TSTP Solution File: LCL242-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL242-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:25:44 EDT 2024
% Result : Unsatisfiable 5.30s 1.17s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 299
% Syntax : Number of formulae : 979 ( 23 unt; 0 def)
% Number of atoms : 3092 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 3935 (1822 ~;1824 |; 0 &)
% ( 289 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 293 ( 291 usr; 290 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 1802 (1802 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7658,plain,
$false,
inference(avatar_sat_refutation,[],[f21,f26,f30,f34,f40,f44,f49,f53,f58,f63,f69,f74,f78,f83,f88,f95,f105,f116,f120,f128,f138,f142,f146,f154,f162,f166,f174,f184,f188,f192,f196,f221,f225,f234,f239,f243,f253,f262,f267,f275,f279,f290,f294,f301,f313,f317,f324,f328,f332,f336,f372,f376,f380,f430,f455,f459,f463,f486,f490,f494,f498,f535,f539,f543,f547,f551,f601,f636,f669,f673,f677,f717,f721,f726,f756,f763,f773,f777,f803,f807,f811,f815,f866,f870,f874,f878,f882,f942,f946,f950,f954,f959,f966,f970,f974,f978,f1023,f1071,f1075,f1079,f1083,f1087,f1099,f1100,f1101,f1102,f1103,f1104,f1105,f1354,f1702,f1765,f1769,f1863,f1867,f1871,f1875,f1879,f1883,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f2109,f2113,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2164,f2168,f2172,f2176,f2180,f2331,f2601,f2605,f2609,f2613,f2617,f2621,f2625,f2629,f2634,f2638,f2642,f2646,f2650,f2654,f2658,f2662,f2666,f2670,f2674,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2799,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3302,f3306,f3310,f3316,f3320,f3324,f3630,f3811,f3815,f3819,f3823,f3829,f3833,f3837,f3841,f3845,f3849,f3853,f3857,f3861,f3865,f3874,f3878,f3882,f4331,f4335,f4341,f4345,f4349,f4353,f4357,f4361,f4365,f4369,f4373,f4377,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f5067,f5071,f5075,f5079,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5128,f5132,f5136,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5173,f5177,f5181,f5185,f5189,f5193,f5197,f5201,f5205,f5209,f5213,f5228,f5232,f5236,f5451,f6269,f6578,f6582,f6586,f6590,f6594,f6598,f6602,f6606,f6610,f6614,f6619,f6623,f6627,f6631,f6635,f6639,f6643,f6647,f6651,f6655,f6659,f6671,f6675,f6679,f6683,f6687,f6691,f6896,f7657]) ).
fof(f7657,plain,
( ~ spl0_41
| spl0_289 ),
inference(avatar_contradiction_clause,[],[f7654]) ).
fof(f7654,plain,
( $false
| ~ spl0_41
| spl0_289 ),
inference(resolution,[],[f6895,f278]) ).
fof(f278,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f277,plain,
( spl0_41
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f6895,plain,
( ~ theorem(or(not(not(q)),not(q)))
| spl0_289 ),
inference(avatar_component_clause,[],[f6893]) ).
fof(f6893,plain,
( spl0_289
<=> theorem(or(not(not(q)),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f6896,plain,
( ~ spl0_289
| ~ spl0_147
| spl0_272 ),
inference(avatar_split_clause,[],[f6660,f6616,f2623,f6893]) ).
fof(f2623,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f6616,plain,
( spl0_272
<=> theorem(or(not(p),or(not(q),not(or(not(p),not(q)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f6660,plain,
( ~ theorem(or(not(not(q)),not(q)))
| ~ spl0_147
| spl0_272 ),
inference(resolution,[],[f6618,f2624]) ).
fof(f2624,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f2623]) ).
fof(f6618,plain,
( ~ theorem(or(not(p),or(not(q),not(or(not(p),not(q))))))
| spl0_272 ),
inference(avatar_component_clause,[],[f6616]) ).
fof(f6691,plain,
( spl0_288
| ~ spl0_16
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f750,f719,f93,f6689]) ).
fof(f6689,plain,
( spl0_288
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(or(X2,X3))
| theorem(or(or(not(or(not(X3),X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f93,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f719,plain,
( spl0_74
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(not(X3),X0)),X1)))
| ~ theorem(or(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f750,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(or(X2,X3))
| theorem(or(or(not(or(not(X3),X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_74 ),
inference(resolution,[],[f720,f94]) ).
fof(f94,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f720,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X2,or(not(or(not(X3),X0)),X1)))
| ~ theorem(or(not(X0),X1))
| ~ theorem(or(X2,X3)) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f6687,plain,
( spl0_287
| ~ spl0_55
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f744,f719,f428,f6685]) ).
fof(f6685,plain,
( spl0_287
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(or(X2,X3))
| theorem(or(X2,or(X1,not(or(not(X3),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f428,plain,
( spl0_55
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f744,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(or(X2,X3))
| theorem(or(X2,or(X1,not(or(not(X3),X0))))) )
| ~ spl0_55
| ~ spl0_74 ),
inference(resolution,[],[f720,f429]) ).
fof(f429,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f6683,plain,
( spl0_286
| ~ spl0_16
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f737,f715,f93,f6681]) ).
fof(f6681,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(or(not(X1),X2),or(not(X1),X2))),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f715,plain,
( spl0_73
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f737,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(or(not(X1),X2),or(not(X1),X2))),X2),X0)) )
| ~ spl0_16
| ~ spl0_73 ),
inference(resolution,[],[f716,f94]) ).
fof(f716,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f6679,plain,
( spl0_285
| ~ spl0_17
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f733,f715,f103,f6677]) ).
fof(f6677,plain,
( spl0_285
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(or(not(X1),X2),or(not(X1),X2))),or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f103,plain,
( spl0_17
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f733,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(or(not(X1),X2),or(not(X1),X2))),or(X0,X2))) )
| ~ spl0_17
| ~ spl0_73 ),
inference(resolution,[],[f716,f104]) ).
fof(f104,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f6675,plain,
( spl0_284
| ~ spl0_55
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f732,f715,f428,f6673]) ).
fof(f6673,plain,
( spl0_284
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(or(not(X1),X2),or(not(X1),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(or(not(X1),X2),or(not(X1),X2)))))) )
| ~ spl0_55
| ~ spl0_73 ),
inference(resolution,[],[f716,f429]) ).
fof(f6671,plain,
( spl0_283
| ~ spl0_6
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f705,f675,f42,f6669]) ).
fof(f6669,plain,
( spl0_283
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| theorem(or(not(or(not(X2),X3)),or(X1,X3)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f42,plain,
( spl0_6
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f675,plain,
( spl0_72
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f705,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| theorem(or(not(or(not(X2),X3)),or(X1,X3)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_72 ),
inference(resolution,[],[f676,f43]) ).
fof(f43,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f676,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f6659,plain,
( spl0_282
| ~ spl0_6
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f693,f671,f42,f6657]) ).
fof(f6657,plain,
( spl0_282
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(X2,or(not(X1),X3))),or(X2,X3)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f671,plain,
( spl0_71
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f693,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(X2,or(not(X1),X3))),or(X2,X3)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_71 ),
inference(resolution,[],[f672,f43]) ).
fof(f672,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f6655,plain,
( spl0_281
| ~ spl0_6
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f681,f667,f42,f6653]) ).
fof(f6653,plain,
( spl0_281
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),or(not(X1),X2)))
| theorem(or(not(or(X3,X1)),or(X3,X2)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f667,plain,
( spl0_70
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(X0,or(not(X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f681,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),or(not(X1),X2)))
| theorem(or(not(or(X3,X1)),or(X3,X2)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_70 ),
inference(resolution,[],[f668,f43]) ).
fof(f668,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(X0,or(not(X2),X3))) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f6651,plain,
( spl0_280
| ~ spl0_50
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f665,f634,f330,f6649]) ).
fof(f6649,plain,
( spl0_280
<=> ! [X4,X0,X3,X2,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(not(X4),X3))
| ~ theorem(or(or(X2,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f330,plain,
( spl0_50
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f634,plain,
( spl0_69
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X1,X3)))
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f665,plain,
( ! [X2,X3,X0,X1,X4] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(not(X4),X3))
| ~ theorem(or(or(X2,X4),X1)) )
| ~ spl0_50
| ~ spl0_69 ),
inference(resolution,[],[f635,f331]) ).
fof(f331,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f635,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X3)))
| theorem(or(X0,or(X1,X2)))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f6647,plain,
( spl0_279
| ~ spl0_32
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f655,f634,f219,f6645]) ).
fof(f6645,plain,
( spl0_279
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X0,X1)),X2)))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(not(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f219,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f655,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X0,X1)),X2)))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(not(X1),X3)) )
| ~ spl0_32
| ~ spl0_69 ),
inference(resolution,[],[f635,f220]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f6643,plain,
( spl0_278
| ~ spl0_60
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f652,f634,f488,f6641]) ).
fof(f6641,plain,
( spl0_278
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f488,plain,
( spl0_60
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f652,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(or(X0,X2)) )
| ~ spl0_60
| ~ spl0_69 ),
inference(resolution,[],[f635,f489]) ).
fof(f489,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f6639,plain,
( spl0_277
| ~ spl0_62
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f647,f634,f496,f6637]) ).
fof(f6637,plain,
( spl0_277
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f496,plain,
( spl0_62
<=> ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f647,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(or(X2,X0)) )
| ~ spl0_62
| ~ spl0_69 ),
inference(resolution,[],[f635,f497]) ).
fof(f497,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f6635,plain,
( spl0_276
| ~ spl0_48
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f645,f634,f322,f6633]) ).
fof(f6633,plain,
( spl0_276
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X0,X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f322,plain,
( spl0_48
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f645,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X0,X3)))
| ~ theorem(or(not(X1),X3))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_69 ),
inference(resolution,[],[f635,f323]) ).
fof(f323,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f6631,plain,
( spl0_275
| ~ spl0_59
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f642,f634,f484,f6629]) ).
fof(f6629,plain,
( spl0_275
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X3)))
| ~ theorem(or(not(X2),X3))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f484,plain,
( spl0_59
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f642,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X3)))
| ~ theorem(or(not(X2),X3))
| ~ theorem(X1) )
| ~ spl0_59
| ~ spl0_69 ),
inference(resolution,[],[f635,f485]) ).
fof(f485,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f6627,plain,
( spl0_274
| ~ spl0_19
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f641,f634,f118,f6625]) ).
fof(f6625,plain,
( spl0_274
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(not(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f118,plain,
( spl0_19
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f641,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(not(X1),X3)) )
| ~ spl0_19
| ~ spl0_69 ),
inference(resolution,[],[f635,f119]) ).
fof(f119,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f6623,plain,
( spl0_273
| ~ spl0_30
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f619,f599,f190,f6621]) ).
fof(f6621,plain,
( spl0_273
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X0,or(X1,X2)),or(X0,or(X1,X2)))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f190,plain,
( spl0_30
<=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f599,plain,
( spl0_68
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f619,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X0,or(X1,X2)),or(X0,or(X1,X2)))),X2))))
| ~ spl0_30
| ~ spl0_68 ),
inference(resolution,[],[f600,f191]) ).
fof(f191,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f600,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X2,or(X1,X3))))
| theorem(or(X0,or(X1,or(X2,X3)))) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f6619,plain,
( ~ spl0_272
| spl0_2
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f6518,f5230,f23,f6616]) ).
fof(f23,plain,
( spl0_2
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(p),or(not(q),r)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f5230,plain,
( spl0_258
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(not(or(not(X2),X3)),or(X0,or(X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f6518,plain,
( ~ theorem(or(not(p),or(not(q),not(or(not(p),not(q))))))
| spl0_2
| ~ spl0_258 ),
inference(resolution,[],[f5231,f25]) ).
fof(f25,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(p),or(not(q),r))))
| spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f5231,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(not(X2),X3)),or(X0,or(X1,X3))))
| ~ theorem(or(X0,or(X1,X2))) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f5230]) ).
fof(f6614,plain,
( spl0_271
| ~ spl0_10
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f609,f599,f61,f6612]) ).
fof(f6612,plain,
( spl0_271
<=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,or(X1,X2)),or(X0,or(X1,X2)))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f61,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f609,plain,
( ! [X2,X0,X1] : theorem(or(not(or(or(X0,or(X1,X2)),or(X0,or(X1,X2)))),or(X1,or(X0,X2))))
| ~ spl0_10
| ~ spl0_68 ),
inference(resolution,[],[f600,f62]) ).
fof(f62,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f6610,plain,
( spl0_270
| ~ spl0_17
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f594,f545,f103,f6608]) ).
fof(f6608,plain,
( spl0_270
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| ~ theorem(X3)
| theorem(or(X1,or(not(or(not(X3),X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f545,plain,
( spl0_66
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f594,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| ~ theorem(X3)
| theorem(or(X1,or(not(or(not(X3),X0)),X2))) )
| ~ spl0_17
| ~ spl0_66 ),
inference(resolution,[],[f546,f104]) ).
fof(f546,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(or(not(X0),X1))
| ~ theorem(X2) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f6606,plain,
( spl0_269
| ~ spl0_55
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f593,f545,f428,f6604]) ).
fof(f6604,plain,
( spl0_269
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| ~ theorem(X3)
| theorem(or(not(or(not(X3),X0)),or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f593,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),or(X1,X2)))
| ~ theorem(X3)
| theorem(or(not(or(not(X3),X0)),or(X2,X1))) )
| ~ spl0_55
| ~ spl0_66 ),
inference(resolution,[],[f546,f429]) ).
fof(f6602,plain,
( spl0_268
| ~ spl0_62
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f570,f541,f496,f6600]) ).
fof(f6600,plain,
( spl0_268
<=> ! [X4,X0,X3,X2,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(X3,or(X4,X2))))
| ~ theorem(or(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f541,plain,
( spl0_65
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f570,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(X3,or(X4,X2))))
| ~ theorem(or(X4,X1)) )
| ~ spl0_62
| ~ spl0_65 ),
inference(resolution,[],[f542,f497]) ).
fof(f542,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X3),X2))
| ~ theorem(or(X0,X3))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f6598,plain,
( spl0_267
| ~ spl0_59
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f567,f541,f484,f6596]) ).
fof(f6596,plain,
( spl0_267
<=> ! [X4,X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,or(not(X2),X3))))
| theorem(or(X0,or(X4,or(X1,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f567,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ theorem(or(X0,or(X1,or(not(X2),X3))))
| theorem(or(X0,or(X4,or(X1,X3))))
| ~ theorem(X2) )
| ~ spl0_59
| ~ spl0_65 ),
inference(resolution,[],[f542,f485]) ).
fof(f6594,plain,
( spl0_266
| ~ spl0_19
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f566,f541,f118,f6592]) ).
fof(f6592,plain,
( spl0_266
<=> ! [X4,X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X1,X4))))
| ~ theorem(or(not(X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f566,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X1,X4))))
| ~ theorem(or(not(X2),X4)) )
| ~ spl0_19
| ~ spl0_65 ),
inference(resolution,[],[f542,f119]) ).
fof(f6590,plain,
( spl0_265
| ~ spl0_51
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f559,f537,f334,f6588]) ).
fof(f6588,plain,
( spl0_265
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(or(not(X0),or(X1,X1)),or(not(X0),or(X1,X1)))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f334,plain,
( spl0_51
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f537,plain,
( spl0_64
<=> ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f559,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(or(not(X0),or(X1,X1)),or(not(X0),or(X1,X1)))),X1)) )
| ~ spl0_51
| ~ spl0_64 ),
inference(resolution,[],[f538,f335]) ).
fof(f335,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f538,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f6586,plain,
( spl0_264
| ~ spl0_31
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f508,f488,f194,f6584]) ).
fof(f6584,plain,
( spl0_264
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X3,not(X1))),X3)))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f194,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f508,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X3,not(X1))),X3)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31
| ~ spl0_60 ),
inference(resolution,[],[f489,f195]) ).
fof(f195,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f6582,plain,
( spl0_263
| ~ spl0_17
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f474,f457,f103,f6580]) ).
fof(f6580,plain,
( spl0_263
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(or(or(X0,X1),X2),or(or(X0,X1),X2))),X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f457,plain,
( spl0_57
<=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f474,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(or(or(X0,X1),X2),or(or(X0,X1),X2))),X2),X1)))
| ~ spl0_17
| ~ spl0_57 ),
inference(resolution,[],[f458,f104]) ).
fof(f458,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f6578,plain,
( spl0_262
| ~ spl0_55
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f473,f457,f428,f6576]) ).
fof(f6576,plain,
( spl0_262
<=> ! [X2,X0,X1] : theorem(or(or(not(or(or(or(X0,X1),X2),or(or(X0,X1),X2))),X2),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f473,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(or(or(X0,X1),X2),or(or(X0,X1),X2))),X2),or(X1,X0)))
| ~ spl0_55
| ~ spl0_57 ),
inference(resolution,[],[f458,f429]) ).
fof(f6269,plain,
( ~ spl0_261
| ~ spl0_20
| spl0_260 ),
inference(avatar_split_clause,[],[f5955,f5448,f126,f6266]) ).
fof(f6266,plain,
( spl0_261
<=> theorem(not(not(not(or(not(p),not(q)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f126,plain,
( spl0_20
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f5448,plain,
( spl0_260
<=> theorem(or(not(not(not(or(not(p),not(q))))),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f5955,plain,
( ~ theorem(not(not(not(or(not(p),not(q))))))
| ~ spl0_20
| spl0_260 ),
inference(resolution,[],[f5450,f127]) ).
fof(f127,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f5450,plain,
( ~ theorem(or(not(not(not(or(not(p),not(q))))),not(q)))
| spl0_260 ),
inference(avatar_component_clause,[],[f5448]) ).
fof(f5451,plain,
( ~ spl0_260
| ~ spl0_165
| spl0_235 ),
inference(avatar_split_clause,[],[f5216,f5125,f2697,f5448]) ).
fof(f2697,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f5125,plain,
( spl0_235
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(r,not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f5216,plain,
( ~ theorem(or(not(not(not(or(not(p),not(q))))),not(q)))
| ~ spl0_165
| spl0_235 ),
inference(resolution,[],[f5127,f2698]) ).
fof(f2698,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f5127,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(r,not(q))))
| spl0_235 ),
inference(avatar_component_clause,[],[f5125]) ).
fof(f5236,plain,
( spl0_259
| ~ spl0_16
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f712,f675,f93,f5234]) ).
fof(f5234,plain,
( spl0_259
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(or(not(or(not(X2),X3)),or(X1,X3)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f712,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(or(not(or(not(X2),X3)),or(X1,X3)),X0)) )
| ~ spl0_16
| ~ spl0_72 ),
inference(resolution,[],[f676,f94]) ).
fof(f5232,plain,
( spl0_258
| ~ spl0_17
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f709,f675,f103,f5230]) ).
fof(f709,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(not(or(not(X2),X3)),or(X0,or(X1,X3)))) )
| ~ spl0_17
| ~ spl0_72 ),
inference(resolution,[],[f676,f104]) ).
fof(f5228,plain,
( spl0_257
| ~ spl0_55
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f708,f675,f428,f5226]) ).
fof(f5226,plain,
( spl0_257
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(or(X1,X3),not(or(not(X2),X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f708,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(or(X1,X3),not(or(not(X2),X3))))) )
| ~ spl0_55
| ~ spl0_72 ),
inference(resolution,[],[f676,f429]) ).
fof(f5213,plain,
( spl0_256
| ~ spl0_68
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f706,f675,f599,f5211]) ).
fof(f5211,plain,
( spl0_256
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X1,or(not(or(not(X2),X3)),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f706,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X1,or(not(or(not(X2),X3)),X3)))) )
| ~ spl0_68
| ~ spl0_72 ),
inference(resolution,[],[f676,f600]) ).
fof(f5209,plain,
( spl0_255
| ~ spl0_16
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f700,f671,f93,f5207]) ).
fof(f5207,plain,
( spl0_255
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,or(not(X1),X3))),or(X2,X3)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f700,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,or(not(X1),X3))),or(X2,X3)),X0)) )
| ~ spl0_16
| ~ spl0_71 ),
inference(resolution,[],[f672,f94]) ).
fof(f5205,plain,
( spl0_254
| ~ spl0_17
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f697,f671,f103,f5203]) ).
fof(f5203,plain,
( spl0_254
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,or(not(X1),X3))),or(X0,or(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f697,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,or(not(X1),X3))),or(X0,or(X2,X3)))) )
| ~ spl0_17
| ~ spl0_71 ),
inference(resolution,[],[f672,f104]) ).
fof(f5201,plain,
( spl0_253
| ~ spl0_55
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f696,f671,f428,f5199]) ).
fof(f5199,plain,
( spl0_253
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(or(X2,X3),not(or(X2,or(not(X1),X3)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f696,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(or(X2,X3),not(or(X2,or(not(X1),X3)))))) )
| ~ spl0_55
| ~ spl0_71 ),
inference(resolution,[],[f672,f429]) ).
fof(f5197,plain,
( spl0_252
| ~ spl0_68
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f694,f671,f599,f5195]) ).
fof(f5195,plain,
( spl0_252
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(not(or(X2,or(not(X1),X3))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f694,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(not(or(X2,or(not(X1),X3))),X3)))) )
| ~ spl0_68
| ~ spl0_71 ),
inference(resolution,[],[f672,f600]) ).
fof(f5193,plain,
( spl0_251
| ~ spl0_16
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f688,f667,f93,f5191]) ).
fof(f5191,plain,
( spl0_251
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(or(not(or(X3,X1)),or(X3,X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f688,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(or(not(or(X3,X1)),or(X3,X2)),X0)) )
| ~ spl0_16
| ~ spl0_70 ),
inference(resolution,[],[f668,f94]) ).
fof(f5189,plain,
( spl0_250
| ~ spl0_17
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f685,f667,f103,f5187]) ).
fof(f5187,plain,
( spl0_250
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(not(or(X3,X1)),or(X0,or(X3,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f685,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(not(or(X3,X1)),or(X0,or(X3,X2)))) )
| ~ spl0_17
| ~ spl0_70 ),
inference(resolution,[],[f668,f104]) ).
fof(f5185,plain,
( spl0_249
| ~ spl0_55
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f684,f667,f428,f5183]) ).
fof(f5183,plain,
( spl0_249
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(or(X3,X2),not(or(X3,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f684,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(or(X3,X2),not(or(X3,X1))))) )
| ~ spl0_55
| ~ spl0_70 ),
inference(resolution,[],[f668,f429]) ).
fof(f5181,plain,
( spl0_248
| ~ spl0_68
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f682,f667,f599,f5179]) ).
fof(f5179,plain,
( spl0_248
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(X3,or(not(or(X3,X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f682,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,or(X3,or(not(or(X3,X1)),X2)))) )
| ~ spl0_68
| ~ spl0_70 ),
inference(resolution,[],[f668,f600]) ).
fof(f5177,plain,
( spl0_247
| ~ spl0_47
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f663,f634,f315,f5175]) ).
fof(f5175,plain,
( spl0_247
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X1,X3)))
| ~ theorem(or(not(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f315,plain,
( spl0_47
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f663,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X1,X3)))
| ~ theorem(or(not(X2),X3)) )
| ~ spl0_47
| ~ spl0_69 ),
inference(resolution,[],[f635,f316]) ).
fof(f316,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f5173,plain,
( ~ spl0_246
| spl0_2
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f3228,f2693,f23,f5170]) ).
fof(f5170,plain,
( spl0_246
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(p),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2693,plain,
( spl0_164
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f3228,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(p),r)))
| spl0_2
| ~ spl0_164 ),
inference(resolution,[],[f2694,f25]) ).
fof(f2694,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f5168,plain,
( spl0_245
| ~ spl0_29
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f654,f634,f186,f5166]) ).
fof(f5166,plain,
( spl0_245
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,or(X0,X2))),X3)))
| ~ theorem(or(not(or(X1,X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f186,plain,
( spl0_29
<=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f654,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(X0,X2))),X3)))
| ~ theorem(or(not(or(X1,X2)),X3)) )
| ~ spl0_29
| ~ spl0_69 ),
inference(resolution,[],[f635,f187]) ).
fof(f187,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f5164,plain,
( spl0_244
| ~ spl0_30
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f653,f634,f190,f5162]) ).
fof(f5162,plain,
( spl0_244
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_30
| ~ spl0_69 ),
inference(resolution,[],[f635,f191]) ).
fof(f5160,plain,
( spl0_243
| ~ spl0_10
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f644,f634,f61,f5158]) ).
fof(f5158,plain,
( spl0_243
<=> ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_10
| ~ spl0_69 ),
inference(resolution,[],[f635,f62]) ).
fof(f5156,plain,
( spl0_242
| ~ spl0_12
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f640,f634,f72,f5154]) ).
fof(f5154,plain,
( spl0_242
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,or(X1,X2))),or(X1,X3)))
| ~ theorem(or(not(or(X0,X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f72,plain,
( spl0_12
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f640,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(X1,X2))),or(X1,X3)))
| ~ theorem(or(not(or(X0,X2)),X3)) )
| ~ spl0_12
| ~ spl0_69 ),
inference(resolution,[],[f635,f73]) ).
fof(f73,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f5152,plain,
( spl0_241
| ~ spl0_50
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f630,f599,f330,f5150]) ).
fof(f5150,plain,
( spl0_241
<=> ! [X4,X0,X3,X2,X1] :
( theorem(or(or(X0,X1),or(X2,or(X3,X4))))
| ~ theorem(or(or(X3,or(X2,X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f630,plain,
( ! [X2,X3,X0,X1,X4] :
( theorem(or(or(X0,X1),or(X2,or(X3,X4))))
| ~ theorem(or(or(X3,or(X2,X4)),X1)) )
| ~ spl0_50
| ~ spl0_68 ),
inference(resolution,[],[f600,f331]) ).
fof(f5148,plain,
( spl0_240
| ~ spl0_32
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f620,f599,f219,f5146]) ).
fof(f5146,plain,
( spl0_240
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(not(or(X0,X2)),X3))))
| ~ theorem(or(not(X2),or(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f620,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(not(or(X0,X2)),X3))))
| ~ theorem(or(not(X2),or(X1,X3))) )
| ~ spl0_32
| ~ spl0_68 ),
inference(resolution,[],[f600,f220]) ).
fof(f5144,plain,
( spl0_239
| ~ spl0_60
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f618,f599,f488,f5142]) ).
fof(f5142,plain,
( spl0_239
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(not(or(or(X1,X2),not(X3))),X2))))
| ~ theorem(or(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f618,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(not(or(or(X1,X2),not(X3))),X2))))
| ~ theorem(or(X0,X3)) )
| ~ spl0_60
| ~ spl0_68 ),
inference(resolution,[],[f600,f489]) ).
fof(f5140,plain,
( spl0_238
| ~ spl0_62
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f612,f599,f496,f5138]) ).
fof(f5138,plain,
( spl0_238
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(not(X0),or(X1,X2))),or(X1,or(X3,X2))))
| ~ theorem(or(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f612,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(not(X0),or(X1,X2))),or(X1,or(X3,X2))))
| ~ theorem(or(X3,X0)) )
| ~ spl0_62
| ~ spl0_68 ),
inference(resolution,[],[f600,f497]) ).
fof(f5136,plain,
( spl0_237
| ~ spl0_48
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f610,f599,f322,f5134]) ).
fof(f5134,plain,
( spl0_237
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(or(X0,or(X1,X2)),not(X3))),or(X1,or(X0,X2))))
| ~ theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f610,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(or(X0,or(X1,X2)),not(X3))),or(X1,or(X0,X2))))
| ~ theorem(X3) )
| ~ spl0_48
| ~ spl0_68 ),
inference(resolution,[],[f600,f323]) ).
fof(f5132,plain,
( spl0_236
| ~ spl0_59
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f607,f599,f484,f5130]) ).
fof(f5130,plain,
( spl0_236
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,or(not(X1),or(X2,X3)))),or(X2,or(X0,X3))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f607,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),or(X2,X3)))),or(X2,or(X0,X3))))
| ~ theorem(X1) )
| ~ spl0_59
| ~ spl0_68 ),
inference(resolution,[],[f600,f485]) ).
fof(f5128,plain,
( ~ spl0_235
| spl0_2
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f3127,f2685,f23,f5125]) ).
fof(f2685,plain,
( spl0_162
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f3127,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(r,not(q))))
| spl0_2
| ~ spl0_162 ),
inference(resolution,[],[f2686,f25]) ).
fof(f2686,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X3,or(X2,X1))))
| ~ theorem(or(X0,or(X1,X2))) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f5123,plain,
( spl0_234
| ~ spl0_19
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f606,f599,f118,f5121]) ).
fof(f5121,plain,
( spl0_234
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,X1)),or(X2,or(X0,X3))))
| ~ theorem(or(not(X1),or(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f606,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,or(X0,X3))))
| ~ theorem(or(not(X1),or(X2,X3))) )
| ~ spl0_19
| ~ spl0_68 ),
inference(resolution,[],[f600,f119]) ).
fof(f5119,plain,
( spl0_233
| ~ spl0_54
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f596,f549,f378,f5117]) ).
fof(f5117,plain,
( spl0_233
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),X3))
| ~ theorem(not(not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f378,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f549,plain,
( spl0_67
<=> ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f596,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),X3))
| ~ theorem(not(not(or(X2,X0)))) )
| ~ spl0_54
| ~ spl0_67 ),
inference(resolution,[],[f550,f379]) ).
fof(f379,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,X1))
| ~ theorem(not(X2)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f550,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f5115,plain,
( spl0_232
| ~ spl0_54
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f591,f545,f378,f5113]) ).
fof(f5113,plain,
( spl0_232
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(not(or(not(X2),X0)),X3))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f591,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(not(or(not(X2),X0)),X3))
| ~ theorem(not(X1)) )
| ~ spl0_54
| ~ spl0_66 ),
inference(resolution,[],[f546,f379]) ).
fof(f5111,plain,
( spl0_231
| ~ spl0_31
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f588,f545,f194,f5109]) ).
fof(f5109,plain,
( spl0_231
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X3,X1))
| ~ theorem(or(X3,or(not(X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f588,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X3,X1))
| ~ theorem(or(X3,or(not(X2),X0))) )
| ~ spl0_31
| ~ spl0_66 ),
inference(resolution,[],[f546,f195]) ).
fof(f5107,plain,
( spl0_230
| ~ spl0_12
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f565,f541,f72,f5105]) ).
fof(f5105,plain,
( spl0_230
<=> ! [X4,X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,or(X2,X3))))
| theorem(or(X0,or(X4,or(X2,or(X1,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f565,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ theorem(or(X0,or(X1,or(X2,X3))))
| theorem(or(X0,or(X4,or(X2,or(X1,X3))))) )
| ~ spl0_12
| ~ spl0_65 ),
inference(resolution,[],[f542,f73]) ).
fof(f5103,plain,
( spl0_229
| ~ spl0_54
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f555,f537,f378,f5101]) ).
fof(f5101,plain,
( spl0_229
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X2))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f555,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X2))
| ~ theorem(not(X1)) )
| ~ spl0_54
| ~ spl0_64 ),
inference(resolution,[],[f538,f379]) ).
fof(f5099,plain,
( spl0_228
| ~ spl0_31
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f553,f537,f194,f5097]) ).
fof(f5097,plain,
( spl0_228
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(or(not(X0),X2),or(not(X0),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f553,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(or(not(X0),X2),or(not(X0),X2)))) )
| ~ spl0_31
| ~ spl0_64 ),
inference(resolution,[],[f538,f195]) ).
fof(f5095,plain,
( spl0_227
| ~ spl0_17
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f520,f492,f103,f5093]) ).
fof(f5093,plain,
( spl0_227
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(or(not(or(or(X2,X3),X0)),X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f492,plain,
( spl0_61
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f520,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(or(not(or(or(X2,X3),X0)),X1),X3))) )
| ~ spl0_17
| ~ spl0_61 ),
inference(resolution,[],[f493,f104]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X2,X0)),X1),X2))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f5091,plain,
( spl0_226
| ~ spl0_55
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f519,f492,f428,f5089]) ).
fof(f5089,plain,
( spl0_226
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(or(X2,X3),X0)),X1),or(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f519,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(or(X2,X3),X0)),X1),or(X3,X2))) )
| ~ spl0_55
| ~ spl0_61 ),
inference(resolution,[],[f493,f429]) ).
fof(f5087,plain,
( spl0_225
| ~ spl0_15
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f512,f488,f86,f5085]) ).
fof(f5085,plain,
( spl0_225
<=> ! [X0,X1] :
( ~ theorem(or(or(not(or(X0,not(X1))),X0),X1))
| theorem(or(not(or(X0,not(X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f86,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ theorem(or(or(not(or(X0,not(X1))),X0),X1))
| theorem(or(not(or(X0,not(X1))),X0)) )
| ~ spl0_15
| ~ spl0_60 ),
inference(resolution,[],[f489,f87]) ).
fof(f87,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f5079,plain,
( spl0_224
| ~ spl0_31
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f477,f461,f194,f5077]) ).
fof(f5077,plain,
( spl0_224
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,not(or(not(X1),not(X1)))))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f461,plain,
( spl0_58
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,not(or(not(X1),not(X1)))))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31
| ~ spl0_58 ),
inference(resolution,[],[f462,f195]) ).
fof(f462,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f5075,plain,
( spl0_223
| ~ spl0_34
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f423,f378,f232,f5073]) ).
fof(f5073,plain,
( spl0_223
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(not(or(X0,X1)),or(X0,X2)),X3))
| ~ theorem(not(not(or(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f232,plain,
( spl0_34
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f423,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(not(or(X0,X1)),or(X0,X2)),X3))
| ~ theorem(not(not(or(not(X1),X2)))) )
| ~ spl0_34
| ~ spl0_54 ),
inference(resolution,[],[f379,f233]) ).
fof(f233,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f5071,plain,
( spl0_222
| ~ spl0_14
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f408,f378,f81,f5069]) ).
fof(f5069,plain,
( spl0_222
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(not(X0),X1)),X2))
| ~ theorem(not(or(not(or(X3,X0)),or(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f81,plain,
( spl0_14
<=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f408,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(not(X0),X1)),X2))
| ~ theorem(not(or(not(or(X3,X0)),or(X3,X1)))) )
| ~ spl0_14
| ~ spl0_54 ),
inference(resolution,[],[f379,f82]) ).
fof(f82,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f5067,plain,
( spl0_221
| ~ spl0_36
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f407,f378,f241,f5065]) ).
fof(f5065,plain,
( spl0_221
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(not(or(not(X1),X3)),or(X0,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f241,plain,
( spl0_36
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(not(or(not(X1),X3)),or(X0,X3)))) )
| ~ spl0_36
| ~ spl0_54 ),
inference(resolution,[],[f379,f242]) ).
fof(f242,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f4410,plain,
( spl0_220
| ~ spl0_47
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f628,f599,f315,f4408]) ).
fof(f4408,plain,
( spl0_220
<=> ! [X0,X3,X2,X1] : theorem(or(or(not(or(X0,or(X1,or(X2,X3)))),X0),or(X2,or(X1,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f628,plain,
( ! [X2,X3,X0,X1] : theorem(or(or(not(or(X0,or(X1,or(X2,X3)))),X0),or(X2,or(X1,X3))))
| ~ spl0_47
| ~ spl0_68 ),
inference(resolution,[],[f600,f316]) ).
fof(f4406,plain,
( spl0_219
| ~ spl0_51
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f595,f545,f334,f4404]) ).
fof(f4404,plain,
( spl0_219
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),or(X1,X1)))
| ~ theorem(X2)
| theorem(or(not(or(not(X2),X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f595,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),or(X1,X1)))
| ~ theorem(X2)
| theorem(or(not(or(not(X2),X0)),X1)) )
| ~ spl0_51
| ~ spl0_66 ),
inference(resolution,[],[f546,f335]) ).
fof(f4402,plain,
( spl0_218
| ~ spl0_15
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f590,f545,f86,f4400]) ).
fof(f4400,plain,
( spl0_218
<=> ! [X0,X1] :
( ~ theorem(or(not(X0),not(or(not(X1),X0))))
| ~ theorem(X1)
| theorem(not(or(not(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f590,plain,
( ! [X0,X1] :
( ~ theorem(or(not(X0),not(or(not(X1),X0))))
| ~ theorem(X1)
| theorem(not(or(not(X1),X0))) )
| ~ spl0_15
| ~ spl0_66 ),
inference(resolution,[],[f546,f87]) ).
fof(f4398,plain,
( spl0_217
| ~ spl0_27
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f583,f541,f172,f4396]) ).
fof(f4396,plain,
( spl0_217
<=> ! [X2,X4,X0,X3,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X4))))
| ~ theorem(or(not(X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f172,plain,
( spl0_27
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f583,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X4))))
| ~ theorem(or(not(X1),X4)) )
| ~ spl0_27
| ~ spl0_65 ),
inference(resolution,[],[f542,f173]) ).
fof(f173,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f4394,plain,
( spl0_216
| ~ spl0_54
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f529,f496,f378,f4392]) ).
fof(f4392,plain,
( spl0_216
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),X3))
| ~ theorem(not(or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),X3))
| ~ theorem(not(or(X0,X2))) )
| ~ spl0_54
| ~ spl0_62 ),
inference(resolution,[],[f497,f379]) ).
fof(f4390,plain,
( spl0_215
| ~ spl0_31
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f524,f496,f194,f4388]) ).
fof(f4388,plain,
( spl0_215
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X2,or(X0,X3)))
| ~ theorem(or(X2,or(not(X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f524,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X2,or(X0,X3)))
| ~ theorem(or(X2,or(not(X1),X3))) )
| ~ spl0_31
| ~ spl0_62 ),
inference(resolution,[],[f497,f195]) ).
fof(f4386,plain,
( spl0_214
| ~ spl0_54
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f517,f492,f378,f4384]) ).
fof(f4384,plain,
( spl0_214
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X3))
| ~ theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f517,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X3))
| ~ theorem(not(X2)) )
| ~ spl0_54
| ~ spl0_61 ),
inference(resolution,[],[f493,f379]) ).
fof(f4382,plain,
( ~ spl0_213
| ~ spl0_20
| spl0_197 ),
inference(avatar_split_clause,[],[f4336,f3867,f126,f4379]) ).
fof(f4379,plain,
( spl0_213
<=> theorem(not(not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f3867,plain,
( spl0_197
<=> theorem(or(not(not(q)),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f4336,plain,
( ~ theorem(not(not(q)))
| ~ spl0_20
| spl0_197 ),
inference(resolution,[],[f3869,f127]) ).
fof(f3869,plain,
( ~ theorem(or(not(not(q)),r))
| spl0_197 ),
inference(avatar_component_clause,[],[f3867]) ).
fof(f4377,plain,
( spl0_212
| ~ spl0_54
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f513,f488,f378,f4375]) ).
fof(f4375,plain,
( spl0_212
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,X2))
| ~ theorem(not(or(not(or(X3,not(X1))),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f513,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,X2))
| ~ theorem(not(or(not(or(X3,not(X1))),X3))) )
| ~ spl0_54
| ~ spl0_60 ),
inference(resolution,[],[f489,f379]) ).
fof(f4373,plain,
( spl0_211
| ~ spl0_53
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f507,f488,f374,f4371]) ).
fof(f4371,plain,
( spl0_211
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X3,not(X1))),X3)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f374,plain,
( spl0_53
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f507,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X3,not(X1))),X3)))
| ~ theorem(X0) )
| ~ spl0_53
| ~ spl0_60 ),
inference(resolution,[],[f489,f375]) ).
fof(f375,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f4369,plain,
( spl0_210
| ~ spl0_54
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f505,f484,f378,f4367]) ).
fof(f4367,plain,
( spl0_210
<=> ! [X0,X3,X2,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),X3))
| ~ theorem(not(or(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f505,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),X3))
| ~ theorem(not(or(X1,X2))) )
| ~ spl0_54
| ~ spl0_59 ),
inference(resolution,[],[f485,f379]) ).
fof(f4365,plain,
( spl0_209
| ~ spl0_31
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f500,f484,f194,f4363]) ).
fof(f4363,plain,
( spl0_209
<=> ! [X0,X3,X2,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,or(X2,or(not(X0),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f500,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,or(X2,or(not(X0),X3)))) )
| ~ spl0_31
| ~ spl0_59 ),
inference(resolution,[],[f485,f195]) ).
fof(f4361,plain,
( spl0_208
| ~ spl0_51
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f475,f457,f334,f4359]) ).
fof(f4359,plain,
( spl0_208
<=> ! [X0,X1] : theorem(or(or(not(or(or(or(X0,X0),X1),or(or(X0,X0),X1))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f475,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(or(X0,X0),X1),or(or(X0,X0),X1))),X1),X0))
| ~ spl0_51
| ~ spl0_57 ),
inference(resolution,[],[f458,f335]) ).
fof(f4357,plain,
( spl0_207
| ~ spl0_17
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f468,f453,f103,f4355]) ).
fof(f4355,plain,
( spl0_207
<=> ! [X0,X3,X2,X1] : theorem(or(X0,or(or(not(or(X1,or(or(X0,X2),X3))),or(X1,X3)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f453,plain,
( spl0_56
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f468,plain,
( ! [X2,X3,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(or(X0,X2),X3))),or(X1,X3)),X2)))
| ~ spl0_17
| ~ spl0_56 ),
inference(resolution,[],[f454,f104]) ).
fof(f454,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f4353,plain,
( spl0_206
| ~ spl0_55
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f467,f453,f428,f4351]) ).
fof(f4351,plain,
( spl0_206
<=> ! [X0,X3,X2,X1] : theorem(or(or(not(or(X0,or(or(X1,X2),X3))),or(X0,X3)),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1] : theorem(or(or(not(or(X0,or(or(X1,X2),X3))),or(X0,X3)),or(X2,X1)))
| ~ spl0_55
| ~ spl0_56 ),
inference(resolution,[],[f454,f429]) ).
fof(f4349,plain,
( spl0_205
| ~ spl0_33
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f421,f378,f223,f4347]) ).
fof(f4347,plain,
( spl0_205
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X0,X3))))
| ~ theorem(or(not(X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f223,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f421,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X0,X3))))
| ~ theorem(or(not(X3),X1)) )
| ~ spl0_33
| ~ spl0_54 ),
inference(resolution,[],[f379,f224]) ).
fof(f224,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),not(or(X2,X0))))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f4345,plain,
( spl0_204
| ~ spl0_32
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f416,f378,f219,f4343]) ).
fof(f4343,plain,
( spl0_204
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X0,X2)),X3)))
| ~ theorem(or(not(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f416,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X0,X2)),X3)))
| ~ theorem(or(not(X2),X3)) )
| ~ spl0_32
| ~ spl0_54 ),
inference(resolution,[],[f379,f220]) ).
fof(f4341,plain,
( spl0_203
| ~ spl0_19
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f406,f378,f118,f4339]) ).
fof(f4339,plain,
( spl0_203
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X0,X3)))
| ~ theorem(or(not(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X0,X3)))
| ~ theorem(or(not(X1),X3)) )
| ~ spl0_19
| ~ spl0_54 ),
inference(resolution,[],[f379,f119]) ).
fof(f4335,plain,
( spl0_202
| ~ spl0_32
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f397,f374,f219,f4333]) ).
fof(f4333,plain,
( spl0_202
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),X3)))
| ~ theorem(X1)
| ~ theorem(or(not(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),X3)))
| ~ theorem(X1)
| ~ theorem(or(not(X2),X3)) )
| ~ spl0_32
| ~ spl0_53 ),
inference(resolution,[],[f375,f220]) ).
fof(f4331,plain,
( spl0_201
| ~ spl0_30
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f395,f374,f190,f4329]) ).
fof(f4329,plain,
( spl0_201
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(X1) )
| ~ spl0_30
| ~ spl0_53 ),
inference(resolution,[],[f375,f191]) ).
fof(f3882,plain,
( spl0_200
| ~ spl0_53
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f587,f545,f374,f3880]) ).
fof(f3880,plain,
( spl0_200
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X3,X1))
| ~ theorem(or(not(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f587,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X3,X1))
| ~ theorem(or(not(X2),X0)) )
| ~ spl0_53
| ~ spl0_66 ),
inference(resolution,[],[f546,f375]) ).
fof(f3878,plain,
( spl0_199
| ~ spl0_26
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f577,f541,f164,f3876]) ).
fof(f3876,plain,
( spl0_199
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(not(or(X3,not(X1))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f164,plain,
( spl0_26
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f577,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(not(or(X3,not(X1))),X3)))) )
| ~ spl0_26
| ~ spl0_65 ),
inference(resolution,[],[f542,f165]) ).
fof(f165,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f3874,plain,
( ~ spl0_197
| ~ spl0_198
| spl0_124
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f3769,f3314,f2115,f3871,f3867]) ).
fof(f3871,plain,
( spl0_198
<=> theorem(p) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2115,plain,
( spl0_124
<=> theorem(or(r,not(or(not(p),not(q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f3314,plain,
( spl0_179
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X1,not(or(not(X2),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f3769,plain,
( ~ theorem(p)
| ~ theorem(or(not(not(q)),r))
| spl0_124
| ~ spl0_179 ),
inference(resolution,[],[f3315,f2117]) ).
fof(f2117,plain,
( ~ theorem(or(r,not(or(not(p),not(q)))))
| spl0_124 ),
inference(avatar_component_clause,[],[f2115]) ).
fof(f3315,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,not(or(not(X2),X0))))
| ~ theorem(X2)
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f3314]) ).
fof(f3865,plain,
( spl0_196
| ~ spl0_53
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f552,f537,f374,f3863]) ).
fof(f3863,plain,
( spl0_196
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(or(not(X0),X2),or(not(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f552,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(or(not(X0),X2),or(not(X0),X2))) )
| ~ spl0_53
| ~ spl0_64 ),
inference(resolution,[],[f538,f375]) ).
fof(f3861,plain,
( spl0_195
| ~ spl0_51
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f521,f492,f334,f3859]) ).
fof(f3859,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(or(X2,X2),X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f521,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(or(X2,X2),X0)),X1),X2)) )
| ~ spl0_51
| ~ spl0_61 ),
inference(resolution,[],[f493,f335]) ).
fof(f3857,plain,
( spl0_194
| ~ spl0_54
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f480,f461,f378,f3855]) ).
fof(f3855,plain,
( spl0_194
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,X2))
| ~ theorem(not(not(or(not(X1),not(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,X2))
| ~ theorem(not(not(or(not(X1),not(X1))))) )
| ~ spl0_54
| ~ spl0_58 ),
inference(resolution,[],[f462,f379]) ).
fof(f3853,plain,
( spl0_193
| ~ spl0_15
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f479,f461,f86,f3851]) ).
fof(f3851,plain,
( spl0_193
<=> ! [X0] :
( ~ theorem(or(not(or(not(X0),not(X0))),X0))
| theorem(not(or(not(X0),not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f479,plain,
( ! [X0] :
( ~ theorem(or(not(or(not(X0),not(X0))),X0))
| theorem(not(or(not(X0),not(X0)))) )
| ~ spl0_15
| ~ spl0_58 ),
inference(resolution,[],[f462,f87]) ).
fof(f3849,plain,
( spl0_192
| ~ spl0_53
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f476,f461,f374,f3847]) ).
fof(f3847,plain,
( spl0_192
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,not(or(not(X1),not(X1)))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,not(or(not(X1),not(X1)))))
| ~ theorem(X0) )
| ~ spl0_53
| ~ spl0_58 ),
inference(resolution,[],[f462,f375]) ).
fof(f3845,plain,
( spl0_191
| ~ spl0_54
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f471,f457,f378,f3843]) ).
fof(f3843,plain,
( spl0_191
<=> ! [X2,X0,X1] :
( theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X2))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X2))
| ~ theorem(not(X0)) )
| ~ spl0_54
| ~ spl0_57 ),
inference(resolution,[],[f458,f379]) ).
fof(f3841,plain,
( spl0_190
| ~ spl0_54
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f465,f453,f378,f3839]) ).
fof(f3839,plain,
( spl0_190
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X3))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f465,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X3))
| ~ theorem(not(X1)) )
| ~ spl0_54
| ~ spl0_56 ),
inference(resolution,[],[f454,f379]) ).
fof(f3837,plain,
( spl0_189
| ~ spl0_28
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f422,f378,f182,f3835]) ).
fof(f3835,plain,
( spl0_189
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,or(X1,X2)),X3))
| ~ theorem(not(not(or(X1,or(X0,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f182,plain,
( spl0_28
<=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f422,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,or(X1,X2)),X3))
| ~ theorem(not(not(or(X1,or(X0,X2))))) )
| ~ spl0_28
| ~ spl0_54 ),
inference(resolution,[],[f379,f183]) ).
fof(f183,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f3833,plain,
( spl0_188
| ~ spl0_29
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f415,f378,f186,f3831]) ).
fof(f3831,plain,
( spl0_188
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,or(X0,X3))),or(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f415,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,or(X0,X3))),or(X2,X3)))) )
| ~ spl0_29
| ~ spl0_54 ),
inference(resolution,[],[f379,f187]) ).
fof(f3829,plain,
( spl0_187
| ~ spl0_30
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f414,f378,f190,f3827]) ).
fof(f3827,plain,
( spl0_187
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(or(X0,X2),or(X0,X2))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(or(X0,X2),or(X0,X2))),X2))) )
| ~ spl0_30
| ~ spl0_54 ),
inference(resolution,[],[f379,f191]) ).
fof(f3823,plain,
( spl0_186
| ~ spl0_12
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f405,f378,f72,f3821]) ).
fof(f3821,plain,
( spl0_186
<=> ! [X0,X3,X2,X1] :
( theorem(or(not(or(X0,or(X1,X2))),X3))
| ~ theorem(not(or(X1,or(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f405,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(X1,X2))),X3))
| ~ theorem(not(or(X1,or(X0,X2)))) )
| ~ spl0_12
| ~ spl0_54 ),
inference(resolution,[],[f379,f73]) ).
fof(f3819,plain,
( spl0_185
| ~ spl0_29
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f396,f374,f186,f3817]) ).
fof(f3817,plain,
( spl0_185
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f396,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(X2) )
| ~ spl0_29
| ~ spl0_53 ),
inference(resolution,[],[f375,f187]) ).
fof(f3815,plain,
( spl0_184
| ~ spl0_14
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f389,f374,f81,f3813]) ).
fof(f3813,plain,
( spl0_184
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(not(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f389,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(not(X2),X3)) )
| ~ spl0_14
| ~ spl0_53 ),
inference(resolution,[],[f375,f82]) ).
fof(f3811,plain,
( spl0_183
| ~ spl0_36
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f388,f374,f241,f3809]) ).
fof(f3809,plain,
( spl0_183
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f388,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X3,X1)) )
| ~ spl0_36
| ~ spl0_53 ),
inference(resolution,[],[f375,f242]) ).
fof(f3630,plain,
( ~ spl0_182
| ~ spl0_97
| spl0_167 ),
inference(avatar_split_clause,[],[f3009,f2796,f972,f3627]) ).
fof(f3627,plain,
( spl0_182
<=> theorem(or(not(q),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f972,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f2796,plain,
( spl0_167
<=> theorem(or(not(q),or(not(p),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f3009,plain,
( ~ theorem(or(not(q),not(p)))
| ~ spl0_97
| spl0_167 ),
inference(resolution,[],[f2798,f973]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f2798,plain,
( ~ theorem(or(not(q),or(not(p),r)))
| spl0_167 ),
inference(avatar_component_clause,[],[f2796]) ).
fof(f3324,plain,
( spl0_181
| ~ spl0_14
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f611,f599,f81,f3322]) ).
fof(f3322,plain,
( spl0_181
<=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(X2,or(not(or(X2,X0)),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f611,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(X2,or(not(or(X2,X0)),X1))))
| ~ spl0_14
| ~ spl0_68 ),
inference(resolution,[],[f600,f82]) ).
fof(f3320,plain,
( spl0_180
| ~ spl0_36
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f608,f599,f241,f3318]) ).
fof(f3318,plain,
( spl0_180
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(not(or(not(X1),X2)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f608,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(not(or(not(X1),X2)),X2))))
| ~ spl0_36
| ~ spl0_68 ),
inference(resolution,[],[f600,f242]) ).
fof(f3316,plain,
( spl0_179
| ~ spl0_16
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f592,f545,f93,f3314]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(or(X1,not(or(not(X2),X0)))) )
| ~ spl0_16
| ~ spl0_66 ),
inference(resolution,[],[f546,f94]) ).
fof(f3310,plain,
( spl0_178
| ~ spl0_22
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f574,f541,f140,f3308]) ).
fof(f3308,plain,
( spl0_178
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(not(X1),not(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f140,plain,
( spl0_22
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f574,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(not(X1),not(X1)))))) )
| ~ spl0_22
| ~ spl0_65 ),
inference(resolution,[],[f542,f141]) ).
fof(f141,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f3306,plain,
( spl0_177
| ~ spl0_48
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f563,f541,f322,f3304]) ).
fof(f3304,plain,
( spl0_177
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,not(X2))))
| theorem(or(X0,or(X3,X1)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f563,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,not(X2))))
| theorem(or(X0,or(X3,X1)))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_65 ),
inference(resolution,[],[f542,f323]) ).
fof(f3302,plain,
( spl0_176
| ~ spl0_16
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f556,f537,f93,f3300]) ).
fof(f3300,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(or(not(X0),X1),or(not(X0),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f556,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(or(not(X0),X1),or(not(X0),X1))))) )
| ~ spl0_16
| ~ spl0_64 ),
inference(resolution,[],[f538,f94]) ).
fof(f3298,plain,
( spl0_175
| ~ spl0_6
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f509,f488,f42,f3296]) ).
fof(f3296,plain,
( spl0_175
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(X2,not(X1))),X2))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f509,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(X2,not(X1))),X2))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_60 ),
inference(resolution,[],[f489,f43]) ).
fof(f3294,plain,
( spl0_174
| ~ spl0_53
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f499,f484,f374,f3292]) ).
fof(f3292,plain,
( spl0_174
<=> ! [X0,X3,X2,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X2,or(not(X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X2,or(not(X0),X3))) )
| ~ spl0_53
| ~ spl0_59 ),
inference(resolution,[],[f485,f375]) ).
fof(f3290,plain,
( spl0_173
| ~ spl0_51
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f469,f453,f334,f3288]) ).
fof(f3288,plain,
( spl0_173
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(or(X1,X1),X2))),or(X0,X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f469,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(or(X1,X1),X2))),or(X0,X2)),X1))
| ~ spl0_51
| ~ spl0_56 ),
inference(resolution,[],[f454,f335]) ).
fof(f3286,plain,
( spl0_172
| ~ spl0_14
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f439,f428,f81,f3284]) ).
fof(f3284,plain,
( spl0_172
<=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(or(X2,X1),not(or(X2,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f439,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(or(X2,X1),not(or(X2,X0)))))
| ~ spl0_14
| ~ spl0_55 ),
inference(resolution,[],[f429,f82]) ).
fof(f3282,plain,
( spl0_171
| ~ spl0_36
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f436,f428,f241,f3280]) ).
fof(f3280,plain,
( spl0_171
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(or(X0,X2),not(or(not(X1),X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f436,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(or(X0,X2),not(or(not(X1),X2)))))
| ~ spl0_36
| ~ spl0_55 ),
inference(resolution,[],[f429,f242]) ).
fof(f3278,plain,
( spl0_170
| ~ spl0_19
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f387,f374,f118,f3276]) ).
fof(f3276,plain,
( spl0_170
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,X3))
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f387,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,X3))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_19
| ~ spl0_53 ),
inference(resolution,[],[f375,f119]) ).
fof(f3274,plain,
( spl0_169
| ~ spl0_33
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f341,f326,f223,f3272]) ).
fof(f3272,plain,
( spl0_169
<=> ! [X0,X1] :
( theorem(or(X0,not(or(X0,X1))))
| ~ theorem(or(not(X1),not(or(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f326,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f341,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(X0,X1))))
| ~ theorem(or(not(X1),not(or(X0,X1)))) )
| ~ spl0_33
| ~ spl0_49 ),
inference(resolution,[],[f327,f224]) ).
fof(f327,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f3270,plain,
( ~ spl0_168
| ~ spl0_90
| spl0_167 ),
inference(avatar_split_clause,[],[f3010,f2796,f944,f3267]) ).
fof(f3267,plain,
( spl0_168
<=> theorem(or(r,not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f944,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f3010,plain,
( ~ theorem(or(r,not(p)))
| ~ spl0_90
| spl0_167 ),
inference(resolution,[],[f2798,f945]) ).
fof(f945,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f2799,plain,
( ~ spl0_167
| spl0_2
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f2794,f2611,f23,f2796]) ).
fof(f2611,plain,
( spl0_144
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2794,plain,
( ~ theorem(or(not(q),or(not(p),r)))
| spl0_2
| ~ spl0_144 ),
inference(resolution,[],[f2612,f25]) ).
fof(f2612,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f2611]) ).
fof(f2703,plain,
( spl0_166
| ~ spl0_26
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f651,f634,f164,f2701]) ).
fof(f2701,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f651,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_26
| ~ spl0_69 ),
inference(resolution,[],[f635,f165]) ).
fof(f2699,plain,
( spl0_165
| ~ spl0_11
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f639,f634,f67,f2697]) ).
fof(f67,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) )
| ~ spl0_11
| ~ spl0_69 ),
inference(resolution,[],[f635,f68]) ).
fof(f68,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f2695,plain,
( spl0_164
| ~ spl0_27
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f622,f599,f172,f2693]) ).
fof(f622,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) )
| ~ spl0_27
| ~ spl0_68 ),
inference(resolution,[],[f600,f173]) ).
fof(f2691,plain,
( spl0_163
| ~ spl0_6
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f589,f545,f42,f2689]) ).
fof(f2689,plain,
( spl0_163
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f589,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) )
| ~ spl0_6
| ~ spl0_66 ),
inference(resolution,[],[f546,f43]) ).
fof(f2687,plain,
( spl0_162
| ~ spl0_11
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f564,f541,f67,f2685]) ).
fof(f564,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X2,X1)))) )
| ~ spl0_11
| ~ spl0_65 ),
inference(resolution,[],[f542,f68]) ).
fof(f2683,plain,
( spl0_161
| ~ spl0_6
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f554,f537,f42,f2681]) ).
fof(f2681,plain,
( spl0_161
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) )
| ~ spl0_6
| ~ spl0_64 ),
inference(resolution,[],[f538,f43]) ).
fof(f2679,plain,
( ~ spl0_160
| spl0_39
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1041,f972,f264,f2676]) ).
fof(f2676,plain,
( spl0_160
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f264,plain,
( spl0_39
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(q),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1041,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),not(q)))
| spl0_39
| ~ spl0_97 ),
inference(resolution,[],[f973,f266]) ).
fof(f266,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(q),r)))
| spl0_39 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f2674,plain,
( spl0_159
| ~ spl0_16
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f530,f496,f93,f2672]) ).
fof(f2672,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f530,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) )
| ~ spl0_16
| ~ spl0_62 ),
inference(resolution,[],[f497,f94]) ).
fof(f2670,plain,
( spl0_158
| ~ spl0_17
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f527,f496,f103,f2668]) ).
fof(f2668,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) )
| ~ spl0_17
| ~ spl0_62 ),
inference(resolution,[],[f497,f104]) ).
fof(f2666,plain,
( spl0_157
| ~ spl0_55
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f526,f496,f428,f2664]) ).
fof(f2664,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f526,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) )
| ~ spl0_55
| ~ spl0_62 ),
inference(resolution,[],[f497,f429]) ).
fof(f2662,plain,
( spl0_156
| ~ spl0_16
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f514,f488,f93,f2660]) ).
fof(f2660,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) )
| ~ spl0_16
| ~ spl0_60 ),
inference(resolution,[],[f489,f94]) ).
fof(f2658,plain,
( spl0_155
| ~ spl0_17
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f511,f488,f103,f2656]) ).
fof(f2656,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f511,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) )
| ~ spl0_17
| ~ spl0_60 ),
inference(resolution,[],[f489,f104]) ).
fof(f2654,plain,
( spl0_154
| ~ spl0_55
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f510,f488,f428,f2652]) ).
fof(f2652,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f510,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) )
| ~ spl0_55
| ~ spl0_60 ),
inference(resolution,[],[f489,f429]) ).
fof(f2650,plain,
( spl0_153
| ~ spl0_16
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f506,f484,f93,f2648]) ).
fof(f2648,plain,
( spl0_153
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f506,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) )
| ~ spl0_16
| ~ spl0_59 ),
inference(resolution,[],[f485,f94]) ).
fof(f2646,plain,
( spl0_152
| ~ spl0_17
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f503,f484,f103,f2644]) ).
fof(f2644,plain,
( spl0_152
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f503,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) )
| ~ spl0_17
| ~ spl0_59 ),
inference(resolution,[],[f485,f104]) ).
fof(f2642,plain,
( spl0_151
| ~ spl0_55
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f502,f484,f428,f2640]) ).
fof(f2640,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f502,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) )
| ~ spl0_55
| ~ spl0_59 ),
inference(resolution,[],[f485,f429]) ).
fof(f2638,plain,
( spl0_150
| ~ spl0_6
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f478,f461,f42,f2636]) ).
fof(f2636,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f478,plain,
( ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_58 ),
inference(resolution,[],[f462,f43]) ).
fof(f2634,plain,
( ~ spl0_149
| spl0_2
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1040,f972,f23,f2631]) ).
fof(f2631,plain,
( spl0_149
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1040,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),not(p)))
| spl0_2
| ~ spl0_97 ),
inference(resolution,[],[f973,f25]) ).
fof(f2629,plain,
( spl0_148
| ~ spl0_50
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f451,f428,f330,f2627]) ).
fof(f2627,plain,
( spl0_148
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) )
| ~ spl0_50
| ~ spl0_55 ),
inference(resolution,[],[f429,f331]) ).
fof(f2625,plain,
( spl0_147
| ~ spl0_32
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f444,f428,f219,f2623]) ).
fof(f444,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) )
| ~ spl0_32
| ~ spl0_55 ),
inference(resolution,[],[f429,f220]) ).
fof(f2621,plain,
( spl0_146
| ~ spl0_48
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f438,f428,f322,f2619]) ).
fof(f2619,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f438,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_55 ),
inference(resolution,[],[f429,f323]) ).
fof(f2617,plain,
( spl0_145
| ~ spl0_19
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f435,f428,f118,f2615]) ).
fof(f2615,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f435,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19
| ~ spl0_55 ),
inference(resolution,[],[f429,f119]) ).
fof(f2613,plain,
( spl0_144
| ~ spl0_12
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f386,f374,f72,f2611]) ).
fof(f386,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) )
| ~ spl0_12
| ~ spl0_53 ),
inference(resolution,[],[f375,f73]) ).
fof(f2609,plain,
( spl0_143
| ~ spl0_17
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f352,f330,f103,f2607]) ).
fof(f2607,plain,
( spl0_143
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(or(X0,X1),X2))
| theorem(or(X0,or(or(X3,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f352,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(or(X0,X1),X2))
| theorem(or(X0,or(or(X3,X2),X1))) )
| ~ spl0_17
| ~ spl0_50 ),
inference(resolution,[],[f331,f104]) ).
fof(f2605,plain,
( spl0_142
| ~ spl0_27
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f348,f326,f172,f2603]) ).
fof(f2603,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f348,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) )
| ~ spl0_27
| ~ spl0_49 ),
inference(resolution,[],[f327,f173]) ).
fof(f2601,plain,
( spl0_141
| ~ spl0_17
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f340,f322,f103,f2599]) ).
fof(f2599,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f340,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) )
| ~ spl0_17
| ~ spl0_48 ),
inference(resolution,[],[f323,f104]) ).
fof(f2331,plain,
( ~ spl0_140
| spl0_2
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1990,f1877,f23,f2328]) ).
fof(f2328,plain,
( spl0_140
<=> theorem(not(or(r,not(not(or(not(p),not(q))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1877,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1990,plain,
( ~ theorem(not(or(r,not(not(or(not(p),not(q)))))))
| spl0_2
| ~ spl0_113 ),
inference(resolution,[],[f1878,f25]) ).
fof(f1878,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f2180,plain,
( spl0_139
| ~ spl0_26
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f617,f599,f164,f2178]) ).
fof(f2178,plain,
( spl0_139
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f617,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2))))
| ~ spl0_26
| ~ spl0_68 ),
inference(resolution,[],[f600,f165]) ).
fof(f2176,plain,
( spl0_138
| ~ spl0_29
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f615,f599,f186,f2174]) ).
fof(f2174,plain,
( spl0_138
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f615,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2))))
| ~ spl0_29
| ~ spl0_68 ),
inference(resolution,[],[f600,f187]) ).
fof(f2172,plain,
( spl0_137
| ~ spl0_11
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f604,f599,f67,f2170]) ).
fof(f2170,plain,
( spl0_137
<=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f604,plain,
( ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1))))
| ~ spl0_11
| ~ spl0_68 ),
inference(resolution,[],[f600,f68]) ).
fof(f2168,plain,
( spl0_136
| ~ spl0_6
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f501,f484,f42,f2166]) ).
fof(f2166,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) )
| ~ spl0_6
| ~ spl0_59 ),
inference(resolution,[],[f485,f43]) ).
fof(f2164,plain,
( spl0_135
| ~ spl0_16
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f481,f461,f93,f2162]) ).
fof(f2162,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) )
| ~ spl0_16
| ~ spl0_58 ),
inference(resolution,[],[f462,f94]) ).
fof(f2158,plain,
( spl0_134
| ~ spl0_47
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f450,f428,f315,f2156]) ).
fof(f2156,plain,
( spl0_134
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f450,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1)))
| ~ spl0_47
| ~ spl0_55 ),
inference(resolution,[],[f429,f316]) ).
fof(f2154,plain,
( spl0_133
| ~ spl0_29
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f443,f428,f186,f2152]) ).
fof(f2152,plain,
( spl0_133
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f443,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2))))))
| ~ spl0_29
| ~ spl0_55 ),
inference(resolution,[],[f429,f187]) ).
fof(f2150,plain,
( spl0_132
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f442,f428,f190,f2148]) ).
fof(f2148,plain,
( spl0_132
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f442,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1))))))
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f429,f191]) ).
fof(f2146,plain,
( spl0_131
| ~ spl0_10
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f437,f428,f61,f2144]) ).
fof(f2144,plain,
( spl0_131
<=> ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f437,plain,
( ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0)))
| ~ spl0_10
| ~ spl0_55 ),
inference(resolution,[],[f429,f62]) ).
fof(f2142,plain,
( spl0_130
| ~ spl0_12
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f434,f428,f72,f2140]) ).
fof(f2140,plain,
( spl0_130
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f434,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1)))
| ~ spl0_12
| ~ spl0_55 ),
inference(resolution,[],[f429,f73]) ).
fof(f2138,plain,
( spl0_129
| ~ spl0_50
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f426,f378,f330,f2136]) ).
fof(f2136,plain,
( spl0_129
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) )
| ~ spl0_50
| ~ spl0_54 ),
inference(resolution,[],[f379,f331]) ).
fof(f2134,plain,
( spl0_128
| ~ spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f418,f378,f172,f2132]) ).
fof(f2132,plain,
( spl0_128
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f418,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) )
| ~ spl0_27
| ~ spl0_54 ),
inference(resolution,[],[f379,f173]) ).
fof(f2130,plain,
( spl0_127
| ~ spl0_48
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f403,f378,f322,f2128]) ).
fof(f2128,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) )
| ~ spl0_48
| ~ spl0_54 ),
inference(resolution,[],[f379,f323]) ).
fof(f2126,plain,
( spl0_126
| ~ spl0_27
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f399,f374,f172,f2124]) ).
fof(f2124,plain,
( spl0_126
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f399,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_53 ),
inference(resolution,[],[f375,f173]) ).
fof(f2122,plain,
( spl0_125
| ~ spl0_12
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f356,f334,f72,f2120]) ).
fof(f2120,plain,
( spl0_125
<=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f356,plain,
( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
| ~ spl0_12
| ~ spl0_51 ),
inference(resolution,[],[f335,f73]) ).
fof(f2118,plain,
( ~ spl0_124
| spl0_76
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f2034,f1902,f753,f2115]) ).
fof(f753,plain,
( spl0_76
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),r)),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1902,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f2034,plain,
( ~ theorem(or(r,not(or(not(p),not(q)))))
| spl0_76
| ~ spl0_119 ),
inference(resolution,[],[f1903,f755]) ).
fof(f755,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),r))
| spl0_76 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f1903,plain,
( ! [X0,X1] :
( theorem(or(not(or(not(X1),X0)),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1902]) ).
fof(f2113,plain,
( spl0_123
| ~ spl0_31
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f337,f322,f194,f2111]) ).
fof(f2111,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f337,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) )
| ~ spl0_31
| ~ spl0_48 ),
inference(resolution,[],[f323,f195]) ).
fof(f2109,plain,
( spl0_122
| ~ spl0_17
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f320,f315,f103,f2107]) ).
fof(f2107,plain,
( spl0_122
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f320,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
| ~ spl0_17
| ~ spl0_47 ),
inference(resolution,[],[f316,f104]) ).
fof(f1912,plain,
( spl0_121
| ~ spl0_10
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f562,f541,f61,f1910]) ).
fof(f1910,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f562,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) )
| ~ spl0_10
| ~ spl0_65 ),
inference(resolution,[],[f542,f62]) ).
fof(f1908,plain,
( spl0_120
| ~ spl0_7
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f560,f541,f47,f1906]) ).
fof(f1906,plain,
( spl0_120
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f47,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f560,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) )
| ~ spl0_7
| ~ spl0_65 ),
inference(resolution,[],[f542,f48]) ).
fof(f48,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f1904,plain,
( spl0_119
| ~ spl0_51
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f528,f496,f334,f1902]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) )
| ~ spl0_51
| ~ spl0_62 ),
inference(resolution,[],[f497,f335]) ).
fof(f1900,plain,
( spl0_118
| ~ spl0_51
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f504,f484,f334,f1898]) ).
fof(f1898,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f504,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
| ~ spl0_51
| ~ spl0_59 ),
inference(resolution,[],[f485,f335]) ).
fof(f1896,plain,
( spl0_117
| ~ spl0_47
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f425,f378,f315,f1894]) ).
fof(f1894,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f425,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) )
| ~ spl0_47
| ~ spl0_54 ),
inference(resolution,[],[f379,f316]) ).
fof(f1892,plain,
( spl0_116
| ~ spl0_25
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f420,f378,f160,f1890]) ).
fof(f1890,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f160,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f420,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) )
| ~ spl0_25
| ~ spl0_54 ),
inference(resolution,[],[f379,f161]) ).
fof(f161,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f1888,plain,
( ~ spl0_115
| ~ spl0_96
| spl0_106 ),
inference(avatar_split_clause,[],[f1791,f1699,f968,f1885]) ).
fof(f1885,plain,
( spl0_115
<=> theorem(not(not(r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f968,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1699,plain,
( spl0_106
<=> theorem(or(or(not(q),r),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1791,plain,
( ~ theorem(not(not(r)))
| ~ spl0_96
| spl0_106 ),
inference(resolution,[],[f1701,f969]) ).
fof(f969,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f968]) ).
fof(f1701,plain,
( ~ theorem(or(or(not(q),r),not(p)))
| spl0_106 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f1883,plain,
( spl0_114
| ~ spl0_26
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f413,f378,f164,f1881]) ).
fof(f1881,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) )
| ~ spl0_26
| ~ spl0_54 ),
inference(resolution,[],[f379,f165]) ).
fof(f1879,plain,
( spl0_113
| ~ spl0_11
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f404,f378,f67,f1877]) ).
fof(f404,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_11
| ~ spl0_54 ),
inference(resolution,[],[f379,f68]) ).
fof(f1875,plain,
( spl0_112
| ~ spl0_26
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f394,f374,f164,f1873]) ).
fof(f1873,plain,
( spl0_112
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f394,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) )
| ~ spl0_26
| ~ spl0_53 ),
inference(resolution,[],[f375,f165]) ).
fof(f1871,plain,
( spl0_111
| ~ spl0_50
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f367,f334,f330,f1869]) ).
fof(f1869,plain,
( spl0_111
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f367,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) )
| ~ spl0_50
| ~ spl0_51 ),
inference(resolution,[],[f335,f331]) ).
fof(f1867,plain,
( spl0_110
| ~ spl0_48
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f359,f334,f322,f1865]) ).
fof(f1865,plain,
( spl0_110
<=> ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f359,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_48
| ~ spl0_51 ),
inference(resolution,[],[f335,f323]) ).
fof(f1863,plain,
( spl0_109
| ~ spl0_19
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f357,f334,f118,f1861]) ).
fof(f1861,plain,
( spl0_109
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f357,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) )
| ~ spl0_19
| ~ spl0_51 ),
inference(resolution,[],[f335,f119]) ).
fof(f1769,plain,
( spl0_108
| ~ spl0_23
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f616,f599,f144,f1767]) ).
fof(f1767,plain,
( spl0_108
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f144,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f616,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
| ~ spl0_23
| ~ spl0_68 ),
inference(resolution,[],[f600,f145]) ).
fof(f145,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f1765,plain,
( spl0_107
| ~ spl0_7
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f602,f599,f47,f1763]) ).
fof(f1763,plain,
( spl0_107
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f602,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
| ~ spl0_7
| ~ spl0_68 ),
inference(resolution,[],[f600,f48]) ).
fof(f1702,plain,
( ~ spl0_106
| spl0_2
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f990,f944,f23,f1699]) ).
fof(f990,plain,
( ~ theorem(or(or(not(q),r),not(p)))
| spl0_2
| ~ spl0_90 ),
inference(resolution,[],[f945,f25]) ).
fof(f1354,plain,
( ~ spl0_105
| spl0_18
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1042,f972,f113,f1351]) ).
fof(f1351,plain,
( spl0_105
<=> theorem(or(not(p),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f113,plain,
( spl0_18
<=> theorem(or(not(p),or(not(q),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1042,plain,
( ~ theorem(or(not(p),not(q)))
| spl0_18
| ~ spl0_97 ),
inference(resolution,[],[f973,f115]) ).
fof(f115,plain,
( ~ theorem(or(not(p),or(not(q),r)))
| spl0_18 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f1105,plain,
( spl0_2
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1090]) ).
fof(f1090,plain,
( $false
| spl0_2
| ~ spl0_95 ),
inference(resolution,[],[f965,f25]) ).
fof(f965,plain,
( ! [X0,X1] : theorem(or(X0,X1))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f964,plain,
( spl0_95
<=> ! [X0,X1] : theorem(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1104,plain,
( spl0_39
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1091]) ).
fof(f1091,plain,
( $false
| spl0_39
| ~ spl0_95 ),
inference(resolution,[],[f965,f266]) ).
fof(f1103,plain,
( spl0_76
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1092]) ).
fof(f1092,plain,
( $false
| spl0_76
| ~ spl0_95 ),
inference(resolution,[],[f965,f755]) ).
fof(f1102,plain,
( spl0_18
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1093]) ).
fof(f1093,plain,
( $false
| spl0_18
| ~ spl0_95 ),
inference(resolution,[],[f965,f115]) ).
fof(f1101,plain,
( spl0_37
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1094]) ).
fof(f1094,plain,
( $false
| spl0_37
| ~ spl0_95 ),
inference(resolution,[],[f965,f252]) ).
fof(f252,plain,
( ~ theorem(or(not(p),r))
| spl0_37 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f250,plain,
( spl0_37
<=> theorem(or(not(p),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1100,plain,
( spl0_35
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1095]) ).
fof(f1095,plain,
( $false
| spl0_35
| ~ spl0_95 ),
inference(resolution,[],[f965,f238]) ).
fof(f238,plain,
( ~ theorem(or(not(q),r))
| spl0_35 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f236,plain,
( spl0_35
<=> theorem(or(not(q),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1099,plain,
( spl0_63
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1096]) ).
fof(f1096,plain,
( $false
| spl0_63
| ~ spl0_95 ),
inference(resolution,[],[f965,f534]) ).
fof(f534,plain,
( ~ theorem(or(not(q),not(or(not(p),not(q)))))
| spl0_63 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f532,plain,
( spl0_63
<=> theorem(or(not(q),not(or(not(p),not(q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1087,plain,
( spl0_104
| spl0_95
| ~ spl0_45
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f417,f378,f299,f964,f1085]) ).
fof(f1085,plain,
( spl0_104
<=> ! [X2,X3] :
( ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f299,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f417,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) )
| ~ spl0_45
| ~ spl0_54 ),
inference(resolution,[],[f379,f300]) ).
fof(f300,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f1083,plain,
( spl0_103
| ~ spl0_22
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f392,f374,f140,f1081]) ).
fof(f1081,plain,
( spl0_103
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f392,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) )
| ~ spl0_22
| ~ spl0_53 ),
inference(resolution,[],[f375,f141]) ).
fof(f1079,plain,
( spl0_102
| ~ spl0_48
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f384,f374,f322,f1077]) ).
fof(f1077,plain,
( spl0_102
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_53 ),
inference(resolution,[],[f375,f323]) ).
fof(f1075,plain,
( spl0_101
| ~ spl0_47
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f366,f334,f315,f1073]) ).
fof(f1073,plain,
( spl0_101
<=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f366,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
| ~ spl0_47
| ~ spl0_51 ),
inference(resolution,[],[f335,f316]) ).
fof(f1071,plain,
( spl0_100
| ~ spl0_10
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f358,f334,f61,f1069]) ).
fof(f1069,plain,
( spl0_100
<=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f358,plain,
( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
| ~ spl0_10
| ~ spl0_51 ),
inference(resolution,[],[f335,f62]) ).
fof(f1023,plain,
( ~ spl0_99
| spl0_39
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f991,f944,f264,f1020]) ).
fof(f1020,plain,
( spl0_99
<=> theorem(or(r,not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f991,plain,
( ~ theorem(or(r,not(q)))
| spl0_39
| ~ spl0_90 ),
inference(resolution,[],[f945,f266]) ).
fof(f978,plain,
( spl0_98
| ~ spl0_45
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f621,f599,f299,f976]) ).
fof(f976,plain,
( spl0_98
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f621,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) )
| ~ spl0_45
| ~ spl0_68 ),
inference(resolution,[],[f600,f300]) ).
fof(f974,plain,
( spl0_97
| ~ spl0_27
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f446,f428,f172,f972]) ).
fof(f446,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_27
| ~ spl0_55 ),
inference(resolution,[],[f429,f173]) ).
fof(f970,plain,
( spl0_96
| ~ spl0_21
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f419,f378,f136,f968]) ).
fof(f136,plain,
( spl0_21
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f419,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_21
| ~ spl0_54 ),
inference(resolution,[],[f379,f137]) ).
fof(f137,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f966,plain,
( spl0_94
| spl0_95
| ~ spl0_23
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f412,f378,f144,f964,f961]) ).
fof(f961,plain,
( spl0_94
<=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f412,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(X2),X2))) )
| ~ spl0_23
| ~ spl0_54 ),
inference(resolution,[],[f379,f145]) ).
fof(f959,plain,
( spl0_93
| ~ spl0_22
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f411,f378,f140,f957]) ).
fof(f957,plain,
( spl0_93
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f411,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) )
| ~ spl0_22
| ~ spl0_54 ),
inference(resolution,[],[f379,f141]) ).
fof(f954,plain,
( spl0_92
| ~ spl0_10
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f402,f378,f61,f952]) ).
fof(f952,plain,
( spl0_92
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f402,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_10
| ~ spl0_54 ),
inference(resolution,[],[f379,f62]) ).
fof(f950,plain,
( spl0_91
| ~ spl0_7
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f400,f378,f47,f948]) ).
fof(f948,plain,
( spl0_91
<=> ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f400,plain,
( ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) )
| ~ spl0_7
| ~ spl0_54 ),
inference(resolution,[],[f379,f48]) ).
fof(f946,plain,
( spl0_90
| ~ spl0_11
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f385,f374,f67,f944]) ).
fof(f385,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_11
| ~ spl0_53 ),
inference(resolution,[],[f375,f68]) ).
fof(f942,plain,
( spl0_89
| ~ spl0_16
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f339,f322,f93,f940]) ).
fof(f940,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f339,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) )
| ~ spl0_16
| ~ spl0_48 ),
inference(resolution,[],[f323,f94]) ).
fof(f882,plain,
( spl0_88
| ~ spl0_26
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f441,f428,f164,f880]) ).
fof(f880,plain,
( spl0_88
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f441,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_26
| ~ spl0_55 ),
inference(resolution,[],[f429,f165]) ).
fof(f878,plain,
( spl0_87
| ~ spl0_6
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f338,f322,f42,f876]) ).
fof(f876,plain,
( spl0_87
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f338,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_48 ),
inference(resolution,[],[f323,f43]) ).
fof(f874,plain,
( spl0_86
| ~ spl0_6
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f767,f761,f42,f872]) ).
fof(f872,plain,
( spl0_86
<=> ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f761,plain,
( spl0_77
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f767,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_77 ),
inference(resolution,[],[f762,f43]) ).
fof(f762,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f870,plain,
( spl0_85
| ~ spl0_17
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f297,f292,f103,f868]) ).
fof(f868,plain,
( spl0_85
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f292,plain,
( spl0_44
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f297,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_44 ),
inference(resolution,[],[f293,f104]) ).
fof(f293,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f866,plain,
( spl0_84
| ~ spl0_17
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f283,f277,f103,f864]) ).
fof(f864,plain,
( spl0_84
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f283,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_41 ),
inference(resolution,[],[f278,f104]) ).
fof(f815,plain,
( spl0_83
| ~ spl0_7
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f381,f374,f47,f813]) ).
fof(f813,plain,
( spl0_83
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f381,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_53 ),
inference(resolution,[],[f375,f48]) ).
fof(f811,plain,
( spl0_82
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f349,f330,f326,f809]) ).
fof(f809,plain,
( spl0_82
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f349,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_49
| ~ spl0_50 ),
inference(resolution,[],[f331,f327]) ).
fof(f807,plain,
( spl0_81
| ~ spl0_43
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f318,f311,f288,f805]) ).
fof(f805,plain,
( spl0_81
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f288,plain,
( spl0_43
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f311,plain,
( spl0_46
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f318,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_43
| ~ spl0_46 ),
inference(resolution,[],[f312,f289]) ).
fof(f289,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f312,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f803,plain,
( spl0_80
| ~ spl0_16
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f309,f299,f93,f801]) ).
fof(f801,plain,
( spl0_80
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f309,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_45 ),
inference(resolution,[],[f300,f94]) ).
fof(f777,plain,
( spl0_79
| ~ spl0_23
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f440,f428,f144,f775]) ).
fof(f775,plain,
( spl0_79
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f440,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_23
| ~ spl0_55 ),
inference(resolution,[],[f429,f145]) ).
fof(f773,plain,
( spl0_78
| ~ spl0_7
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f431,f428,f47,f771]) ).
fof(f771,plain,
( spl0_78
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f431,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_55 ),
inference(resolution,[],[f429,f48]) ).
fof(f763,plain,
( spl0_77
| ~ spl0_16
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f282,f277,f93,f761]) ).
fof(f282,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_41 ),
inference(resolution,[],[f278,f94]) ).
fof(f756,plain,
( ~ spl0_76
| ~ spl0_27
| spl0_39 ),
inference(avatar_split_clause,[],[f268,f264,f172,f753]) ).
fof(f268,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),r))
| ~ spl0_27
| spl0_39 ),
inference(resolution,[],[f266,f173]) ).
fof(f726,plain,
( ~ spl0_75
| ~ spl0_13
| spl0_63 ),
inference(avatar_split_clause,[],[f632,f532,f76,f723]) ).
fof(f723,plain,
( spl0_75
<=> theorem(not(or(not(p),not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f76,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f632,plain,
( ~ theorem(not(or(not(p),not(q))))
| ~ spl0_13
| spl0_63 ),
inference(resolution,[],[f534,f77]) ).
fof(f77,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f721,plain,
( spl0_74
| ~ spl0_31
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f226,f219,f194,f719]) ).
fof(f226,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(not(X3),X0)),X1)))
| ~ theorem(or(X2,X3)) )
| ~ spl0_31
| ~ spl0_32 ),
inference(resolution,[],[f220,f195]) ).
fof(f717,plain,
( spl0_73
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f215,f194,f190,f715]) ).
fof(f215,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_30
| ~ spl0_31 ),
inference(resolution,[],[f195,f191]) ).
fof(f677,plain,
( spl0_72
| ~ spl0_31
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f245,f241,f194,f675]) ).
fof(f245,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) )
| ~ spl0_31
| ~ spl0_36 ),
inference(resolution,[],[f242,f195]) ).
fof(f673,plain,
( spl0_71
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f216,f194,f186,f671]) ).
fof(f216,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) )
| ~ spl0_29
| ~ spl0_31 ),
inference(resolution,[],[f195,f187]) ).
fof(f669,plain,
( spl0_70
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f209,f194,f81,f667]) ).
fof(f209,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(X0,or(not(X2),X3))) )
| ~ spl0_14
| ~ spl0_31 ),
inference(resolution,[],[f195,f82]) ).
fof(f636,plain,
( spl0_69
| ~ spl0_19
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f208,f194,f118,f634]) ).
fof(f208,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X1,X3)))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_19
| ~ spl0_31 ),
inference(resolution,[],[f195,f119]) ).
fof(f601,plain,
( spl0_68
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f207,f194,f72,f599]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) )
| ~ spl0_12
| ~ spl0_31 ),
inference(resolution,[],[f195,f73]) ).
fof(f551,plain,
( spl0_67
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f248,f241,f93,f549]) ).
fof(f248,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
| ~ spl0_16
| ~ spl0_36 ),
inference(resolution,[],[f242,f94]) ).
fof(f547,plain,
( spl0_66
| ~ spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f227,f219,f42,f545]) ).
fof(f227,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) )
| ~ spl0_6
| ~ spl0_32 ),
inference(resolution,[],[f220,f43]) ).
fof(f543,plain,
( spl0_65
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f217,f194,f172,f541]) ).
fof(f217,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_31 ),
inference(resolution,[],[f195,f173]) ).
fof(f539,plain,
( spl0_64
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f201,f190,f42,f537]) ).
fof(f201,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_30 ),
inference(resolution,[],[f191,f43]) ).
fof(f535,plain,
( ~ spl0_63
| spl0_39
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f522,f496,f264,f532]) ).
fof(f522,plain,
( ~ theorem(or(not(q),not(or(not(p),not(q)))))
| spl0_39
| ~ spl0_62 ),
inference(resolution,[],[f497,f266]) ).
fof(f498,plain,
( spl0_62
| ~ spl0_6
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f246,f241,f42,f496]) ).
fof(f246,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_36 ),
inference(resolution,[],[f242,f43]) ).
fof(f494,plain,
( spl0_61
| ~ spl0_16
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f229,f219,f93,f492]) ).
fof(f229,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_32 ),
inference(resolution,[],[f220,f94]) ).
fof(f490,plain,
( spl0_60
| ~ spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f214,f194,f164,f488]) ).
fof(f214,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26
| ~ spl0_31 ),
inference(resolution,[],[f195,f165]) ).
fof(f486,plain,
( spl0_59
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f198,f186,f42,f484]) ).
fof(f198,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f187,f43]) ).
fof(f463,plain,
( spl0_58
| ~ spl0_22
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f212,f194,f140,f461]) ).
fof(f212,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_22
| ~ spl0_31 ),
inference(resolution,[],[f195,f141]) ).
fof(f459,plain,
( spl0_57
| ~ spl0_16
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f203,f190,f93,f457]) ).
fof(f203,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_30 ),
inference(resolution,[],[f191,f94]) ).
fof(f455,plain,
( spl0_56
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f200,f186,f93,f453]) ).
fof(f200,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f187,f94]) ).
fof(f430,plain,
( spl0_55
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f206,f194,f67,f428]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_31 ),
inference(resolution,[],[f195,f68]) ).
fof(f380,plain,
( spl0_54
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f210,f194,f126,f378]) ).
fof(f210,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_20
| ~ spl0_31 ),
inference(resolution,[],[f195,f127]) ).
fof(f376,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f176,f172,f42,f374]) ).
fof(f176,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_27 ),
inference(resolution,[],[f173,f43]) ).
fof(f372,plain,
( ~ spl0_52
| ~ spl0_20
| spl0_35 ),
inference(avatar_split_clause,[],[f254,f236,f126,f369]) ).
fof(f369,plain,
( spl0_52
<=> theorem(not(q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f254,plain,
( ~ theorem(not(q))
| ~ spl0_20
| spl0_35 ),
inference(resolution,[],[f238,f127]) ).
fof(f336,plain,
( spl0_51
| ~ spl0_10
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f205,f194,f61,f334]) ).
fof(f205,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_31 ),
inference(resolution,[],[f195,f62]) ).
fof(f332,plain,
( spl0_50
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f180,f172,f93,f330]) ).
fof(f180,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_27 ),
inference(resolution,[],[f173,f94]) ).
fof(f328,plain,
( spl0_49
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f179,f172,f86,f326]) ).
fof(f179,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f173,f87]) ).
fof(f324,plain,
( spl0_48
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f168,f164,f42,f322]) ).
fof(f168,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f165,f43]) ).
fof(f317,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f170,f164,f93,f315]) ).
fof(f170,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f165,f94]) ).
fof(f313,plain,
( spl0_46
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f148,f140,f42,f311]) ).
fof(f148,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f141,f43]) ).
fof(f301,plain,
( spl0_45
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f134,f126,f103,f299]) ).
fof(f134,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f127,f104]) ).
fof(f294,plain,
( spl0_44
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f158,f144,f93,f292]) ).
fof(f158,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f145,f94]) ).
fof(f290,plain,
( spl0_42
| spl0_43
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f126,f42,f288,f285]) ).
fof(f285,plain,
( spl0_42
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f130,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f127,f43]) ).
fof(f279,plain,
( spl0_41
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f144,f86,f277]) ).
fof(f157,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f145,f87]) ).
fof(f275,plain,
( ~ spl0_40
| ~ spl0_13
| spl0_35 ),
inference(avatar_split_clause,[],[f255,f236,f76,f272]) ).
fof(f272,plain,
( spl0_40
<=> theorem(r) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f255,plain,
( ~ theorem(r)
| ~ spl0_13
| spl0_35 ),
inference(resolution,[],[f238,f77]) ).
fof(f267,plain,
( ~ spl0_39
| spl0_2
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f175,f172,f23,f264]) ).
fof(f175,plain,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(q),r)))
| spl0_2
| ~ spl0_27 ),
inference(resolution,[],[f173,f25]) ).
fof(f262,plain,
( ~ spl0_38
| spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f129,f126,f23,f259]) ).
fof(f259,plain,
( spl0_38
<=> theorem(not(or(not(not(or(not(p),not(q)))),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f129,plain,
( ~ theorem(not(or(not(not(or(not(p),not(q)))),r)))
| spl0_2
| ~ spl0_20 ),
inference(resolution,[],[f127,f25]) ).
fof(f253,plain,
( ~ spl0_37
| spl0_18
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f177,f172,f113,f250]) ).
fof(f177,plain,
( ~ theorem(or(not(p),r))
| spl0_18
| ~ spl0_27 ),
inference(resolution,[],[f173,f115]) ).
fof(f243,plain,
( spl0_36
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f103,f81,f241]) ).
fof(f110,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_14
| ~ spl0_17 ),
inference(resolution,[],[f104,f82]) ).
fof(f239,plain,
( ~ spl0_35
| ~ spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f124,f113,f76,f236]) ).
fof(f124,plain,
( ~ theorem(or(not(q),r))
| ~ spl0_13
| spl0_18 ),
inference(resolution,[],[f115,f77]) ).
fof(f234,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f93,f81,f232]) ).
fof(f100,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[],[f94,f82]) ).
fof(f225,plain,
( spl0_33
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f123,f118,f93,f223]) ).
fof(f123,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) )
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f119,f94]) ).
fof(f221,plain,
( spl0_32
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f118,f103,f219]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) )
| ~ spl0_17
| ~ spl0_19 ),
inference(resolution,[],[f119,f104]) ).
fof(f196,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f118,f42,f194]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[],[f119,f43]) ).
fof(f192,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f103,f61,f190]) ).
fof(f109,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f104,f62]) ).
fof(f188,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f103,f72,f186]) ).
fof(f108,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f104,f73]) ).
fof(f184,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f93,f72,f182]) ).
fof(f99,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f94,f73]) ).
fof(f174,plain,
( spl0_27
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f111,f103,f76,f172]) ).
fof(f111,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f104,f77]) ).
fof(f166,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f103,f67,f164]) ).
fof(f107,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f104,f68]) ).
fof(f162,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f93,f67,f160]) ).
fof(f98,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f94,f68]) ).
fof(f154,plain,
( ~ spl0_24
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f131,f126,f113,f151]) ).
fof(f151,plain,
( spl0_24
<=> theorem(not(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f131,plain,
( ~ theorem(not(p))
| spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f127,f115]) ).
fof(f146,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f106,f103,f47,f144]) ).
fof(f106,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f104,f48]) ).
fof(f142,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f93,f61,f140]) ).
fof(f97,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f94,f62]) ).
fof(f138,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f96,f93,f47,f136]) ).
fof(f96,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f94,f48]) ).
fof(f128,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f101,f93,f76,f126]) ).
fof(f101,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f94,f77]) ).
fof(f120,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f84,f81,f42,f118]) ).
fof(f84,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f82,f43]) ).
fof(f116,plain,
( ~ spl0_18
| spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f89,f76,f23,f113]) ).
fof(f89,plain,
( ~ theorem(or(not(p),or(not(q),r)))
| spl0_2
| ~ spl0_13 ),
inference(resolution,[],[f77,f25]) ).
fof(f105,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f79,f72,f42,f103]) ).
fof(f79,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_6
| ~ spl0_12 ),
inference(resolution,[],[f73,f43]) ).
fof(f95,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f70,f67,f42,f93]) ).
fof(f70,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f68,f43]) ).
fof(f88,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f65,f61,f42,f86]) ).
fof(f65,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f62,f43]) ).
fof(f83,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f59,f56,f19,f81]) ).
fof(f19,plain,
( spl0_1
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f56,plain,
( spl0_9
<=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f59,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_1
| ~ spl0_9 ),
inference(resolution,[],[f57,f20]) ).
fof(f20,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f57,plain,
( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f78,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f64,f47,f42,f76]) ).
fof(f64,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f48,f43]) ).
fof(f74,plain,
( spl0_12
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f54,f51,f19,f72]) ).
fof(f51,plain,
( spl0_8
<=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f54,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f52,f20]) ).
fof(f52,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f69,plain,
( spl0_11
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f45,f38,f19,f67]) ).
fof(f38,plain,
( spl0_5
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f45,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f39,f20]) ).
fof(f39,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f63,plain,
( spl0_10
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f36,f32,f19,f61]) ).
fof(f32,plain,
( spl0_4
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f36,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f33,f20]) ).
fof(f33,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f58,plain,
spl0_9,
inference(avatar_split_clause,[],[f15,f56]) ).
fof(f15,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f6,axiom,
! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f53,plain,
spl0_8,
inference(avatar_split_clause,[],[f16,f51]) ).
fof(f16,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f49,plain,
( spl0_7
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f35,f28,f19,f47]) ).
fof(f28,plain,
( spl0_3
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f35,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f29,f20]) ).
fof(f29,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f44,plain,
spl0_6,
inference(avatar_split_clause,[],[f17,f42]) ).
fof(f17,plain,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f8,axiom,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(implies(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f40,plain,
spl0_5,
inference(avatar_split_clause,[],[f14,f38]) ).
fof(f14,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f34,plain,
spl0_4,
inference(avatar_split_clause,[],[f13,f32]) ).
fof(f13,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f30,plain,
spl0_3,
inference(avatar_split_clause,[],[f12,f28]) ).
fof(f12,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f26,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f11,f23]) ).
fof(f11,plain,
~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(p),or(not(q),r)))),
inference(definition_unfolding,[],[f10,f6,f6,f9,f6,f6]) ).
fof(f9,axiom,
! [X6,X5] : and(X5,X6) = not(or(not(X5),not(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
~ theorem(implies(implies(and(p,q),r),implies(p,implies(q,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f21,plain,
spl0_1,
inference(avatar_split_clause,[],[f7,f19]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : LCL242-3 : TPTP v8.2.0. Released v2.3.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 20 01:22:52 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (16757)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.34 % (16760)WARNING: value z3 for option sas not known
% 0.16/0.35 % (16759)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.35 % (16761)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.35 % (16758)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.35 % (16763)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.35 % (16764)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.35 % (16762)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.35 % (16760)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.35 TRYING [1]
% 0.16/0.35 TRYING [2]
% 0.16/0.35 TRYING [1]
% 0.16/0.35 TRYING [2]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [3]
% 0.16/0.36 TRYING [4]
% 0.16/0.36 TRYING [4]
% 0.16/0.42 TRYING [5]
% 0.16/0.44 TRYING [5]
% 2.73/0.72 TRYING [6]
% 3.11/0.82 TRYING [6]
% 5.30/1.15 % (16762)First to succeed.
% 5.30/1.16 % (16762)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16757"
% 5.30/1.17 % (16762)Refutation found. Thanks to Tanya!
% 5.30/1.17 % SZS status Unsatisfiable for theBenchmark
% 5.30/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 5.92/1.17 % (16762)------------------------------
% 5.92/1.17 % (16762)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.92/1.17 % (16762)Termination reason: Refutation
% 5.92/1.17
% 5.92/1.17 % (16762)Memory used [KB]: 4924
% 5.92/1.17 % (16762)Time elapsed: 0.818 s
% 5.92/1.17 % (16762)Instructions burned: 1683 (million)
% 5.92/1.17 % (16757)Success in time 0.82 s
%------------------------------------------------------------------------------