ),
inference(resolution,[],[f29221,f22998]) ).
fof(f29354,plain,
( spl2_561
| ~ spl2_82
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29267,f29220,f915,f29352]) ).
fof(f915,plain,
( spl2_82
<=> ! [X9,X10] :
( ~ is_a_theorem(and(X10,X9))
| is_a_theorem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_82])]) ).
fof(f29267,plain,
( ! [X22,X23] :
( ~ is_a_theorem(not(implies(X22,X23)))
| is_a_theorem(not(X23)) )
| ~ spl2_82
| ~ spl2_549 ),
inference(resolution,[],[f29221,f916]) ).
fof(f916,plain,
( ! [X10,X9] :
( ~ is_a_theorem(and(X10,X9))
| is_a_theorem(X9) )
| ~ spl2_82 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f29339,plain,
( spl2_560
| ~ spl2_30
| ~ spl2_549 ),
inference(avatar_split_clause,[],[f29265,f29220,f319,f29337]) ).
fof(f29265,plain,
( ! [X18,X19] :
( ~ is_a_theorem(not(implies(X18,X19)))
| is_a_theorem(X18) )
| ~ spl2_30
| ~ spl2_549 ),
inference(resolution,[],[f29221,f320]) ).
fof(f29335,plain,
( spl2_559
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_122
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20163,f19362,f1831,f1050,f810,f344,f29333]) ).
fof(f29333,plain,
( spl2_559
<=> ! [X59,X57,X58,X60] :
( is_a_theorem(strict_implies(X57,and(strict_equiv(X59,X58),X60)))
| ~ is_a_theorem(strict_implies(X57,and(strict_equiv(X58,X59),X60))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_559])]) ).
fof(f20163,plain,
( ! [X58,X59,X57,X60] :
( is_a_theorem(strict_implies(X57,and(strict_equiv(X59,X58),X60)))
| ~ is_a_theorem(strict_implies(X57,and(strict_equiv(X58,X59),X60))) )
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_122
| ~ spl2_486 ),
inference(backward_demodulation,[],[f2326,f20156]) ).
fof(f2326,plain,
( ! [X58,X59,X57,X60] :
( is_a_theorem(strict_implies(X57,and(strict_implies(X58,X59),and(strict_implies(X59,X58),X60))))
| ~ is_a_theorem(strict_implies(X57,and(strict_equiv(X58,X59),X60))) )
| ~ spl2_85
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1051]) ).
fof(f29258,plain,
( spl2_558
| ~ spl2_24
| ~ spl2_539 ),
inference(avatar_split_clause,[],[f28760,f28611,f290,f29256]) ).
fof(f29256,plain,
( spl2_558
<=> ! [X11,X12] :
( ~ is_a_theorem(implies(or(X11,X12),not(X12)))
| is_a_theorem(not(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_558])]) ).
fof(f28611,plain,
( spl2_539
<=> ! [X2,X3] :
( ~ is_a_theorem(implies(implies(X3,X2),not(X2)))
| is_a_theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_539])]) ).
fof(f28760,plain,
( ! [X11,X12] :
( ~ is_a_theorem(implies(or(X11,X12),not(X12)))
| is_a_theorem(not(X12)) )
| ~ spl2_24
| ~ spl2_539 ),
inference(superposition,[],[f28612,f291]) ).
fof(f28612,plain,
( ! [X2,X3] :
( ~ is_a_theorem(implies(implies(X3,X2),not(X2)))
| is_a_theorem(not(X2)) )
| ~ spl2_539 ),
inference(avatar_component_clause,[],[f28611]) ).
fof(f29254,plain,
( spl2_557
| ~ spl2_311
| ~ spl2_538 ),
inference(avatar_split_clause,[],[f28745,f28607,f9479,f29252]) ).
fof(f29252,plain,
( spl2_557
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(and(X0,X2),X1),X0))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_557])]) ).
fof(f28607,plain,
( spl2_538
<=> ! [X22,X21,X23] :
( ~ is_a_theorem(or(X21,and(X23,and(X21,X22))))
| is_a_theorem(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_538])]) ).
fof(f28745,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(and(X0,X2),X1),X0))
| is_a_theorem(X0) )
| ~ spl2_311
| ~ spl2_538 ),
inference(superposition,[],[f28608,f9480]) ).
fof(f28608,plain,
( ! [X21,X22,X23] :
( ~ is_a_theorem(or(X21,and(X23,and(X21,X22))))
| is_a_theorem(X21) )
| ~ spl2_538 ),
inference(avatar_component_clause,[],[f28607]) ).
fof(f29250,plain,
( spl2_556
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_122
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20028,f19362,f1831,f1074,f810,f363,f29248]) ).
fof(f29248,plain,
( spl2_556
<=> ! [X41,X42,X44,X43] :
( is_a_theorem(strict_implies(X41,and(equiv(X43,X42),X44)))
| ~ is_a_theorem(strict_implies(X41,and(equiv(X42,X43),X44))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_556])]) ).
fof(f20028,plain,
( ! [X41,X44,X42,X43] :
( is_a_theorem(strict_implies(X41,and(equiv(X43,X42),X44)))
| ~ is_a_theorem(strict_implies(X41,and(equiv(X42,X43),X44))) )
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_122
| ~ spl2_486 ),
inference(backward_demodulation,[],[f2322,f20021]) ).
fof(f2322,plain,
( ! [X41,X44,X42,X43] :
( is_a_theorem(strict_implies(X41,and(implies(X42,X43),and(implies(X43,X42),X44))))
| ~ is_a_theorem(strict_implies(X41,and(equiv(X42,X43),X44))) )
| ~ spl2_88
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1075]) ).
fof(f29246,plain,
( spl2_555
| ~ spl2_311
| ~ spl2_537 ),
inference(avatar_split_clause,[],[f28687,f28603,f9479,f29244]) ).
fof(f29244,plain,
( spl2_555
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(and(X2,X0),X1),X0))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_555])]) ).
fof(f28603,plain,
( spl2_537
<=> ! [X20,X18,X19] :
( ~ is_a_theorem(or(X18,and(X19,and(X20,X18))))
| is_a_theorem(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_537])]) ).
fof(f28687,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(and(X2,X0),X1),X0))
| is_a_theorem(X0) )
| ~ spl2_311
| ~ spl2_537 ),
inference(superposition,[],[f28604,f9480]) ).
fof(f28604,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(or(X18,and(X19,and(X20,X18))))
| is_a_theorem(X18) )
| ~ spl2_537 ),
inference(avatar_component_clause,[],[f28603]) ).
fof(f29242,plain,
( spl2_554
| ~ spl2_20
| ~ spl2_54
| ~ spl2_535 ),
inference(avatar_split_clause,[],[f28597,f28565,f505,f273,f29240]) ).
fof(f28597,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(possibly(X0),not(and(X1,possibly(X0))))))
| ~ spl2_20
| ~ spl2_54
| ~ spl2_535 ),
inference(forward_demodulation,[],[f28573,f506]) ).
fof(f28573,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(possibly(X0),implies(X1,necessarily(not(X0))))))
| ~ spl2_20
| ~ spl2_535 ),
inference(superposition,[],[f28566,f274]) ).
fof(f29238,plain,
( spl2_553
| ~ spl2_380
| ~ spl2_535 ),
inference(avatar_split_clause,[],[f28572,f28565,f13441,f29236]) ).
fof(f28572,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),implies(X2,X0)))
| ~ spl2_380
| ~ spl2_535 ),
inference(resolution,[],[f28566,f13442]) ).
fof(f29234,plain,
( spl2_552
| ~ spl2_24
| ~ spl2_528 ),
inference(avatar_split_clause,[],[f28184,f28128,f290,f29232]) ).
fof(f29232,plain,
( spl2_552
<=> ! [X12,X11] :
( ~ is_a_theorem(implies(or(X11,X12),not(X11)))
| is_a_theorem(not(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_552])]) ).
fof(f28128,plain,
( spl2_528
<=> ! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_528])]) ).
fof(f28184,plain,
( ! [X11,X12] :
( ~ is_a_theorem(implies(or(X11,X12),not(X11)))
| is_a_theorem(not(X11)) )
| ~ spl2_24
| ~ spl2_528 ),
inference(superposition,[],[f28129,f291]) ).
fof(f28129,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(X0) )
| ~ spl2_528 ),
inference(avatar_component_clause,[],[f28128]) ).
fof(f29230,plain,
( spl2_551
| ~ spl2_33
| ~ spl2_141
| ~ spl2_197
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24666,f23260,f4144,f2474,f340,f29228]) ).
fof(f29228,plain,
( spl2_551
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,strict_equiv(not(X0),X1)))
| is_a_theorem(and(X2,strict_equiv(X1,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_551])]) ).
fof(f4144,plain,
( spl2_197
<=> ! [X4,X5,X3] :
( is_a_theorem(and(X3,strict_equiv(X4,X5)))
| ~ is_a_theorem(and(strict_implies(X5,X4),and(X3,strict_implies(X4,X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_197])]) ).
fof(f24666,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,strict_equiv(not(X0),X1)))
| is_a_theorem(and(X2,strict_equiv(X1,not(X0)))) )
| ~ spl2_33
| ~ spl2_141
| ~ spl2_197
| ~ spl2_504 ),
inference(backward_demodulation,[],[f4384,f24169]) ).
fof(f4384,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X0,X1)),and(X2,strict_implies(X1,not(X0)))))
| is_a_theorem(and(X2,strict_equiv(X1,not(X0)))) )
| ~ spl2_33
| ~ spl2_197 ),
inference(superposition,[],[f4145,f341]) ).
fof(f4145,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(strict_implies(X5,X4),and(X3,strict_implies(X4,X5))))
| is_a_theorem(and(X3,strict_equiv(X4,X5))) )
| ~ spl2_197 ),
inference(avatar_component_clause,[],[f4144]) ).
fof(f29226,plain,
( spl2_550
| ~ spl2_96
| ~ spl2_525 ),
inference(avatar_split_clause,[],[f27878,f27866,f1122,f29224]) ).
fof(f27866,plain,
( spl2_525
<=> ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_525])]) ).
fof(f27878,plain,
( ! [X19,X20] :
( ~ is_a_theorem(not(implies(X20,X19)))
| is_a_theorem(and(not(X19),X20)) )
| ~ spl2_96
| ~ spl2_525 ),
inference(superposition,[],[f27867,f1123]) ).
fof(f27867,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) )
| ~ spl2_525 ),
inference(avatar_component_clause,[],[f27866]) ).
fof(f29222,plain,
( spl2_549
| ~ spl2_29
| ~ spl2_525 ),
inference(avatar_split_clause,[],[f27875,f27866,f315,f29220]) ).
fof(f27875,plain,
( ! [X12,X13] :
( ~ is_a_theorem(not(implies(X12,X13)))
| is_a_theorem(and(X12,not(X13))) )
| ~ spl2_29
| ~ spl2_525 ),
inference(superposition,[],[f27867,f316]) ).
fof(f29162,plain,
( spl2_548
| ~ spl2_33
| ~ spl2_76
| ~ spl2_141
| ~ spl2_190
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20138,f19362,f4074,f2474,f810,f340,f29160]) ).
fof(f29160,plain,
( spl2_548
<=> ! [X2,X0,X1] :
( is_a_theorem(and(strict_equiv(not(X0),X1),X2))
| ~ is_a_theorem(and(strict_equiv(X1,not(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_548])]) ).
fof(f20138,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(strict_equiv(not(X0),X1),X2))
| ~ is_a_theorem(and(strict_equiv(X1,not(X0)),X2)) )
| ~ spl2_33
| ~ spl2_76
| ~ spl2_141
| ~ spl2_190
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4192,f20136]) ).
fof(f4192,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(strict_implies(X1,not(X0)),and(necessarily(or(X0,X1)),X2)))
| ~ is_a_theorem(and(strict_equiv(X1,not(X0)),X2)) )
| ~ spl2_33
| ~ spl2_190 ),
inference(superposition,[],[f4075,f341]) ).
fof(f29011,plain,
( spl2_547
| ~ spl2_76
| ~ spl2_546 ),
inference(avatar_split_clause,[],[f28961,f28951,f810,f29009]) ).
fof(f28961,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X3,implies(and(X3,X2),X4))))
| ~ spl2_76
| ~ spl2_546 ),
inference(superposition,[],[f28952,f811]) ).
fof(f28953,plain,
( spl2_546
| ~ spl2_327
| ~ spl2_542 ),
inference(avatar_split_clause,[],[f28860,f28623,f10547,f28951]) ).
fof(f28860,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X1,X0),X2))))
| ~ spl2_327
| ~ spl2_542 ),
inference(resolution,[],[f28624,f10548]) ).
fof(f28637,plain,
( spl2_545
| ~ spl2_24
| ~ spl2_533 ),
inference(avatar_split_clause,[],[f28526,f28313,f290,f28635]) ).
fof(f28526,plain,
( ! [X11,X12] : is_a_theorem(strict_implies(implies(or(X11,X12),not(X12)),not(X12)))
| ~ spl2_24
| ~ spl2_533 ),
inference(superposition,[],[f28314,f291]) ).
fof(f28633,plain,
( spl2_544
| ~ spl2_34
| ~ spl2_76
| ~ spl2_397
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20174,f19362,f14308,f810,f344,f28631]) ).
fof(f28631,plain,
( spl2_544
<=> ! [X22,X20,X21] :
( is_a_theorem(and(strict_equiv(X21,X20),X22))
| ~ is_a_theorem(strict_equiv(X20,X21))
| ~ is_a_theorem(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_544])]) ).
fof(f14308,plain,
( spl2_397
<=> ! [X22,X20,X21] :
( ~ is_a_theorem(strict_equiv(X20,X21))
| ~ is_a_theorem(X22)
| is_a_theorem(and(strict_implies(X20,X21),and(strict_implies(X21,X20),X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_397])]) ).
fof(f20174,plain,
( ! [X21,X22,X20] :
( is_a_theorem(and(strict_equiv(X21,X20),X22))
| ~ is_a_theorem(strict_equiv(X20,X21))
| ~ is_a_theorem(X22) )
| ~ spl2_34
| ~ spl2_76
| ~ spl2_397
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14309,f20156]) ).
fof(f14309,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(strict_equiv(X20,X21))
| ~ is_a_theorem(X22)
| is_a_theorem(and(strict_implies(X20,X21),and(strict_implies(X21,X20),X22))) )
| ~ spl2_397 ),
inference(avatar_component_clause,[],[f14308]) ).
fof(f28629,plain,
( spl2_543
| ~ spl2_311
| ~ spl2_532 ),
inference(avatar_split_clause,[],[f28485,f28309,f9479,f28627]) ).
fof(f28485,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X0,X2),X1),X0),X0))
| ~ spl2_311
| ~ spl2_532 ),
inference(superposition,[],[f28310,f9480]) ).
fof(f28625,plain,
( spl2_542
| ~ spl2_311
| ~ spl2_531 ),
inference(avatar_split_clause,[],[f28389,f28305,f9479,f28623]) ).
fof(f28389,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(implies(implies(and(X2,X0),X1),X0),X0))
| ~ spl2_311
| ~ spl2_531 ),
inference(superposition,[],[f28306,f9480]) ).
fof(f28621,plain,
( spl2_541
| ~ spl2_24
| ~ spl2_524 ),
inference(avatar_split_clause,[],[f28017,f27818,f290,f28619]) ).
fof(f28619,plain,
( spl2_541
<=> ! [X12,X11] : is_a_theorem(strict_implies(implies(or(X11,X12),not(X11)),not(X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_541])]) ).
fof(f28017,plain,
( ! [X11,X12] : is_a_theorem(strict_implies(implies(or(X11,X12),not(X11)),not(X11)))
| ~ spl2_24
| ~ spl2_524 ),
inference(superposition,[],[f27819,f291]) ).
fof(f28617,plain,
( spl2_540
| ~ spl2_36
| ~ spl2_76
| ~ spl2_395
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20039,f19362,f14216,f810,f363,f28615]) ).
fof(f28615,plain,
( spl2_540
<=> ! [X16,X14,X15] :
( is_a_theorem(and(equiv(X15,X14),X16))
| ~ is_a_theorem(equiv(X14,X15))
| ~ is_a_theorem(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_540])]) ).
fof(f14216,plain,
( spl2_395
<=> ! [X16,X14,X15] :
( ~ is_a_theorem(equiv(X14,X15))
| ~ is_a_theorem(X16)
| is_a_theorem(and(implies(X14,X15),and(implies(X15,X14),X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_395])]) ).
fof(f20039,plain,
( ! [X16,X14,X15] :
( is_a_theorem(and(equiv(X15,X14),X16))
| ~ is_a_theorem(equiv(X14,X15))
| ~ is_a_theorem(X16) )
| ~ spl2_36
| ~ spl2_76
| ~ spl2_395
| ~ spl2_486 ),
inference(backward_demodulation,[],[f14217,f20021]) ).
fof(f14217,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(equiv(X14,X15))
| ~ is_a_theorem(X16)
| is_a_theorem(and(implies(X14,X15),and(implies(X15,X14),X16))) )
| ~ spl2_395 ),
inference(avatar_component_clause,[],[f14216]) ).
fof(f28613,plain,
( spl2_539
| ~ spl2_311
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27856,f27806,f9479,f28611]) ).
fof(f27856,plain,
( ! [X2,X3] :
( ~ is_a_theorem(implies(implies(X3,X2),not(X2)))
| is_a_theorem(not(X2)) )
| ~ spl2_311
| ~ spl2_521 ),
inference(superposition,[],[f27807,f9480]) ).
fof(f28609,plain,
( spl2_538
| ~ spl2_517
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27830,f27806,f26955,f28607]) ).
fof(f27830,plain,
( ! [X21,X22,X23] :
( ~ is_a_theorem(or(X21,and(X23,and(X21,X22))))
| is_a_theorem(X21) )
| ~ spl2_517
| ~ spl2_521 ),
inference(superposition,[],[f27807,f26956]) ).
fof(f28605,plain,
( spl2_537
| ~ spl2_517
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27829,f27806,f26955,f28603]) ).
fof(f27829,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(or(X18,and(X19,and(X20,X18))))
| is_a_theorem(X18) )
| ~ spl2_517
| ~ spl2_521 ),
inference(superposition,[],[f27807,f26956]) ).
fof(f28571,plain,
( spl2_536
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24667,f23260,f6149,f2474,f28569]) ).
fof(f28569,plain,
( spl2_536
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,strict_equiv(not(X0),X1)),and(X2,strict_equiv(X1,not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_536])]) ).
fof(f24667,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,strict_equiv(not(X0),X1)),and(X2,strict_equiv(X1,not(X0)))))
| ~ spl2_141
| ~ spl2_241
| ~ spl2_504 ),
inference(backward_demodulation,[],[f6150,f24169]) ).
fof(f28567,plain,
( spl2_535
| ~ spl2_327
| ~ spl2_533 ),
inference(avatar_split_clause,[],[f28512,f28313,f10547,f28565]) ).
fof(f28512,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(not(X0),implies(X1,X0))))
| ~ spl2_327
| ~ spl2_533 ),
inference(resolution,[],[f28314,f10548]) ).
fof(f28411,plain,
( spl2_534
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20139,f19362,f6129,f2474,f810,f28409]) ).
fof(f28409,plain,
( spl2_534
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X1,not(X0)),X2),and(strict_equiv(not(X0),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_534])]) ).
fof(f20139,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X1,not(X0)),X2),and(strict_equiv(not(X0),X1),X2)))
| ~ spl2_76
| ~ spl2_141
| ~ spl2_236
| ~ spl2_486 ),
inference(backward_demodulation,[],[f6130,f20136]) ).
fof(f28315,plain,
( spl2_533
| ~ spl2_311
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27773,f27681,f9479,f28313]) ).
fof(f27773,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(implies(implies(X3,X2),not(X2)),not(X2)))
| ~ spl2_311
| ~ spl2_520 ),
inference(superposition,[],[f27682,f9480]) ).
fof(f28311,plain,
( spl2_532
| ~ spl2_517
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27747,f27681,f26955,f28309]) ).
fof(f27747,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(or(X21,and(X23,and(X21,X22))),X21))
| ~ spl2_517
| ~ spl2_520 ),
inference(superposition,[],[f27682,f26956]) ).
fof(f28307,plain,
( spl2_531
| ~ spl2_517
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27746,f27681,f26955,f28305]) ).
fof(f27746,plain,
( ! [X18,X19,X20] : is_a_theorem(strict_implies(or(X18,and(X19,and(X20,X18))),X18))
| ~ spl2_517
| ~ spl2_520 ),
inference(superposition,[],[f27682,f26956]) ).
fof(f28265,plain,
( spl2_530
| ~ spl2_382
| ~ spl2_529 ),
inference(avatar_split_clause,[],[f28235,f28204,f13556,f28263]) ).
fof(f28263,plain,
( spl2_530
<=> ! [X6,X5] :
( ~ is_a_theorem(not(possibly(not(X5))))
| is_a_theorem(strict_implies(X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_530])]) ).
fof(f28235,plain,
( ! [X6,X5] :
( ~ is_a_theorem(not(possibly(not(X5))))
| is_a_theorem(strict_implies(X6,X5)) )
| ~ spl2_382
| ~ spl2_529 ),
inference(resolution,[],[f28205,f13557]) ).
fof(f28206,plain,
( spl2_529
| ~ spl2_20
| ~ spl2_525 ),
inference(avatar_split_clause,[],[f27869,f27866,f273,f28204]) ).
fof(f27869,plain,
( ! [X0] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(necessarily(not(X0))) )
| ~ spl2_20
| ~ spl2_525 ),
inference(superposition,[],[f27867,f274]) ).
fof(f28130,plain,
( spl2_528
| ~ spl2_125
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27855,f27806,f1852,f28128]) ).
fof(f27855,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(X0) )
| ~ spl2_125
| ~ spl2_521 ),
inference(superposition,[],[f27807,f1853]) ).
fof(f28067,plain,
( spl2_527
| ~ spl2_76
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27822,f27806,f810,f28065]) ).
fof(f28065,plain,
( spl2_527
<=> ! [X2,X1] :
( ~ is_a_theorem(or(X1,and(X2,X1)))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_527])]) ).
fof(f27822,plain,
( ! [X2,X1] :
( ~ is_a_theorem(or(X1,and(X2,X1)))
| is_a_theorem(X1) )
| ~ spl2_76
| ~ spl2_521 ),
inference(superposition,[],[f27807,f811]) ).
fof(f27885,plain,
( spl2_526
| ~ spl2_34
| ~ spl2_197
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24689,f23260,f4144,f344,f27883]) ).
fof(f27883,plain,
( spl2_526
<=> ! [X4,X5,X3] :
( ~ is_a_theorem(and(X3,strict_equiv(X5,X4)))
| is_a_theorem(and(X3,strict_equiv(X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_526])]) ).
fof(f24689,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(X3,strict_equiv(X5,X4)))
| is_a_theorem(and(X3,strict_equiv(X4,X5))) )
| ~ spl2_34
| ~ spl2_197
| ~ spl2_504 ),
inference(backward_demodulation,[],[f4145,f24170]) ).
fof(f27868,plain,
( spl2_525
| ~ spl2_72
| ~ spl2_83
| ~ spl2_521 ),
inference(avatar_split_clause,[],[f27861,f27806,f1024,f748,f27866]) ).
fof(f27861,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) )
| ~ spl2_72
| ~ spl2_83
| ~ spl2_521 ),
inference(forward_demodulation,[],[f27821,f1025]) ).
fof(f27821,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) )
| ~ spl2_72
| ~ spl2_521 ),
inference(superposition,[],[f27807,f749]) ).
fof(f27820,plain,
( spl2_524
| ~ spl2_125
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27772,f27681,f1852,f27818]) ).
fof(f27772,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(implies(implies(X0,X1),X0),X0))
| ~ spl2_125
| ~ spl2_520 ),
inference(superposition,[],[f27682,f1853]) ).
fof(f27816,plain,
( spl2_523
| ~ spl2_36
| ~ spl2_201
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24592,f23260,f4160,f363,f27814]) ).
fof(f27814,plain,
( spl2_523
<=> ! [X4,X5,X3] :
( ~ is_a_theorem(and(X3,equiv(X5,X4)))
| is_a_theorem(and(X3,equiv(X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_523])]) ).
fof(f24592,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(X3,equiv(X5,X4)))
| is_a_theorem(and(X3,equiv(X4,X5))) )
| ~ spl2_36
| ~ spl2_201
| ~ spl2_504 ),
inference(backward_demodulation,[],[f4161,f24160]) ).
fof(f27812,plain,
( spl2_522
| ~ spl2_76
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27739,f27681,f810,f27810]) ).
fof(f27739,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(or(X1,and(X2,X1)),X1))
| ~ spl2_76
| ~ spl2_520 ),
inference(superposition,[],[f27682,f811]) ).
fof(f27808,plain,
( spl2_521
| ~ spl2_27
| ~ spl2_520 ),
inference(avatar_split_clause,[],[f27714,f27681,f302,f27806]) ).
fof(f27714,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,and(X0,X1))) )
| ~ spl2_27
| ~ spl2_520 ),
inference(resolution,[],[f27682,f303]) ).
fof(f27683,plain,
( spl2_520
| ~ spl2_126
| ~ spl2_319
| ~ spl2_518 ),
inference(avatar_split_clause,[],[f27674,f26959,f9930,f1856,f27681]) ).
fof(f9930,plain,
( spl2_319
<=> ! [X2,X0,X1] : strict_implies(or(X0,X1),X2) = strict_implies(or(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_319])]) ).
fof(f27674,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(or(X0,and(X0,X1)),X0))
| ~ spl2_126
| ~ spl2_319
| ~ spl2_518 ),
inference(forward_demodulation,[],[f27645,f9931]) ).
fof(f9931,plain,
( ! [X2,X0,X1] : strict_implies(or(X0,X1),X2) = strict_implies(or(X1,X0),X2)
| ~ spl2_319 ),
inference(avatar_component_clause,[],[f9930]) ).
fof(f27645,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(or(and(X0,X1),X0),X0))
| ~ spl2_126
| ~ spl2_518 ),
inference(superposition,[],[f26960,f1857]) ).
fof(f26993,plain,
( spl2_519
| ~ spl2_136
| ~ spl2_489 ),
inference(avatar_split_clause,[],[f22837,f22739,f2344,f26991]) ).
fof(f22837,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(X43),or(X43,and(X44,X45))),X44))
| ~ spl2_136
| ~ spl2_489 ),
inference(resolution,[],[f22740,f2345]) ).
fof(f26961,plain,
( spl2_518
| ~ spl2_136
| ~ spl2_487 ),
inference(avatar_split_clause,[],[f22758,f22731,f2344,f26959]) ).
fof(f22758,plain,
( ! [X44,X45,X43] : is_a_theorem(strict_implies(and(not(X43),or(and(X44,X45),X43)),X44))
| ~ spl2_136
| ~ spl2_487 ),
inference(resolution,[],[f22732,f2345]) ).
fof(f26957,plain,
( spl2_517
| ~ spl2_70
| ~ spl2_76
| ~ spl2_298
| ~ spl2_301
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21159,f19362,f9399,f9376,f810,f681,f26955]) ).
fof(f26847,plain,
( spl2_516
| ~ spl2_26
| ~ spl2_493 ),
inference(avatar_split_clause,[],[f23185,f22989,f298,f26845]) ).
fof(f26845,plain,
( spl2_516
<=> ! [X4,X5,X3] :
( is_a_theorem(and(X3,and(X4,X5)))
| ~ is_a_theorem(and(X3,X5))
| ~ is_a_theorem(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_516])]) ).
fof(f22989,plain,
( spl2_493
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,and(X0,X2)))
| is_a_theorem(and(X0,and(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_493])]) ).
fof(f23185,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(X3,and(X4,X5)))
| ~ is_a_theorem(and(X3,X5))
| ~ is_a_theorem(X4) )
| ~ spl2_26
| ~ spl2_493 ),
inference(resolution,[],[f22990,f299]) ).
fof(f22990,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,and(X0,X2)))
| is_a_theorem(and(X0,and(X1,X2))) )
| ~ spl2_493 ),
inference(avatar_component_clause,[],[f22989]) ).
fof(f25561,plain,
( spl2_515
| ~ spl2_29
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f24127,f23256,f315,f25559]) ).
fof(f24127,plain,
( ! [X381,X380,X379] : implies(strict_equiv(X379,X380),X381) = implies(strict_equiv(X380,X379),X381)
| ~ spl2_29
| ~ spl2_503 ),
inference(forward_demodulation,[],[f23824,f316]) ).
fof(f23824,plain,
( ! [X381,X380,X379] : implies(strict_equiv(X379,X380),X381) = not(and(strict_equiv(X380,X379),not(X381)))
| ~ spl2_29
| ~ spl2_503 ),
inference(superposition,[],[f316,f23257]) ).
fof(f25557,plain,
( spl2_514
| ~ spl2_76
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f23715,f23256,f810,f25555]) ).
fof(f25555,plain,
( spl2_514
<=> ! [X9,X8,X10] : and(X10,strict_equiv(X8,X9)) = and(strict_equiv(X9,X8),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_514])]) ).
fof(f23715,plain,
( ! [X10,X8,X9] : and(X10,strict_equiv(X8,X9)) = and(strict_equiv(X9,X8),X10)
| ~ spl2_76
| ~ spl2_503 ),
inference(superposition,[],[f23257,f811]) ).
fof(f25509,plain,
( spl2_513
| ~ spl2_72
| ~ spl2_503 ),
inference(avatar_split_clause,[],[f23714,f23256,f748,f25507]) ).
fof(f23714,plain,
( ! [X6,X7] : strict_equiv(X6,X7) = and(strict_equiv(X7,X6),strict_equiv(X6,X7))
| ~ spl2_72
| ~ spl2_503 ),
inference(superposition,[],[f23257,f749]) ).
fof(f25505,plain,
( spl2_512
| ~ spl2_29
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23688,f23252,f315,f25503]) ).
fof(f23688,plain,
( ! [X399,X400,X398] : implies(equiv(X398,X399),X400) = implies(equiv(X399,X398),X400)
| ~ spl2_29
| ~ spl2_502 ),
inference(forward_demodulation,[],[f23382,f316]) ).
fof(f23382,plain,
( ! [X399,X400,X398] : implies(equiv(X398,X399),X400) = not(and(equiv(X399,X398),not(X400)))
| ~ spl2_29
| ~ spl2_502 ),
inference(superposition,[],[f316,f23253]) ).
fof(f25501,plain,
( spl2_511
| ~ spl2_76
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23268,f23252,f810,f25499]) ).
fof(f25499,plain,
( spl2_511
<=> ! [X9,X8,X10] : and(equiv(X9,X8),X10) = and(X10,equiv(X8,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_511])]) ).
fof(f23268,plain,
( ! [X10,X8,X9] : and(equiv(X9,X8),X10) = and(X10,equiv(X8,X9))
| ~ spl2_76
| ~ spl2_502 ),
inference(superposition,[],[f23253,f811]) ).
fof(f25497,plain,
( spl2_510
| ~ spl2_72
| ~ spl2_502 ),
inference(avatar_split_clause,[],[f23267,f23252,f748,f25495]) ).
fof(f23267,plain,
( ! [X6,X7] : equiv(X6,X7) = and(equiv(X7,X6),equiv(X6,X7))
| ~ spl2_72
| ~ spl2_502 ),
inference(superposition,[],[f23253,f749]) ).
fof(f25493,plain,
( spl2_509
| ~ spl2_34
| ~ spl2_91
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24681,f23260,f1092,f344,f25491]) ).
fof(f24681,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,strict_equiv(X1,X0)),and(X2,strict_equiv(X0,X1))))
| ~ spl2_34
| ~ spl2_91
| ~ spl2_504 ),
inference(backward_demodulation,[],[f1093,f24170]) ).
fof(f24821,plain,
( spl2_508
| ~ spl2_34
| ~ spl2_70
| ~ spl2_91
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24700,f23260,f1092,f681,f344,f24819]) ).
fof(f24700,plain,
( ! [X2,X0,X1] : and(X0,strict_equiv(X1,X2)) = and(X0,strict_equiv(X2,X1))
| ~ spl2_34
| ~ spl2_70
| ~ spl2_91
| ~ spl2_504 ),
inference(forward_demodulation,[],[f24699,f24170]) ).
fof(f24699,plain,
( ! [X2,X0,X1] : and(X0,strict_equiv(X1,X2)) = and(strict_implies(X2,X1),and(X0,strict_implies(X1,X2)))
| ~ spl2_34
| ~ spl2_70
| ~ spl2_91
| ~ spl2_504 ),
inference(subsumption_resolution,[],[f24683,f24681]) ).
fof(f24683,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,strict_equiv(X1,X2)),and(X0,strict_equiv(X2,X1))))
| and(X0,strict_equiv(X1,X2)) = and(strict_implies(X2,X1),and(X0,strict_implies(X1,X2))) )
| ~ spl2_34
| ~ spl2_70
| ~ spl2_91
| ~ spl2_504 ),
inference(backward_demodulation,[],[f1289,f24170]) ).
fof(f1289,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,strict_equiv(X1,X2)),and(strict_implies(X2,X1),and(X0,strict_implies(X1,X2)))))
| and(X0,strict_equiv(X1,X2)) = and(strict_implies(X2,X1),and(X0,strict_implies(X1,X2))) )
| ~ spl2_70
| ~ spl2_91 ),
inference(resolution,[],[f1093,f682]) ).
fof(f24817,plain,
( spl2_507
| ~ spl2_36
| ~ spl2_94
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24584,f23260,f1114,f363,f24815]) ).
fof(f24584,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(X5,equiv(X4,X3)),and(X5,equiv(X3,X4))))
| ~ spl2_36
| ~ spl2_94
| ~ spl2_504 ),
inference(backward_demodulation,[],[f1115,f24160]) ).
fof(f24813,plain,
( spl2_506
| ~ spl2_36
| ~ spl2_70
| ~ spl2_94
| ~ spl2_504 ),
inference(avatar_split_clause,[],[f24603,f23260,f1114,f681,f363,f24811]) ).
fof(f24603,plain,
( ! [X2,X0,X1] : and(X0,equiv(X1,X2)) = and(X0,equiv(X2,X1))
| ~ spl2_36
| ~ spl2_70
| ~ spl2_94
| ~ spl2_504 ),
inference(forward_demodulation,[],[f24602,f24160]) ).
fof(f24602,plain,
( ! [X2,X0,X1] : and(X0,equiv(X1,X2)) = and(implies(X2,X1),and(X0,implies(X1,X2)))
| ~ spl2_36
| ~ spl2_70
| ~ spl2_94
| ~ spl2_504 ),
inference(subsumption_resolution,[],[f24586,f24584]) ).
fof(f24586,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,equiv(X1,X2)),and(X0,equiv(X2,X1))))
| and(X0,equiv(X1,X2)) = and(implies(X2,X1),and(X0,implies(X1,X2))) )
| ~ spl2_36
| ~ spl2_70
| ~ spl2_94
| ~ spl2_504 ),
inference(backward_demodulation,[],[f1348,f24160]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,equiv(X1,X2)),and(implies(X2,X1),and(X0,implies(X1,X2)))))
| and(X0,equiv(X1,X2)) = and(implies(X2,X1),and(X0,implies(X1,X2))) )
| ~ spl2_70
| ~ spl2_94 ),
inference(resolution,[],[f1115,f682]) ).
fof(f23266,plain,
( spl2_505
| ~ spl2_34
| ~ spl2_76
| ~ spl2_190
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20165,f19362,f4074,f810,f344,f23264]) ).
fof(f23264,plain,
( spl2_505
<=> ! [X2,X0,X1] :
( is_a_theorem(and(strict_equiv(X1,X0),X2))
| ~ is_a_theorem(and(strict_equiv(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_505])]) ).
fof(f20165,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(strict_equiv(X1,X0),X2))
| ~ is_a_theorem(and(strict_equiv(X0,X1),X2)) )
| ~ spl2_34
| ~ spl2_76
| ~ spl2_190
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4075,f20156]) ).
fof(f23262,plain,
( spl2_504
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20741,f19362,f18075,f810,f681,f436,f23260]) ).
fof(f23258,plain,
( spl2_503
| ~ spl2_34
| ~ spl2_70
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20180,f19362,f1050,f810,f681,f344,f23256]) ).
fof(f20180,plain,
( ! [X2,X0,X1] : and(strict_equiv(X0,X1),X2) = and(strict_equiv(X1,X0),X2)
| ~ spl2_34
| ~ spl2_70
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20179,f20156]) ).
fof(f20179,plain,
( ! [X2,X0,X1] : and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)) = and(strict_equiv(X0,X1),X2)
| ~ spl2_34
| ~ spl2_70
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(subsumption_resolution,[],[f20158,f20157]) ).
fof(f20157,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_equiv(X1,X0),X2)))
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1051,f20156]) ).
fof(f20158,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(strict_equiv(X1,X0),X2),and(strict_equiv(X0,X1),X2)))
| and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)) = and(strict_equiv(X0,X1),X2) )
| ~ spl2_34
| ~ spl2_70
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1135,f20156]) ).
fof(f1135,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)),and(strict_equiv(X0,X1),X2)))
| and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2)) = and(strict_equiv(X0,X1),X2) )
| ~ spl2_70
| ~ spl2_85 ),
inference(resolution,[],[f1051,f682]) ).
fof(f23254,plain,
( spl2_502
| ~ spl2_36
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20045,f19362,f1074,f810,f681,f363,f23252]) ).
fof(f20045,plain,
( ! [X2,X0,X1] : and(equiv(X0,X1),X2) = and(equiv(X1,X0),X2)
| ~ spl2_36
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20044,f20021]) ).
fof(f20044,plain,
( ! [X2,X0,X1] : and(equiv(X0,X1),X2) = and(implies(X0,X1),and(implies(X1,X0),X2))
| ~ spl2_36
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(subsumption_resolution,[],[f20023,f20022]) ).
fof(f20022,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(equiv(X4,X3),X5)))
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1075,f20021]) ).
fof(f20023,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(equiv(X1,X0),X2),and(equiv(X0,X1),X2)))
| and(equiv(X0,X1),X2) = and(implies(X0,X1),and(implies(X1,X0),X2)) )
| ~ spl2_36
| ~ spl2_70
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(backward_demodulation,[],[f1252,f20021]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(implies(X0,X1),and(implies(X1,X0),X2)),and(equiv(X0,X1),X2)))
| and(equiv(X0,X1),X2) = and(implies(X0,X1),and(implies(X1,X0),X2)) )
| ~ spl2_70
| ~ spl2_88 ),
inference(resolution,[],[f1075,f682]) ).
fof(f23250,plain,
( spl2_501
| ~ spl2_36
| ~ spl2_76
| ~ spl2_192
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20030,f19362,f4124,f810,f363,f23248]) ).
fof(f23248,plain,
( spl2_501
<=> ! [X4,X5,X3] :
( is_a_theorem(and(equiv(X4,X3),X5))
| ~ is_a_theorem(and(equiv(X3,X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_501])]) ).
fof(f20030,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(equiv(X4,X3),X5))
| ~ is_a_theorem(and(equiv(X3,X4),X5)) )
| ~ spl2_36
| ~ spl2_76
| ~ spl2_192
| ~ spl2_486 ),
inference(backward_demodulation,[],[f4125,f20021]) ).
fof(f23236,plain,
( spl2_500
| ~ spl2_20
| ~ spl2_104
| ~ spl2_494 ),
inference(avatar_split_clause,[],[f23046,f22993,f1388,f273,f23234]) ).
fof(f23234,plain,
( spl2_500
<=> ! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(possibly(X0))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_500])]) ).
fof(f22993,plain,
( spl2_494
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_494])]) ).
fof(f23046,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(possibly(X0))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_104
| ~ spl2_494 ),
inference(forward_demodulation,[],[f23033,f1389]) ).
fof(f23033,plain,
( ! [X0,X1] :
( ~ is_a_theorem(possibly(X0))
| ~ is_a_theorem(or(X1,necessarily(not(X0))))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_494 ),
inference(superposition,[],[f22994,f274]) ).
fof(f22994,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(X1))
| ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X0) )
| ~ spl2_494 ),
inference(avatar_component_clause,[],[f22993]) ).
fof(f23219,plain,
( spl2_499
| ~ spl2_20
| ~ spl2_104
| ~ spl2_491 ),
inference(avatar_split_clause,[],[f22937,f22905,f1388,f273,f23217]) ).
fof(f23217,plain,
( spl2_499
<=> ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),implies(possibly(X0),X1)))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_499])]) ).
fof(f22937,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),implies(possibly(X0),X1)))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_104
| ~ spl2_491 ),
inference(forward_demodulation,[],[f22913,f1389]) ).
fof(f22913,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(possibly(X0),or(X1,necessarily(not(X0)))))
| is_a_theorem(X1) )
| ~ spl2_20
| ~ spl2_491 ),
inference(superposition,[],[f22906,f274]) ).
fof(f23140,plain,
( spl2_498
| ~ spl2_20
| ~ spl2_104
| ~ spl2_487 ),
inference(avatar_split_clause,[],[f22799,f22731,f1388,f273,f23138]) ).
fof(f22799,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),implies(possibly(X0),X1)),X1))
| ~ spl2_20
| ~ spl2_104
| ~ spl2_487 ),
inference(forward_demodulation,[],[f22766,f1389]) ).
fof(f22766,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),or(X1,necessarily(not(X0)))),X1))
| ~ spl2_20
| ~ spl2_487 ),
inference(superposition,[],[f22732,f274]) ).
fof(f23094,plain,
( spl2_497
| ~ spl2_26
| ~ spl2_495 ),
inference(avatar_split_clause,[],[f23055,f22997,f298,f23092]) ).
fof(f23055,plain,
( ! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(X0)))
| ~ is_a_theorem(not(X0)) )
| ~ spl2_26
| ~ spl2_495 ),
inference(resolution,[],[f22998,f299]) ).
fof(f23003,plain,
( spl2_496
| ~ spl2_26
| ~ spl2_492 ),
inference(avatar_split_clause,[],[f22950,f22909,f298,f23001]) ).
fof(f23001,plain,
( spl2_496
<=> ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X0))
| ~ is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_496])]) ).
fof(f22950,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X0))
| ~ is_a_theorem(not(X1)) )
| ~ spl2_26
| ~ spl2_492 ),
inference(resolution,[],[f22910,f299]) ).
fof(f22999,plain,
( spl2_495
| ~ spl2_83
| ~ spl2_491 ),
inference(avatar_split_clause,[],[f22926,f22905,f1024,f22997]) ).
fof(f22926,plain,
( ! [X0] :
( ~ is_a_theorem(and(not(X0),not(not(X0))))
| is_a_theorem(X0) )
| ~ spl2_83
| ~ spl2_491 ),
inference(superposition,[],[f22906,f1025]) ).
fof(f22995,plain,
( spl2_494
| ~ spl2_26
| ~ spl2_491 ),
inference(avatar_split_clause,[],[f22912,f22905,f298,f22993]) ).
fof(f22912,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1)) )
| ~ spl2_26
| ~ spl2_491 ),
inference(resolution,[],[f22906,f299]) ).
fof(f22991,plain,
( spl2_493
| ~ spl2_66
| ~ spl2_76
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20194,f19362,f810,f623,f22989]) ).
fof(f623,plain,
( spl2_66
<=> ! [X2,X0,X1] :
( is_a_theorem(and(X0,and(X1,X2)))
| ~ is_a_theorem(and(and(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_66])]) ).
fof(f20194,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,and(X0,X2)))
| is_a_theorem(and(X0,and(X1,X2))) )
| ~ spl2_66
| ~ spl2_76
| ~ spl2_486 ),
inference(backward_demodulation,[],[f624,f19383]) ).
fof(f624,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(and(X0,X1),X2))
| is_a_theorem(and(X0,and(X1,X2))) )
| ~ spl2_66 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f22911,plain,
( spl2_492
| ~ spl2_27
| ~ spl2_489 ),
inference(avatar_split_clause,[],[f22821,f22739,f302,f22909]) ).
fof(f22821,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X1,X0))) )
| ~ spl2_27
| ~ spl2_489 ),
inference(resolution,[],[f22740,f303]) ).
fof(f22907,plain,
( spl2_491
| ~ spl2_27
| ~ spl2_487 ),
inference(avatar_split_clause,[],[f22742,f22731,f302,f22905]) ).
fof(f22742,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(not(X1),or(X0,X1))) )
| ~ spl2_27
| ~ spl2_487 ),
inference(resolution,[],[f22732,f303]) ).
fof(f22903,plain,
( spl2_490
| ~ spl2_34
| ~ spl2_76
| ~ spl2_85
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20157,f19362,f1050,f810,f344,f22901]) ).
fof(f22741,plain,
( spl2_489
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_443
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f21011,f19362,f18075,f16094,f1122,f810,f681,f436,f286,f22739]) ).
fof(f16094,plain,
( spl2_443
<=> ! [X203,X204] : is_a_theorem(necessarily(not(and(or(X204,X203),and(not(X203),not(X204)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_443])]) ).
fof(f21011,plain,
( ! [X203,X204] : is_a_theorem(strict_implies(and(not(X204),or(X204,X203)),X203))
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_443
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21010,f811]) ).
fof(f21010,plain,
( ! [X203,X204] : is_a_theorem(strict_implies(and(or(X204,X203),not(X204)),X203))
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_443
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f21009,f287]) ).
fof(f21009,plain,
( ! [X203,X204] : is_a_theorem(necessarily(implies(and(or(X204,X203),not(X204)),X203)))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_443
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20818,f1123]) ).
fof(f20818,plain,
( ! [X203,X204] : is_a_theorem(necessarily(not(and(not(X203),and(or(X204,X203),not(X204))))))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_443
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f16095,f20741]) ).
fof(f16095,plain,
( ! [X203,X204] : is_a_theorem(necessarily(not(and(or(X204,X203),and(not(X203),not(X204))))))
| ~ spl2_443 ),
inference(avatar_component_clause,[],[f16094]) ).
fof(f22737,plain,
( spl2_488
| ~ spl2_36
| ~ spl2_76
| ~ spl2_88
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20022,f19362,f1074,f810,f363,f22735]) ).
fof(f22733,plain,
( spl2_487
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_442
| ~ spl2_471
| ~ spl2_486 ),
inference(avatar_split_clause,[],[f20990,f19362,f18075,f15708,f1122,f810,f681,f436,f286,f22731]) ).
fof(f15708,plain,
( spl2_442
<=> ! [X20,X19] : is_a_theorem(necessarily(not(and(or(X19,X20),and(not(X19),not(X20)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_442])]) ).
fof(f20990,plain,
( ! [X19,X20] : is_a_theorem(strict_implies(and(not(X20),or(X19,X20)),X19))
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_442
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20989,f811]) ).
fof(f20989,plain,
( ! [X19,X20] : is_a_theorem(strict_implies(and(or(X19,X20),not(X20)),X19))
| ~ spl2_23
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_442
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20988,f287]) ).
fof(f20988,plain,
( ! [X19,X20] : is_a_theorem(necessarily(implies(and(or(X19,X20),not(X20)),X19)))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_96
| ~ spl2_442
| ~ spl2_471
| ~ spl2_486 ),
inference(forward_demodulation,[],[f20811,f1123]) ).
fof(f20811,plain,
( ! [X19,X20] : is_a_theorem(necessarily(not(and(not(X19),and(or(X19,X20),not(X20))))))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_76
| ~ spl2_442
| ~ spl2_471
| ~ spl2_486 ),
inference(backward_demodulation,[],[f15709,f20741]) ).
fof(f15709,plain,
( ! [X19,X20] : is_a_theorem(necessarily(not(and(or(X19,X20),and(not(X19),not(X20))))))
| ~ spl2_442 ),
inference(avatar_component_clause,[],[f15708]) ).
fof(f19364,plain,
( spl2_486
| ~ spl2_70
| ~ spl2_466 ),
inference(avatar_split_clause,[],[f19333,f17967,f681,f19362]) ).
fof(f17967,plain,
( spl2_466
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_466])]) ).
fof(f19333,plain,
( ! [X18,X19,X20] : and(and(X18,X19),X20) = and(and(X18,X20),X19)
| ~ spl2_70
| ~ spl2_466 ),
inference(subsumption_resolution,[],[f19285,f17968]) ).
fof(f17968,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X0,X2),X1)))
| ~ spl2_466 ),
inference(avatar_component_clause,[],[f17967]) ).
fof(f19285,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(strict_implies(and(and(X18,X19),X20),and(and(X18,X20),X19)))
| and(and(X18,X19),X20) = and(and(X18,X20),X19) )
| ~ spl2_70
| ~ spl2_466 ),
inference(resolution,[],[f17968,f682]) ).
fof(f19278,plain,
( spl2_485
| ~ spl2_56
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f693,f681,f529,f19276]) ).
fof(f19276,plain,
( spl2_485
<=> ! [X6,X7] :
( ~ is_a_theorem(strict_implies(or(X6,X7),equiv(not(X6),X7)))
| or(X6,X7) = equiv(not(X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_485])]) ).
fof(f693,plain,
( ! [X6,X7] :
( ~ is_a_theorem(strict_implies(or(X6,X7),equiv(not(X6),X7)))
| or(X6,X7) = equiv(not(X6),X7) )
| ~ spl2_56
| ~ spl2_70 ),
inference(resolution,[],[f682,f530]) ).
fof(f18719,plain,
( spl2_484
| ~ spl2_302
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16368,f16331,f9403,f18717]) ).
fof(f18717,plain,
( spl2_484
<=> ! [X76,X75,X74] :
( ~ is_a_theorem(and(X74,X75))
| is_a_theorem(and(X74,and(X75,strict_implies(X76,X76)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_484])]) ).
fof(f9403,plain,
( spl2_302
<=> ! [X34,X36,X35] :
( ~ is_a_theorem(and(X36,and(X34,X35)))
| is_a_theorem(and(X34,and(X35,X36))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_302])]) ).
fof(f16368,plain,
( ! [X76,X74,X75] :
( ~ is_a_theorem(and(X74,X75))
| is_a_theorem(and(X74,and(X75,strict_implies(X76,X76)))) )
| ~ spl2_302
| ~ spl2_448 ),
inference(resolution,[],[f16332,f9404]) ).
fof(f9404,plain,
( ! [X36,X34,X35] :
( ~ is_a_theorem(and(X36,and(X34,X35)))
| is_a_theorem(and(X34,and(X35,X36))) )
| ~ spl2_302 ),
inference(avatar_component_clause,[],[f9403]) ).
fof(f18715,plain,
( spl2_483
| ~ spl2_309
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16346,f16331,f9471,f18713]) ).
fof(f18713,plain,
( spl2_483
<=> ! [X27,X28,X26] :
( ~ is_a_theorem(X26)
| ~ is_a_theorem(X27)
| is_a_theorem(and(X26,and(strict_implies(X28,X28),X27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_483])]) ).
fof(f9471,plain,
( spl2_309
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X2,and(X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_309])]) ).
fof(f16346,plain,
( ! [X28,X26,X27] :
( ~ is_a_theorem(X26)
| ~ is_a_theorem(X27)
| is_a_theorem(and(X26,and(strict_implies(X28,X28),X27))) )
| ~ spl2_309
| ~ spl2_448 ),
inference(resolution,[],[f16332,f9472]) ).
fof(f9472,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X2,and(X3,X4))) )
| ~ spl2_309 ),
inference(avatar_component_clause,[],[f9471]) ).
fof(f18711,plain,
( spl2_482
| ~ spl2_120
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16341,f16331,f1712,f18709]) ).
fof(f18709,plain,
( spl2_482
<=> ! [X13,X14,X15] :
( ~ is_a_theorem(X13)
| ~ is_a_theorem(X14)
| is_a_theorem(and(strict_implies(X15,X15),and(X13,X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_482])]) ).
fof(f16341,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(X13)
| ~ is_a_theorem(X14)
| is_a_theorem(and(strict_implies(X15,X15),and(X13,X14))) )
| ~ spl2_120
| ~ spl2_448 ),
inference(resolution,[],[f16332,f1713]) ).
fof(f18307,plain,
( spl2_481
| ~ spl2_27
| ~ spl2_381 ),
inference(avatar_split_clause,[],[f15179,f13497,f302,f18305]) ).
fof(f18305,plain,
( spl2_481
<=> ! [X14,X15] :
( ~ is_a_theorem(necessarily(not(equiv(X14,X15))))
| is_a_theorem(X15)
| ~ is_a_theorem(implies(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_481])]) ).
fof(f13497,plain,
( spl2_381
<=> ! [X9,X8] :
( ~ is_a_theorem(necessarily(not(equiv(X8,X9))))
| is_a_theorem(strict_implies(implies(X8,X9),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_381])]) ).
fof(f15179,plain,
( ! [X14,X15] :
( ~ is_a_theorem(necessarily(not(equiv(X14,X15))))
| is_a_theorem(X15)
| ~ is_a_theorem(implies(X14,X15)) )
| ~ spl2_27
| ~ spl2_381 ),
inference(resolution,[],[f13498,f303]) ).
fof(f13498,plain,
( ! [X8,X9] :
( is_a_theorem(strict_implies(implies(X8,X9),X9))
| ~ is_a_theorem(necessarily(not(equiv(X8,X9)))) )
| ~ spl2_381 ),
inference(avatar_component_clause,[],[f13497]) ).
fof(f18303,plain,
( spl2_480
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13552,f13441,f373,f286,f273,f18301]) ).
fof(f18301,plain,
( spl2_480
<=> ! [X32,X31,X33] :
( is_a_theorem(strict_implies(and(possibly(X31),X33),X32))
| ~ is_a_theorem(strict_implies(possibly(X31),X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_480])]) ).
fof(f13552,plain,
( ! [X31,X32,X33] :
( is_a_theorem(strict_implies(and(possibly(X31),X33),X32))
| ~ is_a_theorem(strict_implies(possibly(X31),X32)) )
| ~ spl2_20
| ~ spl2_23
| ~ spl2_37
| ~ spl2_380 ),
inference(forward_demodulation,[],[f13551,f274]) ).
fof(f13551,plain,
( ! [X31,X32,X33] :
( ~ is_a_theorem(strict_implies(possibly(X31),X32))
| is_a_theorem(strict_implies(and(not(necessarily(not(X31))),X33),X32)) )
| ~ spl2_23
| ~ spl2_37
| ~ spl2_380 ),
inference(forward_demodulation,[],[f13540,f287]) ).
fof(f13540,plain,
( ! [X31,X32,X33] :
( ~ is_a_theorem(necessarily(implies(possibly(X31),X32)))
| is_a_theorem(strict_implies(and(not(necessarily(not(X31))),X33),X32)) )
| ~ spl2_37
| ~ spl2_380 ),
inference(superposition,[],[f13442,f374]) ).
fof(f18299,plain,
( spl2_479
| ~ spl2_79
| ~ spl2_313 ),
inference(avatar_split_clause,[],[f13135,f9487,f822,f18297]) ).
fof(f18297,plain,
( spl2_479
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(necessarily(not(X1)),not(X0)))
| is_a_theorem(strict_implies(possibly(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_479])]) ).
fof(f822,plain,
( spl2_79
<=> ! [X25,X24] : strict_equiv(X24,X25) = strict_equiv(X25,X24) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_79])]) ).
fof(f9487,plain,
( spl2_313
<=> ! [X9,X10] :
( is_a_theorem(strict_implies(possibly(X9),X10))
| ~ is_a_theorem(strict_equiv(not(X10),necessarily(not(X9)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_313])]) ).
fof(f13135,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(necessarily(not(X1)),not(X0)))
| is_a_theorem(strict_implies(possibly(X1),X0)) )
| ~ spl2_79
| ~ spl2_313 ),
inference(superposition,[],[f9488,f823]) ).
fof(f823,plain,
( ! [X24,X25] : strict_equiv(X24,X25) = strict_equiv(X25,X24)
| ~ spl2_79 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f9488,plain,
( ! [X10,X9] :
( ~ is_a_theorem(strict_equiv(not(X10),necessarily(not(X9))))
| is_a_theorem(strict_implies(possibly(X9),X10)) )
| ~ spl2_313 ),
inference(avatar_component_clause,[],[f9487]) ).
fof(f18233,plain,
( spl2_478
| ~ spl2_23
| ~ spl2_310
| ~ spl2_311 ),
inference(avatar_split_clause,[],[f13063,f9479,f9475,f286,f18231]) ).
fof(f18231,plain,
( spl2_478
<=> ! [X4,X5,X3] :
( ~ is_a_theorem(strict_implies(implies(X5,X4),X3))
| is_a_theorem(necessarily(or(X3,not(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_478])]) ).
fof(f9475,plain,
( spl2_310
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(necessarily(or(X0,and(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_310])]) ).
fof(f13063,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(strict_implies(implies(X5,X4),X3))
| is_a_theorem(necessarily(or(X3,not(X4)))) )
| ~ spl2_23
| ~ spl2_310
| ~ spl2_311 ),
inference(forward_demodulation,[],[f12966,f287]) ).
fof(f12966,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(necessarily(implies(implies(X5,X4),X3)))
| is_a_theorem(necessarily(or(X3,not(X4)))) )
| ~ spl2_310
| ~ spl2_311 ),
inference(superposition,[],[f9476,f9480]) ).
fof(f9476,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(X1,X2))))
| is_a_theorem(necessarily(or(X0,X1))) )
| ~ spl2_310 ),
inference(avatar_component_clause,[],[f9475]) ).
fof(f18229,plain,
( spl2_477
| ~ spl2_81
| ~ spl2_317 ),
inference(avatar_split_clause,[],[f11161,f9822,f911,f18227]) ).
fof(f18227,plain,
( spl2_477
<=> ! [X20,X21,X19] :
( is_a_theorem(strict_implies(and(X19,not(X20)),X21))
| ~ is_a_theorem(necessarily(or(X20,X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_477])]) ).
fof(f9822,plain,
( spl2_317
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X2,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_317])]) ).
fof(f11161,plain,
( ! [X21,X19,X20] :
( is_a_theorem(strict_implies(and(X19,not(X20)),X21))
| ~ is_a_theorem(necessarily(or(X20,X21))) )
| ~ spl2_81
| ~ spl2_317 ),
inference(resolution,[],[f9823,f912]) ).
fof(f9823,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,not(X0)))
| is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(necessarily(or(X0,X1))) )
| ~ spl2_317 ),
inference(avatar_component_clause,[],[f9822]) ).
fof(f18225,plain,
( spl2_476
| ~ spl2_75
| ~ spl2_306 ),
inference(avatar_split_clause,[],[f10367,f9459,f806,f18223]) ).
fof(f18223,plain,
( spl2_476
<=> ! [X2,X1] : is_a_theorem(strict_implies(equiv(necessarily(not(X2)),X1),not(and(possibly(X2),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_476])]) ).
fof(f10367,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(equiv(necessarily(not(X2)),X1),not(and(possibly(X2),X1))))
| ~ spl2_75
| ~ spl2_306 ),
inference(superposition,[],[f9460,f807]) ).
fof(f18221,plain,
( spl2_475
| ~ spl2_27
| ~ spl2_306 ),
inference(avatar_split_clause,[],[f10354,f9459,f302,f18219]) ).
fof(f18219,plain,
( spl2_475
<=> ! [X9,X10] :
( is_a_theorem(not(and(possibly(X9),X10)))
| ~ is_a_theorem(equiv(X10,necessarily(not(X9)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_475])]) ).
fof(f10354,plain,
( ! [X10,X9] :
( is_a_theorem(not(and(possibly(X9),X10)))
| ~ is_a_theorem(equiv(X10,necessarily(not(X9)))) )
| ~ spl2_27
| ~ spl2_306 ),
inference(resolution,[],[f9460,f303]) ).
fof(f18146,plain,
( spl2_474
| ~ spl2_76
| ~ spl2_301 ),
inference(avatar_split_clause,[],[f10155,f9399,f810,f18144]) ).
fof(f18144,plain,
( spl2_474
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(and(X3,X4),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_474])]) ).
fof(f10155,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(and(X3,X4),X2)))
| ~ spl2_76
| ~ spl2_301 ),
inference(superposition,[],[f9400,f811]) ).
fof(f18142,plain,
( spl2_473
| ~ spl2_27
| ~ spl2_301 ),
inference(avatar_split_clause,[],[f10137,f9399,f302,f18140]) ).
fof(f18140,plain,
( spl2_473
<=> ! [X22,X24,X23] :
( is_a_theorem(and(and(X22,X23),X24))
| ~ is_a_theorem(and(and(X24,X22),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_473])]) ).
fof(f10137,plain,
( ! [X24,X22,X23] :
( is_a_theorem(and(and(X22,X23),X24))
| ~ is_a_theorem(and(and(X24,X22),X23)) )
| ~ spl2_27
| ~ spl2_301 ),
inference(resolution,[],[f9400,f303]) ).
fof(f18138,plain,
( spl2_472
| ~ spl2_76
| ~ spl2_299 ),
inference(avatar_split_clause,[],[f9646,f9380,f810,f18136]) ).
fof(f18136,plain,
( spl2_472
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X3,and(X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_472])]) ).
fof(f9380,plain,
( spl2_299
<=> ! [X20,X21,X19] :
( ~ is_a_theorem(and(and(X20,X19),X21))
| is_a_theorem(and(X19,and(X20,X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_299])]) ).
fof(f9646,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X3,and(X2,X4))) )
| ~ spl2_76
| ~ spl2_299 ),
inference(superposition,[],[f9381,f811]) ).
fof(f9381,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(and(X20,X19),X21))
| is_a_theorem(and(X19,and(X20,X21))) )
| ~ spl2_299 ),
inference(avatar_component_clause,[],[f9380]) ).
fof(f18077,plain,
( spl2_471
| ~ spl2_76
| ~ spl2_298 ),
inference(avatar_split_clause,[],[f9588,f9376,f810,f18075]) ).
fof(f9588,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,and(X4,X3))))
| ~ spl2_76
| ~ spl2_298 ),
inference(superposition,[],[f9377,f811]) ).
fof(f18073,plain,
( spl2_470
| ~ spl2_27
| ~ spl2_298 ),
inference(avatar_split_clause,[],[f9570,f9376,f302,f18071]) ).
fof(f18071,plain,
( spl2_470
<=> ! [X22,X24,X23] :
( is_a_theorem(and(X22,and(X23,X24)))
| ~ is_a_theorem(and(and(X22,X24),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_470])]) ).
fof(f9570,plain,
( ! [X24,X22,X23] :
( is_a_theorem(and(X22,and(X23,X24)))
| ~ is_a_theorem(and(and(X22,X24),X23)) )
| ~ spl2_27
| ~ spl2_298 ),
inference(resolution,[],[f9377,f303]) ).
fof(f18069,plain,
( spl2_469
| ~ spl2_275
| ~ spl2_298 ),
inference(avatar_split_clause,[],[f9563,f9376,f8172,f18067]) ).
fof(f18067,plain,
( spl2_469
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X2,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_469])]) ).
fof(f9563,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X2,X1),X0)))
| ~ spl2_275
| ~ spl2_298 ),
inference(resolution,[],[f9377,f8173]) ).
fof(f18065,plain,
( spl2_468
| ~ spl2_76
| ~ spl2_297 ),
inference(avatar_split_clause,[],[f9532,f9372,f810,f18063]) ).
fof(f18063,plain,
( spl2_468
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(and(X2,X4),X3),and(X4,and(X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_468])]) ).
fof(f9372,plain,
( spl2_297
<=> ! [X13,X14,X15] : is_a_theorem(strict_implies(and(and(X14,X13),X15),and(X13,and(X14,X15)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_297])]) ).
fof(f9532,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X2,X4),X3),and(X4,and(X3,X2))))
| ~ spl2_76
| ~ spl2_297 ),
inference(superposition,[],[f9373,f811]) ).
fof(f9373,plain,
( ! [X14,X15,X13] : is_a_theorem(strict_implies(and(and(X14,X13),X15),and(X13,and(X14,X15))))
| ~ spl2_297 ),
inference(avatar_component_clause,[],[f9372]) ).
fof(f17973,plain,
( spl2_467
| ~ spl2_76
| ~ spl2_297 ),
inference(avatar_split_clause,[],[f9527,f9372,f810,f17971]) ).
fof(f17971,plain,
( spl2_467
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X3,and(X2,X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_467])]) ).
fof(f9527,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X3,and(X2,X4))))
| ~ spl2_76
| ~ spl2_297 ),
inference(superposition,[],[f9373,f811]) ).
fof(f17969,plain,
( spl2_466
| ~ spl2_275
| ~ spl2_297 ),
inference(avatar_split_clause,[],[f9502,f9372,f8172,f17967]) ).
fof(f9502,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X0,X2),X1)))
| ~ spl2_275
| ~ spl2_297 ),
inference(resolution,[],[f9373,f8173]) ).
fof(f17965,plain,
( spl2_465
| ~ spl2_137
| ~ spl2_279 ),
inference(avatar_split_clause,[],[f9276,f8188,f2369,f17963]) ).
fof(f17963,plain,
( spl2_465
<=> ! [X41,X40,X42,X39] : is_a_theorem(strict_implies(and(and(strict_equiv(X39,X40),X41),X42),strict_equiv(X40,X39))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_465])]) ).
fof(f2369,plain,
( spl2_137
<=> ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_137])]) ).
fof(f9276,plain,
( ! [X40,X41,X39,X42] : is_a_theorem(strict_implies(and(and(strict_equiv(X39,X40),X41),X42),strict_equiv(X40,X39)))
| ~ spl2_137
| ~ spl2_279 ),
inference(resolution,[],[f8189,f2370]) ).
fof(f2370,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),X4))
| ~ spl2_137 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f17565,plain,
( spl2_464
| ~ spl2_137
| ~ spl2_278 ),
inference(avatar_split_clause,[],[f9247,f8184,f2369,f17563]) ).
fof(f17563,plain,
( spl2_464
<=> ! [X41,X40,X42,X39] : is_a_theorem(strict_implies(and(and(strict_equiv(X39,X40),X41),X42),strict_implies(X39,X39))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_464])]) ).
fof(f9247,plain,
( ! [X40,X41,X39,X42] : is_a_theorem(strict_implies(and(and(strict_equiv(X39,X40),X41),X42),strict_implies(X39,X39)))
| ~ spl2_137
| ~ spl2_278 ),
inference(resolution,[],[f8185,f2370]) ).
fof(f17561,plain,
( spl2_463
| ~ spl2_137
| ~ spl2_275 ),
inference(avatar_split_clause,[],[f8486,f8172,f2369,f17559]) ).
fof(f17559,plain,
( spl2_463
<=> ! [X94,X95,X93,X92] : is_a_theorem(strict_implies(and(and(and(X92,X93),X94),X95),and(X93,X92))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_463])]) ).
fof(f8486,plain,
( ! [X94,X95,X92,X93] : is_a_theorem(strict_implies(and(and(and(X92,X93),X94),X95),and(X93,X92)))
| ~ spl2_137
| ~ spl2_275 ),
inference(resolution,[],[f8173,f2370]) ).
fof(f17557,plain,
( spl2_462
| ~ spl2_137
| ~ spl2_274 ),
inference(avatar_split_clause,[],[f8393,f8168,f2369,f17555]) ).
fof(f17555,plain,
( spl2_462
<=> ! [X38,X41,X40,X39] : is_a_theorem(strict_implies(and(and(equiv(X38,X39),X40),X41),equiv(X39,X38))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_462])]) ).
fof(f8393,plain,
( ! [X40,X38,X41,X39] : is_a_theorem(strict_implies(and(and(equiv(X38,X39),X40),X41),equiv(X39,X38)))
| ~ spl2_137
| ~ spl2_274 ),
inference(resolution,[],[f8169,f2370]) ).
fof(f17553,plain,
( spl2_461
| ~ spl2_33
| ~ spl2_150 ),
inference(avatar_split_clause,[],[f2657,f2620,f340,f17551]) ).
fof(f2657,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(not(X0),X1),X2),necessarily(or(X0,X1))))
| ~ spl2_33
| ~ spl2_150 ),
inference(superposition,[],[f2621,f341]) ).
fof(f17447,plain,
( spl2_460
| ~ spl2_122
| ~ spl2_137 ),
inference(avatar_split_clause,[],[f2443,f2369,f1831,f17445]) ).
fof(f17445,plain,
( spl2_460
<=> ! [X0,X3,X2,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,and(and(X1,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_460])]) ).
fof(f2443,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,and(and(X1,X2),X3))) )
| ~ spl2_122
| ~ spl2_137 ),
inference(resolution,[],[f2370,f1832]) ).
fof(f17443,plain,
( spl2_459
| ~ spl2_87
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2329,f1831,f1058,f17441]) ).
fof(f2329,plain,
( ! [X68,X69,X67] :
( is_a_theorem(strict_implies(X67,strict_implies(X68,X68)))
| ~ is_a_theorem(strict_implies(X67,strict_equiv(X69,X68))) )
| ~ spl2_87
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1059]) ).
fof(f17196,plain,
( spl2_458
| ~ spl2_33
| ~ spl2_455 ),
inference(avatar_split_clause,[],[f16897,f16877,f340,f17194]) ).
fof(f16897,plain,
( ! [X3,X4] : is_a_theorem(and(strict_implies(X4,X4),necessarily(or(X3,not(X3)))))
| ~ spl2_33
| ~ spl2_455 ),
inference(superposition,[],[f16878,f341]) ).
fof(f17192,plain,
( spl2_457
| ~ spl2_33
| ~ spl2_455 ),
inference(avatar_split_clause,[],[f16893,f16877,f340,f17190]) ).
fof(f16893,plain,
( ! [X3,X4] : is_a_theorem(and(necessarily(or(X3,not(X3))),strict_implies(X4,X4)))
| ~ spl2_33
| ~ spl2_455 ),
inference(superposition,[],[f16878,f341]) ).
fof(f17089,plain,
( spl2_456
| ~ spl2_216
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16366,f16331,f4859,f17087]) ).
fof(f4859,plain,
( spl2_216
<=> ! [X13,X14,X15] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(X13,and(X14,X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_216])]) ).
fof(f16366,plain,
( ! [X70,X71,X69] :
( ~ is_a_theorem(and(X69,X70))
| is_a_theorem(and(strict_implies(X71,X71),X69)) )
| ~ spl2_216
| ~ spl2_448 ),
inference(resolution,[],[f16332,f4860]) ).
fof(f4860,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(and(X13,and(X14,X15)))
| is_a_theorem(and(X13,X14)) )
| ~ spl2_216 ),
inference(avatar_component_clause,[],[f4859]) ).
fof(f16879,plain,
( spl2_387
| spl2_455
| ~ spl2_449
| ~ spl2_452 ),
inference(avatar_split_clause,[],[f16792,f16780,f16395,f16877,f14075]) ).
fof(f16395,plain,
( spl2_449
<=> ! [X11,X10] :
( ~ is_a_theorem(X10)
| is_a_theorem(and(X10,strict_implies(X11,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_449])]) ).
fof(f16780,plain,
( spl2_452
<=> ! [X61,X60,X62] :
( ~ is_a_theorem(and(X60,X61))
| is_a_theorem(and(X61,strict_implies(X62,X62))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_452])]) ).
fof(f16792,plain,
( ! [X31,X32,X30] :
( is_a_theorem(and(strict_implies(X30,X30),strict_implies(X31,X31)))
| ~ is_a_theorem(X32) )
| ~ spl2_449
| ~ spl2_452 ),
inference(resolution,[],[f16781,f16396]) ).
fof(f16396,plain,
( ! [X10,X11] :
( is_a_theorem(and(X10,strict_implies(X11,X11)))
| ~ is_a_theorem(X10) )
| ~ spl2_449 ),
inference(avatar_component_clause,[],[f16395]) ).
fof(f16781,plain,
( ! [X62,X60,X61] :
( ~ is_a_theorem(and(X60,X61))
| is_a_theorem(and(X61,strict_implies(X62,X62))) )
| ~ spl2_452 ),
inference(avatar_component_clause,[],[f16780]) ).
fof(f16875,plain,
( spl2_454
| ~ spl2_210
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16365,f16331,f4562,f16873]) ).
fof(f16873,plain,
( spl2_454
<=> ! [X66,X68,X67] :
( ~ is_a_theorem(and(X66,X67))
| is_a_theorem(and(strict_implies(X68,X68),X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_454])]) ).
fof(f4562,plain,
( spl2_210
<=> ! [X13,X14,X15] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(X13,and(X15,X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_210])]) ).
fof(f16365,plain,
( ! [X68,X66,X67] :
( ~ is_a_theorem(and(X66,X67))
| is_a_theorem(and(strict_implies(X68,X68),X67)) )
| ~ spl2_210
| ~ spl2_448 ),
inference(resolution,[],[f16332,f4563]) ).
fof(f4563,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(and(X13,and(X15,X14)))
| is_a_theorem(and(X13,X14)) )
| ~ spl2_210 ),
inference(avatar_component_clause,[],[f4562]) ).
fof(f16871,plain,
( spl2_453
| ~ spl2_206
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16364,f16331,f4546,f16869]) ).
fof(f4546,plain,
( spl2_206
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_206])]) ).
fof(f16364,plain,
( ! [X65,X63,X64] :
( ~ is_a_theorem(and(X63,X64))
| is_a_theorem(and(X63,strict_implies(X65,X65))) )
| ~ spl2_206
| ~ spl2_448 ),
inference(resolution,[],[f16332,f4547]) ).
fof(f4547,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X2,X4)) )
| ~ spl2_206 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f16782,plain,
( spl2_452
| ~ spl2_199
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16363,f16331,f4152,f16780]) ).
fof(f4152,plain,
( spl2_199
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_199])]) ).
fof(f16363,plain,
( ! [X62,X60,X61] :
( ~ is_a_theorem(and(X60,X61))
| is_a_theorem(and(X61,strict_implies(X62,X62))) )
| ~ spl2_199
| ~ spl2_448 ),
inference(resolution,[],[f16332,f4153]) ).
fof(f4153,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X3,X4)) )
| ~ spl2_199 ),
inference(avatar_component_clause,[],[f4152]) ).
fof(f16619,plain,
( spl2_451
| ~ spl2_33
| ~ spl2_449 ),
inference(avatar_split_clause,[],[f16508,f16395,f340,f16617]) ).
fof(f16508,plain,
( ! [X3,X4] :
( is_a_theorem(and(X4,necessarily(or(X3,not(X3)))))
| ~ is_a_theorem(X4) )
| ~ spl2_33
| ~ spl2_449 ),
inference(superposition,[],[f16396,f341]) ).
fof(f16524,plain,
( spl2_450
| ~ spl2_33
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16378,f16331,f340,f16522]) ).
fof(f16378,plain,
( ! [X3,X4] :
( is_a_theorem(and(necessarily(or(X3,not(X3))),X4))
| ~ is_a_theorem(X4) )
| ~ spl2_33
| ~ spl2_448 ),
inference(superposition,[],[f16332,f341]) ).
fof(f16397,plain,
( spl2_449
| ~ spl2_31
| ~ spl2_448 ),
inference(avatar_split_clause,[],[f16339,f16331,f330,f16395]) ).
fof(f16339,plain,
( ! [X10,X11] :
( ~ is_a_theorem(X10)
| is_a_theorem(and(X10,strict_implies(X11,X11))) )
| ~ spl2_31
| ~ spl2_448 ),
inference(resolution,[],[f16332,f331]) ).
fof(f16333,plain,
( spl2_448
| ~ spl2_71
| ~ spl2_78
| ~ spl2_111
| ~ spl2_397 ),
inference(avatar_split_clause,[],[f16329,f14308,f1499,f818,f738,f16331]) ).
fof(f818,plain,
( spl2_78
<=> ! [X19] : strict_equiv(X19,X19) = strict_implies(X19,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_78])]) ).
fof(f16329,plain,
( ! [X0,X1] :
( is_a_theorem(and(strict_implies(X0,X0),X1))
| ~ is_a_theorem(X1) )
| ~ spl2_71
| ~ spl2_78
| ~ spl2_111
| ~ spl2_397 ),
inference(forward_demodulation,[],[f16328,f1500]) ).
fof(f16328,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(and(strict_implies(X0,X0),and(strict_implies(X0,X0),X1))) )
| ~ spl2_71
| ~ spl2_78
| ~ spl2_397 ),
inference(subsumption_resolution,[],[f16324,f739]) ).
fof(f16324,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X0))
| ~ is_a_theorem(X1)
| is_a_theorem(and(strict_implies(X0,X0),and(strict_implies(X0,X0),X1))) )
| ~ spl2_78
| ~ spl2_397 ),
inference(superposition,[],[f14309,f819]) ).
fof(f819,plain,
( ! [X19] : strict_equiv(X19,X19) = strict_implies(X19,X19)
| ~ spl2_78 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f16321,plain,
( spl2_447
| ~ spl2_84
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2310,f1831,f1046,f16319]) ).
fof(f16319,plain,
( spl2_447
<=> ! [X6,X5,X7] :
( is_a_theorem(strict_implies(X5,implies(X6,X7)))
| ~ is_a_theorem(strict_implies(X5,equiv(X7,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_447])]) ).
fof(f2310,plain,
( ! [X6,X7,X5] :
( is_a_theorem(strict_implies(X5,implies(X6,X7)))
| ~ is_a_theorem(strict_implies(X5,equiv(X7,X6))) )
| ~ spl2_84
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1047]) ).
fof(f16317,plain,
( spl2_446
| ~ spl2_27
| ~ spl2_131 ),
inference(avatar_split_clause,[],[f2236,f2224,f302,f16315]) ).
fof(f16315,plain,
( spl2_446
<=> ! [X1] :
( ~ is_a_theorem(necessarily(not(possibly(X1))))
| is_a_theorem(necessarily(not(X1)))
| ~ is_a_theorem(possibly(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_446])]) ).
fof(f2224,plain,
( spl2_131
<=> ! [X0] : necessarily(not(possibly(X0))) = strict_implies(possibly(X0),necessarily(not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_131])]) ).
fof(f2236,plain,
( ! [X1] :
( ~ is_a_theorem(necessarily(not(possibly(X1))))
| is_a_theorem(necessarily(not(X1)))
| ~ is_a_theorem(possibly(X1)) )
| ~ spl2_27
| ~ spl2_131 ),
inference(superposition,[],[f303,f2225]) ).
fof(f2225,plain,
( ! [X0] : necessarily(not(possibly(X0))) = strict_implies(possibly(X0),necessarily(not(X0)))
| ~ spl2_131 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f16313,plain,
( spl2_445
| ~ spl2_23
| ~ spl2_104
| ~ spl2_110 ),
inference(avatar_split_clause,[],[f1682,f1481,f1388,f286,f16311]) ).
fof(f1682,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(strict_equiv(necessarily(not(X11)),not(X10)),strict_implies(possibly(X11),X10)))
| ~ spl2_23
| ~ spl2_104
| ~ spl2_110 ),
inference(forward_demodulation,[],[f1670,f287]) ).
fof(f1670,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(strict_equiv(necessarily(not(X11)),not(X10)),necessarily(implies(possibly(X11),X10))))
| ~ spl2_104
| ~ spl2_110 ),
inference(superposition,[],[f1482,f1389]) ).
fof(f16309,plain,
( spl2_444
| ~ spl2_54
| ~ spl2_84 ),
inference(avatar_split_clause,[],[f1067,f1046,f505,f16307]) ).
fof(f1067,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(equiv(necessarily(not(X3)),X2),not(and(X2,possibly(X3)))))
| ~ spl2_54
| ~ spl2_84 ),
inference(superposition,[],[f1047,f506]) ).
fof(f16096,plain,
( spl2_443
| ~ spl2_24
| ~ spl2_25
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f14002,f12444,f1856,f1499,f810,f315,f294,f290,f16094]) ).
fof(f14002,plain,
( ! [X203,X204] : is_a_theorem(necessarily(not(and(or(X204,X203),and(not(X203),not(X204))))))
| ~ spl2_24
| ~ spl2_25
| ~ spl2_29
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13870,f13940]) ).
fof(f13870,plain,
( ! [X203,X204] : is_a_theorem(necessarily(not(and(and(not(X203),not(X204)),or(X204,X203)))))
| ~ spl2_25
| ~ spl2_371 ),
inference(superposition,[],[f295,f12445]) ).
fof(f15710,plain,
( spl2_442
| ~ spl2_24
| ~ spl2_29
| ~ spl2_71
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(avatar_split_clause,[],[f13954,f12444,f1856,f1499,f810,f738,f315,f290,f15708]) ).
fof(f13954,plain,
( ! [X19,X20] : is_a_theorem(necessarily(not(and(or(X19,X20),and(not(X19),not(X20))))))
| ~ spl2_24
| ~ spl2_29
| ~ spl2_71
| ~ spl2_76
| ~ spl2_111
| ~ spl2_126
| ~ spl2_371 ),
inference(forward_demodulation,[],[f13819,f13940]) ).
fof(f13819,plain,
( ! [X19,X20] : is_a_theorem(necessarily(not(and(and(not(X19),not(X20)),or(X19,X20)))))
| ~ spl2_71
| ~ spl2_371 ),
inference(superposition,[],[f739,f12445]) ).
fof(f15693,plain,
( spl2_441
| ~ spl2_74
| ~ spl2_83
| ~ spl2_439 ),
inference(avatar_split_clause,[],[f15227,f15221,f1024,f802,f15691]) ).
fof(f802,plain,
( spl2_74
<=> ! [X1] : implies(X1,X1) = equiv(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).
fof(f15227,plain,
( ! [X0] :
( is_a_theorem(necessarily(not(not(X0))))
| ~ is_a_theorem(necessarily(not(implies(X0,X0)))) )
| ~ spl2_74
| ~ spl2_83
| ~ spl2_439 ),
inference(forward_demodulation,[],[f15224,f1025]) ).
fof(f15224,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(not(implies(X0,X0))))
| is_a_theorem(necessarily(or(X0,X0))) )
| ~ spl2_74
| ~ spl2_439 ),
inference(superposition,[],[f15222,f803]) ).
fof(f803,plain,
( ! [X1] : implies(X1,X1) = equiv(X1,X1)
| ~ spl2_74 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f15231,plain,
( spl2_440
| ~ spl2_75
| ~ spl2_439 ),
inference(avatar_split_clause,[],[f15225,f15221,f806,f15229]) ).
fof(f15225,plain,
( ! [X2,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X2,X1))))
| is_a_theorem(necessarily(or(X2,X1))) )
| ~ spl2_75
| ~ spl2_439 ),
inference(superposition,[],[f15222,f807]) ).
fof(f15223,plain,
( spl2_439
| ~ spl2_327
| ~ spl2_381 ),
inference(avatar_split_clause,[],[f15173,f13497,f10547,f15221]) ).
fof(f15173,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(equiv(X0,X1))))
| is_a_theorem(necessarily(or(X1,X0))) )
| ~ spl2_327
| ~ spl2_381 ),
inference(resolution,[],[f13498,f10548]) ).
fof(f15219,plain,
( spl2_438
| ~ spl2_26
| ~ spl2_201 ),
inference(avatar_split_clause,[],[f4506,f4160,f298,f15217]) ).
fof(f15217,plain,
( spl2_438
<=> ! [X4,X2,X3] :
( is_a_theorem(and(X2,equiv(X3,X4)))
| ~ is_a_theorem(and(X2,implies(X3,X4)))
| ~ is_a_theorem(implies(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_438])]) ).
fof(f4506,plain,
( ! [X2,X3,X4] :
( is_a_theorem(and(X2,equiv(X3,X4)))
| ~ is_a_theorem(and(X2,implies(X3,X4)))
| ~ is_a_theorem(implies(X4,X3)) )
| ~ spl2_26
| ~ spl2_201 ),
inference(resolution,[],[f4161,f299]) ).
fof(f15139,plain,
( spl2_387
| spl2_433
| ~ spl2_26
| ~ spl2_427 ),
inference(avatar_split_clause,[],[f15070,f14908,f298,f15091,f14075]) ).
fof(f15070,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(not(X1))) )
| ~ spl2_26
| ~ spl2_427 ),
inference(resolution,[],[f14909,f299]) ).
fof(f15138,plain,
( spl2_437
| ~ spl2_26
| ~ spl2_197 ),
inference(avatar_split_clause,[],[f4383,f4144,f298,f15136]) ).
fof(f15136,plain,
( spl2_437
<=> ! [X4,X2,X3] :
( is_a_theorem(and(X2,strict_equiv(X3,X4)))
| ~ is_a_theorem(and(X2,strict_implies(X3,X4)))
| ~ is_a_theorem(strict_implies(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_437])]) ).
fof(f4383,plain,
( ! [X2,X3,X4] :
( is_a_theorem(and(X2,strict_equiv(X3,X4)))
| ~ is_a_theorem(and(X2,strict_implies(X3,X4)))
| ~ is_a_theorem(strict_implies(X4,X3)) )
| ~ spl2_26
| ~ spl2_197 ),
inference(resolution,[],[f4145,f299]) ).
fof(f15134,plain,
( spl2_436
| ~ spl2_76
| ~ spl2_424 ),
inference(avatar_split_clause,[],[f14995,f14896,f810,f15132]) ).
fof(f14995,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(not(and(possibly(X11),X9))) )
| ~ spl2_76
| ~ spl2_424 ),
inference(superposition,[],[f14897,f811]) ).
fof(f15130,plain,
( spl2_387
| spl2_431
| ~ spl2_26
| ~ spl2_424 ),
inference(avatar_split_clause,[],[f14980,f14896,f298,f15004,f14075]) ).
fof(f14980,plain,
( ! [X2,X0,X1] :
( is_a_theorem(not(and(possibly(X0),X1)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(X1)) )
| ~ spl2_26
| ~ spl2_424 ),
inference(resolution,[],[f14897,f299]) ).
fof(f15129,plain,
( spl2_435
| ~ spl2_27
| ~ spl2_423 ),
inference(avatar_split_clause,[],[f14944,f14892,f302,f15127]) ).
fof(f14944,plain,
( ! [X18,X19,X17] :
( is_a_theorem(implies(possibly(X17),X18))
| ~ is_a_theorem(and(X19,not(not(X18)))) )
| ~ spl2_27
| ~ spl2_423 ),
inference(resolution,[],[f14893,f303]) ).
fof(f15125,plain,
( spl2_434
| ~ spl2_26
| ~ spl2_189 ),
inference(avatar_split_clause,[],[f3862,f3772,f298,f15123]) ).
fof(f3862,plain,
( ! [X8,X7] :
( is_a_theorem(equiv(not(X7),not(X8)))
| ~ is_a_theorem(or(X8,not(X7)))
| ~ is_a_theorem(or(X7,not(X8))) )
| ~ spl2_26
| ~ spl2_189 ),
inference(superposition,[],[f299,f3773]) ).
fof(f15093,plain,
( spl2_433
| ~ spl2_72
| ~ spl2_427 ),
inference(avatar_split_clause,[],[f15082,f14908,f748,f15091]) ).
fof(f15082,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(implies(possibly(X1),X0)) )
| ~ spl2_72
| ~ spl2_427 ),
inference(superposition,[],[f14909,f749]) ).
fof(f15069,plain,
( spl2_432
| ~ spl2_80
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3523,f2750,f856,f15067]) ).
fof(f15006,plain,
( spl2_431
| ~ spl2_72
| ~ spl2_424 ),
inference(avatar_split_clause,[],[f14994,f14896,f748,f15004]) ).
fof(f14994,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(possibly(X8),X7))) )
| ~ spl2_72
| ~ spl2_424 ),
inference(superposition,[],[f14897,f749]) ).
fof(f15002,plain,
( spl2_430
| ~ spl2_80
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3476,f2734,f856,f15000]) ).
fof(f3476,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(equiv(or(X10,X11),and(X11,not(not(X10)))),not(equiv(not(X10),X11))))
| ~ spl2_80
| ~ spl2_157 ),
inference(superposition,[],[f2735,f857]) ).
fof(f14919,plain,
( spl2_387
| spl2_420
| ~ spl2_26
| ~ spl2_417 ),
inference(avatar_split_clause,[],[f14850,f14629,f298,f14870,f14075]) ).
fof(f14850,plain,
( ! [X2,X0,X1] :
( is_a_theorem(not(and(X0,possibly(X1))))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(X0)) )
| ~ spl2_26
| ~ spl2_417 ),
inference(resolution,[],[f14630,f299]) ).
fof(f14918,plain,
( spl2_429
| ~ spl2_23
| ~ spl2_104
| ~ spl2_154 ),
inference(avatar_split_clause,[],[f3427,f2673,f1388,f286,f14916]) ).
fof(f14916,plain,
( spl2_429
<=> ! [X20,X21,X19] :
( ~ is_a_theorem(and(strict_implies(possibly(X20),X19),strict_implies(necessarily(not(X20)),X21)))
| is_a_theorem(necessarily(or(X19,X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_429])]) ).
fof(f3427,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(strict_implies(possibly(X20),X19),strict_implies(necessarily(not(X20)),X21)))
| is_a_theorem(necessarily(or(X19,X21))) )
| ~ spl2_23
| ~ spl2_104
| ~ spl2_154 ),
inference(forward_demodulation,[],[f3412,f287]) ).
fof(f3412,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(necessarily(implies(possibly(X20),X19)),strict_implies(necessarily(not(X20)),X21)))
| is_a_theorem(necessarily(or(X19,X21))) )
| ~ spl2_104
| ~ spl2_154 ),
inference(superposition,[],[f2674,f1389]) ).
fof(f14914,plain,
( spl2_428
| ~ spl2_27
| ~ spl2_416 ),
inference(avatar_split_clause,[],[f14810,f14625,f302,f14912]) ).
fof(f14810,plain,
( ! [X26,X24,X25] :
( is_a_theorem(not(and(X24,possibly(X25))))
| ~ is_a_theorem(and(X26,not(X24))) )
| ~ spl2_27
| ~ spl2_416 ),
inference(resolution,[],[f14626,f303]) ).
fof(f14910,plain,
( spl2_427
| ~ spl2_27
| ~ spl2_412 ),
inference(avatar_split_clause,[],[f14694,f14609,f302,f14908]) ).
fof(f14694,plain,
( ! [X18,X19,X17] :
( is_a_theorem(implies(possibly(X17),X18))
| ~ is_a_theorem(and(not(not(X18)),X19)) )
| ~ spl2_27
| ~ spl2_412 ),
inference(resolution,[],[f14610,f303]) ).
fof(f14906,plain,
( spl2_426
| ~ spl2_76
| ~ spl2_411 ),
inference(avatar_split_clause,[],[f14657,f14605,f810,f14904]) ).
fof(f14657,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),not(and(possibly(X11),X9))))
| ~ spl2_76
| ~ spl2_411 ),
inference(superposition,[],[f14606,f811]) ).
fof(f14902,plain,
( spl2_425
| ~ spl2_23
| ~ spl2_104
| ~ spl2_151 ),
inference(avatar_split_clause,[],[f3392,f2643,f1388,f286,f14900]) ).
fof(f14900,plain,
( spl2_425
<=> ! [X20,X21,X19] :
( ~ is_a_theorem(and(strict_implies(X21,not(X19)),strict_implies(possibly(X20),X19)))
| is_a_theorem(strict_implies(X21,necessarily(not(X20)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_425])]) ).
fof(f3392,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(strict_implies(X21,not(X19)),strict_implies(possibly(X20),X19)))
| is_a_theorem(strict_implies(X21,necessarily(not(X20)))) )
| ~ spl2_23
| ~ spl2_104
| ~ spl2_151 ),
inference(forward_demodulation,[],[f3372,f287]) ).
fof(f3372,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(strict_implies(X21,not(X19)),necessarily(implies(possibly(X20),X19))))
| is_a_theorem(strict_implies(X21,necessarily(not(X20)))) )
| ~ spl2_104
| ~ spl2_151 ),
inference(superposition,[],[f2644,f1389]) ).
fof(f14898,plain,
( spl2_424
| ~ spl2_27
| ~ spl2_411 ),
inference(avatar_split_clause,[],[f14643,f14605,f302,f14896]) ).
fof(f14643,plain,
( ! [X26,X24,X25] :
( is_a_theorem(not(and(possibly(X24),X25)))
| ~ is_a_theorem(and(not(X25),X26)) )
| ~ spl2_27
| ~ spl2_411 ),
inference(resolution,[],[f14606,f303]) ).
fof(f14894,plain,
( spl2_423
| ~ spl2_104
| ~ spl2_393 ),
inference(avatar_split_clause,[],[f14243,f14161,f1388,f14892]) ).
fof(f14243,plain,
( ! [X18,X16,X17] : is_a_theorem(strict_implies(and(X18,not(not(X16))),implies(possibly(X17),X16)))
| ~ spl2_104
| ~ spl2_393 ),
inference(superposition,[],[f14162,f1389]) ).
fof(f14890,plain,
( spl2_422
| ~ spl2_20
| ~ spl2_388 ),
inference(avatar_split_clause,[],[f14088,f14079,f273,f14888]) ).
fof(f14888,plain,
( spl2_422
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_422])]) ).
fof(f14088,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X1,possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X2)) )
| ~ spl2_20
| ~ spl2_388 ),
inference(superposition,[],[f14080,f274]) ).
fof(f14876,plain,
( spl2_421
| ~ spl2_33
| ~ spl2_151 ),
inference(avatar_split_clause,[],[f3385,f2643,f340,f14874]) ).
fof(f14874,plain,
( spl2_421
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X2)))
| ~ is_a_theorem(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_421])]) ).
fof(f3385,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X2)))
| ~ is_a_theorem(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2)))) )
| ~ spl2_33
| ~ spl2_151 ),
inference(forward_demodulation,[],[f3363,f341]) ).
fof(f3363,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2))))
| is_a_theorem(strict_implies(not(X0),X2)) )
| ~ spl2_33
| ~ spl2_151 ),
inference(superposition,[],[f2644,f341]) ).
fof(f14872,plain,
( spl2_420
| ~ spl2_72
| ~ spl2_417 ),
inference(avatar_split_clause,[],[f14864,f14629,f748,f14870]) ).
fof(f14864,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(not(and(X7,possibly(X8)))) )
| ~ spl2_72
| ~ spl2_417 ),
inference(superposition,[],[f14630,f749]) ).
fof(f14802,plain,
( spl2_419
| ~ spl2_20
| ~ spl2_148 ),
inference(avatar_split_clause,[],[f3245,f2598,f273,f14800]) ).
fof(f14800,plain,
( spl2_419
<=> ! [X2,X0,X1] : possibly(strict_implies(X0,and(X1,not(X2)))) = not(necessarily(possibly(and(X0,implies(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_419])]) ).
fof(f3245,plain,
( ! [X2,X0,X1] : possibly(strict_implies(X0,and(X1,not(X2)))) = not(necessarily(possibly(and(X0,implies(X1,X2)))))
| ~ spl2_20
| ~ spl2_148 ),
inference(superposition,[],[f274,f2599]) ).
fof(f14635,plain,
( spl2_418
| ~ spl2_23
| ~ spl2_104
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3163,f2558,f1388,f286,f14633]) ).
fof(f3163,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(necessarily(or(X19,X21)),strict_implies(X21,necessarily(not(X20)))),strict_implies(possibly(X20),X19)))
| ~ spl2_23
| ~ spl2_104
| ~ spl2_146 ),
inference(forward_demodulation,[],[f3137,f287]) ).
fof(f3137,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(necessarily(or(X19,X21)),strict_implies(X21,necessarily(not(X20)))),necessarily(implies(possibly(X20),X19))))
| ~ spl2_104
| ~ spl2_146 ),
inference(superposition,[],[f2559,f1389]) ).
fof(f14631,plain,
( spl2_417
| ~ spl2_27
| ~ spl2_408 ),
inference(avatar_split_clause,[],[f14508,f14494,f302,f14629]) ).
fof(f14508,plain,
( ! [X26,X24,X25] :
( is_a_theorem(not(and(X24,possibly(X25))))
| ~ is_a_theorem(and(not(X24),X26)) )
| ~ spl2_27
| ~ spl2_408 ),
inference(resolution,[],[f14495,f303]) ).
fof(f14627,plain,
( spl2_416
| ~ spl2_54
| ~ spl2_385 ),
inference(avatar_split_clause,[],[f14060,f13747,f505,f14625]) ).
fof(f14060,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,not(X0)),not(and(X0,possibly(X1)))))
| ~ spl2_54
| ~ spl2_385 ),
inference(superposition,[],[f13748,f506]) ).
fof(f14623,plain,
( spl2_415
| ~ spl2_20
| ~ spl2_385 ),
inference(avatar_split_clause,[],[f14047,f13747,f273,f14621]) ).
fof(f14047,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X1,possibly(X0)),implies(necessarily(not(X0)),X2)))
| ~ spl2_20
| ~ spl2_385 ),
inference(superposition,[],[f13748,f274]) ).
fof(f14619,plain,
( spl2_414
| ~ spl2_23
| ~ spl2_104
| ~ spl2_146 ),
inference(avatar_split_clause,[],[f3145,f2558,f1388,f286,f14617]) ).
fof(f3145,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(strict_implies(possibly(X20),X19),strict_implies(necessarily(not(X20)),X21)),necessarily(or(X19,X21))))
| ~ spl2_23
| ~ spl2_104
| ~ spl2_146 ),
inference(forward_demodulation,[],[f3123,f287]) ).
fof(f3123,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(necessarily(implies(possibly(X20),X19)),strict_implies(necessarily(not(X20)),X21)),necessarily(or(X19,X21))))
| ~ spl2_104
| ~ spl2_146 ),
inference(superposition,[],[f2559,f1389]) ).
fof(f14615,plain,
( spl2_413
| ~ spl2_20
| ~ spl2_384 ),
inference(avatar_split_clause,[],[f13752,f13659,f273,f14613]) ).
fof(f14613,plain,
( spl2_413
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(and(possibly(X0),X1))
| is_a_theorem(implies(necessarily(not(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_413])]) ).
fof(f13752,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(possibly(X0),X1))
| is_a_theorem(implies(necessarily(not(X0)),X2)) )
| ~ spl2_20
| ~ spl2_384 ),
inference(superposition,[],[f13660,f274]) ).
fof(f14611,plain,
( spl2_412
| ~ spl2_334
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13522,f13441,f11028,f14609]) ).
fof(f13522,plain,
( ! [X83,X84,X85] : is_a_theorem(strict_implies(and(not(not(X83)),X84),implies(possibly(X85),X83)))
| ~ spl2_334
| ~ spl2_380 ),
inference(resolution,[],[f13442,f11029]) ).
fof(f14607,plain,
( spl2_411
| ~ spl2_335
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13506,f13441,f11032,f14605]) ).
fof(f13506,plain,
( ! [X21,X22,X23] : is_a_theorem(strict_implies(and(not(X21),X22),not(and(possibly(X23),X21))))
| ~ spl2_335
| ~ spl2_380 ),
inference(resolution,[],[f13442,f11033]) ).
fof(f14555,plain,
( spl2_410
| ~ spl2_23
| ~ spl2_104
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f3015,f2528,f1388,f286,f14553]) ).
fof(f3015,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(strict_implies(X21,not(X19)),strict_implies(possibly(X20),X19)),strict_implies(X21,necessarily(not(X20)))))
| ~ spl2_23
| ~ spl2_104
| ~ spl2_142 ),
inference(forward_demodulation,[],[f2993,f287]) ).
fof(f2993,plain,
( ! [X21,X19,X20] : is_a_theorem(strict_implies(and(strict_implies(X21,not(X19)),necessarily(implies(possibly(X20),X19))),strict_implies(X21,necessarily(not(X20)))))
| ~ spl2_104
| ~ spl2_142 ),
inference(superposition,[],[f2529,f1389]) ).
fof(f14500,plain,
( spl2_409
| ~ spl2_20
| ~ spl2_383 ),
inference(avatar_split_clause,[],[f13627,f13618,f273,f14498]) ).
fof(f13627,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(possibly(X0),X1),implies(necessarily(not(X0)),X2)))
| ~ spl2_20
| ~ spl2_383 ),
inference(superposition,[],[f13619,f274]) ).
fof(f14496,plain,
( spl2_408
| ~ spl2_332
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13501,f13441,f10702,f14494]) ).
fof(f13501,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(not(X2),X3),not(and(X2,possibly(X4)))))
| ~ spl2_332
| ~ spl2_380 ),
inference(resolution,[],[f13442,f10703]) ).
fof(f14492,plain,
( spl2_407
| ~ spl2_33
| ~ spl2_142 ),
inference(avatar_split_clause,[],[f3008,f2528,f340,f14490]) ).
fof(f3008,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2))),necessarily(or(X0,X2))))
| ~ spl2_33
| ~ spl2_142 ),
inference(forward_demodulation,[],[f2984,f341]) ).
fof(f2984,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,not(X1))),necessarily(or(X1,X2))),strict_implies(not(X0),X2)))
| ~ spl2_33
| ~ spl2_142 ),
inference(superposition,[],[f2529,f341]) ).
fof(f14474,plain,
( spl2_406
| ~ spl2_20
| ~ spl2_382 ),
inference(avatar_split_clause,[],[f13559,f13556,f273,f14472]) ).
fof(f13559,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(possibly(X0))))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) )
| ~ spl2_20
| ~ spl2_382 ),
inference(superposition,[],[f13557,f274]) ).
fof(f14449,plain,
( spl2_405
| ~ spl2_76
| ~ spl2_398 ),
inference(avatar_split_clause,[],[f14341,f14312,f810,f14447]) ).
fof(f14341,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,not(not(X2))))
| is_a_theorem(or(X4,X2)) )
| ~ spl2_76
| ~ spl2_398 ),
inference(superposition,[],[f14313,f811]) ).
fof(f14445,plain,
( spl2_404
| ~ spl2_46
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2324,f1831,f450,f14443]) ).
fof(f14443,plain,
( spl2_404
<=> ! [X51,X50,X49,X52] :
( is_a_theorem(strict_implies(X49,strict_implies(X50,X51)))
| ~ is_a_theorem(strict_implies(X49,and(strict_implies(X50,X52),strict_implies(X52,X51)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_404])]) ).
fof(f2324,plain,
( ! [X50,X51,X49,X52] :
( is_a_theorem(strict_implies(X49,strict_implies(X50,X51)))
| ~ is_a_theorem(strict_implies(X49,and(strict_implies(X50,X52),strict_implies(X52,X51)))) )
| ~ spl2_46
| ~ spl2_122 ),
inference(resolution,[],[f1832,f451]) ).
fof(f14441,plain,
( spl2_387
| spl2_402
| ~ spl2_26
| ~ spl2_398 ),
inference(avatar_split_clause,[],[f14328,f14312,f298,f14352,f14075]) ).
fof(f14328,plain,
( ! [X2,X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(not(X1))) )
| ~ spl2_26
| ~ spl2_398 ),
inference(resolution,[],[f14313,f299]) ).
fof(f14374,plain,
( spl2_403
| ~ spl2_43
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2323,f1831,f436,f14372]) ).
fof(f2323,plain,
( ! [X48,X46,X47,X45] :
( is_a_theorem(strict_implies(X45,and(X46,and(X47,X48))))
| ~ is_a_theorem(strict_implies(X45,and(and(X46,X47),X48))) )
| ~ spl2_43
| ~ spl2_122 ),
inference(resolution,[],[f1832,f437]) ).
fof(f14354,plain,
( spl2_402
| ~ spl2_72
| ~ spl2_398 ),
inference(avatar_split_clause,[],[f14340,f14312,f748,f14352]) ).
fof(f14340,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) )
| ~ spl2_72
| ~ spl2_398 ),
inference(superposition,[],[f14313,f749]) ).
fof(f14327,plain,
( spl2_387
| spl2_396
| ~ spl2_26
| ~ spl2_394 ),
inference(avatar_split_clause,[],[f14264,f14165,f298,f14288,f14075]) ).
fof(f14264,plain,
( ! [X2,X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(not(X0))) )
| ~ spl2_26
| ~ spl2_394 ),
inference(resolution,[],[f14166,f299]) ).
fof(f14326,plain,
( spl2_401
| ~ spl2_114
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2317,f1831,f1640,f14324]) ).
fof(f14324,plain,
( spl2_401
<=> ! [X25,X27,X26] :
( is_a_theorem(strict_implies(X25,not(and(X26,possibly(X27)))))
| ~ is_a_theorem(strict_implies(X25,equiv(X26,necessarily(not(X27))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_401])]) ).
fof(f2317,plain,
( ! [X26,X27,X25] :
( is_a_theorem(strict_implies(X25,not(and(X26,possibly(X27)))))
| ~ is_a_theorem(strict_implies(X25,equiv(X26,necessarily(not(X27))))) )
| ~ spl2_114
| ~ spl2_122 ),
inference(resolution,[],[f1832,f1641]) ).
fof(f14322,plain,
( spl2_400
| ~ spl2_27
| ~ spl2_393 ),
inference(avatar_split_clause,[],[f14224,f14161,f302,f14320]) ).
fof(f14224,plain,
( ! [X18,X19,X17] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(X19,not(not(X17)))) )
| ~ spl2_27
| ~ spl2_393 ),
inference(resolution,[],[f14162,f303]) ).
fof(f14318,plain,
( spl2_399
| ~ spl2_76
| ~ spl2_391 ),
inference(avatar_split_clause,[],[f14185,f14153,f810,f14316]) ).
fof(f14185,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,not(not(X2))),or(X4,X2)))
| ~ spl2_76
| ~ spl2_391 ),
inference(superposition,[],[f14154,f811]) ).
fof(f14314,plain,
( spl2_398
| ~ spl2_27
| ~ spl2_391 ),
inference(avatar_split_clause,[],[f14173,f14153,f302,f14312]) ).
fof(f14173,plain,
( ! [X18,X19,X17] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(not(not(X18)),X19)) )
| ~ spl2_27
| ~ spl2_391 ),
inference(resolution,[],[f14154,f303]) ).
fof(f14310,plain,
( spl2_397
| ~ spl2_34
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f2290,f1712,f344,f14308]) ).
fof(f2290,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(strict_equiv(X20,X21))
| ~ is_a_theorem(X22)
| is_a_theorem(and(strict_implies(X20,X21),and(strict_implies(X21,X20),X22))) )
| ~ spl2_34
| ~ spl2_120 ),
inference(superposition,[],[f1713,f345]) ).
fof(f14290,plain,
( spl2_396
| ~ spl2_72
| ~ spl2_394 ),
inference(avatar_split_clause,[],[f14276,f14165,f748,f14288]) ).
fof(f14276,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) )
| ~ spl2_72
| ~ spl2_394 ),
inference(superposition,[],[f14166,f749]) ).
fof(f14218,plain,
( spl2_395
| ~ spl2_36
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f2288,f1712,f363,f14216]) ).
fof(f2288,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(equiv(X14,X15))
| ~ is_a_theorem(X16)
| is_a_theorem(and(implies(X14,X15),and(implies(X15,X14),X16))) )
| ~ spl2_36
| ~ spl2_120 ),
inference(superposition,[],[f1713,f364]) ).
fof(f14167,plain,
( spl2_394
| ~ spl2_27
| ~ spl2_390 ),
inference(avatar_split_clause,[],[f14110,f14102,f302,f14165]) ).
fof(f14110,plain,
( ! [X18,X19,X17] :
( is_a_theorem(or(X17,X18))
| ~ is_a_theorem(and(not(not(X17)),X19)) )
| ~ spl2_27
| ~ spl2_390 ),
inference(resolution,[],[f14103,f303]) ).
fof(f14163,plain,
( spl2_393
| ~ spl2_24
| ~ spl2_385 ),
inference(avatar_split_clause,[],[f14062,f13747,f290,f14161]) ).
fof(f14062,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X9,not(not(X7))),or(X7,X8)))
| ~ spl2_24
| ~ spl2_385 ),
inference(superposition,[],[f13748,f291]) ).
fof(f14159,plain,
( spl2_392
| ~ spl2_32
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1943,f1558,f336,f14157]) ).
fof(f14157,plain,
( spl2_392
<=> ! [X9,X8] : not(necessarily(possibly(strict_implies(X8,necessarily(not(X9)))))) = possibly(necessarily(possibly(and(X8,possibly(X9))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_392])]) ).
fof(f1943,plain,
( ! [X8,X9] : not(necessarily(possibly(strict_implies(X8,necessarily(not(X9)))))) = possibly(necessarily(possibly(and(X8,possibly(X9)))))
| ~ spl2_32
| ~ spl2_112 ),
inference(superposition,[],[f337,f1559]) ).
fof(f14155,plain,
( spl2_391
| ~ spl2_331
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13521,f13441,f10620,f14153]) ).
fof(f13521,plain,
( ! [X82,X80,X81] : is_a_theorem(strict_implies(and(not(not(X80)),X81),or(X82,X80)))
| ~ spl2_331
| ~ spl2_380 ),
inference(resolution,[],[f13442,f10621]) ).
fof(f14104,plain,
( spl2_390
| ~ spl2_330
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13520,f13441,f10591,f14102]) ).
fof(f13520,plain,
( ! [X78,X79,X77] : is_a_theorem(strict_implies(and(not(not(X77)),X78),or(X77,X79)))
| ~ spl2_330
| ~ spl2_380 ),
inference(resolution,[],[f13442,f10592]) ).
fof(f14085,plain,
( spl2_389
| ~ spl2_29
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1942,f1558,f315,f14083]) ).
fof(f14083,plain,
( spl2_389
<=> ! [X6,X5,X7] : implies(X7,strict_implies(X5,necessarily(not(X6)))) = not(and(X7,possibly(and(X5,possibly(X6))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_389])]) ).
fof(f1942,plain,
( ! [X6,X7,X5] : implies(X7,strict_implies(X5,necessarily(not(X6)))) = not(and(X7,possibly(and(X5,possibly(X6)))))
| ~ spl2_29
| ~ spl2_112 ),
inference(superposition,[],[f316,f1559]) ).
fof(f14081,plain,
( spl2_388
| ~ spl2_76
| ~ spl2_384 ),
inference(avatar_split_clause,[],[f13765,f13659,f810,f14079]) ).
fof(f13765,plain,
( ! [X10,X11,X9] :
( ~ is_a_theorem(and(X10,not(X9)))
| is_a_theorem(implies(X9,X11)) )
| ~ spl2_76
| ~ spl2_384 ),
inference(superposition,[],[f13660,f811]) ).
fof(f14077,plain,
( spl2_387
| spl2_386
| ~ spl2_26
| ~ spl2_384 ),
inference(avatar_split_clause,[],[f13750,f13659,f298,f13770,f14075]) ).
fof(f13770,plain,
( spl2_386
<=> ! [X7,X8] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(implies(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_386])]) ).
fof(f13750,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(not(X0)) )
| ~ spl2_26
| ~ spl2_384 ),
inference(resolution,[],[f13660,f299]) ).
fof(f13772,plain,
( spl2_386
| ~ spl2_72
| ~ spl2_384 ),
inference(avatar_split_clause,[],[f13764,f13659,f748,f13770]) ).
fof(f13764,plain,
( ! [X8,X7] :
( ~ is_a_theorem(not(X7))
| is_a_theorem(implies(X7,X8)) )
| ~ spl2_72
| ~ spl2_384 ),
inference(superposition,[],[f13660,f749]) ).
fof(f13749,plain,
( spl2_385
| ~ spl2_76
| ~ spl2_383 ),
inference(avatar_split_clause,[],[f13640,f13618,f810,f13747]) ).
fof(f13640,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X10,not(X9)),implies(X9,X11)))
| ~ spl2_76
| ~ spl2_383 ),
inference(superposition,[],[f13619,f811]) ).
fof(f13661,plain,
( spl2_384
| ~ spl2_27
| ~ spl2_383 ),
inference(avatar_split_clause,[],[f13626,f13618,f302,f13659]) ).
fof(f13626,plain,
( ! [X18,X19,X17] :
( is_a_theorem(implies(X17,X18))
| ~ is_a_theorem(and(not(X17),X19)) )
| ~ spl2_27
| ~ spl2_383 ),
inference(resolution,[],[f13619,f303]) ).
fof(f13620,plain,
( spl2_383
| ~ spl2_328
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13507,f13441,f10566,f13618]) ).
fof(f13507,plain,
( ! [X26,X24,X25] : is_a_theorem(strict_implies(and(not(X24),X25),implies(X24,X26)))
| ~ spl2_328
| ~ spl2_380 ),
inference(resolution,[],[f13442,f10567]) ).
fof(f13558,plain,
( spl2_382
| ~ spl2_83
| ~ spl2_126
| ~ spl2_380 ),
inference(avatar_split_clause,[],[f13542,f13441,f1856,f1024,f13556]) ).
fof(f13542,plain,
( ! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(not(not(X0)))) )
| ~ spl2_83
| ~ spl2_126
| ~ spl2_380 ),
inference(forward_demodulation,[],[f13531,f1857]) ).
fof(f13531,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(strict_implies(and(not(X0),X1),X0)) )
| ~ spl2_83
| ~ spl2_380 ),
inference(superposition,[],[f13442,f1025]) ).
fof(f13499,plain,
( spl2_381
| ~ spl2_136
| ~ spl2_325 ),
inference(avatar_split_clause,[],[f11606,f10415,f2344,f13497]) ).
fof(f11606,plain,
( ! [X8,X9] :
( ~ is_a_theorem(necessarily(not(equiv(X8,X9))))
| is_a_theorem(strict_implies(implies(X8,X9),X9)) )
| ~ spl2_136
| ~ spl2_325 ),
inference(superposition,[],[f2345,f10416]) ).
fof(f13443,plain,
( spl2_380
| ~ spl2_19
| ~ spl2_317 ),
inference(avatar_split_clause,[],[f11160,f9822,f269,f13441]) ).
fof(f11160,plain,
( ! [X18,X16,X17] :
( is_a_theorem(strict_implies(and(not(X16),X17),X18))
| ~ is_a_theorem(necessarily(or(X16,X18))) )
| ~ spl2_19
| ~ spl2_317 ),
inference(resolution,[],[f9823,f270]) ).
fof(f12661,plain,
( spl2_379
| ~ spl2_36
| ~ spl2_373 ),
inference(avatar_split_clause,[],[f12545,f12452,f363,f12659]) ).
fof(f12545,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),implies(equiv(X0,X1),X2))))
| ~ spl2_36
| ~ spl2_373 ),
inference(superposition,[],[f12453,f364]) ).
fof(f12657,plain,
( spl2_378
| ~ spl2_24
| ~ spl2_373 ),
inference(avatar_split_clause,[],[f12540,f12452,f290,f12655]) ).
fof(f12540,plain,
( ! [X10,X11,X9,X12] : is_a_theorem(necessarily(or(X11,implies(and(or(X9,X10),X11),X12))))
| ~ spl2_24
| ~ spl2_373 ),
inference(superposition,[],[f12453,f291]) ).
fof(f12486,plain,
( spl2_377
| ~ spl2_75
| ~ spl2_367 ),
inference(avatar_split_clause,[],[f12409,f12251,f806,f12484]) ).
fof(f12409,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(or(X2,X1),not(equiv(X2,not(X1))))))
| ~ spl2_75
| ~ spl2_367 ),
inference(superposition,[],[f12252,f807]) ).
fof(f12482,plain,
( spl2_376
| ~ spl2_36
| ~ spl2_364 ),
inference(avatar_split_clause,[],[f12359,f12239,f363,f12480]) ).
fof(f12359,plain,
( ! [X11,X12,X13] : is_a_theorem(necessarily(or(implies(X11,X12),implies(equiv(X11,X12),X13))))
| ~ spl2_36
| ~ spl2_364 ),
inference(superposition,[],[f12240,f364]) ).
fof(f12462,plain,
( spl2_375
| ~ spl2_24
| ~ spl2_364 ),
inference(avatar_split_clause,[],[f12351,f12239,f290,f12460]) ).
fof(f12351,plain,
( ! [X10,X11,X9,X12] : is_a_theorem(necessarily(or(X11,implies(and(X11,or(X9,X10)),X12))))
| ~ spl2_24
| ~ spl2_364 ),
inference(superposition,[],[f12240,f291]) ).
fof(f12458,plain,
( spl2_374
| ~ spl2_27
| ~ spl2_361 ),
inference(avatar_split_clause,[],[f12269,f12227,f302,f12456]) ).
fof(f12456,plain,
( spl2_374
<=> ! [X18,X17] :
( is_a_theorem(not(and(possibly(X17),necessarily(not(X18)))))
| ~ is_a_theorem(possibly(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_374])]) ).
fof(f12269,plain,
( ! [X18,X17] :
( is_a_theorem(not(and(possibly(X17),necessarily(not(X18)))))
| ~ is_a_theorem(possibly(X18)) )
| ~ spl2_27
| ~ spl2_361 ),
inference(resolution,[],[f12228,f303]) ).
fof(f12454,plain,
( spl2_373
| ~ spl2_29
| ~ spl2_351 ),
inference(avatar_split_clause,[],[f11959,f11933,f315,f12452]) ).
fof(f11959,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(necessarily(or(X17,implies(and(implies(X15,X16),X17),X18))))
| ~ spl2_29
| ~ spl2_351 ),
inference(superposition,[],[f11934,f316]) ).
fof(f12450,plain,
( spl2_372
| ~ spl2_24
| ~ spl2_344 ),
inference(avatar_split_clause,[],[f11727,f11551,f290,f12448]) ).
fof(f11727,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(or(X5,X6),not(equiv(X6,not(X5))))))
| ~ spl2_24
| ~ spl2_344 ),
inference(superposition,[],[f11552,f291]) ).
fof(f12446,plain,
( spl2_371
| ~ spl2_24
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3514,f2750,f290,f12444]) ).
fof(f3514,plain,
( ! [X2,X0,X1] : strict_implies(X2,and(not(X0),not(X1))) = necessarily(not(and(X2,or(X0,X1))))
| ~ spl2_24
| ~ spl2_161 ),
inference(superposition,[],[f2751,f291]) ).
fof(f12375,plain,
( spl2_370
| ~ spl2_24
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3467,f2734,f290,f12373]) ).
fof(f3467,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X2,and(not(X0),not(X1))),not(and(X2,or(X0,X1)))))
| ~ spl2_24
| ~ spl2_157 ),
inference(superposition,[],[f2735,f291]) ).
fof(f12261,plain,
( spl2_369
| ~ spl2_26
| ~ spl2_141 ),
inference(avatar_split_clause,[],[f2868,f2474,f298,f12259]) ).
fof(f2868,plain,
( ! [X8,X9] :
( is_a_theorem(strict_equiv(not(X8),X9))
| ~ is_a_theorem(strict_implies(X9,not(X8)))
| ~ is_a_theorem(necessarily(or(X8,X9))) )
| ~ spl2_26
| ~ spl2_141 ),
inference(superposition,[],[f299,f2475]) ).
fof(f12257,plain,
( spl2_368
| ~ spl2_75
| ~ spl2_83
| ~ spl2_356 ),
inference(avatar_split_clause,[],[f12184,f12080,f1024,f806,f12255]) ).
fof(f12184,plain,
( ! [X8] : is_a_theorem(necessarily(or(not(not(X8)),not(equiv(X8,not(X8))))))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_356 ),
inference(forward_demodulation,[],[f12163,f807]) ).
fof(f12163,plain,
( ! [X8] : is_a_theorem(necessarily(or(not(not(X8)),not(equiv(not(X8),X8)))))
| ~ spl2_83
| ~ spl2_356 ),
inference(superposition,[],[f12081,f1025]) ).
fof(f12253,plain,
( spl2_367
| ~ spl2_97
| ~ spl2_356 ),
inference(avatar_split_clause,[],[f12164,f12080,f1233,f12251]) ).
fof(f12164,plain,
( ! [X10,X9] : is_a_theorem(necessarily(or(or(X10,X9),not(equiv(not(X9),X10)))))
| ~ spl2_97
| ~ spl2_356 ),
inference(superposition,[],[f12081,f1234]) ).
fof(f12249,plain,
( spl2_366
| ~ spl2_27
| ~ spl2_354 ),
inference(avatar_split_clause,[],[f12098,f12072,f302,f12247]) ).
fof(f12247,plain,
( spl2_366
<=> ! [X18,X17] :
( is_a_theorem(not(and(necessarily(not(X17)),possibly(X18))))
| ~ is_a_theorem(possibly(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_366])]) ).
fof(f12098,plain,
( ! [X18,X17] :
( is_a_theorem(not(and(necessarily(not(X17)),possibly(X18))))
| ~ is_a_theorem(possibly(X17)) )
| ~ spl2_27
| ~ spl2_354 ),
inference(resolution,[],[f12073,f303]) ).
fof(f12245,plain,
( spl2_365
| ~ spl2_65
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2333,f1831,f602,f12243]) ).
fof(f12243,plain,
( spl2_365
<=> ! [X80,X81,X79] :
( is_a_theorem(strict_implies(X79,necessarily(or(X80,not(X80)))))
| ~ is_a_theorem(strict_implies(X79,strict_equiv(not(X80),X81))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_365])]) ).
fof(f2333,plain,
( ! [X80,X81,X79] :
( is_a_theorem(strict_implies(X79,necessarily(or(X80,not(X80)))))
| ~ is_a_theorem(strict_implies(X79,strict_equiv(not(X80),X81))) )
| ~ spl2_65
| ~ spl2_122 ),
inference(resolution,[],[f1832,f603]) ).
fof(f12241,plain,
( spl2_364
| ~ spl2_29
| ~ spl2_348 ),
inference(avatar_split_clause,[],[f11904,f11897,f315,f12239]) ).
fof(f11904,plain,
( ! [X18,X16,X17,X15] : is_a_theorem(necessarily(or(X17,implies(and(X17,implies(X15,X16)),X18))))
| ~ spl2_29
| ~ spl2_348 ),
inference(superposition,[],[f11898,f316]) ).
fof(f12237,plain,
( spl2_363
| ~ spl2_23
| ~ spl2_29
| ~ spl2_38
| ~ spl2_336 ),
inference(avatar_split_clause,[],[f11149,f11086,f377,f315,f286,f12235]) ).
fof(f12235,plain,
( spl2_363
<=> ! [X9,X8,X10] :
( is_a_theorem(implies(strict_implies(X8,X9),X10))
| ~ is_a_theorem(not(strict_implies(X8,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_363])]) ).
fof(f11149,plain,
( ! [X10,X8,X9] :
( is_a_theorem(implies(strict_implies(X8,X9),X10))
| ~ is_a_theorem(not(strict_implies(X8,X9))) )
| ~ spl2_23
| ~ spl2_29
| ~ spl2_38
| ~ spl2_336 ),
inference(forward_demodulation,[],[f11148,f287]) ).
fof(f11148,plain,
( ! [X10,X8,X9] :
( is_a_theorem(implies(necessarily(implies(X8,X9)),X10))
| ~ is_a_theorem(not(strict_implies(X8,X9))) )
| ~ spl2_29
| ~ spl2_38
| ~ spl2_336 ),
inference(forward_demodulation,[],[f11143,f316]) ).
fof(f11143,plain,
( ! [X10,X8,X9] :
( ~ is_a_theorem(not(strict_implies(X8,X9)))
| is_a_theorem(implies(necessarily(not(and(X8,not(X9)))),X10)) )
| ~ spl2_38
| ~ spl2_336 ),
inference(superposition,[],[f11087,f378]) ).
fof(f12233,plain,
( spl2_362
| ~ spl2_20
| ~ spl2_32
| ~ spl2_336 ),
inference(avatar_split_clause,[],[f11147,f11086,f336,f273,f12231]) ).
fof(f11147,plain,
( ! [X0,X1] :
( is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(not(necessarily(possibly(X0)))) )
| ~ spl2_20
| ~ spl2_32
| ~ spl2_336 ),
inference(forward_demodulation,[],[f11140,f274]) ).
fof(f11140,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(necessarily(possibly(X0))))
| is_a_theorem(implies(necessarily(not(necessarily(not(X0)))),X1)) )
| ~ spl2_32
| ~ spl2_336 ),
inference(superposition,[],[f11087,f337]) ).
fof(f12229,plain,
( spl2_361
| ~ spl2_23
| ~ spl2_37
| ~ spl2_335 ),
inference(avatar_split_clause,[],[f11137,f11032,f373,f286,f12227]) ).
fof(f11137,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(possibly(X1),necessarily(not(X0))))))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_335 ),
inference(forward_demodulation,[],[f11131,f287]) ).
fof(f11131,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(possibly(X0),not(and(possibly(X1),necessarily(not(X0)))))))
| ~ spl2_37
| ~ spl2_335 ),
inference(superposition,[],[f11033,f374]) ).
fof(f12225,plain,
( spl2_360
| ~ spl2_104
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f2165,f1696,f1388,f12223]) ).
fof(f12223,plain,
( spl2_360
<=> ! [X11,X12,X10] : or(X12,strict_implies(X10,necessarily(not(X11)))) = implies(possibly(and(X10,possibly(X11))),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_360])]) ).
fof(f2165,plain,
( ! [X10,X11,X12] : or(X12,strict_implies(X10,necessarily(not(X11)))) = implies(possibly(and(X10,possibly(X11))),X12)
| ~ spl2_104
| ~ spl2_116 ),
inference(superposition,[],[f1389,f1697]) ).
fof(f12159,plain,
( spl2_359
| ~ spl2_24
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1941,f1558,f290,f12157]) ).
fof(f12157,plain,
( spl2_359
<=> ! [X4,X2,X3] : or(strict_implies(X2,necessarily(not(X3))),X4) = implies(possibly(and(X2,possibly(X3))),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_359])]) ).
fof(f1941,plain,
( ! [X2,X3,X4] : or(strict_implies(X2,necessarily(not(X3))),X4) = implies(possibly(and(X2,possibly(X3))),X4)
| ~ spl2_24
| ~ spl2_112 ),
inference(superposition,[],[f291,f1559]) ).
fof(f12090,plain,
( spl2_358
| ~ spl2_27
| ~ spl2_347 ),
inference(avatar_split_clause,[],[f12018,f11776,f302,f12088]) ).
fof(f12018,plain,
( ! [X21,X22,X20] :
( is_a_theorem(implies(and(not(X20),X21),X22))
| ~ is_a_theorem(implies(X21,X20)) )
| ~ spl2_27
| ~ spl2_347 ),
inference(resolution,[],[f11777,f303]) ).
fof(f12086,plain,
( spl2_357
| ~ spl2_27
| ~ spl2_346 ),
inference(avatar_split_clause,[],[f11815,f11772,f302,f12084]) ).
fof(f12084,plain,
( spl2_357
<=> ! [X22,X20,X21] :
( is_a_theorem(implies(and(X20,not(X21)),X22))
| ~ is_a_theorem(implies(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_357])]) ).
fof(f11815,plain,
( ! [X21,X22,X20] :
( is_a_theorem(implies(and(X20,not(X21)),X22))
| ~ is_a_theorem(implies(X20,X21)) )
| ~ spl2_27
| ~ spl2_346 ),
inference(resolution,[],[f11773,f303]) ).
fof(f12082,plain,
( spl2_356
| ~ spl2_80
| ~ spl2_337 ),
inference(avatar_split_clause,[],[f11222,f11206,f856,f12080]) ).
fof(f11222,plain,
( ! [X16,X15] : is_a_theorem(necessarily(or(or(X15,X16),not(equiv(not(X15),X16)))))
| ~ spl2_80
| ~ spl2_337 ),
inference(superposition,[],[f11207,f857]) ).
fof(f12078,plain,
( spl2_355
| ~ spl2_52
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f701,f681,f489,f12076]) ).
fof(f12076,plain,
( spl2_355
<=> ! [X22,X23] :
( ~ is_a_theorem(strict_implies(strict_implies(X22,X22),strict_equiv(X22,X23)))
| strict_implies(X22,X22) = strict_equiv(X22,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_355])]) ).
fof(f701,plain,
( ! [X22,X23] :
( ~ is_a_theorem(strict_implies(strict_implies(X22,X22),strict_equiv(X22,X23)))
| strict_implies(X22,X22) = strict_equiv(X22,X23) )
| ~ spl2_52
| ~ spl2_70 ),
inference(resolution,[],[f682,f490]) ).
fof(f12074,plain,
( spl2_354
| ~ spl2_23
| ~ spl2_37
| ~ spl2_332 ),
inference(avatar_split_clause,[],[f10728,f10702,f373,f286,f12072]) ).
fof(f10728,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),not(and(necessarily(not(X0)),possibly(X1)))))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_332 ),
inference(forward_demodulation,[],[f10722,f287]) ).
fof(f10722,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(possibly(X0),not(and(necessarily(not(X0)),possibly(X1))))))
| ~ spl2_37
| ~ spl2_332 ),
inference(superposition,[],[f10703,f374]) ).
fof(f11990,plain,
( spl2_353
| ~ spl2_40
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f700,f681,f406,f11988]) ).
fof(f11988,plain,
( spl2_353
<=> ! [X20,X21] :
( ~ is_a_theorem(strict_implies(strict_implies(X20,X21),strict_equiv(X20,X21)))
| strict_implies(X20,X21) = strict_equiv(X20,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_353])]) ).
fof(f700,plain,
( ! [X21,X20] :
( ~ is_a_theorem(strict_implies(strict_implies(X20,X21),strict_equiv(X20,X21)))
| strict_implies(X20,X21) = strict_equiv(X20,X21) )
| ~ spl2_40
| ~ spl2_70 ),
inference(resolution,[],[f682,f407]) ).
fof(f11986,plain,
( spl2_352
| ~ spl2_76
| ~ spl2_349 ),
inference(avatar_split_clause,[],[f11944,f11925,f810,f11984]) ).
fof(f11944,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,implies(and(possibly(X3),X2),X4))))
| ~ spl2_76
| ~ spl2_349 ),
inference(superposition,[],[f11926,f811]) ).
fof(f11935,plain,
( spl2_351
| ~ spl2_76
| ~ spl2_348 ),
inference(avatar_split_clause,[],[f11911,f11897,f810,f11933]) ).
fof(f11911,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,implies(and(not(X3),X2),X4))))
| ~ spl2_76
| ~ spl2_348 ),
inference(superposition,[],[f11898,f811]) ).
fof(f11931,plain,
( spl2_350
| ~ spl2_44
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f691,f681,f440,f11929]) ).
fof(f11929,plain,
( spl2_350
<=> ! [X2,X3] :
( ~ is_a_theorem(strict_implies(implies(X2,X3),equiv(X2,X3)))
| implies(X2,X3) = equiv(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_350])]) ).
fof(f691,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_implies(implies(X2,X3),equiv(X2,X3)))
| implies(X2,X3) = equiv(X2,X3) )
| ~ spl2_44
| ~ spl2_70 ),
inference(resolution,[],[f682,f441]) ).
fof(f11927,plain,
( spl2_349
| ~ spl2_20
| ~ spl2_348 ),
inference(avatar_split_clause,[],[f11900,f11897,f273,f11925]) ).
fof(f11900,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X1,implies(and(X1,possibly(X0)),X2))))
| ~ spl2_20
| ~ spl2_348 ),
inference(superposition,[],[f11898,f274]) ).
fof(f11899,plain,
( spl2_348
| ~ spl2_97
| ~ spl2_327
| ~ spl2_346 ),
inference(avatar_split_clause,[],[f11840,f11772,f10547,f1233,f11897]) ).
fof(f11840,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(X0,implies(and(X0,not(X1)),X2))))
| ~ spl2_97
| ~ spl2_327
| ~ spl2_346 ),
inference(forward_demodulation,[],[f11809,f1234]) ).
fof(f11809,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(or(implies(and(X0,not(X1)),X2),X0)))
| ~ spl2_327
| ~ spl2_346 ),
inference(resolution,[],[f11773,f10548]) ).
fof(f11778,plain,
( spl2_347
| ~ spl2_23
| ~ spl2_300
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10585,f10566,f9395,f286,f11776]) ).
fof(f10585,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(implies(X6,X5),implies(and(not(X5),X6),X7)))
| ~ spl2_23
| ~ spl2_300
| ~ spl2_328 ),
inference(forward_demodulation,[],[f10578,f287]) ).
fof(f10578,plain,
( ! [X6,X7,X5] : is_a_theorem(necessarily(implies(implies(X6,X5),implies(and(not(X5),X6),X7))))
| ~ spl2_300
| ~ spl2_328 ),
inference(superposition,[],[f10567,f9396]) ).
fof(f11774,plain,
( spl2_346
| ~ spl2_23
| ~ spl2_58
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10584,f10566,f544,f286,f11772]) ).
fof(f10584,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,not(X3)),X4)))
| ~ spl2_23
| ~ spl2_58
| ~ spl2_328 ),
inference(forward_demodulation,[],[f10577,f287]) ).
fof(f10577,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(implies(implies(X2,X3),implies(and(X2,not(X3)),X4))))
| ~ spl2_58
| ~ spl2_328 ),
inference(superposition,[],[f10567,f545]) ).
fof(f11738,plain,
( spl2_345
| ~ spl2_318
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10574,f10566,f9826,f11736]) ).
fof(f10574,plain,
( ! [X11,X12,X13] : is_a_theorem(necessarily(or(or(X11,X12),implies(or(X12,X11),X13))))
| ~ spl2_318
| ~ spl2_328 ),
inference(superposition,[],[f10567,f9827]) ).
fof(f11553,plain,
( spl2_344
| ~ spl2_36
| ~ spl2_340 ),
inference(avatar_split_clause,[],[f11471,f11376,f363,f11551]) ).
fof(f11471,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(implies(X1,X0),not(equiv(X0,X1)))))
| ~ spl2_36
| ~ spl2_340 ),
inference(superposition,[],[f11377,f364]) ).
fof(f11549,plain,
( spl2_343
| ~ spl2_76
| ~ spl2_339 ),
inference(avatar_split_clause,[],[f11452,f11372,f810,f11547]) ).
fof(f11452,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(or(X3,X4),X2)))))
| ~ spl2_76
| ~ spl2_339 ),
inference(superposition,[],[f11373,f811]) ).
fof(f11545,plain,
( spl2_342
| ~ spl2_24
| ~ spl2_338 ),
inference(avatar_split_clause,[],[f11395,f11234,f290,f11543]) ).
fof(f11395,plain,
( ! [X8,X9,X7] : is_a_theorem(necessarily(or(not(X9),implies(or(X7,X8),X9))))
| ~ spl2_24
| ~ spl2_338 ),
inference(superposition,[],[f11235,f291]) ).
fof(f11382,plain,
( spl2_341
| ~ spl2_36
| ~ spl2_337 ),
inference(avatar_split_clause,[],[f11219,f11206,f363,f11380]) ).
fof(f11219,plain,
( ! [X8,X9] : is_a_theorem(necessarily(or(implies(X8,X9),not(equiv(X8,X9)))))
| ~ spl2_36
| ~ spl2_337 ),
inference(superposition,[],[f11207,f364]) ).
fof(f11378,plain,
( spl2_340
| ~ spl2_76
| ~ spl2_337 ),
inference(avatar_split_clause,[],[f11217,f11206,f810,f11376]) ).
fof(f11217,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(implies(X3,X4),X2)))))
| ~ spl2_76
| ~ spl2_337 ),
inference(superposition,[],[f11207,f811]) ).
fof(f11374,plain,
( spl2_339
| ~ spl2_24
| ~ spl2_337 ),
inference(avatar_split_clause,[],[f11211,f11206,f290,f11372]) ).
fof(f11211,plain,
( ! [X8,X9,X7] : is_a_theorem(necessarily(or(X9,not(and(X9,or(X7,X8))))))
| ~ spl2_24
| ~ spl2_337 ),
inference(superposition,[],[f11207,f291]) ).
fof(f11236,plain,
( spl2_338
| ~ spl2_125
| ~ spl2_330 ),
inference(avatar_split_clause,[],[f10609,f10591,f1852,f11234]) ).
fof(f10609,plain,
( ! [X14,X15,X13] : is_a_theorem(necessarily(or(not(X13),implies(implies(X14,X15),X13))))
| ~ spl2_125
| ~ spl2_330 ),
inference(superposition,[],[f10592,f1853]) ).
fof(f11208,plain,
( spl2_337
| ~ spl2_77
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10570,f10566,f814,f11206]) ).
fof(f10570,plain,
( ! [X2,X3,X4] : is_a_theorem(necessarily(or(X2,not(and(X2,implies(X3,X4))))))
| ~ spl2_77
| ~ spl2_328 ),
inference(superposition,[],[f10567,f815]) ).
fof(f11088,plain,
( spl2_336
| ~ spl2_27
| ~ spl2_333 ),
inference(avatar_split_clause,[],[f10983,f10706,f302,f11086]) ).
fof(f10983,plain,
( ! [X10,X9] :
( is_a_theorem(implies(necessarily(not(X9)),X10))
| ~ is_a_theorem(possibly(X9)) )
| ~ spl2_27
| ~ spl2_333 ),
inference(resolution,[],[f10707,f303]) ).
fof(f11034,plain,
( spl2_335
| ~ spl2_76
| ~ spl2_332 ),
inference(avatar_split_clause,[],[f10717,f10702,f810,f11032]) ).
fof(f10717,plain,
( ! [X2,X1] : is_a_theorem(necessarily(or(X1,not(and(possibly(X2),X1)))))
| ~ spl2_76
| ~ spl2_332 ),
inference(superposition,[],[f10703,f811]) ).
fof(f11030,plain,
( spl2_334
| ~ spl2_104
| ~ spl2_330 ),
inference(avatar_split_clause,[],[f10610,f10591,f1388,f11028]) ).
fof(f10610,plain,
( ! [X16,X17] : is_a_theorem(necessarily(or(not(X16),implies(possibly(X17),X16))))
| ~ spl2_104
| ~ spl2_330 ),
inference(superposition,[],[f10592,f1389]) ).
fof(f10708,plain,
( spl2_333
| ~ spl2_23
| ~ spl2_37
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10583,f10566,f373,f286,f10706]) ).
fof(f10583,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(possibly(X0),implies(necessarily(not(X0)),X1)))
| ~ spl2_23
| ~ spl2_37
| ~ spl2_328 ),
inference(forward_demodulation,[],[f10576,f287]) ).
fof(f10576,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(possibly(X0),implies(necessarily(not(X0)),X1))))
| ~ spl2_37
| ~ spl2_328 ),
inference(superposition,[],[f10567,f374]) ).
fof(f10704,plain,
( spl2_332
| ~ spl2_54
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10569,f10566,f505,f10702]) ).
fof(f10569,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X0,not(and(X0,possibly(X1))))))
| ~ spl2_54
| ~ spl2_328 ),
inference(superposition,[],[f10567,f506]) ).
fof(f10622,plain,
( spl2_331
| ~ spl2_97
| ~ spl2_330 ),
inference(avatar_split_clause,[],[f10607,f10591,f1233,f10620]) ).
fof(f10607,plain,
( ! [X10,X9] : is_a_theorem(necessarily(or(not(X9),or(X10,X9))))
| ~ spl2_97
| ~ spl2_330 ),
inference(superposition,[],[f10592,f1234]) ).
fof(f10593,plain,
( spl2_330
| ~ spl2_24
| ~ spl2_328 ),
inference(avatar_split_clause,[],[f10571,f10566,f290,f10591]) ).
fof(f10571,plain,
( ! [X6,X5] : is_a_theorem(necessarily(or(not(X5),or(X5,X6))))
| ~ spl2_24
| ~ spl2_328 ),
inference(superposition,[],[f10567,f291]) ).
fof(f10589,plain,
( spl2_329
| ~ spl2_30
| ~ spl2_252 ),
inference(avatar_split_clause,[],[f7026,f6967,f319,f10587]) ).
fof(f7026,plain,
( ! [X44,X42,X43] :
( ~ is_a_theorem(equiv(and(X43,not(X44)),X42))
| is_a_theorem(not(and(X42,implies(X43,X44)))) )
| ~ spl2_30
| ~ spl2_252 ),
inference(superposition,[],[f320,f6968]) ).
fof(f10568,plain,
( spl2_328
| ~ spl2_71
| ~ spl2_97
| ~ spl2_327 ),
inference(avatar_split_clause,[],[f10558,f10547,f1233,f738,f10566]) ).
fof(f10558,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(X0,implies(X0,X1))))
| ~ spl2_71
| ~ spl2_97
| ~ spl2_327 ),
inference(forward_demodulation,[],[f10550,f1234]) ).
fof(f10550,plain,
( ! [X0,X1] : is_a_theorem(necessarily(or(implies(X0,X1),X0)))
| ~ spl2_71
| ~ spl2_327 ),
inference(resolution,[],[f10548,f739]) ).
fof(f10549,plain,
( spl2_327
| ~ spl2_23
| ~ spl2_125
| ~ spl2_310 ),
inference(avatar_split_clause,[],[f10540,f9475,f1852,f286,f10547]) ).
fof(f10540,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(strict_implies(implies(X12,X13),X11))
| is_a_theorem(necessarily(or(X11,X12))) )
| ~ spl2_23
| ~ spl2_125
| ~ spl2_310 ),
inference(forward_demodulation,[],[f10527,f287]) ).
fof(f10527,plain,
( ! [X11,X12,X13] :
( ~ is_a_theorem(necessarily(implies(implies(X12,X13),X11)))
| is_a_theorem(necessarily(or(X11,X12))) )
| ~ spl2_125
| ~ spl2_310 ),
inference(superposition,[],[f9476,f1853]) ).
fof(f10545,plain,
( spl2_326
| ~ spl2_53
| ~ spl2_166 ),
inference(avatar_split_clause,[],[f3588,f2770,f495,f10543]) ).
fof(f10543,plain,
( spl2_326
<=> ! [X6,X7] :
( ~ is_a_theorem(implies(X6,not(X7)))
| ~ is_a_theorem(or(X7,X6))
| is_a_theorem(equiv(X6,not(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_326])]) ).
fof(f495,plain,
( spl2_53
<=> ! [X2,X3] :
( is_a_theorem(equiv(X3,X2))
| ~ is_a_theorem(equiv(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
fof(f2770,plain,
( spl2_166
<=> ! [X6,X7] :
( is_a_theorem(equiv(not(X6),X7))
| ~ is_a_theorem(implies(X7,not(X6)))
| ~ is_a_theorem(or(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_166])]) ).
fof(f3588,plain,
( ! [X6,X7] :
( ~ is_a_theorem(implies(X6,not(X7)))
| ~ is_a_theorem(or(X7,X6))
| is_a_theorem(equiv(X6,not(X7))) )
| ~ spl2_53
| ~ spl2_166 ),
inference(resolution,[],[f2771,f496]) ).
fof(f496,plain,
( ! [X2,X3] :
( ~ is_a_theorem(equiv(X2,X3))
| is_a_theorem(equiv(X3,X2)) )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f2771,plain,
( ! [X6,X7] :
( is_a_theorem(equiv(not(X6),X7))
| ~ is_a_theorem(implies(X7,not(X6)))
| ~ is_a_theorem(or(X6,X7)) )
| ~ spl2_166 ),
inference(avatar_component_clause,[],[f2770]) ).
fof(f10417,plain,
( spl2_325
| ~ spl2_36
| ~ spl2_161 ),
inference(avatar_split_clause,[],[f3522,f2750,f363,f10415]) ).
fof(f3522,plain,
( ! [X8,X9] : strict_implies(implies(X8,X9),and(X9,not(X8))) = necessarily(not(equiv(X8,X9)))
| ~ spl2_36
| ~ spl2_161 ),
inference(superposition,[],[f2751,f364]) ).
fof(f10242,plain,
( spl2_324
| ~ spl2_36
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3475,f2734,f363,f10240]) ).
fof(f3475,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(equiv(implies(X8,X9),and(X9,not(X8))),not(equiv(X8,X9))))
| ~ spl2_36
| ~ spl2_157 ),
inference(superposition,[],[f2735,f364]) ).
fof(f10116,plain,
( spl2_323
| ~ spl2_27
| ~ spl2_157 ),
inference(avatar_split_clause,[],[f3455,f2734,f302,f10114]) ).
fof(f3455,plain,
( ! [X8,X9,X7] :
( is_a_theorem(not(and(X7,implies(X8,X9))))
| ~ is_a_theorem(equiv(X7,and(X8,not(X9)))) )
| ~ spl2_27
| ~ spl2_157 ),
inference(resolution,[],[f2735,f303]) ).
fof(f10112,plain,
( spl2_322
| ~ spl2_27
| ~ spl2_321 ),
inference(avatar_split_clause,[],[f10079,f10072,f302,f10110]) ).
fof(f10079,plain,
( ! [X10,X9] :
( is_a_theorem(or(X9,X10))
| ~ is_a_theorem(or(X10,X9)) )
| ~ spl2_27
| ~ spl2_321 ),
inference(resolution,[],[f10073,f303]) ).
fof(f10074,plain,
( spl2_321
| ~ spl2_71
| ~ spl2_319 ),
inference(avatar_split_clause,[],[f9948,f9930,f738,f10072]) ).
fof(f9948,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(or(X4,X3),or(X3,X4)))
| ~ spl2_71
| ~ spl2_319 ),
inference(superposition,[],[f739,f9931]) ).
fof(f9936,plain,
( spl2_320
| ~ spl2_26
| ~ spl2_154 ),
inference(avatar_split_clause,[],[f3405,f2673,f298,f9934]) ).
fof(f9934,plain,
( spl2_320
<=> ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(necessarily(or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_320])]) ).
fof(f3405,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(necessarily(or(X0,X2))) )
| ~ spl2_26
| ~ spl2_154 ),
inference(resolution,[],[f2674,f299]) ).
fof(f9932,plain,
( spl2_319
| ~ spl2_23
| ~ spl2_318 ),
inference(avatar_split_clause,[],[f9921,f9826,f286,f9930]) ).
fof(f9921,plain,
( ! [X2,X0,X1] : strict_implies(or(X0,X1),X2) = strict_implies(or(X1,X0),X2)
| ~ spl2_23
| ~ spl2_318 ),
inference(forward_demodulation,[],[f9843,f287]) ).
fof(f9843,plain,
( ! [X2,X0,X1] : strict_implies(or(X0,X1),X2) = necessarily(implies(or(X1,X0),X2))
| ~ spl2_23
| ~ spl2_318 ),
inference(superposition,[],[f287,f9827]) ).
fof(f9828,plain,
( spl2_318
| ~ spl2_24
| ~ spl2_58
| ~ spl2_300 ),
inference(avatar_split_clause,[],[f9740,f9395,f544,f290,f9826]) ).
fof(f9740,plain,
( ! [X3,X4,X5] : implies(or(X4,X3),X5) = implies(or(X3,X4),X5)
| ~ spl2_24
| ~ spl2_58
| ~ spl2_300 ),
inference(forward_demodulation,[],[f9739,f291]) ).
fof(f9739,plain,
( ! [X3,X4,X5] : implies(implies(not(X3),X4),X5) = implies(or(X4,X3),X5)
| ~ spl2_24
| ~ spl2_58
| ~ spl2_300 ),
inference(forward_demodulation,[],[f9669,f291]) ).
fof(f9669,plain,
( ! [X3,X4,X5] : implies(implies(not(X3),X4),X5) = implies(implies(not(X4),X3),X5)
| ~ spl2_58
| ~ spl2_300 ),
inference(superposition,[],[f9396,f545]) ).
fof(f9824,plain,
( spl2_317
| ~ spl2_33
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2339,f1831,f340,f9822]) ).
fof(f2339,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X2,not(X0))) )
| ~ spl2_33
| ~ spl2_122 ),
inference(superposition,[],[f1832,f341]) ).
fof(f9501,plain,
( spl2_316
| ~ spl2_60
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2332,f1831,f558,f9499]) ).
fof(f9499,plain,
( spl2_316
<=> ! [X77,X76,X78] :
( is_a_theorem(strict_implies(X76,necessarily(or(X77,X78))))
| ~ is_a_theorem(strict_implies(X76,strict_equiv(not(X77),X78))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_316])]) ).
fof(f2332,plain,
( ! [X78,X76,X77] :
( is_a_theorem(strict_implies(X76,necessarily(or(X77,X78))))
| ~ is_a_theorem(strict_implies(X76,strict_equiv(not(X77),X78))) )
| ~ spl2_60
| ~ spl2_122 ),
inference(resolution,[],[f1832,f559]) ).
fof(f9497,plain,
( spl2_315
| ~ spl2_31
| ~ spl2_272 ),
inference(avatar_split_clause,[],[f8301,f8160,f330,f9495]) ).
fof(f9495,plain,
( spl2_315
<=> ! [X38,X37,X39] :
( ~ is_a_theorem(X37)
| ~ is_a_theorem(X38)
| ~ is_a_theorem(X39)
| is_a_theorem(and(and(X38,X37),X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_315])]) ).
fof(f8160,plain,
( spl2_272
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(and(X1,and(X2,X0)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_272])]) ).
fof(f8301,plain,
( ! [X38,X39,X37] :
( ~ is_a_theorem(X37)
| ~ is_a_theorem(X38)
| ~ is_a_theorem(X39)
| is_a_theorem(and(and(X38,X37),X39)) )
| ~ spl2_31
| ~ spl2_272 ),
inference(resolution,[],[f8161,f331]) ).
fof(f8161,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X1,and(X2,X0)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) )
| ~ spl2_272 ),
inference(avatar_component_clause,[],[f8160]) ).
fof(f9493,plain,
( spl2_314
| ~ spl2_75
| ~ spl2_271 ),
inference(avatar_split_clause,[],[f8268,f8076,f806,f9491]) ).
fof(f9491,plain,
( spl2_314
<=> ! [X2,X1] :
( ~ is_a_theorem(equiv(necessarily(not(X2)),X1))
| is_a_theorem(not(and(X1,possibly(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_314])]) ).
fof(f8076,plain,
( spl2_271
<=> ! [X2,X3] :
( is_a_theorem(not(and(X2,possibly(X3))))
| ~ is_a_theorem(equiv(X2,necessarily(not(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_271])]) ).
fof(f8268,plain,
( ! [X2,X1] :
( ~ is_a_theorem(equiv(necessarily(not(X2)),X1))
| is_a_theorem(not(and(X1,possibly(X2)))) )
| ~ spl2_75
| ~ spl2_271 ),
inference(superposition,[],[f8077,f807]) ).
fof(f8077,plain,
( ! [X2,X3] :
( ~ is_a_theorem(equiv(X2,necessarily(not(X3))))
| is_a_theorem(not(and(X2,possibly(X3)))) )
| ~ spl2_271 ),
inference(avatar_component_clause,[],[f8076]) ).
fof(f9489,plain,
( spl2_313
| ~ spl2_27
| ~ spl2_270 ),
inference(avatar_split_clause,[],[f8199,f8072,f302,f9487]) ).
fof(f8199,plain,
( ! [X10,X9] :
( is_a_theorem(strict_implies(possibly(X9),X10))
| ~ is_a_theorem(strict_equiv(not(X10),necessarily(not(X9)))) )
| ~ spl2_27
| ~ spl2_270 ),
inference(resolution,[],[f8073,f303]) ).
fof(f9485,plain,
( spl2_312
| ~ spl2_20
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1940,f1558,f273,f9483]) ).
fof(f9483,plain,
( spl2_312
<=> ! [X0,X1] : possibly(strict_implies(X0,necessarily(not(X1)))) = not(necessarily(possibly(and(X0,possibly(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_312])]) ).
fof(f1940,plain,
( ! [X0,X1] : possibly(strict_implies(X0,necessarily(not(X1)))) = not(necessarily(possibly(and(X0,possibly(X1)))))
| ~ spl2_20
| ~ spl2_112 ),
inference(superposition,[],[f274,f1559]) ).
fof(f9481,plain,
( spl2_311
| ~ spl2_76
| ~ spl2_125 ),
inference(avatar_split_clause,[],[f2377,f1852,f810,f9479]) ).
fof(f9477,plain,
( spl2_310
| ~ spl2_33
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f2367,f2344,f340,f9475]) ).
fof(f2367,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(necessarily(or(X0,and(X1,X2)))) )
| ~ spl2_33
| ~ spl2_136 ),
inference(forward_demodulation,[],[f2364,f341]) ).
fof(f2364,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(X1,X2))))
| is_a_theorem(strict_implies(not(X0),X1)) )
| ~ spl2_33
| ~ spl2_136 ),
inference(superposition,[],[f2345,f341]) ).
fof(f9473,plain,
( spl2_309
| ~ spl2_76
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f2284,f1712,f810,f9471]) ).
fof(f2284,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X2,and(X3,X4))) )
| ~ spl2_76
| ~ spl2_120 ),
inference(superposition,[],[f1713,f811]) ).
fof(f9469,plain,
( spl2_308
| ~ spl2_76
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f2158,f1696,f810,f9467]) ).
fof(f9467,plain,
( spl2_308
<=> ! [X2,X1] : strict_implies(X1,necessarily(not(X2))) = necessarily(not(and(possibly(X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_308])]) ).
fof(f2158,plain,
( ! [X2,X1] : strict_implies(X1,necessarily(not(X2))) = necessarily(not(and(possibly(X2),X1)))
| ~ spl2_76
| ~ spl2_116 ),
inference(superposition,[],[f1697,f811]) ).
fof(f9465,plain,
( spl2_307
| ~ spl2_33
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f705,f681,f340,f9463]) ).
fof(f705,plain,
( ! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_implies(X1,not(X0)))
| not(X0) = X1 )
| ~ spl2_33
| ~ spl2_70 ),
inference(superposition,[],[f682,f341]) ).
fof(f9461,plain,
( spl2_306
| ~ spl2_76
| ~ spl2_114 ),
inference(avatar_split_clause,[],[f2078,f1640,f810,f9459]) ).
fof(f2078,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(equiv(X1,necessarily(not(X2))),not(and(possibly(X2),X1))))
| ~ spl2_76
| ~ spl2_114 ),
inference(superposition,[],[f1641,f811]) ).
fof(f9457,plain,
( spl2_305
| ~ spl2_46
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f881,f810,f450,f9455]) ).
fof(f881,plain,
( ! [X46,X47,X45] : is_a_theorem(strict_implies(and(strict_implies(X46,X47),strict_implies(X45,X46)),strict_implies(X45,X47)))
| ~ spl2_46
| ~ spl2_76 ),
inference(superposition,[],[f451,f811]) ).
fof(f9453,plain,
( spl2_304
| ~ spl2_69
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f880,f810,f644,f9451]) ).
fof(f9451,plain,
( spl2_304
<=> ! [X43,X44,X42] :
( ~ is_a_theorem(and(strict_implies(X43,X44),strict_implies(X42,X43)))
| is_a_theorem(strict_implies(X42,X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_304])]) ).
fof(f644,plain,
( spl2_69
<=> ! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(and(strict_implies(X0,X2),strict_implies(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).
fof(f880,plain,
( ! [X44,X42,X43] :
( ~ is_a_theorem(and(strict_implies(X43,X44),strict_implies(X42,X43)))
| is_a_theorem(strict_implies(X42,X44)) )
| ~ spl2_69
| ~ spl2_76 ),
inference(superposition,[],[f645,f811]) ).
fof(f645,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X0,X2),strict_implies(X2,X1)))
| is_a_theorem(strict_implies(X0,X1)) )
| ~ spl2_69 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f9409,plain,
( spl2_303
| ~ spl2_43
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f878,f810,f436,f9407]) ).
fof(f878,plain,
( ! [X38,X39,X37] : is_a_theorem(strict_implies(and(X39,and(X37,X38)),and(X37,and(X38,X39))))
| ~ spl2_43
| ~ spl2_76 ),
inference(superposition,[],[f437,f811]) ).
fof(f9405,plain,
( spl2_302
| ~ spl2_66
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f877,f810,f623,f9403]) ).
fof(f877,plain,
( ! [X36,X34,X35] :
( ~ is_a_theorem(and(X36,and(X34,X35)))
| is_a_theorem(and(X34,and(X35,X36))) )
| ~ spl2_66
| ~ spl2_76 ),
inference(superposition,[],[f624,f811]) ).
fof(f9401,plain,
( spl2_301
| ~ spl2_43
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f875,f810,f436,f9399]) ).
fof(f875,plain,
( ! [X31,X29,X30] : is_a_theorem(strict_implies(and(and(X29,X30),X31),and(and(X30,X31),X29)))
| ~ spl2_43
| ~ spl2_76 ),
inference(superposition,[],[f437,f811]) ).
fof(f9397,plain,
( spl2_300
| ~ spl2_58
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f872,f810,f544,f9395]) ).
fof(f872,plain,
( ! [X24,X22,X23] : implies(implies(X22,X23),X24) = or(and(not(X23),X22),X24)
| ~ spl2_58
| ~ spl2_76 ),
inference(superposition,[],[f545,f811]) ).
fof(f9382,plain,
( spl2_299
| ~ spl2_66
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f871,f810,f623,f9380]) ).
fof(f871,plain,
( ! [X21,X19,X20] :
( ~ is_a_theorem(and(and(X20,X19),X21))
| is_a_theorem(and(X19,and(X20,X21))) )
| ~ spl2_66
| ~ spl2_76 ),
inference(superposition,[],[f624,f811]) ).
fof(f9378,plain,
( spl2_298
| ~ spl2_43
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f870,f810,f436,f9376]) ).
fof(f870,plain,
( ! [X18,X16,X17] : is_a_theorem(strict_implies(and(and(X18,X16),X17),and(X18,and(X17,X16))))
| ~ spl2_43
| ~ spl2_76 ),
inference(superposition,[],[f437,f811]) ).
fof(f9374,plain,
( spl2_297
| ~ spl2_43
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f869,f810,f436,f9372]) ).
fof(f869,plain,
( ! [X14,X15,X13] : is_a_theorem(strict_implies(and(and(X14,X13),X15),and(X13,and(X14,X15))))
| ~ spl2_43
| ~ spl2_76 ),
inference(superposition,[],[f437,f811]) ).
fof(f9370,plain,
( spl2_296
| ~ spl2_56
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2312,f1831,f529,f9368]) ).
fof(f2312,plain,
( ! [X11,X12,X13] :
( is_a_theorem(strict_implies(X11,or(X12,X13)))
| ~ is_a_theorem(strict_implies(X11,equiv(not(X12),X13))) )
| ~ spl2_56
| ~ spl2_122 ),
inference(resolution,[],[f1832,f530]) ).
fof(f9351,plain,
( spl2_295
| ~ spl2_278
| ~ spl2_290 ),
inference(avatar_split_clause,[],[f9246,f9064,f8184,f9349]) ).
fof(f9246,plain,
( ! [X38,X36,X37] : is_a_theorem(strict_implies(and(X36,strict_equiv(X37,X38)),strict_implies(X38,X38)))
| ~ spl2_278
| ~ spl2_290 ),
inference(resolution,[],[f8185,f9065]) ).
fof(f9332,plain,
( spl2_294
| ~ spl2_278
| ~ spl2_288 ),
inference(avatar_split_clause,[],[f9253,f8822,f8184,f9330]) ).
fof(f9253,plain,
( ! [X68,X69,X67] : is_a_theorem(strict_implies(and(strict_equiv(X67,X68),X69),strict_implies(X68,X68)))
| ~ spl2_278
| ~ spl2_288 ),
inference(resolution,[],[f8185,f8823]) ).
fof(f9328,plain,
( spl2_293
| ~ spl2_24
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1477,f1462,f290,f9326]) ).
fof(f9326,plain,
( spl2_293
<=> ! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,not(X0)))
| not(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_293])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,not(X0)))
| not(X0) = X1 )
| ~ spl2_24
| ~ spl2_106 ),
inference(superposition,[],[f1463,f291]) ).
fof(f9309,plain,
( spl2_292
| ~ spl2_81
| ~ spl2_278 ),
inference(avatar_split_clause,[],[f9239,f8184,f911,f9307]) ).
fof(f9239,plain,
( ! [X6,X7,X5] : is_a_theorem(strict_implies(and(X5,strict_equiv(X6,X7)),strict_implies(X6,X6)))
| ~ spl2_81
| ~ spl2_278 ),
inference(resolution,[],[f8185,f912]) ).
fof(f9265,plain,
( spl2_291
| ~ spl2_19
| ~ spl2_278 ),
inference(avatar_split_clause,[],[f9238,f8184,f269,f9263]) ).
fof(f9238,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(strict_equiv(X2,X3),X4),strict_implies(X2,X2)))
| ~ spl2_19
| ~ spl2_278 ),
inference(resolution,[],[f8185,f270]) ).
fof(f9066,plain,
( spl2_290
| ~ spl2_34
| ~ spl2_286 ),
inference(avatar_split_clause,[],[f8890,f8725,f344,f9064]) ).
fof(f8890,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(X41,strict_equiv(X39,X40)),strict_equiv(X40,X39)))
| ~ spl2_34
| ~ spl2_286 ),
inference(forward_demodulation,[],[f8846,f345]) ).
fof(f8846,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(X41,strict_equiv(X39,X40)),and(strict_implies(X40,X39),strict_implies(X39,X40))))
| ~ spl2_34
| ~ spl2_286 ),
inference(superposition,[],[f8726,f345]) ).
fof(f9062,plain,
( spl2_289
| ~ spl2_27
| ~ spl2_286 ),
inference(avatar_split_clause,[],[f8832,f8725,f302,f9060]) ).
fof(f8832,plain,
( ! [X24,X22,X23] :
( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(and(X24,and(X23,X22))) )
| ~ spl2_27
| ~ spl2_286 ),
inference(resolution,[],[f8726,f303]) ).
fof(f8824,plain,
( spl2_288
| ~ spl2_34
| ~ spl2_285 ),
inference(avatar_split_clause,[],[f8708,f8551,f344,f8822]) ).
fof(f8551,plain,
( spl2_285
<=> ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X5,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_285])]) ).
fof(f8708,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(strict_equiv(X39,X40),X41),strict_equiv(X40,X39)))
| ~ spl2_34
| ~ spl2_285 ),
inference(forward_demodulation,[],[f8664,f345]) ).
fof(f8664,plain,
( ! [X40,X41,X39] : is_a_theorem(strict_implies(and(strict_equiv(X39,X40),X41),and(strict_implies(X40,X39),strict_implies(X39,X40))))
| ~ spl2_34
| ~ spl2_285 ),
inference(superposition,[],[f8552,f345]) ).
fof(f8552,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X5,X4)))
| ~ spl2_285 ),
inference(avatar_component_clause,[],[f8551]) ).
fof(f8731,plain,
( spl2_287
| ~ spl2_27
| ~ spl2_285 ),
inference(avatar_split_clause,[],[f8650,f8551,f302,f8729]) ).
fof(f8729,plain,
( spl2_287
<=> ! [X22,X24,X23] :
( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(and(and(X23,X22),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_287])]) ).
fof(f8650,plain,
( ! [X24,X22,X23] :
( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(and(and(X23,X22),X24)) )
| ~ spl2_27
| ~ spl2_285 ),
inference(resolution,[],[f8552,f303]) ).
fof(f8727,plain,
( spl2_286
| ~ spl2_81
| ~ spl2_275 ),
inference(avatar_split_clause,[],[f8461,f8172,f911,f8725]) ).
fof(f8461,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),and(X9,X8)))
| ~ spl2_81
| ~ spl2_275 ),
inference(resolution,[],[f8173,f912]) ).
fof(f8553,plain,
( spl2_285
| ~ spl2_19
| ~ spl2_275 ),
inference(avatar_split_clause,[],[f8460,f8172,f269,f8551]) ).
fof(f8460,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X5,X4)))
| ~ spl2_19
| ~ spl2_275 ),
inference(resolution,[],[f8173,f270]) ).
fof(f8437,plain,
( spl2_284
| ~ spl2_81
| ~ spl2_274 ),
inference(avatar_split_clause,[],[f8386,f8168,f911,f8435]) ).
fof(f8386,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,equiv(X8,X9)),equiv(X9,X8)))
| ~ spl2_81
| ~ spl2_274 ),
inference(resolution,[],[f8169,f912]) ).
fof(f8433,plain,
( spl2_283
| ~ spl2_77
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1355,f1114,f814,f8431]) ).
fof(f1355,plain,
( ! [X8,X6,X9,X7] : is_a_theorem(strict_implies(and(implies(and(X7,not(X8)),X6),and(X9,not(and(X6,implies(X7,X8))))),and(X9,equiv(X6,and(X7,not(X8))))))
| ~ spl2_77
| ~ spl2_94 ),
inference(superposition,[],[f1115,f815]) ).
fof(f8409,plain,
( spl2_282
| ~ spl2_19
| ~ spl2_274 ),
inference(avatar_split_clause,[],[f8385,f8168,f269,f8407]) ).
fof(f8385,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(equiv(X4,X5),X6),equiv(X5,X4)))
| ~ spl2_19
| ~ spl2_274 ),
inference(resolution,[],[f8169,f270]) ).
fof(f8382,plain,
( spl2_281
| ~ spl2_77
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1352,f1114,f814,f8380]) ).
fof(f8380,plain,
( spl2_281
<=> ! [X9,X7,X6,X8] : is_a_theorem(strict_implies(and(not(and(X6,implies(X7,X8))),and(X9,implies(and(X7,not(X8)),X6))),and(X9,equiv(and(X7,not(X8)),X6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_281])]) ).
fof(f1352,plain,
( ! [X8,X6,X9,X7] : is_a_theorem(strict_implies(and(not(and(X6,implies(X7,X8))),and(X9,implies(and(X7,not(X8)),X6))),and(X9,equiv(and(X7,not(X8)),X6))))
| ~ spl2_77
| ~ spl2_94 ),
inference(superposition,[],[f1115,f815]) ).
fof(f8194,plain,
( spl2_280
| ~ spl2_77
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f1265,f1074,f814,f8192]) ).
fof(f8192,plain,
( spl2_280
<=> ! [X9,X7,X6,X8] : is_a_theorem(strict_implies(and(equiv(and(X7,not(X8)),X6),X9),and(implies(and(X7,not(X8)),X6),and(not(and(X6,implies(X7,X8))),X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_280])]) ).
fof(f1265,plain,
( ! [X8,X6,X9,X7] : is_a_theorem(strict_implies(and(equiv(and(X7,not(X8)),X6),X9),and(implies(and(X7,not(X8)),X6),and(not(and(X6,implies(X7,X8))),X9))))
| ~ spl2_77
| ~ spl2_88 ),
inference(superposition,[],[f1075,f815]) ).
fof(f8190,plain,
( spl2_279
| ~ spl2_41
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2331,f1831,f410,f8188]) ).
fof(f2331,plain,
( ! [X73,X74,X75] :
( is_a_theorem(strict_implies(X73,strict_equiv(X74,X75)))
| ~ is_a_theorem(strict_implies(X73,strict_equiv(X75,X74))) )
| ~ spl2_41
| ~ spl2_122 ),
inference(resolution,[],[f1832,f411]) ).
fof(f8186,plain,
( spl2_278
| ~ spl2_52
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2328,f1831,f489,f8184]) ).
fof(f2328,plain,
( ! [X65,X66,X64] :
( is_a_theorem(strict_implies(X64,strict_implies(X65,X65)))
| ~ is_a_theorem(strict_implies(X64,strict_equiv(X65,X66))) )
| ~ spl2_52
| ~ spl2_122 ),
inference(resolution,[],[f1832,f490]) ).
fof(f8182,plain,
( spl2_277
| ~ spl2_40
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2327,f1831,f406,f8180]) ).
fof(f2327,plain,
( ! [X62,X63,X61] :
( is_a_theorem(strict_implies(X61,strict_implies(X62,X63)))
| ~ is_a_theorem(strict_implies(X61,strict_equiv(X62,X63))) )
| ~ spl2_40
| ~ spl2_122 ),
inference(resolution,[],[f1832,f407]) ).
fof(f8178,plain,
( spl2_276
| ~ spl2_77
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f1262,f1074,f814,f8176]) ).
fof(f8176,plain,
( spl2_276
<=> ! [X9,X7,X6,X8] : is_a_theorem(strict_implies(and(equiv(X6,and(X7,not(X8))),X9),and(not(and(X6,implies(X7,X8))),and(implies(and(X7,not(X8)),X6),X9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_276])]) ).
fof(f1262,plain,
( ! [X8,X6,X9,X7] : is_a_theorem(strict_implies(and(equiv(X6,and(X7,not(X8))),X9),and(not(and(X6,implies(X7,X8))),and(implies(and(X7,not(X8)),X6),X9))))
| ~ spl2_77
| ~ spl2_88 ),
inference(superposition,[],[f1075,f815]) ).
fof(f8174,plain,
( spl2_275
| ~ spl2_25
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2319,f1831,f294,f8172]) ).
fof(f2319,plain,
( ! [X31,X32,X33] :
( is_a_theorem(strict_implies(X31,and(X32,X33)))
| ~ is_a_theorem(strict_implies(X31,and(X33,X32))) )
| ~ spl2_25
| ~ spl2_122 ),
inference(resolution,[],[f1832,f295]) ).
fof(f8170,plain,
( spl2_274
| ~ spl2_45
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2311,f1831,f444,f8168]) ).
fof(f2311,plain,
( ! [X10,X8,X9] :
( is_a_theorem(strict_implies(X8,equiv(X9,X10)))
| ~ is_a_theorem(strict_implies(X8,equiv(X10,X9))) )
| ~ spl2_45
| ~ spl2_122 ),
inference(resolution,[],[f1832,f445]) ).
fof(f8166,plain,
( spl2_273
| ~ spl2_44
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2309,f1831,f440,f8164]) ).
fof(f2309,plain,
( ! [X2,X3,X4] :
( is_a_theorem(strict_implies(X2,implies(X3,X4)))
| ~ is_a_theorem(strict_implies(X2,equiv(X3,X4))) )
| ~ spl2_44
| ~ spl2_122 ),
inference(resolution,[],[f1832,f441]) ).
fof(f8162,plain,
( spl2_272
| ~ spl2_26
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f2282,f1712,f298,f8160]) ).
fof(f2282,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(and(X1,and(X2,X0)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) )
| ~ spl2_26
| ~ spl2_120 ),
inference(resolution,[],[f1713,f299]) ).
fof(f8078,plain,
( spl2_271
| ~ spl2_27
| ~ spl2_114 ),
inference(avatar_split_clause,[],[f2066,f1640,f302,f8076]) ).
fof(f2066,plain,
( ! [X2,X3] :
( is_a_theorem(not(and(X2,possibly(X3))))
| ~ is_a_theorem(equiv(X2,necessarily(not(X3)))) )
| ~ spl2_27
| ~ spl2_114 ),
inference(resolution,[],[f1641,f303]) ).
fof(f8074,plain,
( spl2_270
| ~ spl2_23
| ~ spl2_60
| ~ spl2_104 ),
inference(avatar_split_clause,[],[f1450,f1388,f558,f286,f8072]) ).
fof(f1450,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(strict_equiv(not(X3),necessarily(not(X4))),strict_implies(possibly(X4),X3)))
| ~ spl2_23
| ~ spl2_60
| ~ spl2_104 ),
inference(forward_demodulation,[],[f1425,f287]) ).
fof(f1425,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(strict_equiv(not(X3),necessarily(not(X4))),necessarily(implies(possibly(X4),X3))))
| ~ spl2_60
| ~ spl2_104 ),
inference(superposition,[],[f559,f1389]) ).
fof(f8070,plain,
( spl2_269
| ~ spl2_55
| ~ spl2_61 ),
inference(avatar_split_clause,[],[f672,f568,f510,f8068]) ).
fof(f8068,plain,
( spl2_269
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(strict_implies(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_269])]) ).
fof(f510,plain,
( spl2_55
<=> ! [X0,X1] :
( is_a_theorem(strict_implies(X0,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_55])]) ).
fof(f568,plain,
( spl2_61
<=> ! [X6,X7] :
( is_a_theorem(strict_equiv(X6,X7))
| ~ is_a_theorem(strict_implies(X7,X6))
| ~ is_a_theorem(strict_implies(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).
fof(f672,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(strict_implies(X1,X1)) )
| ~ spl2_55
| ~ spl2_61 ),
inference(resolution,[],[f569,f511]) ).
fof(f511,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X0)) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f569,plain,
( ! [X6,X7] :
( is_a_theorem(strict_equiv(X6,X7))
| ~ is_a_theorem(strict_implies(X7,X6))
| ~ is_a_theorem(strict_implies(X6,X7)) )
| ~ spl2_61 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f7964,plain,
( spl2_268
| ~ spl2_27
| ~ spl2_264 ),
inference(avatar_split_clause,[],[f7785,f7546,f302,f7962]) ).
fof(f7962,plain,
( spl2_268
<=> ! [X9,X10] :
( is_a_theorem(strict_implies(X9,X10))
| ~ is_a_theorem(strict_equiv(X10,and(X9,not(X10)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_268])]) ).
fof(f7785,plain,
( ! [X10,X9] :
( is_a_theorem(strict_implies(X9,X10))
| ~ is_a_theorem(strict_equiv(X10,and(X9,not(X10)))) )
| ~ spl2_27
| ~ spl2_264 ),
inference(resolution,[],[f7547,f303]) ).
fof(f7560,plain,
( spl2_267
| ~ spl2_75
| ~ spl2_255 ),
inference(avatar_split_clause,[],[f7436,f6979,f806,f7558]) ).
fof(f7558,plain,
( spl2_267
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,equiv(X3,not(X2))))
| is_a_theorem(or(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_267])]) ).
fof(f6979,plain,
( spl2_255
<=> ! [X9,X8,X7] :
( is_a_theorem(or(X7,X8))
| ~ is_a_theorem(and(X9,equiv(not(X8),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_255])]) ).
fof(f7436,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,equiv(X3,not(X2))))
| is_a_theorem(or(X3,X2)) )
| ~ spl2_75
| ~ spl2_255 ),
inference(superposition,[],[f6980,f807]) ).
fof(f6980,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(X9,equiv(not(X8),X7)))
| is_a_theorem(or(X7,X8)) )
| ~ spl2_255 ),
inference(avatar_component_clause,[],[f6979]) ).
fof(f7556,plain,
( spl2_266
| ~ spl2_27
| ~ spl2_250 ),
inference(avatar_split_clause,[],[f7306,f6959,f302,f7554]) ).
fof(f7554,plain,
( spl2_266
<=> ! [X8,X7] :
( is_a_theorem(strict_implies(X7,X8))
| ~ is_a_theorem(strict_equiv(X8,and(not(X8),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_266])]) ).
fof(f7306,plain,
( ! [X8,X7] :
( is_a_theorem(strict_implies(X7,X8))
| ~ is_a_theorem(strict_equiv(X8,and(not(X8),X7))) )
| ~ spl2_27
| ~ spl2_250 ),
inference(resolution,[],[f6960,f303]) ).
fof(f7552,plain,
( spl2_265
| ~ spl2_27
| ~ spl2_248 ),
inference(avatar_split_clause,[],[f7169,f6951,f302,f7550]) ).
fof(f7550,plain,
( spl2_265
<=> ! [X6,X5] :
( is_a_theorem(implies(X5,X6))
| ~ is_a_theorem(equiv(X6,and(X5,not(X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_265])]) ).
fof(f7169,plain,
( ! [X6,X5] :
( is_a_theorem(implies(X5,X6))
| ~ is_a_theorem(equiv(X6,and(X5,not(X6)))) )
| ~ spl2_27
| ~ spl2_248 ),
inference(resolution,[],[f6952,f303]) ).
fof(f7548,plain,
( spl2_264
| ~ spl2_40
| ~ spl2_79
| ~ spl2_128 ),
inference(avatar_split_clause,[],[f2128,f2062,f822,f406,f7546]) ).
fof(f2128,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(strict_equiv(X9,and(X8,not(X9))),strict_implies(X8,X9)))
| ~ spl2_40
| ~ spl2_79
| ~ spl2_128 ),
inference(forward_demodulation,[],[f2113,f823]) ).
fof(f2113,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(strict_equiv(and(X8,not(X9)),X9),strict_implies(X8,X9)))
| ~ spl2_40
| ~ spl2_128 ),
inference(superposition,[],[f407,f2063]) ).
fof(f7544,plain,
( spl2_263
| ~ spl2_54
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1354,f1114,f505,f7542]) ).
fof(f7542,plain,
( spl2_263
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(implies(necessarily(not(X4)),X3),and(X5,not(and(X3,possibly(X4))))),and(X5,equiv(X3,necessarily(not(X4)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_263])]) ).
fof(f1354,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(implies(necessarily(not(X4)),X3),and(X5,not(and(X3,possibly(X4))))),and(X5,equiv(X3,necessarily(not(X4))))))
| ~ spl2_54
| ~ spl2_94 ),
inference(superposition,[],[f1115,f506]) ).
fof(f7540,plain,
( spl2_262
| ~ spl2_27
| ~ spl2_128 ),
inference(avatar_split_clause,[],[f2110,f2062,f302,f7538]) ).
fof(f2110,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_implies(X2,X3))
| is_a_theorem(X3)
| ~ is_a_theorem(and(X2,not(X3))) )
| ~ spl2_27
| ~ spl2_128 ),
inference(superposition,[],[f303,f2063]) ).
fof(f7491,plain,
( spl2_261
| ~ spl2_54
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1351,f1114,f505,f7489]) ).
fof(f7489,plain,
( spl2_261
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(not(and(X3,possibly(X4))),and(X5,implies(necessarily(not(X4)),X3))),and(X5,equiv(necessarily(not(X4)),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_261])]) ).
fof(f1351,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(not(and(X3,possibly(X4))),and(X5,implies(necessarily(not(X4)),X3))),and(X5,equiv(necessarily(not(X4)),X3))))
| ~ spl2_54
| ~ spl2_94 ),
inference(superposition,[],[f1115,f506]) ).
fof(f7375,plain,
( spl2_260
| ~ spl2_54
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f1264,f1074,f505,f7373]) ).
fof(f7373,plain,
( spl2_260
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(equiv(necessarily(not(X4)),X3),X5),and(implies(necessarily(not(X4)),X3),and(not(and(X3,possibly(X4))),X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_260])]) ).
fof(f1264,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(necessarily(not(X4)),X3),X5),and(implies(necessarily(not(X4)),X3),and(not(and(X3,possibly(X4))),X5))))
| ~ spl2_54
| ~ spl2_88 ),
inference(superposition,[],[f1075,f506]) ).
fof(f7199,plain,
( spl2_259
| ~ spl2_54
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f1261,f1074,f505,f7197]) ).
fof(f7197,plain,
( spl2_259
<=> ! [X4,X5,X3] : is_a_theorem(strict_implies(and(equiv(X3,necessarily(not(X4))),X5),and(not(and(X3,possibly(X4))),and(implies(necessarily(not(X4)),X3),X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_259])]) ).
fof(f1261,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(X3,necessarily(not(X4))),X5),and(not(and(X3,possibly(X4))),and(implies(necessarily(not(X4)),X3),X5))))
| ~ spl2_54
| ~ spl2_88 ),
inference(superposition,[],[f1075,f506]) ).
fof(f7166,plain,
( spl2_258
| ~ spl2_75
| ~ spl2_244 ),
inference(avatar_split_clause,[],[f6816,f6161,f806,f7164]) ).
fof(f7164,plain,
( spl2_258
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(and(equiv(X3,not(X2)),X4))
| is_a_theorem(or(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_258])]) ).
fof(f6161,plain,
( spl2_244
<=> ! [X9,X8,X7] :
( is_a_theorem(or(X7,X8))
| ~ is_a_theorem(and(equiv(not(X8),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_244])]) ).
fof(f6816,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(equiv(X3,not(X2)),X4))
| is_a_theorem(or(X3,X2)) )
| ~ spl2_75
| ~ spl2_244 ),
inference(superposition,[],[f6162,f807]) ).
fof(f6162,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(equiv(not(X8),X7),X9))
| is_a_theorem(or(X7,X8)) )
| ~ spl2_244 ),
inference(avatar_component_clause,[],[f6161]) ).
fof(f7162,plain,
( spl2_257
| ~ spl2_27
| ~ spl2_242 ),
inference(avatar_split_clause,[],[f6691,f6153,f302,f7160]) ).
fof(f7160,plain,
( spl2_257
<=> ! [X6,X5] :
( is_a_theorem(not(not(X5)))
| ~ is_a_theorem(and(X6,equiv(X5,not(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_257])]) ).
fof(f6691,plain,
( ! [X6,X5] :
( is_a_theorem(not(not(X5)))
| ~ is_a_theorem(and(X6,equiv(X5,not(X5)))) )
| ~ spl2_27
| ~ spl2_242 ),
inference(resolution,[],[f6154,f303]) ).
fof(f7158,plain,
( spl2_256
| ~ spl2_75
| ~ spl2_240 ),
inference(avatar_split_clause,[],[f6664,f6145,f806,f7156]) ).
fof(f6664,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,equiv(X3,not(X2))),or(X3,X2)))
| ~ spl2_75
| ~ spl2_240 ),
inference(superposition,[],[f6146,f807]) ).
fof(f6981,plain,
( spl2_255
| ~ spl2_27
| ~ spl2_240 ),
inference(avatar_split_clause,[],[f6653,f6145,f302,f6979]) ).
fof(f6653,plain,
( ! [X8,X9,X7] :
( is_a_theorem(or(X7,X8))
| ~ is_a_theorem(and(X9,equiv(not(X8),X7))) )
| ~ spl2_27
| ~ spl2_240 ),
inference(resolution,[],[f6146,f303]) ).
fof(f6977,plain,
( spl2_254
| ~ spl2_75
| ~ spl2_238 ),
inference(avatar_split_clause,[],[f6534,f6137,f806,f6975]) ).
fof(f6975,plain,
( spl2_254
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,equiv(X3,not(X2))))
| is_a_theorem(or(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_254])]) ).
fof(f6137,plain,
( spl2_238
<=> ! [X18,X17,X19] :
( ~ is_a_theorem(and(X19,equiv(not(X17),X18)))
| is_a_theorem(or(X17,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_238])]) ).
fof(f6534,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,equiv(X3,not(X2))))
| is_a_theorem(or(X2,X3)) )
| ~ spl2_75
| ~ spl2_238 ),
inference(superposition,[],[f6138,f807]) ).
fof(f6138,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(X19,equiv(not(X17),X18)))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_238 ),
inference(avatar_component_clause,[],[f6137]) ).
fof(f6973,plain,
( spl2_253
| ~ spl2_27
| ~ spl2_237 ),
inference(avatar_split_clause,[],[f6494,f6133,f302,f6971]) ).
fof(f6971,plain,
( spl2_253
<=> ! [X6,X5] :
( is_a_theorem(implies(X5,X6))
| ~ is_a_theorem(equiv(X6,and(not(X6),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_253])]) ).
fof(f6494,plain,
( ! [X6,X5] :
( is_a_theorem(implies(X5,X6))
| ~ is_a_theorem(equiv(X6,and(not(X6),X5))) )
| ~ spl2_27
| ~ spl2_237 ),
inference(resolution,[],[f6134,f303]) ).
fof(f6969,plain,
( spl2_252
| ~ spl2_36
| ~ spl2_76
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f934,f814,f810,f363,f6967]) ).
fof(f934,plain,
( ! [X3,X4,X5] : equiv(and(X4,not(X5)),X3) = and(not(and(X3,implies(X4,X5))),implies(and(X4,not(X5)),X3))
| ~ spl2_36
| ~ spl2_76
| ~ spl2_77 ),
inference(forward_demodulation,[],[f925,f811]) ).
fof(f925,plain,
( ! [X3,X4,X5] : equiv(and(X4,not(X5)),X3) = and(implies(and(X4,not(X5)),X3),not(and(X3,implies(X4,X5))))
| ~ spl2_36
| ~ spl2_77 ),
inference(superposition,[],[f364,f815]) ).
fof(f6965,plain,
( spl2_251
| ~ spl2_24
| ~ spl2_175 ),
inference(avatar_split_clause,[],[f3653,f3354,f290,f6963]) ).
fof(f3653,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X2,equiv(X1,not(X0))),or(X0,X1)))
| ~ spl2_24
| ~ spl2_175 ),
inference(superposition,[],[f3355,f291]) ).
fof(f6961,plain,
( spl2_250
| ~ spl2_40
| ~ spl2_79
| ~ spl2_126 ),
inference(avatar_split_clause,[],[f2036,f1856,f822,f406,f6959]) ).
fof(f2036,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(strict_equiv(X7,and(not(X7),X8)),strict_implies(X8,X7)))
| ~ spl2_40
| ~ spl2_79
| ~ spl2_126 ),
inference(forward_demodulation,[],[f2021,f823]) ).
fof(f2021,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(strict_equiv(and(not(X7),X8),X7),strict_implies(X8,X7)))
| ~ spl2_40
| ~ spl2_126 ),
inference(superposition,[],[f407,f1857]) ).
fof(f6957,plain,
( spl2_249
| ~ spl2_27
| ~ spl2_126 ),
inference(avatar_split_clause,[],[f2018,f1856,f302,f6955]) ).
fof(f2018,plain,
( ! [X2,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(and(not(X1),X2)) )
| ~ spl2_27
| ~ spl2_126 ),
inference(superposition,[],[f303,f1857]) ).
fof(f6953,plain,
( spl2_248
| ~ spl2_44
| ~ spl2_75
| ~ spl2_123 ),
inference(avatar_split_clause,[],[f1905,f1844,f806,f440,f6951]) ).
fof(f1844,plain,
( spl2_123
<=> ! [X45,X44] : implies(and(X45,not(X44)),X44) = implies(X45,X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_123])]) ).
fof(f1905,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(equiv(X8,and(X7,not(X8))),implies(X7,X8)))
| ~ spl2_44
| ~ spl2_75
| ~ spl2_123 ),
inference(forward_demodulation,[],[f1873,f807]) ).
fof(f1873,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(equiv(and(X7,not(X8)),X8),implies(X7,X8)))
| ~ spl2_44
| ~ spl2_123 ),
inference(superposition,[],[f441,f1845]) ).
fof(f1845,plain,
( ! [X44,X45] : implies(and(X45,not(X44)),X44) = implies(X45,X44)
| ~ spl2_123 ),
inference(avatar_component_clause,[],[f1844]) ).
fof(f6175,plain,
( spl2_247
| ~ spl2_27
| ~ spl2_231 ),
inference(avatar_split_clause,[],[f6090,f5603,f302,f6173]) ).
fof(f6173,plain,
( spl2_247
<=> ! [X6,X5] :
( is_a_theorem(not(not(X5)))
| ~ is_a_theorem(and(equiv(X5,not(X5)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_247])]) ).
fof(f6090,plain,
( ! [X6,X5] :
( is_a_theorem(not(not(X5)))
| ~ is_a_theorem(and(equiv(X5,not(X5)),X6)) )
| ~ spl2_27
| ~ spl2_231 ),
inference(resolution,[],[f5604,f303]) ).
fof(f6171,plain,
( spl2_246
| ~ spl2_75
| ~ spl2_230 ),
inference(avatar_split_clause,[],[f6063,f5599,f806,f6169]) ).
fof(f6063,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(equiv(X3,not(X2)),X4),or(X3,X2)))
| ~ spl2_75
| ~ spl2_230 ),
inference(superposition,[],[f5600,f807]) ).
fof(f6167,plain,
( spl2_245
| ~ spl2_33
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f1292,f1092,f340,f6165]) ).
fof(f6165,plain,
( spl2_245
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X1,not(X0)),and(X2,necessarily(or(X0,X1)))),and(X2,strict_equiv(not(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_245])]) ).
fof(f1292,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X1,not(X0)),and(X2,necessarily(or(X0,X1)))),and(X2,strict_equiv(not(X0),X1))))
| ~ spl2_33
| ~ spl2_91 ),
inference(superposition,[],[f1093,f341]) ).
fof(f6163,plain,
( spl2_244
| ~ spl2_27
| ~ spl2_230 ),
inference(avatar_split_clause,[],[f6052,f5599,f302,f6161]) ).
fof(f6052,plain,
( ! [X8,X9,X7] :
( is_a_theorem(or(X7,X8))
| ~ is_a_theorem(and(equiv(not(X8),X7),X9)) )
| ~ spl2_27
| ~ spl2_230 ),
inference(resolution,[],[f5600,f303]) ).
fof(f6159,plain,
( spl2_243
| ~ spl2_75
| ~ spl2_228 ),
inference(avatar_split_clause,[],[f5997,f5538,f806,f6157]) ).
fof(f6157,plain,
( spl2_243
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(and(equiv(X3,not(X2)),X4))
| is_a_theorem(or(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_243])]) ).
fof(f5538,plain,
( spl2_228
<=> ! [X18,X17,X19] :
( ~ is_a_theorem(and(equiv(not(X17),X18),X19))
| is_a_theorem(or(X17,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_228])]) ).
fof(f5997,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(equiv(X3,not(X2)),X4))
| is_a_theorem(or(X2,X3)) )
| ~ spl2_75
| ~ spl2_228 ),
inference(superposition,[],[f5539,f807]) ).
fof(f5539,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(equiv(not(X17),X18),X19))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_228 ),
inference(avatar_component_clause,[],[f5538]) ).
fof(f6155,plain,
( spl2_242
| ~ spl2_75
| ~ spl2_83
| ~ spl2_227 ),
inference(avatar_split_clause,[],[f5928,f5534,f1024,f806,f6153]) ).
fof(f5928,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(X8,equiv(X7,not(X7))),not(not(X7))))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_227 ),
inference(forward_demodulation,[],[f5914,f807]) ).
fof(f5914,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(X8,equiv(not(X7),X7)),not(not(X7))))
| ~ spl2_83
| ~ spl2_227 ),
inference(superposition,[],[f5535,f1025]) ).
fof(f6151,plain,
( spl2_241
| ~ spl2_33
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f1291,f1092,f340,f6149]) ).
fof(f1291,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),and(X2,strict_implies(X1,not(X0)))),and(X2,strict_equiv(X1,not(X0)))))
| ~ spl2_33
| ~ spl2_91 ),
inference(superposition,[],[f1093,f341]) ).
fof(f6147,plain,
( spl2_240
| ~ spl2_97
| ~ spl2_227 ),
inference(avatar_split_clause,[],[f5915,f5534,f1233,f6145]) ).
fof(f5915,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(X11,equiv(not(X9),X10)),or(X10,X9)))
| ~ spl2_97
| ~ spl2_227 ),
inference(superposition,[],[f5535,f1234]) ).
fof(f6143,plain,
( spl2_239
| ~ spl2_24
| ~ spl2_163 ),
inference(avatar_split_clause,[],[f3033,f2758,f290,f6141]) ).
fof(f3033,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X1,not(X0)),X2),or(X0,X1)))
| ~ spl2_24
| ~ spl2_163 ),
inference(superposition,[],[f2759,f291]) ).
fof(f6139,plain,
( spl2_238
| ~ spl2_80
| ~ spl2_143 ),
inference(avatar_split_clause,[],[f2550,f2532,f856,f6137]) ).
fof(f2550,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(X19,equiv(not(X17),X18)))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_80
| ~ spl2_143 ),
inference(superposition,[],[f2533,f857]) ).
fof(f6135,plain,
( spl2_237
| ~ spl2_44
| ~ spl2_75
| ~ spl2_118 ),
inference(avatar_split_clause,[],[f1789,f1704,f806,f440,f6133]) ).
fof(f1789,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(equiv(X6,and(not(X6),X7)),implies(X7,X6)))
| ~ spl2_44
| ~ spl2_75
| ~ spl2_118 ),
inference(forward_demodulation,[],[f1754,f807]) ).
fof(f1754,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(equiv(and(not(X6),X7),X6),implies(X7,X6)))
| ~ spl2_44
| ~ spl2_118 ),
inference(superposition,[],[f441,f1705]) ).
fof(f6131,plain,
( spl2_236
| ~ spl2_33
| ~ spl2_85 ),
inference(avatar_split_clause,[],[f1144,f1050,f340,f6129]) ).
fof(f1144,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X1,not(X0)),X2),and(strict_implies(X1,not(X0)),and(necessarily(or(X0,X1)),X2))))
| ~ spl2_33
| ~ spl2_85 ),
inference(superposition,[],[f1051,f341]) ).
fof(f6127,plain,
( spl2_235
| ~ spl2_34
| ~ spl2_113 ),
inference(avatar_split_clause,[],[f1572,f1562,f344,f6125]) ).
fof(f1562,plain,
( spl2_113
<=> ! [X2,X1] : and(X2,X1) = and(X1,and(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_113])]) ).
fof(f1572,plain,
( ! [X14,X13] : strict_equiv(X13,X14) = and(strict_implies(X14,X13),strict_equiv(X13,X14))
| ~ spl2_34
| ~ spl2_113 ),
inference(superposition,[],[f1563,f345]) ).
fof(f1563,plain,
( ! [X2,X1] : and(X2,X1) = and(X1,and(X2,X1))
| ~ spl2_113 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f6123,plain,
( spl2_234
| ~ spl2_36
| ~ spl2_113 ),
inference(avatar_split_clause,[],[f1570,f1562,f363,f6121]) ).
fof(f1570,plain,
( ! [X10,X9] : equiv(X9,X10) = and(implies(X10,X9),equiv(X9,X10))
| ~ spl2_36
| ~ spl2_113 ),
inference(superposition,[],[f1563,f364]) ).
fof(f6119,plain,
( spl2_233
| ~ spl2_20
| ~ spl2_75
| ~ spl2_101 ),
inference(avatar_split_clause,[],[f1376,f1310,f806,f273,f6117]) ).
fof(f6117,plain,
( spl2_233
<=> ! [X0] :
( ~ is_a_theorem(equiv(possibly(X0),necessarily(not(X0))))
| is_a_theorem(not(possibly(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_233])]) ).
fof(f1310,plain,
( spl2_101
<=> ! [X1] :
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(equiv(X1,not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_101])]) ).
fof(f1376,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(possibly(X0),necessarily(not(X0))))
| is_a_theorem(not(possibly(X0))) )
| ~ spl2_20
| ~ spl2_75
| ~ spl2_101 ),
inference(forward_demodulation,[],[f1371,f807]) ).
fof(f1371,plain,
( ! [X0] :
( ~ is_a_theorem(equiv(necessarily(not(X0)),possibly(X0)))
| is_a_theorem(not(possibly(X0))) )
| ~ spl2_20
| ~ spl2_101 ),
inference(superposition,[],[f1311,f274]) ).
fof(f1311,plain,
( ! [X1] :
( ~ is_a_theorem(equiv(X1,not(X1)))
| is_a_theorem(not(not(X1))) )
| ~ spl2_101 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f6115,plain,
( spl2_232
| ~ spl2_33
| ~ spl2_85 ),
inference(avatar_split_clause,[],[f1143,f1050,f340,f6113]) ).
fof(f6113,plain,
( spl2_232
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(not(X0),X1),X2),and(necessarily(or(X0,X1)),and(strict_implies(X1,not(X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_232])]) ).
fof(f1143,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(not(X0),X1),X2),and(necessarily(or(X0,X1)),and(strict_implies(X1,not(X0)),X2))))
| ~ spl2_33
| ~ spl2_85 ),
inference(superposition,[],[f1051,f341]) ).
fof(f5605,plain,
( spl2_231
| ~ spl2_75
| ~ spl2_83
| ~ spl2_223 ),
inference(avatar_split_clause,[],[f5460,f5421,f1024,f806,f5603]) ).
fof(f5460,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(equiv(X7,not(X7)),X8),not(not(X7))))
| ~ spl2_75
| ~ spl2_83
| ~ spl2_223 ),
inference(forward_demodulation,[],[f5446,f807]) ).
fof(f5446,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(and(equiv(not(X7),X7),X8),not(not(X7))))
| ~ spl2_83
| ~ spl2_223 ),
inference(superposition,[],[f5422,f1025]) ).
fof(f5601,plain,
( spl2_230
| ~ spl2_97
| ~ spl2_223 ),
inference(avatar_split_clause,[],[f5447,f5421,f1233,f5599]) ).
fof(f5447,plain,
( ! [X10,X11,X9] : is_a_theorem(strict_implies(and(equiv(not(X9),X10),X11),or(X10,X9)))
| ~ spl2_97
| ~ spl2_223 ),
inference(superposition,[],[f5422,f1234]) ).
fof(f5597,plain,
( spl2_229
| ~ spl2_20
| ~ spl2_135 ),
inference(avatar_split_clause,[],[f5333,f2305,f273,f5595]) ).
fof(f5595,plain,
( spl2_229
<=> ! [X0,X1] : possibly(necessarily(or(X0,X1))) = possibly(necessarily(or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_229])]) ).
fof(f2305,plain,
( spl2_135
<=> ! [X2,X3] : not(necessarily(or(X3,X2))) = not(necessarily(or(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_135])]) ).
fof(f5333,plain,
( ! [X0,X1] : possibly(necessarily(or(X0,X1))) = possibly(necessarily(or(X1,X0)))
| ~ spl2_20
| ~ spl2_135 ),
inference(forward_demodulation,[],[f5203,f274]) ).
fof(f5203,plain,
( ! [X0,X1] : possibly(necessarily(or(X0,X1))) = not(necessarily(not(necessarily(or(X1,X0)))))
| ~ spl2_20
| ~ spl2_135 ),
inference(superposition,[],[f274,f2306]) ).
fof(f2306,plain,
( ! [X2,X3] : not(necessarily(or(X3,X2))) = not(necessarily(or(X2,X3)))
| ~ spl2_135 ),
inference(avatar_component_clause,[],[f2305]) ).
fof(f5540,plain,
( spl2_228
| ~ spl2_80
| ~ spl2_139 ),
inference(avatar_split_clause,[],[f2502,f2466,f856,f5538]) ).
fof(f2466,plain,
( spl2_139
<=> ! [X9,X7,X8] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(and(X7,X8),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_139])]) ).
fof(f2502,plain,
( ! [X18,X19,X17] :
( ~ is_a_theorem(and(equiv(not(X17),X18),X19))
| is_a_theorem(or(X17,X18)) )
| ~ spl2_80
| ~ spl2_139 ),
inference(superposition,[],[f2467,f857]) ).
fof(f2467,plain,
( ! [X8,X9,X7] :
( ~ is_a_theorem(and(and(X7,X8),X9))
| is_a_theorem(X7) )
| ~ spl2_139 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f5536,plain,
( spl2_227
| ~ spl2_80
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2487,f2462,f856,f5534]) ).
fof(f2487,plain,
( ! [X18,X19,X17] : is_a_theorem(strict_implies(and(X19,equiv(not(X17),X18)),or(X17,X18)))
| ~ spl2_80
| ~ spl2_138 ),
inference(superposition,[],[f2463,f857]) ).
fof(f5532,plain,
( spl2_226
| ~ spl2_34
| ~ spl2_111 ),
inference(avatar_split_clause,[],[f1508,f1499,f344,f5530]) ).
fof(f5530,plain,
( spl2_226
<=> ! [X11,X12] : strict_equiv(X11,X12) = and(strict_implies(X11,X12),strict_equiv(X11,X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_226])]) ).
fof(f1508,plain,
( ! [X11,X12] : strict_equiv(X11,X12) = and(strict_implies(X11,X12),strict_equiv(X11,X12))
| ~ spl2_34
| ~ spl2_111 ),
inference(superposition,[],[f1500,f345]) ).
fof(f5468,plain,
( spl2_225
| ~ spl2_36
| ~ spl2_111 ),
inference(avatar_split_clause,[],[f1506,f1499,f363,f5466]) ).
fof(f5466,plain,
( spl2_225
<=> ! [X8,X7] : equiv(X7,X8) = and(implies(X7,X8),equiv(X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_225])]) ).
fof(f1506,plain,
( ! [X8,X7] : equiv(X7,X8) = and(implies(X7,X8),equiv(X7,X8))
| ~ spl2_36
| ~ spl2_111 ),
inference(superposition,[],[f1500,f364]) ).
fof(f5464,plain,
( spl2_224
| ~ spl2_20
| ~ spl2_75
| ~ spl2_98 ),
inference(avatar_split_clause,[],[f1282,f1273,f806,f273,f5462]) ).
fof(f1282,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(possibly(X0),necessarily(not(X0))),not(possibly(X0))))
| ~ spl2_20
| ~ spl2_75
| ~ spl2_98 ),
inference(forward_demodulation,[],[f1278,f807]) ).
fof(f1278,plain,
( ! [X0] : is_a_theorem(strict_implies(equiv(necessarily(not(X0)),possibly(X0)),not(possibly(X0))))
| ~ spl2_20
| ~ spl2_98 ),
inference(superposition,[],[f1274,f274]) ).
fof(f5423,plain,
( spl2_223
| ~ spl2_80
| ~ spl2_137 ),
inference(avatar_split_clause,[],[f2453,f2369,f856,f5421]) ).
fof(f2453,plain,
( ! [X18,X19,X17] : is_a_theorem(strict_implies(and(equiv(not(X17),X18),X19),or(X17,X18)))
| ~ spl2_80
| ~ spl2_137 ),
inference(superposition,[],[f2370,f857]) ).
fof(f4970,plain,
( spl2_222
| ~ spl2_24
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1350,f1114,f290,f4968]) ).
fof(f1350,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(or(X0,X1),and(X2,implies(X1,not(X0)))),and(X2,equiv(X1,not(X0)))))
| ~ spl2_24
| ~ spl2_94 ),
inference(superposition,[],[f1115,f291]) ).
fof(f4937,plain,
( spl2_221
| ~ spl2_76
| ~ spl2_214 ),
inference(avatar_split_clause,[],[f4880,f4851,f810,f4935]) ).
fof(f4935,plain,
( spl2_221
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,equiv(X2,X3)))
| is_a_theorem(equiv(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_221])]) ).
fof(f4880,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,equiv(X2,X3)))
| is_a_theorem(equiv(X3,X2)) )
| ~ spl2_76
| ~ spl2_214 ),
inference(superposition,[],[f4852,f811]) ).
fof(f4933,plain,
( spl2_220
| ~ spl2_24
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f1263,f1074,f290,f4931]) ).
fof(f4931,plain,
( spl2_220
<=> ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X1,not(X0)),X2),and(implies(X1,not(X0)),and(or(X0,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_220])]) ).
fof(f1263,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(equiv(X1,not(X0)),X2),and(implies(X1,not(X0)),and(or(X0,X1),X2))))
| ~ spl2_24
| ~ spl2_88 ),
inference(superposition,[],[f1075,f291]) ).
fof(f4929,plain,
( spl2_219
| ~ spl2_76
| ~ spl2_213 ),
inference(avatar_split_clause,[],[f4871,f4847,f810,f4927]) ).
fof(f4927,plain,
( spl2_219
<=> ! [X2,X4,X3] :
( ~ is_a_theorem(and(X4,strict_equiv(X2,X3)))
| is_a_theorem(strict_equiv(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_219])]) ).
fof(f4871,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,strict_equiv(X2,X3)))
| is_a_theorem(strict_equiv(X3,X2)) )
| ~ spl2_76
| ~ spl2_213 ),
inference(superposition,[],[f4848,f811]) ).
fof(f4887,plain,
( spl2_218
| ~ spl2_43
| ~ spl2_76
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f1022,f856,f810,f436,f4885]) ).
fof(f4885,plain,
( spl2_218
<=> ! [X16,X17,X15] : is_a_theorem(strict_implies(and(implies(X16,not(X15)),and(X17,or(X15,X16))),and(X17,equiv(not(X15),X16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_218])]) ).
fof(f1022,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(implies(X16,not(X15)),and(X17,or(X15,X16))),and(X17,equiv(not(X15),X16))))
| ~ spl2_43
| ~ spl2_76
| ~ spl2_80 ),
inference(forward_demodulation,[],[f1004,f811]) ).
fof(f1004,plain,
( ! [X16,X17,X15] : is_a_theorem(strict_implies(and(and(X17,or(X15,X16)),implies(X16,not(X15))),and(X17,equiv(not(X15),X16))))
| ~ spl2_43
| ~ spl2_80 ),
inference(superposition,[],[f437,f857]) ).
fof(f4865,plain,
( spl2_217
| ~ spl2_26
| ~ spl2_208 ),
inference(avatar_split_clause,[],[f4785,f4554,f298,f4863]) ).
fof(f4554,plain,
( spl2_208
<=> ! [X13,X14,X15] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X14,X15),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_208])]) ).
fof(f4785,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(and(X1,X2)) )
| ~ spl2_26
| ~ spl2_208 ),
inference(resolution,[],[f4555,f299]) ).
fof(f4555,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(and(and(X14,X15),X13))
| is_a_theorem(and(X13,X14)) )
| ~ spl2_208 ),
inference(avatar_component_clause,[],[f4554]) ).
fof(f4861,plain,
( spl2_216
| ~ spl2_27
| ~ spl2_207 ),
inference(avatar_split_clause,[],[f4754,f4550,f302,f4859]) ).
fof(f4754,plain,
( ! [X14,X15,X13] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(X13,and(X14,X15))) )
| ~ spl2_27
| ~ spl2_207 ),
inference(resolution,[],[f4551,f303]) ).
fof(f4857,plain,
( spl2_215
| ~ spl2_66
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f1005,f856,f623,f4855]) ).
fof(f1005,plain,
( ! [X18,X19,X20] :
( ~ is_a_theorem(and(equiv(not(X18),X19),X20))
| is_a_theorem(and(or(X18,X19),and(implies(X19,not(X18)),X20))) )
| ~ spl2_66
| ~ spl2_80 ),
inference(superposition,[],[f624,f857]) ).
fof(f4853,plain,
( spl2_214
| ~ spl2_36
| ~ spl2_192
| ~ spl2_206 ),
inference(avatar_split_clause,[],[f4747,f4546,f4124,f363,f4851]) ).
fof(f4747,plain,
( ! [X3,X4,X5] :
( is_a_theorem(equiv(X3,X4))
| ~ is_a_theorem(and(equiv(X4,X3),X5)) )
| ~ spl2_36
| ~ spl2_192
| ~ spl2_206 ),
inference(forward_demodulation,[],[f4728,f364]) ).
fof(f4728,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(implies(X3,X4),implies(X4,X3)))
| ~ is_a_theorem(and(equiv(X4,X3),X5)) )
| ~ spl2_192
| ~ spl2_206 ),
inference(resolution,[],[f4547,f4125]) ).
fof(f4849,plain,
( spl2_213
| ~ spl2_34
| ~ spl2_190
| ~ spl2_206 ),
inference(avatar_split_clause,[],[f4746,f4546,f4074,f344,f4847]) ).
fof(f4746,plain,
( ! [X2,X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(and(strict_equiv(X1,X0),X2)) )
| ~ spl2_34
| ~ spl2_190
| ~ spl2_206 ),
inference(forward_demodulation,[],[f4727,f345]) ).
fof(f4727,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X0)))
| ~ is_a_theorem(and(strict_equiv(X1,X0),X2)) )
| ~ spl2_190
| ~ spl2_206 ),
inference(resolution,[],[f4547,f4075]) ).
fof(f4831,plain,
( spl2_212
| ~ spl2_43
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f1003,f856,f436,f4829]) ).
fof(f4829,plain,
( spl2_212
<=> ! [X13,X12,X14] : is_a_theorem(strict_implies(and(equiv(not(X12),X13),X14),and(or(X12,X13),and(implies(X13,not(X12)),X14)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_212])]) ).
fof(f1003,plain,
( ! [X14,X12,X13] : is_a_theorem(strict_implies(and(equiv(not(X12),X13),X14),and(or(X12,X13),and(implies(X13,not(X12)),X14))))
| ~ spl2_43
| ~ spl2_80 ),
inference(superposition,[],[f437,f857]) ).
fof(f4568,plain,
( spl2_211
| ~ spl2_26
| ~ spl2_204 ),
inference(avatar_split_clause,[],[f4485,f4172,f298,f4566]) ).
fof(f4566,plain,
( spl2_211
<=> ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(and(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_211])]) ).
fof(f4172,plain,
( spl2_204
<=> ! [X13,X14,X15] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X15,X14),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_204])]) ).
fof(f4485,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(and(X2,X1)) )
| ~ spl2_26
| ~ spl2_204 ),
inference(resolution,[],[f4173,f299]) ).
fof(f4173,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(and(and(X15,X14),X13))
| is_a_theorem(and(X13,X14)) )
| ~ spl2_204 ),
inference(avatar_component_clause,[],[f4172]) ).
fof(f4564,plain,
( spl2_210
| ~ spl2_27
| ~ spl2_203 ),
inference(avatar_split_clause,[],[f4456,f4168,f302,f4562]) ).
fof(f4456,plain,
( ! [X14,X15,X13] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(X13,and(X15,X14))) )
| ~ spl2_27
| ~ spl2_203 ),
inference(resolution,[],[f4169,f303]) ).
fof(f4560,plain,
( spl2_209
| ~ spl2_36
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f520,f505,f363,f4558]) ).
fof(f520,plain,
( ! [X4,X5] : equiv(X4,necessarily(not(X5))) = and(not(and(X4,possibly(X5))),implies(necessarily(not(X5)),X4))
| ~ spl2_36
| ~ spl2_54 ),
inference(superposition,[],[f364,f506]) ).
fof(f4556,plain,
( spl2_208
| ~ spl2_27
| ~ spl2_202 ),
inference(avatar_split_clause,[],[f4417,f4164,f302,f4554]) ).
fof(f4164,plain,
( spl2_202
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(and(X2,X4),X3),and(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_202])]) ).
fof(f4417,plain,
( ! [X14,X15,X13] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X14,X15),X13)) )
| ~ spl2_27
| ~ spl2_202 ),
inference(resolution,[],[f4165,f303]) ).
fof(f4165,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X2,X4),X3),and(X3,X2)))
| ~ spl2_202 ),
inference(avatar_component_clause,[],[f4164]) ).
fof(f4552,plain,
( spl2_207
| ~ spl2_76
| ~ spl2_200 ),
inference(avatar_split_clause,[],[f4371,f4156,f810,f4550]) ).
fof(f4371,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,and(X2,X4)),and(X3,X2)))
| ~ spl2_76
| ~ spl2_200 ),
inference(superposition,[],[f4157,f811]) ).
fof(f4548,plain,
( spl2_206
| ~ spl2_76
| ~ spl2_198 ),
inference(avatar_split_clause,[],[f4325,f4148,f810,f4546]) ).
fof(f4148,plain,
( spl2_198
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(and(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_198])]) ).
fof(f4325,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X2,X4)) )
| ~ spl2_76
| ~ spl2_198 ),
inference(superposition,[],[f4149,f811]) ).
fof(f4149,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(and(X3,X4)) )
| ~ spl2_198 ),
inference(avatar_component_clause,[],[f4148]) ).
fof(f4544,plain,
( spl2_205
| ~ spl2_76
| ~ spl2_196 ),
inference(avatar_split_clause,[],[f4304,f4140,f810,f4542]) ).
fof(f4140,plain,
( spl2_196
<=> ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_196])]) ).
fof(f4304,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X4)
| is_a_theorem(and(X3,X4)) )
| ~ spl2_76
| ~ spl2_196 ),
inference(superposition,[],[f4141,f811]) ).
fof(f4141,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) )
| ~ spl2_196 ),
inference(avatar_component_clause,[],[f4140]) ).
fof(f4174,plain,
( spl2_204
| ~ spl2_27
| ~ spl2_186 ),
inference(avatar_split_clause,[],[f4038,f3567,f302,f4172]) ).
fof(f3567,plain,
( spl2_186
<=> ! [X2,X4,X3] : is_a_theorem(strict_implies(and(and(X4,X2),X3),and(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_186])]) ).
fof(f4038,plain,
( ! [X14,X15,X13] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X15,X14),X13)) )
| ~ spl2_27
| ~ spl2_186 ),
inference(resolution,[],[f3568,f303]) ).
fof(f3568,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X4,X2),X3),and(X3,X2)))
| ~ spl2_186 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f4170,plain,
( spl2_203
| ~ spl2_76
| ~ spl2_185 ),
inference(avatar_split_clause,[],[f4023,f3511,f810,f4168]) ).
fof(f4023,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X3,and(X4,X2)),and(X3,X2)))
| ~ spl2_76
| ~ spl2_185 ),
inference(superposition,[],[f3512,f811]) ).
fof(f4166,plain,
( spl2_202
| ~ spl2_76
| ~ spl2_184 ),
inference(avatar_split_clause,[],[f3987,f3507,f810,f4164]) ).
fof(f3507,plain,
( spl2_184
<=> ! [X4,X2,X3] : is_a_theorem(strict_implies(and(and(X3,X2),X4),and(X3,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_184])]) ).
fof(f3987,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X2,X4),X3),and(X3,X2)))
| ~ spl2_76
| ~ spl2_184 ),
inference(superposition,[],[f3508,f811]) ).
fof(f3508,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X3,X2),X4),and(X3,X4)))
| ~ spl2_184 ),
inference(avatar_component_clause,[],[f3507]) ).
fof(f4162,plain,
( spl2_201
| ~ spl2_27
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1349,f1114,f302,f4160]) ).
fof(f1349,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(X3,equiv(X4,X5)))
| ~ is_a_theorem(and(implies(X5,X4),and(X3,implies(X4,X5)))) )
| ~ spl2_27
| ~ spl2_94 ),
inference(resolution,[],[f1115,f303]) ).
fof(f4158,plain,
( spl2_200
| ~ spl2_76
| ~ spl2_184 ),
inference(avatar_split_clause,[],[f3982,f3507,f810,f4156]) ).
fof(f3982,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X2,X4)))
| ~ spl2_76
| ~ spl2_184 ),
inference(superposition,[],[f3508,f811]) ).
fof(f4154,plain,
( spl2_199
| ~ spl2_76
| ~ spl2_183 ),
inference(avatar_split_clause,[],[f3961,f3503,f810,f4152]) ).
fof(f3503,plain,
( spl2_183
<=> ! [X13,X14,X15] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X15,X13),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_183])]) ).
fof(f3961,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X2,X3)))
| is_a_theorem(and(X3,X4)) )
| ~ spl2_76
| ~ spl2_183 ),
inference(superposition,[],[f3504,f811]) ).
fof(f3504,plain,
( ! [X14,X15,X13] :
( ~ is_a_theorem(and(and(X15,X13),X14))
| is_a_theorem(and(X13,X14)) )
| ~ spl2_183 ),
inference(avatar_component_clause,[],[f3503]) ).
fof(f4150,plain,
( spl2_198
| ~ spl2_76
| ~ spl2_183 ),
inference(avatar_split_clause,[],[f3951,f3503,f810,f4148]) ).
fof(f3951,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(and(X3,X4)) )
| ~ spl2_76
| ~ spl2_183 ),
inference(superposition,[],[f3504,f811]) ).
fof(f4146,plain,
( spl2_197
| ~ spl2_27
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f1290,f1092,f302,f4144]) ).
fof(f1290,plain,
( ! [X3,X4,X5] :
( is_a_theorem(and(X3,strict_equiv(X4,X5)))
| ~ is_a_theorem(and(strict_implies(X5,X4),and(X3,strict_implies(X4,X5)))) )
| ~ spl2_27
| ~ spl2_91 ),
inference(resolution,[],[f1093,f303]) ).
fof(f4142,plain,
( spl2_196
| ~ spl2_26
| ~ spl2_183 ),
inference(avatar_split_clause,[],[f3949,f3503,f298,f4140]) ).
fof(f3949,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X0)) )
| ~ spl2_26
| ~ spl2_183 ),
inference(resolution,[],[f3504,f299]) ).
fof(f4138,plain,
( spl2_195
| ~ spl2_27
| ~ spl2_179 ),
inference(avatar_split_clause,[],[f3748,f3438,f302,f4136]) ).
fof(f3748,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(X11,and(X12,X9)))) )
| ~ spl2_27
| ~ spl2_179 ),
inference(resolution,[],[f3439,f303]) ).
fof(f4134,plain,
( spl2_194
| ~ spl2_27
| ~ spl2_174 ),
inference(avatar_split_clause,[],[f3621,f3350,f302,f4132]) ).
fof(f3621,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(X11,and(X9,X12)))) )
| ~ spl2_27
| ~ spl2_174 ),
inference(resolution,[],[f3351,f303]) ).
fof(f4130,plain,
( spl2_193
| ~ spl2_34
| ~ spl2_147 ),
inference(avatar_split_clause,[],[f2609,f2594,f344,f4128]) ).
fof(f4128,plain,
( spl2_193
<=> ! [X22,X20,X21] :
( ~ is_a_theorem(and(X22,strict_equiv(X20,X21)))
| is_a_theorem(strict_implies(X21,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_193])]) ).
fof(f2609,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(X22,strict_equiv(X20,X21)))
| is_a_theorem(strict_implies(X21,X20)) )
| ~ spl2_34
| ~ spl2_147 ),
inference(superposition,[],[f2595,f345]) ).
fof(f4126,plain,
( spl2_192
| ~ spl2_36
| ~ spl2_66 ),
inference(avatar_split_clause,[],[f746,f623,f363,f4124]) ).
fof(f746,plain,
( ! [X3,X4,X5] :
( ~ is_a_theorem(and(equiv(X3,X4),X5))
| is_a_theorem(and(implies(X3,X4),and(implies(X4,X3),X5))) )
| ~ spl2_36
| ~ spl2_66 ),
inference(superposition,[],[f624,f364]) ).
fof(f4122,plain,
( spl2_191
| ~ spl2_36
| ~ spl2_147 ),
inference(avatar_split_clause,[],[f2607,f2594,f363,f4120]) ).
fof(f4120,plain,
( spl2_191
<=> ! [X16,X14,X15] :
( ~ is_a_theorem(and(X16,equiv(X14,X15)))
| is_a_theorem(implies(X15,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_191])]) ).
fof(f2607,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(X16,equiv(X14,X15)))
| is_a_theorem(implies(X15,X14)) )
| ~ spl2_36
| ~ spl2_147 ),
inference(superposition,[],[f2595,f364]) ).
fof(f4076,plain,
( spl2_190
| ~ spl2_34
| ~ spl2_66 ),
inference(avatar_split_clause,[],[f745,f623,f344,f4074]) ).
fof(f745,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_equiv(X0,X1),X2))
| is_a_theorem(and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2))) )
| ~ spl2_34
| ~ spl2_66 ),
inference(superposition,[],[f624,f345]) ).
fof(f3774,plain,
( spl2_189
| ~ spl2_24
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f996,f856,f290,f3772]) ).
fof(f996,plain,
( ! [X0,X1] : equiv(not(X1),not(X0)) = and(or(X1,not(X0)),or(X0,not(X1)))
| ~ spl2_24
| ~ spl2_80 ),
inference(superposition,[],[f857,f291]) ).
fof(f3577,plain,
( spl2_188
| ~ spl2_27
| ~ spl2_169 ),
inference(avatar_split_clause,[],[f3191,f2782,f302,f3575]) ).
fof(f3575,plain,
( spl2_188
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(X10,and(X11,X9)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_188])]) ).
fof(f2782,plain,
( spl2_169
<=> ! [X34,X32,X31,X33] : is_a_theorem(strict_implies(and(and(X31,and(X32,X33)),X34),X33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_169])]) ).
fof(f3191,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(X10,and(X11,X9)),X12)) )
| ~ spl2_27
| ~ spl2_169 ),
inference(resolution,[],[f2783,f303]) ).
fof(f2783,plain,
( ! [X31,X34,X32,X33] : is_a_theorem(strict_implies(and(and(X31,and(X32,X33)),X34),X33))
| ~ spl2_169 ),
inference(avatar_component_clause,[],[f2782]) ).
fof(f3573,plain,
( spl2_187
| ~ spl2_27
| ~ spl2_168 ),
inference(avatar_split_clause,[],[f3166,f2778,f302,f3571]) ).
fof(f3571,plain,
( spl2_187
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(and(X10,X9),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_187])]) ).
fof(f2778,plain,
( spl2_168
<=> ! [X29,X27,X28,X30] : is_a_theorem(strict_implies(and(and(and(X27,X28),X29),X30),X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_168])]) ).
fof(f3166,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(and(X10,X9),X11),X12)) )
| ~ spl2_27
| ~ spl2_168 ),
inference(resolution,[],[f2779,f303]) ).
fof(f2779,plain,
( ! [X28,X29,X27,X30] : is_a_theorem(strict_implies(and(and(and(X27,X28),X29),X30),X28))
| ~ spl2_168 ),
inference(avatar_component_clause,[],[f2778]) ).
fof(f3569,plain,
( spl2_186
| ~ spl2_76
| ~ spl2_167 ),
inference(avatar_split_clause,[],[f3101,f2774,f810,f3567]) ).
fof(f2774,plain,
( spl2_167
<=> ! [X25,X24,X26] : is_a_theorem(strict_implies(and(and(X24,X25),X26),and(X25,X26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_167])]) ).
fof(f3101,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X4,X2),X3),and(X3,X2)))
| ~ spl2_76
| ~ spl2_167 ),
inference(superposition,[],[f2775,f811]) ).
fof(f2775,plain,
( ! [X26,X24,X25] : is_a_theorem(strict_implies(and(and(X24,X25),X26),and(X25,X26)))
| ~ spl2_167 ),
inference(avatar_component_clause,[],[f2774]) ).
fof(f3513,plain,
( spl2_185
| ~ spl2_76
| ~ spl2_167 ),
inference(avatar_split_clause,[],[f3096,f2774,f810,f3511]) ).
fof(f3096,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X2,X3)),and(X3,X4)))
| ~ spl2_76
| ~ spl2_167 ),
inference(superposition,[],[f2775,f811]) ).
fof(f3509,plain,
( spl2_184
| ~ spl2_76
| ~ spl2_167 ),
inference(avatar_split_clause,[],[f3087,f2774,f810,f3507]) ).
fof(f3087,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X3,X2),X4),and(X3,X4)))
| ~ spl2_76
| ~ spl2_167 ),
inference(superposition,[],[f2775,f811]) ).
fof(f3505,plain,
( spl2_183
| ~ spl2_27
| ~ spl2_167 ),
inference(avatar_split_clause,[],[f3085,f2774,f302,f3503]) ).
fof(f3085,plain,
( ! [X14,X15,X13] :
( is_a_theorem(and(X13,X14))
| ~ is_a_theorem(and(and(X15,X13),X14)) )
| ~ spl2_27
| ~ spl2_167 ),
inference(resolution,[],[f2775,f303]) ).
fof(f3452,plain,
( spl2_182
| ~ spl2_27
| ~ spl2_165 ),
inference(avatar_split_clause,[],[f3058,f2766,f302,f3450]) ).
fof(f3450,plain,
( spl2_182
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(and(X11,X9),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_182])]) ).
fof(f2766,plain,
( spl2_165
<=> ! [X13,X12,X11,X10] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_165])]) ).
fof(f3058,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(and(X11,X9),X12))) )
| ~ spl2_27
| ~ spl2_165 ),
inference(resolution,[],[f2767,f303]) ).
fof(f2767,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X12))
| ~ spl2_165 ),
inference(avatar_component_clause,[],[f2766]) ).
fof(f3448,plain,
( spl2_181
| ~ spl2_27
| ~ spl2_162 ),
inference(avatar_split_clause,[],[f2954,f2754,f302,f3446]) ).
fof(f3446,plain,
( spl2_181
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(X10,and(X9,X11)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_181])]) ).
fof(f2754,plain,
( spl2_162
<=> ! [X13,X12,X11,X10] : is_a_theorem(strict_implies(and(and(X10,and(X11,X12)),X13),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_162])]) ).
fof(f2954,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(X10,and(X9,X11)),X12)) )
| ~ spl2_27
| ~ spl2_162 ),
inference(resolution,[],[f2755,f303]) ).
fof(f2755,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(X10,and(X11,X12)),X13),X11))
| ~ spl2_162 ),
inference(avatar_component_clause,[],[f2754]) ).
fof(f3444,plain,
( spl2_180
| ~ spl2_27
| ~ spl2_155 ),
inference(avatar_split_clause,[],[f2795,f2726,f302,f3442]) ).
fof(f3442,plain,
( spl2_180
<=> ! [X11,X9,X12,X10] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(and(X9,X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_180])]) ).
fof(f2726,plain,
( spl2_155
<=> ! [X13,X12,X11,X10] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_155])]) ).
fof(f2795,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(X10,and(and(X9,X11),X12))) )
| ~ spl2_27
| ~ spl2_155 ),
inference(resolution,[],[f2727,f303]) ).
fof(f2727,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X11))
| ~ spl2_155 ),
inference(avatar_component_clause,[],[f2726]) ).
fof(f3440,plain,
( spl2_179
| ~ spl2_144
| ~ spl2_152 ),
inference(avatar_split_clause,[],[f2681,f2665,f2536,f3438]) ).
fof(f2681,plain,
( ! [X16,X14,X17,X15] : is_a_theorem(strict_implies(and(X14,and(X15,and(X16,X17))),X17))
| ~ spl2_144
| ~ spl2_152 ),
inference(resolution,[],[f2666,f2537]) ).
fof(f3404,plain,
( spl2_178
| ~ spl2_34
| ~ spl2_145 ),
inference(avatar_split_clause,[],[f2587,f2540,f344,f3402]) ).
fof(f2540,plain,
( spl2_145
<=> ! [X4,X2,X3] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_145])]) ).
fof(f2587,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X21,X20)) )
| ~ spl2_34
| ~ spl2_145 ),
inference(superposition,[],[f2541,f345]) ).
fof(f2541,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(X2) )
| ~ spl2_145 ),
inference(avatar_component_clause,[],[f2540]) ).
fof(f3400,plain,
( spl2_177
| ~ spl2_36
| ~ spl2_145 ),
inference(avatar_split_clause,[],[f2585,f2540,f363,f3398]) ).
fof(f2585,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X15,X14)) )
| ~ spl2_36
| ~ spl2_145 ),
inference(superposition,[],[f2541,f364]) ).
fof(f3396,plain,
( spl2_176
| ~ spl2_34
| ~ spl2_144 ),
inference(avatar_split_clause,[],[f2572,f2536,f344,f3394]) ).
fof(f2572,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X21,X20)))
| ~ spl2_34
| ~ spl2_144 ),
inference(superposition,[],[f2537,f345]) ).
fof(f3356,plain,
( spl2_175
| ~ spl2_36
| ~ spl2_144 ),
inference(avatar_split_clause,[],[f2570,f2536,f363,f3354]) ).
fof(f2570,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X15,X14)))
| ~ spl2_36
| ~ spl2_144 ),
inference(superposition,[],[f2537,f364]) ).
fof(f3352,plain,
( spl2_174
| ~ spl2_136
| ~ spl2_144 ),
inference(avatar_split_clause,[],[f2564,f2536,f2344,f3350]) ).
fof(f2564,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(X11,and(X12,X13))),X12))
| ~ spl2_136
| ~ spl2_144 ),
inference(resolution,[],[f2537,f2345]) ).
fof(f3348,plain,
( spl2_173
| ~ spl2_34
| ~ spl2_143 ),
inference(avatar_split_clause,[],[f2551,f2532,f344,f3346]) ).
fof(f3346,plain,
( spl2_173
<=> ! [X22,X20,X21] :
( ~ is_a_theorem(and(X22,strict_equiv(X20,X21)))
| is_a_theorem(strict_implies(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_173])]) ).
fof(f2551,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(X22,strict_equiv(X20,X21)))
| is_a_theorem(strict_implies(X20,X21)) )
| ~ spl2_34
| ~ spl2_143 ),
inference(superposition,[],[f2533,f345]) ).
fof(f3344,plain,
( spl2_172
| ~ spl2_36
| ~ spl2_143 ),
inference(avatar_split_clause,[],[f2549,f2532,f363,f3342]) ).
fof(f3342,plain,
( spl2_172
<=> ! [X16,X14,X15] :
( ~ is_a_theorem(and(X16,equiv(X14,X15)))
| is_a_theorem(implies(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_172])]) ).
fof(f2549,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(X16,equiv(X14,X15)))
| is_a_theorem(implies(X14,X15)) )
| ~ spl2_36
| ~ spl2_143 ),
inference(superposition,[],[f2533,f364]) ).
fof(f2792,plain,
( spl2_171
| ~ spl2_27
| ~ spl2_153 ),
inference(avatar_split_clause,[],[f2703,f2669,f302,f2790]) ).
fof(f2790,plain,
( spl2_171
<=> ! [X10,X11,X12,X9] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(and(X9,X10),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_171])]) ).
fof(f2669,plain,
( spl2_153
<=> ! [X10,X11,X13,X12] : is_a_theorem(strict_implies(and(and(and(X10,X11),X12),X13),X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_153])]) ).
fof(f2703,plain,
( ! [X10,X11,X9,X12] :
( is_a_theorem(X9)
| ~ is_a_theorem(and(and(and(X9,X10),X11),X12)) )
| ~ spl2_27
| ~ spl2_153 ),
inference(resolution,[],[f2670,f303]) ).
fof(f2670,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(and(X10,X11),X12),X13),X10))
| ~ spl2_153 ),
inference(avatar_component_clause,[],[f2669]) ).
fof(f2788,plain,
( spl2_170
| ~ spl2_24
| ~ spl2_80
| ~ spl2_94
| ~ spl2_111 ),
inference(avatar_split_clause,[],[f1542,f1499,f1114,f856,f290,f2786]) ).
fof(f1542,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(equiv(not(X10),X11),and(or(X10,X11),equiv(X11,not(X10)))))
| ~ spl2_24
| ~ spl2_80
| ~ spl2_94
| ~ spl2_111 ),
inference(backward_demodulation,[],[f1368,f1507]) ).
fof(f1507,plain,
( ! [X10,X9] : equiv(not(X9),X10) = and(or(X9,X10),equiv(not(X9),X10))
| ~ spl2_80
| ~ spl2_111 ),
inference(superposition,[],[f1500,f857]) ).
fof(f1368,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(and(or(X10,X11),equiv(not(X10),X11)),and(or(X10,X11),equiv(X11,not(X10)))))
| ~ spl2_24
| ~ spl2_80
| ~ spl2_94 ),
inference(forward_demodulation,[],[f1360,f291]) ).
fof(f1360,plain,
( ! [X10,X11] : is_a_theorem(strict_implies(and(implies(not(X10),X11),equiv(not(X10),X11)),and(or(X10,X11),equiv(X11,not(X10)))))
| ~ spl2_80
| ~ spl2_94 ),
inference(superposition,[],[f1115,f857]) ).
fof(f2784,plain,
( spl2_169
| ~ spl2_140
| ~ spl2_152 ),
inference(avatar_split_clause,[],[f2686,f2665,f2470,f2782]) ).
fof(f2470,plain,
( spl2_140
<=> ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X3,X2),X4),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_140])]) ).
fof(f2686,plain,
( ! [X31,X34,X32,X33] : is_a_theorem(strict_implies(and(and(X31,and(X32,X33)),X34),X33))
| ~ spl2_140
| ~ spl2_152 ),
inference(resolution,[],[f2666,f2471]) ).
fof(f2471,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X3,X2),X4),X2))
| ~ spl2_140 ),
inference(avatar_component_clause,[],[f2470]) ).
fof(f2780,plain,
( spl2_168
| ~ spl2_137
| ~ spl2_152 ),
inference(avatar_split_clause,[],[f2685,f2665,f2369,f2778]) ).
fof(f2685,plain,
( ! [X28,X29,X27,X30] : is_a_theorem(strict_implies(and(and(and(X27,X28),X29),X30),X28))
| ~ spl2_137
| ~ spl2_152 ),
inference(resolution,[],[f2666,f2370]) ).
fof(f2776,plain,
( spl2_167
| ~ spl2_43
| ~ spl2_152 ),
inference(avatar_split_clause,[],[f2684,f2665,f436,f2774]) ).
fof(f2684,plain,
( ! [X26,X24,X25] : is_a_theorem(strict_implies(and(and(X24,X25),X26),and(X25,X26)))
| ~ spl2_43
| ~ spl2_152 ),
inference(resolution,[],[f2666,f437]) ).
fof(f2772,plain,
( spl2_166
| ~ spl2_26
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f1000,f856,f298,f2770]) ).
fof(f1000,plain,
( ! [X6,X7] :
( is_a_theorem(equiv(not(X6),X7))
| ~ is_a_theorem(implies(X7,not(X6)))
| ~ is_a_theorem(or(X6,X7)) )
| ~ spl2_26
| ~ spl2_80 ),
inference(superposition,[],[f299,f857]) ).
fof(f2768,plain,
( spl2_165
| ~ spl2_138
| ~ spl2_152 ),
inference(avatar_split_clause,[],[f2680,f2665,f2462,f2766]) ).
fof(f2680,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X12))
| ~ spl2_138
| ~ spl2_152 ),
inference(resolution,[],[f2666,f2463]) ).
fof(f2764,plain,
( spl2_164
| ~ spl2_34
| ~ spl2_140 ),
inference(avatar_split_clause,[],[f2520,f2470,f344,f2762]) ).
fof(f2520,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(strict_equiv(X20,X21),X22),strict_implies(X21,X20)))
| ~ spl2_34
| ~ spl2_140 ),
inference(superposition,[],[f2471,f345]) ).
fof(f2760,plain,
( spl2_163
| ~ spl2_36
| ~ spl2_140 ),
inference(avatar_split_clause,[],[f2518,f2470,f363,f2758]) ).
fof(f2518,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(equiv(X14,X15),X16),implies(X15,X14)))
| ~ spl2_36
| ~ spl2_140 ),
inference(superposition,[],[f2471,f364]) ).
fof(f2756,plain,
( spl2_162
| ~ spl2_136
| ~ spl2_140 ),
inference(avatar_split_clause,[],[f2512,f2470,f2344,f2754]) ).
fof(f2512,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(X10,and(X11,X12)),X13),X11))
| ~ spl2_136
| ~ spl2_140 ),
inference(resolution,[],[f2471,f2345]) ).
fof(f2752,plain,
( spl2_161
| ~ spl2_23
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f927,f814,f286,f2750]) ).
fof(f927,plain,
( ! [X10,X11,X9] : strict_implies(X9,and(X10,not(X11))) = necessarily(not(and(X9,implies(X10,X11))))
| ~ spl2_23
| ~ spl2_77 ),
inference(superposition,[],[f287,f815]) ).
fof(f2748,plain,
( spl2_160
| ~ spl2_34
| ~ spl2_139 ),
inference(avatar_split_clause,[],[f2503,f2466,f344,f2746]) ).
fof(f2503,plain,
( ! [X21,X22,X20] :
( ~ is_a_theorem(and(strict_equiv(X20,X21),X22))
| is_a_theorem(strict_implies(X20,X21)) )
| ~ spl2_34
| ~ spl2_139 ),
inference(superposition,[],[f2467,f345]) ).
fof(f2744,plain,
( spl2_159
| ~ spl2_36
| ~ spl2_139 ),
inference(avatar_split_clause,[],[f2501,f2466,f363,f2742]) ).
fof(f2501,plain,
( ! [X16,X14,X15] :
( ~ is_a_theorem(and(equiv(X14,X15),X16))
| is_a_theorem(implies(X14,X15)) )
| ~ spl2_36
| ~ spl2_139 ),
inference(superposition,[],[f2467,f364]) ).
fof(f2740,plain,
( spl2_158
| ~ spl2_34
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2488,f2462,f344,f2738]) ).
fof(f2488,plain,
( ! [X21,X22,X20] : is_a_theorem(strict_implies(and(X22,strict_equiv(X20,X21)),strict_implies(X20,X21)))
| ~ spl2_34
| ~ spl2_138 ),
inference(superposition,[],[f2463,f345]) ).
fof(f2736,plain,
( spl2_157
| ~ spl2_44
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f924,f814,f440,f2734]) ).
fof(f924,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(equiv(X0,and(X1,not(X2))),not(and(X0,implies(X1,X2)))))
| ~ spl2_44
| ~ spl2_77 ),
inference(superposition,[],[f441,f815]) ).
fof(f2732,plain,
( spl2_156
| ~ spl2_36
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2486,f2462,f363,f2730]) ).
fof(f2486,plain,
( ! [X16,X14,X15] : is_a_theorem(strict_implies(and(X16,equiv(X14,X15)),implies(X14,X15)))
| ~ spl2_36
| ~ spl2_138 ),
inference(superposition,[],[f2463,f364]) ).
fof(f2728,plain,
( spl2_155
| ~ spl2_136
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2480,f2462,f2344,f2726]) ).
fof(f2480,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(X10,and(and(X11,X12),X13)),X11))
| ~ spl2_136
| ~ spl2_138 ),
inference(resolution,[],[f2463,f2345]) ).
fof(f2675,plain,
( spl2_154
| ~ spl2_33
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f800,f644,f340,f2673]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( is_a_theorem(necessarily(or(X0,X2)))
| ~ is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X1,X2))) )
| ~ spl2_33
| ~ spl2_69 ),
inference(forward_demodulation,[],[f796,f341]) ).
fof(f796,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X1,X2)))
| is_a_theorem(strict_implies(not(X0),X2)) )
| ~ spl2_33
| ~ spl2_69 ),
inference(superposition,[],[f645,f341]) ).
fof(f2671,plain,
( spl2_153
| ~ spl2_136
| ~ spl2_137 ),
inference(avatar_split_clause,[],[f2446,f2369,f2344,f2669]) ).
fof(f2446,plain,
( ! [X10,X11,X12,X13] : is_a_theorem(strict_implies(and(and(and(X10,X11),X12),X13),X10))
| ~ spl2_136
| ~ spl2_137 ),
inference(resolution,[],[f2370,f2345]) ).
fof(f2667,plain,
( spl2_152
| ~ spl2_81
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2320,f1831,f911,f2665]) ).
fof(f2320,plain,
( ! [X36,X34,X35] :
( is_a_theorem(strict_implies(X34,X35))
| ~ is_a_theorem(strict_implies(X34,and(X36,X35))) )
| ~ spl2_81
| ~ spl2_122 ),
inference(resolution,[],[f1832,f912]) ).
fof(f2645,plain,
( spl2_151
| ~ spl2_33
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f797,f644,f340,f2643]) ).
fof(f797,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))))
| is_a_theorem(strict_implies(X2,X1)) )
| ~ spl2_33
| ~ spl2_69 ),
inference(superposition,[],[f645,f341]) ).
fof(f2622,plain,
( spl2_150
| ~ spl2_85
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f2355,f2344,f1050,f2620]) ).
fof(f2355,plain,
( ! [X24,X22,X23] : is_a_theorem(strict_implies(and(strict_equiv(X22,X23),X24),strict_implies(X22,X23)))
| ~ spl2_85
| ~ spl2_136 ),
inference(resolution,[],[f2345,f1051]) ).
fof(f2618,plain,
( spl2_149
| ~ spl2_88
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f2352,f2344,f1074,f2616]) ).
fof(f2352,plain,
( ! [X14,X15,X13] : is_a_theorem(strict_implies(and(equiv(X13,X14),X15),implies(X13,X14)))
| ~ spl2_88
| ~ spl2_136 ),
inference(resolution,[],[f2345,f1075]) ).
fof(f2600,plain,
( spl2_148
| ~ spl2_29
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f500,f377,f315,f2598]) ).
fof(f500,plain,
( ! [X2,X3,X4] : not(strict_implies(X4,and(X2,not(X3)))) = possibly(and(X4,implies(X2,X3)))
| ~ spl2_29
| ~ spl2_38 ),
inference(superposition,[],[f378,f316]) ).
fof(f2596,plain,
( spl2_147
| ~ spl2_76
| ~ spl2_143 ),
inference(avatar_split_clause,[],[f2545,f2532,f810,f2594]) ).
fof(f2545,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(X4,and(X3,X2)))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_143 ),
inference(superposition,[],[f2533,f811]) ).
fof(f2560,plain,
( spl2_146
| ~ spl2_33
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f486,f450,f340,f2558]) ).
fof(f486,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),strict_implies(X1,X2)),necessarily(or(X0,X2))))
| ~ spl2_33
| ~ spl2_46 ),
inference(forward_demodulation,[],[f482,f341]) ).
fof(f482,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(necessarily(or(X0,X1)),strict_implies(X1,X2)),strict_implies(not(X0),X2)))
| ~ spl2_33
| ~ spl2_46 ),
inference(superposition,[],[f451,f341]) ).
fof(f2542,plain,
( spl2_145
| ~ spl2_76
| ~ spl2_139 ),
inference(avatar_split_clause,[],[f2497,f2466,f810,f2540]) ).
fof(f2497,plain,
( ! [X2,X3,X4] :
( ~ is_a_theorem(and(and(X3,X2),X4))
| is_a_theorem(X2) )
| ~ spl2_76
| ~ spl2_139 ),
inference(superposition,[],[f2467,f811]) ).
fof(f2538,plain,
( spl2_144
| ~ spl2_76
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2482,f2462,f810,f2536]) ).
fof(f2482,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(X4,and(X3,X2)),X2))
| ~ spl2_76
| ~ spl2_138 ),
inference(superposition,[],[f2463,f811]) ).
fof(f2534,plain,
( spl2_143
| ~ spl2_27
| ~ spl2_138 ),
inference(avatar_split_clause,[],[f2479,f2462,f302,f2532]) ).
fof(f2479,plain,
( ! [X8,X9,X7] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(X8,and(X7,X9))) )
| ~ spl2_27
| ~ spl2_138 ),
inference(resolution,[],[f2463,f303]) ).
fof(f2530,plain,
( spl2_142
| ~ spl2_33
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f483,f450,f340,f2528]) ).
fof(f483,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X2,not(X0)),necessarily(or(X0,X1))),strict_implies(X2,X1)))
| ~ spl2_33
| ~ spl2_46 ),
inference(superposition,[],[f451,f341]) ).
fof(f2476,plain,
( spl2_141
| ~ spl2_33
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f388,f344,f340,f2474]) ).
fof(f388,plain,
( ! [X0,X1] : strict_equiv(not(X0),X1) = and(necessarily(or(X0,X1)),strict_implies(X1,not(X0)))
| ~ spl2_33
| ~ spl2_34 ),
inference(superposition,[],[f345,f341]) ).
fof(f2472,plain,
( spl2_140
| ~ spl2_76
| ~ spl2_137 ),
inference(avatar_split_clause,[],[f2448,f2369,f810,f2470]) ).
fof(f2448,plain,
( ! [X2,X3,X4] : is_a_theorem(strict_implies(and(and(X3,X2),X4),X2))
| ~ spl2_76
| ~ spl2_137 ),
inference(superposition,[],[f2370,f811]) ).
fof(f2468,plain,
( spl2_139
| ~ spl2_27
| ~ spl2_137 ),
inference(avatar_split_clause,[],[f2445,f2369,f302,f2466]) ).
fof(f2445,plain,
( ! [X8,X9,X7] :
( is_a_theorem(X7)
| ~ is_a_theorem(and(and(X7,X8),X9)) )
| ~ spl2_27
| ~ spl2_137 ),
inference(resolution,[],[f2370,f303]) ).
fof(f2464,plain,
( spl2_138
| ~ spl2_81
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f2350,f2344,f911,f2462]) ).
fof(f2350,plain,
( ! [X8,X9,X7] : is_a_theorem(strict_implies(and(X7,and(X8,X9)),X8))
| ~ spl2_81
| ~ spl2_136 ),
inference(resolution,[],[f2345,f912]) ).
fof(f2371,plain,
( spl2_137
| ~ spl2_19
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f2349,f2344,f269,f2369]) ).
fof(f2349,plain,
( ! [X6,X4,X5] : is_a_theorem(strict_implies(and(and(X4,X5),X6),X4))
| ~ spl2_19
| ~ spl2_136 ),
inference(resolution,[],[f2345,f270]) ).
fof(f2346,plain,
( spl2_136
| ~ spl2_19
| ~ spl2_122 ),
inference(avatar_split_clause,[],[f2318,f1831,f269,f2344]) ).
fof(f2318,plain,
( ! [X28,X29,X30] :
( is_a_theorem(strict_implies(X28,X29))
| ~ is_a_theorem(strict_implies(X28,and(X29,X30))) )
| ~ spl2_19
| ~ spl2_122 ),
inference(resolution,[],[f1832,f270]) ).
fof(f2307,plain,
( spl2_135
| ~ spl2_33
| ~ spl2_38
| ~ spl2_108 ),
inference(avatar_split_clause,[],[f1636,f1470,f377,f340,f2305]) ).
fof(f1470,plain,
( spl2_108
<=> ! [X25,X26] : not(strict_implies(X25,X26)) = possibly(and(not(X26),X25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_108])]) ).
fof(f1636,plain,
( ! [X2,X3] : not(necessarily(or(X3,X2))) = not(necessarily(or(X2,X3)))
| ~ spl2_33
| ~ spl2_38
| ~ spl2_108 ),
inference(forward_demodulation,[],[f1635,f341]) ).
fof(f1635,plain,
( ! [X2,X3] : not(strict_implies(not(X2),X3)) = not(necessarily(or(X3,X2)))
| ~ spl2_33
| ~ spl2_38
| ~ spl2_108 ),
inference(forward_demodulation,[],[f1626,f341]) ).
fof(f1626,plain,
( ! [X2,X3] : not(strict_implies(not(X2),X3)) = not(strict_implies(not(X3),X2))
| ~ spl2_38
| ~ spl2_108 ),
inference(superposition,[],[f1471,f378]) ).
fof(f1471,plain,
( ! [X26,X25] : not(strict_implies(X25,X26)) = possibly(and(not(X26),X25))
| ~ spl2_108 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f2303,plain,
( spl2_134
| ~ spl2_20
| ~ spl2_108
| ~ spl2_112 ),
inference(avatar_split_clause,[],[f1628,f1558,f1470,f273,f2301]) ).
fof(f1628,plain,
( ! [X0,X1] : possibly(and(X1,possibly(X0))) = possibly(and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_108
| ~ spl2_112 ),
inference(forward_demodulation,[],[f1618,f1559]) ).
fof(f1618,plain,
( ! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_108 ),
inference(superposition,[],[f1471,f274]) ).
fof(f2299,plain,
( spl2_133
| ~ spl2_20
| ~ spl2_54
| ~ spl2_96 ),
inference(avatar_split_clause,[],[f1195,f1122,f505,f273,f2297]) ).
fof(f1195,plain,
( ! [X0,X1] : not(and(X1,possibly(X0))) = not(and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_54
| ~ spl2_96 ),
inference(forward_demodulation,[],[f1166,f506]) ).
fof(f1166,plain,
( ! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(possibly(X0),X1))
| ~ spl2_20
| ~ spl2_96 ),
inference(superposition,[],[f1123,f274]) ).
fof(f2295,plain,
( spl2_132
| ~ spl2_70
| ~ spl2_81 ),
inference(avatar_split_clause,[],[f937,f911,f681,f2293]) ).
fof(f2293,plain,
( spl2_132
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X0)))
| and(X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_132])]) ).
fof(f937,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X0)))
| and(X1,X0) = X0 )
| ~ spl2_70
| ~ spl2_81 ),
inference(resolution,[],[f912,f682]) ).
fof(f2226,plain,
( spl2_131
| ~ spl2_72
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f2157,f1696,f748,f2224]) ).
fof(f2157,plain,
( ! [X0] : necessarily(not(possibly(X0))) = strict_implies(possibly(X0),necessarily(not(X0)))
| ~ spl2_72
| ~ spl2_116 ),
inference(superposition,[],[f1697,f749]) ).
fof(f2153,plain,
( spl2_130
| ~ spl2_65
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f976,f822,f602,f2151]) ).
fof(f976,plain,
( ! [X21,X22] : is_a_theorem(strict_implies(strict_equiv(X22,not(X21)),necessarily(or(X21,not(X21)))))
| ~ spl2_65
| ~ spl2_79 ),
inference(superposition,[],[f603,f823]) ).
fof(f2140,plain,
( spl2_129
| ~ spl2_19
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f694,f681,f269,f2138]) ).
fof(f694,plain,
( ! [X8,X9] :
( ~ is_a_theorem(strict_implies(X8,and(X8,X9)))
| and(X8,X9) = X8 )
| ~ spl2_19
| ~ spl2_70 ),
inference(resolution,[],[f682,f270]) ).
fof(f2064,plain,
( spl2_128
| ~ spl2_23
| ~ spl2_123 ),
inference(avatar_split_clause,[],[f1898,f1844,f286,f2062]) ).
fof(f1898,plain,
( ! [X2,X1] : strict_implies(X1,X2) = strict_implies(and(X1,not(X2)),X2)
| ~ spl2_23
| ~ spl2_123 ),
inference(forward_demodulation,[],[f1870,f287]) ).
fof(f1870,plain,
( ! [X2,X1] : necessarily(implies(X1,X2)) = strict_implies(and(X1,not(X2)),X2)
| ~ spl2_23
| ~ spl2_123 ),
inference(superposition,[],[f287,f1845]) ).
fof(f1862,plain,
( spl2_127
| ~ spl2_27
| ~ spl2_119 ),
inference(avatar_split_clause,[],[f1807,f1708,f302,f1860]) ).
fof(f1860,plain,
( spl2_127
<=> ! [X2,X3] :
( is_a_theorem(necessarily(or(X2,X3)))
| ~ is_a_theorem(strict_equiv(X2,not(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_127])]) ).
fof(f1807,plain,
( ! [X2,X3] :
( is_a_theorem(necessarily(or(X2,X3)))
| ~ is_a_theorem(strict_equiv(X2,not(X3))) )
| ~ spl2_27
| ~ spl2_119 ),
inference(resolution,[],[f1709,f303]) ).
fof(f1858,plain,
( spl2_126
| ~ spl2_23
| ~ spl2_118 ),
inference(avatar_split_clause,[],[f1784,f1704,f286,f1856]) ).
fof(f1784,plain,
( ! [X0,X1] : strict_implies(X1,X0) = strict_implies(and(not(X0),X1),X0)
| ~ spl2_23
| ~ spl2_118 ),
inference(forward_demodulation,[],[f1751,f287]) ).
fof(f1751,plain,
( ! [X0,X1] : strict_implies(and(not(X0),X1),X0) = necessarily(implies(X1,X0))
| ~ spl2_23
| ~ spl2_118 ),
inference(superposition,[],[f287,f1705]) ).
fof(f1854,plain,
( spl2_125
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f933,f814,f810,f315,f290,f1852]) ).
fof(f933,plain,
( ! [X2,X0,X1] : or(X0,and(X1,not(X2))) = implies(implies(X1,X2),X0)
| ~ spl2_24
| ~ spl2_29
| ~ spl2_76
| ~ spl2_77 ),
inference(forward_demodulation,[],[f923,f874]) ).
fof(f874,plain,
( ! [X28,X27] : implies(X27,X28) = not(and(not(X28),X27))
| ~ spl2_29
| ~ spl2_76 ),
inference(superposition,[],[f316,f811]) ).
fof(f923,plain,
( ! [X2,X0,X1] : or(X0,and(X1,not(X2))) = not(and(not(X0),implies(X1,X2)))
| ~ spl2_24
| ~ spl2_77 ),
inference(superposition,[],[f815,f291]) ).
fof(f1850,plain,
( spl2_124
| ~ spl2_27
| ~ spl2_117 ),
inference(avatar_split_clause,[],[f1720,f1700,f302,f1848]) ).
fof(f1848,plain,
( spl2_124
<=> ! [X2,X3] :
( is_a_theorem(necessarily(or(X2,X3)))
| ~ is_a_theorem(strict_equiv(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_124])]) ).
fof(f1720,plain,
( ! [X2,X3] :
( is_a_theorem(necessarily(or(X2,X3)))
| ~ is_a_theorem(strict_equiv(not(X3),X2)) )
| ~ spl2_27
| ~ spl2_117 ),
inference(resolution,[],[f1701,f303]) ).
fof(f1846,plain,
( spl2_123
| ~ spl2_29
| ~ spl2_96
| ~ spl2_113 ),
inference(avatar_split_clause,[],[f1613,f1562,f1122,f315,f1844]) ).
fof(f1613,plain,
( ! [X44,X45] : implies(and(X45,not(X44)),X44) = implies(X45,X44)
| ~ spl2_29
| ~ spl2_96
| ~ spl2_113 ),
inference(forward_demodulation,[],[f1590,f316]) ).
fof(f1590,plain,
( ! [X44,X45] : implies(and(X45,not(X44)),X44) = not(and(X45,not(X44)))
| ~ spl2_96
| ~ spl2_113 ),
inference(superposition,[],[f1123,f1563]) ).
fof(f1833,plain,
( spl2_122
| ~ spl2_26
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f795,f644,f298,f1831]) ).
fof(f795,plain,
( ! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2)) )
| ~ spl2_26
| ~ spl2_69 ),
inference(resolution,[],[f645,f299]) ).
fof(f1718,plain,
( spl2_121
| ~ spl2_27
| ~ spl2_115 ),
inference(avatar_split_clause,[],[f1688,f1684,f302,f1716]) ).
fof(f1716,plain,
( spl2_121
<=> ! [X1] :
( is_a_theorem(necessarily(not(not(X1))))
| ~ is_a_theorem(strict_equiv(X1,not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_121])]) ).
fof(f1688,plain,
( ! [X1] :
( is_a_theorem(necessarily(not(not(X1))))
| ~ is_a_theorem(strict_equiv(X1,not(X1))) )
| ~ spl2_27
| ~ spl2_115 ),
inference(resolution,[],[f1685,f303]) ).
fof(f1714,plain,
( spl2_120
| ~ spl2_26
| ~ spl2_66 ),
inference(avatar_split_clause,[],[f744,f623,f298,f1712]) ).
fof(f744,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X0,and(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(and(X0,X1)) )
| ~ spl2_26
| ~ spl2_66 ),
inference(resolution,[],[f624,f299]) ).
fof(f1710,plain,
( spl2_119
| ~ spl2_97
| ~ spl2_110 ),
inference(avatar_split_clause,[],[f1668,f1481,f1233,f1708]) ).
fof(f1668,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(strict_equiv(X7,not(X6)),necessarily(or(X7,X6))))
| ~ spl2_97
| ~ spl2_110 ),
inference(superposition,[],[f1482,f1234]) ).
fof(f1706,plain,
( spl2_118
| ~ spl2_96
| ~ spl2_111 ),
inference(avatar_split_clause,[],[f1554,f1499,f1122,f1704]) ).
fof(f1554,plain,
( ! [X41,X42] : implies(and(not(X41),X42),X41) = implies(X42,X41)
| ~ spl2_96
| ~ spl2_111 ),
inference(forward_demodulation,[],[f1525,f1123]) ).
fof(f1525,plain,
( ! [X41,X42] : implies(and(not(X41),X42),X41) = not(and(not(X41),X42))
| ~ spl2_96
| ~ spl2_111 ),
inference(superposition,[],[f1123,f1500]) ).
fof(f1702,plain,
( spl2_117
| ~ spl2_60
| ~ spl2_97 ),
inference(avatar_split_clause,[],[f1242,f1233,f558,f1700]) ).
fof(f1242,plain,
( ! [X8,X7] : is_a_theorem(strict_implies(strict_equiv(not(X7),X8),necessarily(or(X8,X7))))
| ~ spl2_60
| ~ spl2_97 ),
inference(superposition,[],[f559,f1234]) ).
fof(f1698,plain,
( spl2_116
| ~ spl2_23
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f521,f505,f286,f1696]) ).
fof(f521,plain,
( ! [X6,X7] : strict_implies(X6,necessarily(not(X7))) = necessarily(not(and(X6,possibly(X7))))
| ~ spl2_23
| ~ spl2_54 ),
inference(superposition,[],[f287,f506]) ).
fof(f1686,plain,
( spl2_115
| ~ spl2_25
| ~ spl2_33
| ~ spl2_34
| ~ spl2_60
| ~ spl2_70
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f1039,f1024,f681,f558,f344,f340,f294,f1684]) ).
fof(f1039,plain,
( ! [X1] : is_a_theorem(strict_implies(strict_equiv(X1,not(X1)),necessarily(not(not(X1)))))
| ~ spl2_25
| ~ spl2_33
| ~ spl2_34
| ~ spl2_60
| ~ spl2_70
| ~ spl2_83 ),
inference(forward_demodulation,[],[f1030,f728]) ).
fof(f728,plain,
( ! [X0,X1] : strict_equiv(not(X0),X1) = strict_equiv(X1,not(X0))
| ~ spl2_25
| ~ spl2_33
| ~ spl2_34
| ~ spl2_70 ),
inference(forward_demodulation,[],[f725,f388]) ).
fof(f725,plain,
( ! [X0,X1] : and(necessarily(or(X0,X1)),strict_implies(X1,not(X0))) = strict_equiv(X1,not(X0))
| ~ spl2_25
| ~ spl2_33
| ~ spl2_34
| ~ spl2_70 ),
inference(backward_demodulation,[],[f389,f720]) ).
fof(f720,plain,
( ! [X10,X11] : and(X10,X11) = and(X11,X10)
| ~ spl2_25
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f695,f295]) ).
fof(f695,plain,
( ! [X10,X11] :
( ~ is_a_theorem(strict_implies(and(X10,X11),and(X11,X10)))
| and(X10,X11) = and(X11,X10) )
| ~ spl2_25
| ~ spl2_70 ),
inference(resolution,[],[f682,f295]) ).
fof(f389,plain,
( ! [X0,X1] : strict_equiv(X1,not(X0)) = and(strict_implies(X1,not(X0)),necessarily(or(X0,X1)))
| ~ spl2_33
| ~ spl2_34 ),
inference(superposition,[],[f345,f341]) ).
fof(f1030,plain,
( ! [X1] : is_a_theorem(strict_implies(strict_equiv(not(X1),X1),necessarily(not(not(X1)))))
| ~ spl2_60
| ~ spl2_83 ),
inference(superposition,[],[f559,f1025]) ).
fof(f1642,plain,
( spl2_114
| ~ spl2_44
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f518,f505,f440,f1640]) ).
fof(f518,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,necessarily(not(X1))),not(and(X0,possibly(X1)))))
| ~ spl2_44
| ~ spl2_54 ),
inference(superposition,[],[f441,f506]) ).
fof(f1564,plain,
( spl2_113
| ~ spl2_76
| ~ spl2_111 ),
inference(avatar_split_clause,[],[f1503,f1499,f810,f1562]) ).
fof(f1503,plain,
( ! [X2,X1] : and(X2,X1) = and(X1,and(X2,X1))
| ~ spl2_76
| ~ spl2_111 ),
inference(superposition,[],[f1500,f811]) ).
fof(f1560,plain,
( spl2_112
| ~ spl2_20
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f499,f377,f273,f1558]) ).
fof(f499,plain,
( ! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0)))
| ~ spl2_20
| ~ spl2_38 ),
inference(superposition,[],[f378,f274]) ).
fof(f1501,plain,
( spl2_111
| ~ spl2_70
| ~ spl2_81
| ~ spl2_105 ),
inference(avatar_split_clause,[],[f1492,f1458,f911,f681,f1499]) ).
fof(f1458,plain,
( spl2_105
<=> ! [X6,X7] : is_a_theorem(strict_implies(and(X6,X7),and(X6,and(X6,X7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_105])]) ).
fof(f1492,plain,
( ! [X0,X1] : and(X0,X1) = and(X0,and(X0,X1))
| ~ spl2_70
| ~ spl2_81
| ~ spl2_105 ),
inference(subsumption_resolution,[],[f1484,f912]) ).
fof(f1484,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,and(X0,X1)),and(X0,X1)))
| and(X0,X1) = and(X0,and(X0,X1)) )
| ~ spl2_70
| ~ spl2_105 ),
inference(resolution,[],[f1459,f682]) ).
fof(f1459,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(and(X6,X7),and(X6,and(X6,X7))))
| ~ spl2_105 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f1483,plain,
( spl2_110
| ~ spl2_60
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f978,f822,f558,f1481]) ).
fof(f978,plain,
( ! [X26,X25] : is_a_theorem(strict_implies(strict_equiv(X26,not(X25)),necessarily(or(X25,X26))))
| ~ spl2_60
| ~ spl2_79 ),
inference(superposition,[],[f559,f823]) ).
fof(f1476,plain,
( spl2_109
| ~ spl2_62
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f977,f822,f582,f1474]) ).
fof(f1474,plain,
( spl2_109
<=> ! [X24,X23] :
( ~ is_a_theorem(strict_equiv(X24,not(X23)))
| is_a_theorem(necessarily(or(X23,X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_109])]) ).
fof(f582,plain,
( spl2_62
<=> ! [X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_equiv(not(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_62])]) ).
fof(f977,plain,
( ! [X24,X23] :
( ~ is_a_theorem(strict_equiv(X24,not(X23)))
| is_a_theorem(necessarily(or(X23,X24))) )
| ~ spl2_62
| ~ spl2_79 ),
inference(superposition,[],[f583,f823]) ).
fof(f583,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(not(X0),X1))
| is_a_theorem(necessarily(or(X0,X1))) )
| ~ spl2_62 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f1472,plain,
( spl2_108
| ~ spl2_38
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f873,f810,f377,f1470]) ).
fof(f873,plain,
( ! [X26,X25] : not(strict_implies(X25,X26)) = possibly(and(not(X26),X25))
| ~ spl2_38
| ~ spl2_76 ),
inference(superposition,[],[f378,f811]) ).
fof(f1468,plain,
( spl2_107
| ~ spl2_66
| ~ spl2_72 ),
inference(avatar_split_clause,[],[f761,f748,f623,f1466]) ).
fof(f1466,plain,
( spl2_107
<=> ! [X11,X10] :
( ~ is_a_theorem(and(X10,X11))
| is_a_theorem(and(X10,and(X10,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_107])]) ).
fof(f761,plain,
( ! [X10,X11] :
( ~ is_a_theorem(and(X10,X11))
| is_a_theorem(and(X10,and(X10,X11))) )
| ~ spl2_66
| ~ spl2_72 ),
inference(superposition,[],[f624,f749]) ).
fof(f1464,plain,
( spl2_106
| ~ spl2_22
| ~ spl2_63 ),
inference(avatar_split_clause,[],[f686,f594,f281,f1462]) ).
fof(f594,plain,
( spl2_63
<=> ! [X6,X7] :
( is_a_theorem(equiv(X6,X7))
| ~ is_a_theorem(implies(X7,X6))
| ~ is_a_theorem(implies(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).
fof(f686,plain,
( ! [X4,X5] :
( ~ is_a_theorem(implies(X4,X5))
| ~ is_a_theorem(implies(X5,X4))
| X4 = X5 )
| ~ spl2_22
| ~ spl2_63 ),
inference(resolution,[],[f595,f282]) ).
fof(f595,plain,
( ! [X6,X7] :
( is_a_theorem(equiv(X6,X7))
| ~ is_a_theorem(implies(X7,X6))
| ~ is_a_theorem(implies(X6,X7)) )
| ~ spl2_63 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f1460,plain,
( spl2_105
| ~ spl2_43
| ~ spl2_72 ),
inference(avatar_split_clause,[],[f759,f748,f436,f1458]) ).
fof(f759,plain,
( ! [X6,X7] : is_a_theorem(strict_implies(and(X6,X7),and(X6,and(X6,X7))))
| ~ spl2_43
| ~ spl2_72 ),
inference(superposition,[],[f437,f749]) ).
fof(f1390,plain,
( spl2_104
| ~ spl2_24
| ~ spl2_29
| ~ spl2_54
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f905,f810,f505,f315,f290,f1388]) ).
fof(f905,plain,
( ! [X0,X1] : or(X0,necessarily(not(X1))) = implies(possibly(X1),X0)
| ~ spl2_24
| ~ spl2_29
| ~ spl2_54
| ~ spl2_76 ),
inference(backward_demodulation,[],[f517,f874]) ).
fof(f517,plain,
( ! [X0,X1] : or(X0,necessarily(not(X1))) = not(and(not(X0),possibly(X1)))
| ~ spl2_24
| ~ spl2_54 ),
inference(superposition,[],[f506,f291]) ).
fof(f1386,plain,
( spl2_103
| ~ spl2_27
| ~ spl2_100 ),
inference(avatar_split_clause,[],[f1331,f1306,f302,f1384]) ).
fof(f1384,plain,
( spl2_103
<=> ! [X2,X3] :
( is_a_theorem(or(X2,X3))
| ~ is_a_theorem(equiv(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_103])]) ).
fof(f1331,plain,
( ! [X2,X3] :
( is_a_theorem(or(X2,X3))
| ~ is_a_theorem(equiv(not(X3),X2)) )
| ~ spl2_27
| ~ spl2_100 ),
inference(resolution,[],[f1307,f303]) ).
fof(f1382,plain,
( spl2_102
| ~ spl2_27
| ~ spl2_99 ),
inference(avatar_split_clause,[],[f1314,f1286,f302,f1380]) ).
fof(f1380,plain,
( spl2_102
<=> ! [X2,X3] :
( is_a_theorem(or(X2,X3))
| ~ is_a_theorem(equiv(X2,not(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_102])]) ).
fof(f1314,plain,
( ! [X2,X3] :
( is_a_theorem(or(X2,X3))
| ~ is_a_theorem(equiv(X2,not(X3))) )
| ~ spl2_27
| ~ spl2_99 ),
inference(resolution,[],[f1287,f303]) ).
fof(f1312,plain,
( spl2_101
| ~ spl2_27
| ~ spl2_98 ),
inference(avatar_split_clause,[],[f1277,f1273,f302,f1310]) ).
fof(f1277,plain,
( ! [X1] :
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(equiv(X1,not(X1))) )
| ~ spl2_27
| ~ spl2_98 ),
inference(resolution,[],[f1274,f303]) ).
fof(f1308,plain,
( spl2_100
| ~ spl2_56
| ~ spl2_97 ),
inference(avatar_split_clause,[],[f1243,f1233,f529,f1306]) ).
fof(f1243,plain,
( ! [X10,X9] : is_a_theorem(strict_implies(equiv(not(X9),X10),or(X10,X9)))
| ~ spl2_56
| ~ spl2_97 ),
inference(superposition,[],[f530,f1234]) ).
fof(f1288,plain,
( spl2_99
| ~ spl2_95
| ~ spl2_97 ),
inference(avatar_split_clause,[],[f1240,f1233,f1118,f1286]) ).
fof(f1240,plain,
( ! [X3,X4] : is_a_theorem(strict_implies(equiv(X4,not(X3)),or(X4,X3)))
| ~ spl2_95
| ~ spl2_97 ),
inference(superposition,[],[f1119,f1234]) ).
fof(f1275,plain,
( spl2_98
| ~ spl2_56
| ~ spl2_75
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f1040,f1024,f806,f529,f1273]) ).
fof(f1040,plain,
( ! [X2] : is_a_theorem(strict_implies(equiv(X2,not(X2)),not(not(X2))))
| ~ spl2_56
| ~ spl2_75
| ~ spl2_83 ),
inference(forward_demodulation,[],[f1031,f807]) ).
fof(f1031,plain,
( ! [X2] : is_a_theorem(strict_implies(equiv(not(X2),X2),not(not(X2))))
| ~ spl2_56
| ~ spl2_83 ),
inference(superposition,[],[f530,f1025]) ).
fof(f1235,plain,
( spl2_97
| ~ spl2_24
| ~ spl2_29
| ~ spl2_96 ),
inference(avatar_split_clause,[],[f1200,f1122,f315,f290,f1233]) ).
fof(f1200,plain,
( ! [X2,X3] : or(X2,X3) = or(X3,X2)
| ~ spl2_24
| ~ spl2_29
| ~ spl2_96 ),
inference(forward_demodulation,[],[f1199,f291]) ).
fof(f1199,plain,
( ! [X2,X3] : implies(not(X2),X3) = or(X3,X2)
| ~ spl2_24
| ~ spl2_29
| ~ spl2_96 ),
inference(forward_demodulation,[],[f1172,f291]) ).
fof(f1172,plain,
( ! [X2,X3] : implies(not(X2),X3) = implies(not(X3),X2)
| ~ spl2_29
| ~ spl2_96 ),
inference(superposition,[],[f1123,f316]) ).
fof(f1124,plain,
( spl2_96
| ~ spl2_29
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f874,f810,f315,f1122]) ).
fof(f1120,plain,
( spl2_95
| ~ spl2_56
| ~ spl2_75 ),
inference(avatar_split_clause,[],[f845,f806,f529,f1118]) ).
fof(f845,plain,
( ! [X18,X17] : is_a_theorem(strict_implies(equiv(X18,not(X17)),or(X17,X18)))
| ~ spl2_56
| ~ spl2_75 ),
inference(superposition,[],[f530,f807]) ).
fof(f1116,plain,
( spl2_94
| ~ spl2_25
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f724,f681,f436,f363,f294,f1114]) ).
fof(f724,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(implies(X4,X3),and(X5,implies(X3,X4))),and(X5,equiv(X3,X4))))
| ~ spl2_25
| ~ spl2_36
| ~ spl2_43
| ~ spl2_70 ),
inference(backward_demodulation,[],[f468,f720]) ).
fof(f468,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(and(X5,implies(X3,X4)),implies(X4,X3)),and(X5,equiv(X3,X4))))
| ~ spl2_36
| ~ spl2_43 ),
inference(superposition,[],[f437,f364]) ).
fof(f1112,plain,
( spl2_93
| ~ spl2_57
| ~ spl2_75 ),
inference(avatar_split_clause,[],[f844,f806,f540,f1110]) ).
fof(f1110,plain,
( spl2_93
<=> ! [X16,X15] :
( ~ is_a_theorem(equiv(X16,not(X15)))
| is_a_theorem(or(X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).
fof(f540,plain,
( spl2_57
<=> ! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
fof(f844,plain,
( ! [X16,X15] :
( ~ is_a_theorem(equiv(X16,not(X15)))
| is_a_theorem(or(X15,X16)) )
| ~ spl2_57
| ~ spl2_75 ),
inference(superposition,[],[f541,f807]) ).
fof(f541,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) )
| ~ spl2_57 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f1108,plain,
( spl2_92
| ~ spl2_25
| ~ spl2_33
| ~ spl2_34
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f728,f681,f344,f340,f294,f1106]) ).
fof(f1106,plain,
( spl2_92
<=> ! [X0,X1] : strict_equiv(not(X0),X1) = strict_equiv(X1,not(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).
fof(f1094,plain,
( spl2_91
| ~ spl2_25
| ~ spl2_34
| ~ spl2_43
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f723,f681,f436,f344,f294,f1092]) ).
fof(f723,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X1,X0),and(X2,strict_implies(X0,X1))),and(X2,strict_equiv(X0,X1))))
| ~ spl2_25
| ~ spl2_34
| ~ spl2_43
| ~ spl2_70 ),
inference(backward_demodulation,[],[f467,f720]) ).
fof(f467,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X2,strict_implies(X0,X1)),strict_implies(X1,X0)),and(X2,strict_equiv(X0,X1))))
| ~ spl2_34
| ~ spl2_43 ),
inference(superposition,[],[f437,f345]) ).
fof(f1090,plain,
( spl2_90
| ~ spl2_34
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f945,f915,f344,f1088]) ).
fof(f1088,plain,
( spl2_90
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
fof(f945,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) )
| ~ spl2_34
| ~ spl2_82 ),
inference(superposition,[],[f916,f345]) ).
fof(f1086,plain,
( spl2_89
| ~ spl2_34
| ~ spl2_81 ),
inference(avatar_split_clause,[],[f939,f911,f344,f1084]) ).
fof(f939,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X1,X0)))
| ~ spl2_34
| ~ spl2_81 ),
inference(superposition,[],[f912,f345]) ).
fof(f1076,plain,
( spl2_88
| ~ spl2_36
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f466,f436,f363,f1074]) ).
fof(f466,plain,
( ! [X3,X4,X5] : is_a_theorem(strict_implies(and(equiv(X3,X4),X5),and(implies(X3,X4),and(implies(X4,X3),X5))))
| ~ spl2_36
| ~ spl2_43 ),
inference(superposition,[],[f437,f364]) ).
fof(f1060,plain,
( spl2_87
| ~ spl2_52
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f972,f822,f489,f1058]) ).
fof(f972,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(strict_equiv(X13,X12),strict_implies(X12,X12)))
| ~ spl2_52
| ~ spl2_79 ),
inference(superposition,[],[f490,f823]) ).
fof(f1056,plain,
( spl2_86
| ~ spl2_51
| ~ spl2_75 ),
inference(avatar_split_clause,[],[f841,f806,f478,f1054]) ).
fof(f1054,plain,
( spl2_86
<=> ! [X9,X8] :
( ~ is_a_theorem(equiv(X9,X8))
| is_a_theorem(implies(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
fof(f478,plain,
( spl2_51
<=> ! [X4,X5] :
( ~ is_a_theorem(equiv(X4,X5))
| is_a_theorem(implies(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
fof(f841,plain,
( ! [X8,X9] :
( ~ is_a_theorem(equiv(X9,X8))
| is_a_theorem(implies(X8,X9)) )
| ~ spl2_51
| ~ spl2_75 ),
inference(superposition,[],[f479,f807]) ).
fof(f479,plain,
( ! [X4,X5] :
( ~ is_a_theorem(equiv(X4,X5))
| is_a_theorem(implies(X4,X5)) )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f1052,plain,
( spl2_85
| ~ spl2_34
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f465,f436,f344,f1050]) ).
fof(f465,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_equiv(X0,X1),X2),and(strict_implies(X0,X1),and(strict_implies(X1,X0),X2))))
| ~ spl2_34
| ~ spl2_43 ),
inference(superposition,[],[f437,f345]) ).
fof(f1048,plain,
( spl2_84
| ~ spl2_44
| ~ spl2_75 ),
inference(avatar_split_clause,[],[f838,f806,f440,f1046]) ).
fof(f838,plain,
( ! [X2,X3] : is_a_theorem(strict_implies(equiv(X3,X2),implies(X2,X3)))
| ~ spl2_44
| ~ spl2_75 ),
inference(superposition,[],[f441,f807]) ).
fof(f1026,plain,
( spl2_83
| ~ spl2_24
| ~ spl2_29
| ~ spl2_72 ),
inference(avatar_split_clause,[],[f774,f748,f315,f290,f1024]) ).
fof(f774,plain,
( ! [X15] : not(not(X15)) = or(X15,X15)
| ~ spl2_24
| ~ spl2_29
| ~ spl2_72 ),
inference(forward_demodulation,[],[f764,f291]) ).
fof(f764,plain,
( ! [X15] : implies(not(X15),X15) = not(not(X15))
| ~ spl2_29
| ~ spl2_72 ),
inference(superposition,[],[f316,f749]) ).
fof(f917,plain,
( spl2_82
| ~ spl2_30
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f867,f810,f319,f915]) ).
fof(f867,plain,
( ! [X10,X9] :
( ~ is_a_theorem(and(X10,X9))
| is_a_theorem(X9) )
| ~ spl2_30
| ~ spl2_76 ),
inference(superposition,[],[f320,f811]) ).
fof(f913,plain,
( spl2_81
| ~ spl2_19
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f863,f810,f269,f911]) ).
fof(f863,plain,
( ! [X2,X1] : is_a_theorem(strict_implies(and(X2,X1),X1))
| ~ spl2_19
| ~ spl2_76 ),
inference(superposition,[],[f270,f811]) ).
fof(f858,plain,
( spl2_80
| ~ spl2_24
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f413,f363,f290,f856]) ).
fof(f413,plain,
( ! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0)))
| ~ spl2_24
| ~ spl2_36 ),
inference(superposition,[],[f364,f291]) ).
fof(f824,plain,
( spl2_79
| ~ spl2_41
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f736,f681,f410,f822]) ).
fof(f736,plain,
( ! [X24,X25] : strict_equiv(X24,X25) = strict_equiv(X25,X24)
| ~ spl2_41
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f702,f411]) ).
fof(f702,plain,
( ! [X24,X25] :
( ~ is_a_theorem(strict_implies(strict_equiv(X24,X25),strict_equiv(X25,X24)))
| strict_equiv(X24,X25) = strict_equiv(X25,X24) )
| ~ spl2_41
| ~ spl2_70 ),
inference(resolution,[],[f682,f411]) ).
fof(f820,plain,
( spl2_78
| ~ spl2_39
| ~ spl2_40
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f731,f681,f406,f402,f818]) ).
fof(f402,plain,
( spl2_39
<=> ! [X1] : is_a_theorem(strict_implies(strict_implies(X1,X1),strict_equiv(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
fof(f731,plain,
( ! [X19] : strict_equiv(X19,X19) = strict_implies(X19,X19)
| ~ spl2_39
| ~ spl2_40
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f699,f407]) ).
fof(f699,plain,
( ! [X19] :
( ~ is_a_theorem(strict_implies(strict_equiv(X19,X19),strict_implies(X19,X19)))
| strict_equiv(X19,X19) = strict_implies(X19,X19) )
| ~ spl2_39
| ~ spl2_70 ),
inference(resolution,[],[f682,f403]) ).
fof(f403,plain,
( ! [X1] : is_a_theorem(strict_implies(strict_implies(X1,X1),strict_equiv(X1,X1)))
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f816,plain,
( spl2_77
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f325,f315,f814]) ).
fof(f325,plain,
( ! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3)))
| ~ spl2_29 ),
inference(superposition,[],[f316,f316]) ).
fof(f812,plain,
( spl2_76
| ~ spl2_25
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f720,f681,f294,f810]) ).
fof(f808,plain,
( spl2_75
| ~ spl2_45
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f719,f681,f444,f806]) ).
fof(f719,plain,
( ! [X4,X5] : equiv(X4,X5) = equiv(X5,X4)
| ~ spl2_45
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f692,f445]) ).
fof(f692,plain,
( ! [X4,X5] :
( ~ is_a_theorem(strict_implies(equiv(X4,X5),equiv(X5,X4)))
| equiv(X4,X5) = equiv(X5,X4) )
| ~ spl2_45
| ~ spl2_70 ),
inference(resolution,[],[f682,f445]) ).
fof(f804,plain,
( spl2_74
| ~ spl2_42
| ~ spl2_44
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f710,f681,f440,f432,f802]) ).
fof(f432,plain,
( spl2_42
<=> ! [X1] : is_a_theorem(strict_implies(implies(X1,X1),equiv(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
fof(f710,plain,
( ! [X1] : implies(X1,X1) = equiv(X1,X1)
| ~ spl2_42
| ~ spl2_44
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f690,f441]) ).
fof(f690,plain,
( ! [X1] :
( ~ is_a_theorem(strict_implies(equiv(X1,X1),implies(X1,X1)))
| implies(X1,X1) = equiv(X1,X1) )
| ~ spl2_42
| ~ spl2_70 ),
inference(resolution,[],[f682,f433]) ).
fof(f433,plain,
( ! [X1] : is_a_theorem(strict_implies(implies(X1,X1),equiv(X1,X1)))
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f782,plain,
( spl2_73
| ~ spl2_18
| ~ spl2_19
| ~ spl2_35
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f709,f681,f359,f269,f265,f780]) ).
fof(f265,plain,
( spl2_18
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f359,plain,
( spl2_35
<=> ! [X0] : is_a_theorem(necessarily(or(X0,and(not(X0),not(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f709,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,not(X0))))
| ~ spl2_18
| ~ spl2_19
| ~ spl2_35
| ~ spl2_70 ),
inference(backward_demodulation,[],[f360,f706]) ).
fof(f706,plain,
( ! [X0] : and(X0,X0) = X0
| ~ spl2_18
| ~ spl2_19
| ~ spl2_70 ),
inference(subsumption_resolution,[],[f689,f270]) ).
fof(f689,plain,
( ! [X0] :
( ~ is_a_theorem(strict_implies(and(X0,X0),X0))
| and(X0,X0) = X0 )
| ~ spl2_18
| ~ spl2_70 ),
inference(resolution,[],[f682,f266]) ).
fof(f266,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f360,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f750,plain,
( spl2_72
| ~ spl2_18
| ~ spl2_19
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f706,f681,f269,f265,f748]) ).
fof(f740,plain,
( spl2_71
| ~ spl2_18
| ~ spl2_19
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f708,f681,f269,f265,f738]) ).
fof(f708,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,X0))
| ~ spl2_18
| ~ spl2_19
| ~ spl2_70 ),
inference(backward_demodulation,[],[f266,f706]) ).
fof(f683,plain,
( spl2_70
| ~ spl2_21
| ~ spl2_61 ),
inference(avatar_split_clause,[],[f675,f568,f277,f681]) ).
fof(f277,plain,
( spl2_21
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f675,plain,
( ! [X6,X7] :
( ~ is_a_theorem(strict_implies(X6,X7))
| ~ is_a_theorem(strict_implies(X7,X6))
| X6 = X7 )
| ~ spl2_21
| ~ spl2_61 ),
inference(resolution,[],[f569,f278]) ).
fof(f278,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f646,plain,
( spl2_69
| ~ spl2_27
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f481,f450,f302,f644]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(and(strict_implies(X0,X2),strict_implies(X2,X1))) )
| ~ spl2_27
| ~ spl2_46 ),
inference(resolution,[],[f451,f303]) ).
fof(f633,plain,
( spl2_68
| ~ spl2_27
| ~ spl2_65 ),
inference(avatar_split_clause,[],[f612,f602,f302,f631]) ).
fof(f631,plain,
( spl2_68
<=> ! [X0,X1] :
( is_a_theorem(necessarily(or(X0,not(X0))))
| ~ is_a_theorem(strict_equiv(not(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
fof(f612,plain,
( ! [X0,X1] :
( is_a_theorem(necessarily(or(X0,not(X0))))
| ~ is_a_theorem(strict_equiv(not(X0),X1)) )
| ~ spl2_27
| ~ spl2_65 ),
inference(resolution,[],[f603,f303]) ).
fof(f629,plain,
( spl2_67
| ~ spl2_27
| ~ spl2_64 ),
inference(avatar_split_clause,[],[f605,f598,f302,f627]) ).
fof(f627,plain,
( spl2_67
<=> ! [X0] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_67])]) ).
fof(f598,plain,
( spl2_64
<=> ! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
fof(f605,plain,
( ! [X0] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,not(X0))) )
| ~ spl2_27
| ~ spl2_64 ),
inference(resolution,[],[f599,f303]) ).
fof(f599,plain,
( ! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0))))
| ~ spl2_64 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f625,plain,
( spl2_66
| ~ spl2_27
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f464,f436,f302,f623]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( is_a_theorem(and(X0,and(X1,X2)))
| ~ is_a_theorem(and(and(X0,X1),X2)) )
| ~ spl2_27
| ~ spl2_43 ),
inference(resolution,[],[f437,f303]) ).
fof(f604,plain,
( spl2_65
| ~ spl2_33
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f493,f489,f340,f602]) ).
fof(f493,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,not(X0)))))
| ~ spl2_33
| ~ spl2_52 ),
inference(superposition,[],[f490,f341]) ).
fof(f600,plain,
( spl2_64
| ~ spl2_24
| ~ spl2_42 ),
inference(avatar_split_clause,[],[f448,f432,f290,f598]) ).
fof(f448,plain,
( ! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0))))
| ~ spl2_24
| ~ spl2_42 ),
inference(superposition,[],[f433,f291]) ).
fof(f596,plain,
( spl2_63
| ~ spl2_26
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f419,f363,f298,f594]) ).
fof(f419,plain,
( ! [X6,X7] :
( is_a_theorem(equiv(X6,X7))
| ~ is_a_theorem(implies(X7,X6))
| ~ is_a_theorem(implies(X6,X7)) )
| ~ spl2_26
| ~ spl2_36 ),
inference(superposition,[],[f299,f364]) ).
fof(f584,plain,
( spl2_62
| ~ spl2_27
| ~ spl2_60 ),
inference(avatar_split_clause,[],[f571,f558,f302,f582]) ).
fof(f571,plain,
( ! [X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(strict_equiv(not(X0),X1)) )
| ~ spl2_27
| ~ spl2_60 ),
inference(resolution,[],[f559,f303]) ).
fof(f570,plain,
( spl2_61
| ~ spl2_26
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f394,f344,f298,f568]) ).
fof(f394,plain,
( ! [X6,X7] :
( is_a_theorem(strict_equiv(X6,X7))
| ~ is_a_theorem(strict_implies(X7,X6))
| ~ is_a_theorem(strict_implies(X6,X7)) )
| ~ spl2_26
| ~ spl2_34 ),
inference(superposition,[],[f299,f345]) ).
fof(f560,plain,
( spl2_60
| ~ spl2_33
| ~ spl2_40 ),
inference(avatar_split_clause,[],[f429,f406,f340,f558]) ).
fof(f429,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,X1))))
| ~ spl2_33
| ~ spl2_40 ),
inference(superposition,[],[f407,f341]) ).
fof(f556,plain,
( spl2_59
| ~ spl2_27
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f355,f340,f302,f554]) ).
fof(f554,plain,
( spl2_59
<=> ! [X2,X1] :
( ~ is_a_theorem(necessarily(or(X1,X2)))
| is_a_theorem(X2)
| ~ is_a_theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_59])]) ).
fof(f355,plain,
( ! [X2,X1] :
( ~ is_a_theorem(necessarily(or(X1,X2)))
| is_a_theorem(X2)
| ~ is_a_theorem(not(X1)) )
| ~ spl2_27
| ~ spl2_33 ),
inference(superposition,[],[f303,f341]) ).
fof(f546,plain,
( spl2_58
| ~ spl2_24
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f326,f315,f290,f544]) ).
fof(f326,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2)
| ~ spl2_24
| ~ spl2_29 ),
inference(superposition,[],[f291,f316]) ).
fof(f542,plain,
( spl2_57
| ~ spl2_27
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f532,f529,f302,f540]) ).
fof(f532,plain,
( ! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) )
| ~ spl2_27
| ~ spl2_56 ),
inference(resolution,[],[f530,f303]) ).
fof(f531,plain,
( spl2_56
| ~ spl2_24
| ~ spl2_44 ),
inference(avatar_split_clause,[],[f454,f440,f290,f529]) ).
fof(f454,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(equiv(not(X0),X1),or(X0,X1)))
| ~ spl2_24
| ~ spl2_44 ),
inference(superposition,[],[f441,f291]) ).
fof(f512,plain,
( spl2_55
| ~ spl2_27
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f492,f489,f302,f510]) ).
fof(f492,plain,
( ! [X0,X1] :
( is_a_theorem(strict_implies(X0,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ spl2_27
| ~ spl2_52 ),
inference(resolution,[],[f490,f303]) ).
fof(f507,plain,
( spl2_54
| ~ spl2_20
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f324,f315,f273,f505]) ).
fof(f324,plain,
( ! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0)))
| ~ spl2_20
| ~ spl2_29 ),
inference(superposition,[],[f316,f274]) ).
fof(f497,plain,
( spl2_53
| ~ spl2_31
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f423,f363,f330,f495]) ).
fof(f423,plain,
( ! [X2,X3] :
( is_a_theorem(equiv(X3,X2))
| ~ is_a_theorem(equiv(X2,X3)) )
| ~ spl2_31
| ~ spl2_36 ),
inference(forward_demodulation,[],[f417,f364]) ).
fof(f417,plain,
( ! [X2,X3] :
( ~ is_a_theorem(equiv(X2,X3))
| is_a_theorem(and(implies(X3,X2),implies(X2,X3))) )
| ~ spl2_31
| ~ spl2_36 ),
inference(superposition,[],[f331,f364]) ).
fof(f491,plain,
( spl2_52
| ~ spl2_34
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f484,f450,f344,f489]) ).
fof(f484,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0)))
| ~ spl2_34
| ~ spl2_46 ),
inference(superposition,[],[f451,f345]) ).
fof(f480,plain,
( spl2_51
| ~ spl2_30
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f418,f363,f319,f478]) ).
fof(f418,plain,
( ! [X4,X5] :
( ~ is_a_theorem(equiv(X4,X5))
| is_a_theorem(implies(X4,X5)) )
| ~ spl2_30
| ~ spl2_36 ),
inference(superposition,[],[f320,f364]) ).
fof(f476,plain,
( spl2_50
| ~ spl2_28
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f415,f363,f311,f474]) ).
fof(f474,plain,
( spl2_50
<=> ! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
fof(f311,plain,
( spl2_28
<=> ! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f415,plain,
( ! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) )
| ~ spl2_28
| ~ spl2_36 ),
inference(superposition,[],[f312,f364]) ).
fof(f312,plain,
( ! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f472,plain,
( spl2_49
| ~ spl2_31
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f398,f344,f330,f470]) ).
fof(f398,plain,
( ! [X2,X3] :
( is_a_theorem(strict_equiv(X3,X2))
| ~ is_a_theorem(strict_equiv(X2,X3)) )
| ~ spl2_31
| ~ spl2_34 ),
inference(forward_demodulation,[],[f392,f345]) ).
fof(f392,plain,
( ! [X2,X3] :
( ~ is_a_theorem(strict_equiv(X2,X3))
| is_a_theorem(and(strict_implies(X3,X2),strict_implies(X2,X3))) )
| ~ spl2_31
| ~ spl2_34 ),
inference(superposition,[],[f331,f345]) ).
fof(f463,plain,
( spl2_48
| ~ spl2_30
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f393,f344,f319,f461]) ).
fof(f461,plain,
( spl2_48
<=> ! [X4,X5] :
( ~ is_a_theorem(strict_equiv(X4,X5))
| is_a_theorem(strict_implies(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
fof(f393,plain,
( ! [X4,X5] :
( ~ is_a_theorem(strict_equiv(X4,X5))
| is_a_theorem(strict_implies(X4,X5)) )
| ~ spl2_30
| ~ spl2_34 ),
inference(superposition,[],[f320,f345]) ).
fof(f459,plain,
( spl2_47
| ~ spl2_28
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f390,f344,f311,f457]) ).
fof(f457,plain,
( spl2_47
<=> ! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
fof(f390,plain,
( ! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) )
| ~ spl2_28
| ~ spl2_34 ),
inference(superposition,[],[f312,f345]) ).
fof(f452,plain,
spl2_46,
inference(avatar_split_clause,[],[f178,f450]) ).
fof(f178,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))),
inference(subsumption_resolution,[],[f161,f132]) ).
fof(f132,plain,
axiom_m5,
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_axiom_m5) ).
fof(f161,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
( axiom_m5
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(unused_predicate_definition_removal,[],[f49]) ).
fof(f49,axiom,
( axiom_m5
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',axiom_m5) ).
fof(f446,plain,
( spl2_45
| ~ spl2_25
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f424,f363,f294,f444]) ).
fof(f424,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(equiv(X9,X8),equiv(X8,X9)))
| ~ spl2_25
| ~ spl2_36 ),
inference(forward_demodulation,[],[f420,f364]) ).
fof(f420,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(and(implies(X9,X8),implies(X8,X9)),equiv(X8,X9)))
| ~ spl2_25
| ~ spl2_36 ),
inference(superposition,[],[f295,f364]) ).
fof(f442,plain,
( spl2_44
| ~ spl2_19
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f422,f363,f269,f440]) ).
fof(f422,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(equiv(X12,X13),implies(X12,X13)))
| ~ spl2_19
| ~ spl2_36 ),
inference(superposition,[],[f270,f364]) ).
fof(f438,plain,
spl2_43,
inference(avatar_split_clause,[],[f177,f436]) ).
fof(f177,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))),
inference(subsumption_resolution,[],[f160,f134]) ).
fof(f134,plain,
axiom_m3,
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
axiom_m3,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_axiom_m3) ).
fof(f160,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
( axiom_m3
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f47,axiom,
( axiom_m3
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',axiom_m3) ).
fof(f434,plain,
( spl2_42
| ~ spl2_18
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f416,f363,f265,f432]) ).
fof(f416,plain,
( ! [X1] : is_a_theorem(strict_implies(implies(X1,X1),equiv(X1,X1)))
| ~ spl2_18
| ~ spl2_36 ),
inference(superposition,[],[f266,f364]) ).
fof(f412,plain,
( spl2_41
| ~ spl2_25
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f399,f344,f294,f410]) ).
fof(f399,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(strict_equiv(X9,X8),strict_equiv(X8,X9)))
| ~ spl2_25
| ~ spl2_34 ),
inference(forward_demodulation,[],[f395,f345]) ).
fof(f395,plain,
( ! [X8,X9] : is_a_theorem(strict_implies(and(strict_implies(X9,X8),strict_implies(X8,X9)),strict_equiv(X8,X9)))
| ~ spl2_25
| ~ spl2_34 ),
inference(superposition,[],[f295,f345]) ).
fof(f408,plain,
( spl2_40
| ~ spl2_19
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f397,f344,f269,f406]) ).
fof(f397,plain,
( ! [X12,X13] : is_a_theorem(strict_implies(strict_equiv(X12,X13),strict_implies(X12,X13)))
| ~ spl2_19
| ~ spl2_34 ),
inference(superposition,[],[f270,f345]) ).
fof(f404,plain,
( spl2_39
| ~ spl2_18
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f391,f344,f265,f402]) ).
fof(f391,plain,
( ! [X1] : is_a_theorem(strict_implies(strict_implies(X1,X1),strict_equiv(X1,X1)))
| ~ spl2_18
| ~ spl2_34 ),
inference(superposition,[],[f266,f345]) ).
fof(f379,plain,
( spl2_38
| ~ spl2_20
| ~ spl2_23
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f328,f315,f286,f273,f377]) ).
fof(f328,plain,
( ! [X3,X4] : possibly(and(X3,not(X4))) = not(strict_implies(X3,X4))
| ~ spl2_20
| ~ spl2_23
| ~ spl2_29 ),
inference(forward_demodulation,[],[f327,f287]) ).
fof(f327,plain,
( ! [X3,X4] : possibly(and(X3,not(X4))) = not(necessarily(implies(X3,X4)))
| ~ spl2_20
| ~ spl2_29 ),
inference(superposition,[],[f274,f316]) ).
fof(f375,plain,
( spl2_37
| ~ spl2_20
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f305,f290,f273,f373]) ).
fof(f305,plain,
( ! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1)
| ~ spl2_20
| ~ spl2_24 ),
inference(superposition,[],[f291,f274]) ).
fof(f365,plain,
spl2_36,
inference(avatar_split_clause,[],[f168,f363]) ).
fof(f168,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(subsumption_resolution,[],[f151,f142]) ).
fof(f142,plain,
op_equiv,
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
op_equiv,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',hilbert_op_equiv) ).
fof(f151,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_equiv) ).
fof(f361,plain,
( spl2_35
| ~ spl2_18
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f354,f340,f265,f359]) ).
fof(f354,plain,
( ! [X0] : is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))
| ~ spl2_18
| ~ spl2_33 ),
inference(superposition,[],[f266,f341]) ).
fof(f346,plain,
spl2_34,
inference(avatar_split_clause,[],[f165,f344]) ).
fof(f165,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(subsumption_resolution,[],[f149,f139]) ).
fof(f139,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_op_strict_equiv) ).
fof(f149,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_strict_equiv) ).
fof(f342,plain,
( spl2_33
| ~ spl2_23
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f306,f290,f286,f340]) ).
fof(f306,plain,
( ! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1))
| ~ spl2_23
| ~ spl2_24 ),
inference(superposition,[],[f287,f291]) ).
fof(f338,plain,
( spl2_32
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f284,f273,f336]) ).
fof(f284,plain,
( ! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0)))
| ~ spl2_20 ),
inference(superposition,[],[f274,f274]) ).
fof(f332,plain,
( spl2_31
| ~ spl2_25
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f309,f302,f294,f330]) ).
fof(f309,plain,
( ! [X3,X4] :
( is_a_theorem(and(X3,X4))
| ~ is_a_theorem(and(X4,X3)) )
| ~ spl2_25
| ~ spl2_27 ),
inference(resolution,[],[f303,f295]) ).
fof(f321,plain,
( spl2_30
| ~ spl2_19
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f308,f302,f269,f319]) ).
fof(f308,plain,
( ! [X2,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(and(X1,X2)) )
| ~ spl2_19
| ~ spl2_27 ),
inference(resolution,[],[f303,f270]) ).
fof(f317,plain,
spl2_29,
inference(avatar_split_clause,[],[f164,f315]) ).
fof(f164,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(subsumption_resolution,[],[f148,f138]) ).
fof(f138,plain,
op_implies_and,
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',hilbert_op_implies_and) ).
fof(f148,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_implies_and) ).
fof(f313,plain,
( spl2_28
| ~ spl2_18
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f307,f302,f265,f311]) ).
fof(f307,plain,
( ! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) )
| ~ spl2_18
| ~ spl2_27 ),
inference(resolution,[],[f303,f266]) ).
fof(f304,plain,
spl2_27,
inference(avatar_split_clause,[],[f176,f302]) ).
fof(f176,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f159,f130]) ).
fof(f130,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_modus_ponens_strict_implies) ).
fof(f159,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,plain,
( modus_ponens_strict_implies
=> ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f33,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',modus_ponens_strict_implies) ).
fof(f300,plain,
spl2_26,
inference(avatar_split_clause,[],[f175,f298]) ).
fof(f175,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f158,f137]) ).
fof(f137,plain,
adjunction,
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_adjunction) ).
fof(f158,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
( adjunction
=> ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',adjunction) ).
fof(f296,plain,
spl2_25,
inference(avatar_split_clause,[],[f172,f294]) ).
fof(f172,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(subsumption_resolution,[],[f155,f136]) ).
fof(f136,plain,
axiom_m1,
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_axiom_m1) ).
fof(f155,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
( axiom_m1
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f45,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',axiom_m1) ).
fof(f292,plain,
spl2_24,
inference(avatar_split_clause,[],[f167,f290]) ).
fof(f167,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f166,f164]) ).
fof(f166,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(subsumption_resolution,[],[f150,f143]) ).
fof(f143,plain,
op_or,
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
op_or,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',hilbert_op_or) ).
fof(f150,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_or) ).
fof(f288,plain,
spl2_23,
inference(avatar_split_clause,[],[f163,f286]) ).
fof(f163,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(subsumption_resolution,[],[f147,f141]) ).
fof(f141,plain,
op_strict_implies,
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_op_strict_implies) ).
fof(f147,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_strict_implies) ).
fof(f283,plain,
spl2_22,
inference(avatar_split_clause,[],[f174,f281]) ).
fof(f174,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(subsumption_resolution,[],[f157,f129]) ).
fof(f129,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',substitution_of_equivalents) ).
fof(f157,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',substitution_of_equivalents) ).
fof(f279,plain,
spl2_21,
inference(avatar_split_clause,[],[f173,f277]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(subsumption_resolution,[],[f156,f131]) ).
fof(f131,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_substitution_strict_equiv) ).
fof(f156,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
( substitution_strict_equiv
=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',substitution_strict_equiv) ).
fof(f275,plain,
spl2_20,
inference(avatar_split_clause,[],[f162,f273]) ).
fof(f162,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(subsumption_resolution,[],[f146,f140]) ).
fof(f140,plain,
op_possibly,
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
op_possibly,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_op_possibly) ).
fof(f146,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',op_possibly) ).
fof(f271,plain,
spl2_19,
inference(avatar_split_clause,[],[f171,f269]) ).
fof(f171,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(subsumption_resolution,[],[f154,f135]) ).
fof(f135,plain,
axiom_m2,
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_axiom_m2) ).
fof(f154,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
( axiom_m2
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f46,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',axiom_m2) ).
fof(f267,plain,
spl2_18,
inference(avatar_split_clause,[],[f170,f265]) ).
fof(f170,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(subsumption_resolution,[],[f153,f133]) ).
fof(f133,plain,
axiom_m4,
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',s1_0_axiom_m4) ).
fof(f153,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,plain,
( axiom_m4
=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f48]) ).
fof(f48,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',axiom_m4) ).
fof(f263,plain,
spl2_17,
inference(avatar_split_clause,[],[f143,f260]) ).
fof(f260,plain,
( spl2_17
<=> op_or ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f258,plain,
spl2_16,
inference(avatar_split_clause,[],[f142,f255]) ).
fof(f255,plain,
( spl2_16
<=> op_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f253,plain,
spl2_15,
inference(avatar_split_clause,[],[f141,f250]) ).
fof(f250,plain,
( spl2_15
<=> op_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f248,plain,
spl2_14,
inference(avatar_split_clause,[],[f140,f245]) ).
fof(f245,plain,
( spl2_14
<=> op_possibly ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f243,plain,
spl2_13,
inference(avatar_split_clause,[],[f139,f240]) ).
fof(f240,plain,
( spl2_13
<=> op_strict_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f238,plain,
spl2_12,
inference(avatar_split_clause,[],[f138,f235]) ).
fof(f235,plain,
( spl2_12
<=> op_implies_and ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f233,plain,
spl2_11,
inference(avatar_split_clause,[],[f137,f230]) ).
fof(f230,plain,
( spl2_11
<=> adjunction ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f228,plain,
spl2_10,
inference(avatar_split_clause,[],[f136,f225]) ).
fof(f225,plain,
( spl2_10
<=> axiom_m1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f223,plain,
spl2_9,
inference(avatar_split_clause,[],[f135,f220]) ).
fof(f220,plain,
( spl2_9
<=> axiom_m2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f218,plain,
spl2_8,
inference(avatar_split_clause,[],[f134,f215]) ).
fof(f215,plain,
( spl2_8
<=> axiom_m3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f213,plain,
spl2_7,
inference(avatar_split_clause,[],[f133,f210]) ).
fof(f210,plain,
( spl2_7
<=> axiom_m4 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f208,plain,
spl2_6,
inference(avatar_split_clause,[],[f132,f205]) ).
fof(f205,plain,
( spl2_6
<=> axiom_m5 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f203,plain,
spl2_5,
inference(avatar_split_clause,[],[f131,f200]) ).
fof(f200,plain,
( spl2_5
<=> substitution_strict_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f198,plain,
spl2_4,
inference(avatar_split_clause,[],[f130,f195]) ).
fof(f195,plain,
( spl2_4
<=> modus_ponens_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f193,plain,
spl2_3,
inference(avatar_split_clause,[],[f129,f190]) ).
fof(f190,plain,
( spl2_3
<=> substitution_of_equivalents ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f188,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f169,f185]) ).
fof(f169,plain,
~ is_a_theorem(implies(sK0,or(sK0,sK1))),
inference(subsumption_resolution,[],[f152,f128]) ).
fof(f128,plain,
~ or_1,
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
~ or_1,
inference(flattening,[],[f78]) ).
fof(f78,negated_conjecture,
~ or_1,
inference(negated_conjecture,[],[f77]) ).
fof(f77,conjecture,
or_1,
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',hilbert_or_1) ).
fof(f152,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f114,f126]) ).
fof(f126,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1)))
=> ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146',or_1) ).
fof(f183,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f128,f180]) ).
fof(f180,plain,
( spl2_1
<=> or_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n010.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 : Thu Aug 24 21:04:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.ZC74EU7L4d/Vampire---4.8_9146
% 0.15/0.37 % (9313)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (9318)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (9319)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.43 % (9317)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (9316)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.43 % (9314)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (9315)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (9320)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.43 % (9317)Refutation not found, incomplete strategy% (9317)------------------------------
% 0.22/0.43 % (9317)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (9317)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (9317)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (9317)Memory used [KB]: 5628
% 0.22/0.43 % (9317)Time elapsed: 0.004 s
% 0.22/0.43 % (9317)------------------------------
% 0.22/0.43 % (9317)------------------------------
% 0.22/0.49 % (9321)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_401 on Vampire---4 for (401ds/0Mi)
% 34.30/5.30 % (9315)First to succeed.
% 34.84/5.35 % (9315)Refutation found. Thanks to Tanya!
% 34.84/5.35 % SZS status Theorem for Vampire---4
% 34.84/5.35 % SZS output start Proof for Vampire---4
% See solution above
% 34.84/5.38 % (9315)------------------------------
% 34.84/5.38 % (9315)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 34.84/5.38 % (9315)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 34.84/5.38 % (9315)Termination reason: Refutation
% 34.84/5.38
% 34.84/5.38 % (9315)Memory used [KB]: 145328
% 34.84/5.38 % (9315)Time elapsed: 4.902 s
% 34.84/5.38 % (9315)------------------------------
% 34.84/5.38 % (9315)------------------------------
% 34.84/5.38 % (9313)Success in time 4.956 s
% 34.84/5.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------