TSTP Solution File: LCL231-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL231-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:44:51 EDT 2024
% Result : Unsatisfiable 3.48s 0.87s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 271
% Syntax : Number of formulae : 918 ( 22 unt; 0 def)
% Number of atoms : 2842 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 3571 (1647 ~;1662 |; 0 &)
% ( 262 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 266 ( 264 usr; 263 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 1588 (1588 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7064,plain,
$false,
inference(avatar_sat_refutation,[],[f20,f25,f29,f33,f39,f43,f48,f52,f57,f62,f68,f73,f77,f82,f87,f94,f104,f115,f119,f127,f137,f141,f145,f153,f161,f165,f173,f183,f187,f191,f195,f220,f224,f233,f238,f242,f252,f261,f266,f274,f278,f289,f293,f300,f312,f316,f323,f327,f331,f335,f371,f375,f379,f429,f454,f458,f462,f485,f489,f493,f497,f533,f537,f541,f545,f549,f599,f635,f668,f672,f676,f716,f720,f729,f758,f768,f772,f798,f802,f814,f815,f816,f817,f818,f819,f820,f821,f822,f823,f824,f848,f1025,f1278,f1304,f1308,f1359,f1363,f1367,f1371,f1431,f1435,f1439,f1443,f1447,f1451,f1458,f1462,f1466,f1470,f1515,f1562,f1566,f1570,f1574,f1578,f1591,f1592,f1593,f1594,f1595,f1596,f1597,f1598,f1967,f2252,f2256,f2348,f2352,f2356,f2360,f2364,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2397,f2600,f2605,f2609,f2613,f2617,f2621,f2625,f2629,f2633,f2637,f2641,f2645,f2650,f2654,f2658,f2662,f2666,f2670,f2674,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3153,f3157,f3161,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3264,f3482,f3760,f3764,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3797,f3801,f3805,f3809,f3813,f4295,f4299,f4303,f4308,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4354,f4358,f4362,f4814,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4958,f5246,f5557,f5561,f5565,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5657,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5707,f5711,f5715,f5719,f5723,f6745,f7063]) ).
fof(f7063,plain,
( ~ spl0_7
| spl0_262 ),
inference(avatar_contradiction_clause,[],[f7055]) ).
fof(f7055,plain,
( $false
| ~ spl0_7
| spl0_262 ),
inference(resolution,[],[f6744,f47]) ).
fof(f47,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f46,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f6744,plain,
( ~ theorem(or(not(q),or(not(p),q)))
| spl0_262 ),
inference(avatar_component_clause,[],[f6742]) ).
fof(f6742,plain,
( spl0_262
<=> theorem(or(not(q),or(not(p),q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f6745,plain,
( ~ spl0_262
| spl0_2
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f6429,f5631,f22,f6742]) ).
fof(f22,plain,
( spl0_2
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f5631,plain,
( spl0_239
<=> ! [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_239])]) ).
fof(f6429,plain,
( ~ theorem(or(not(q),or(not(p),q)))
| spl0_2
| ~ spl0_239 ),
inference(resolution,[],[f5632,f24]) ).
fof(f24,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r))))
| spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f5632,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(not(X0),or(X1,X2))),or(X1,or(X3,X2))))
| ~ theorem(or(X3,X0)) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f5631]) ).
fof(f5723,plain,
( spl0_261
| ~ spl0_16
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f711,f674,f92,f5721]) ).
fof(f5721,plain,
( spl0_261
<=> ! [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_261])]) ).
fof(f92,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f674,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(f711,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,[],[f675,f93]) ).
fof(f93,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f675,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,[],[f674]) ).
fof(f5719,plain,
( spl0_260
| ~ spl0_17
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f708,f674,f102,f5717]) ).
fof(f5717,plain,
( spl0_260
<=> ! [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_260])]) ).
fof(f102,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(f708,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,[],[f675,f103]) ).
fof(f103,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f5715,plain,
( spl0_259
| ~ spl0_55
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f707,f674,f427,f5713]) ).
fof(f5713,plain,
( spl0_259
<=> ! [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_259])]) ).
fof(f427,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(f707,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,[],[f675,f428]) ).
fof(f428,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f5711,plain,
( spl0_258
| ~ spl0_68
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f705,f674,f597,f5709]) ).
fof(f5709,plain,
( spl0_258
<=> ! [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_258])]) ).
fof(f597,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(f705,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,[],[f675,f598]) ).
fof(f598,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,[],[f597]) ).
fof(f5707,plain,
( ~ spl0_257
| spl0_2
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f3712,f3179,f22,f5704]) ).
fof(f5704,plain,
( spl0_257
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3179,plain,
( spl0_165
<=> ! [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_165])]) ).
fof(f3712,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),r)))
| spl0_2
| ~ spl0_165 ),
inference(resolution,[],[f3180,f24]) ).
fof(f3180,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f3179]) ).
fof(f5702,plain,
( spl0_256
| ~ spl0_16
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f699,f670,f92,f5700]) ).
fof(f5700,plain,
( spl0_256
<=> ! [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_256])]) ).
fof(f670,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(f699,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,[],[f671,f93]) ).
fof(f671,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,[],[f670]) ).
fof(f5698,plain,
( spl0_255
| ~ spl0_17
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f696,f670,f102,f5696]) ).
fof(f5696,plain,
( spl0_255
<=> ! [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_255])]) ).
fof(f696,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,[],[f671,f103]) ).
fof(f5694,plain,
( spl0_254
| ~ spl0_55
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f695,f670,f427,f5692]) ).
fof(f5692,plain,
( spl0_254
<=> ! [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_254])]) ).
fof(f695,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,[],[f671,f428]) ).
fof(f5690,plain,
( spl0_253
| ~ spl0_68
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f693,f670,f597,f5688]) ).
fof(f5688,plain,
( spl0_253
<=> ! [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_253])]) ).
fof(f693,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,[],[f671,f598]) ).
fof(f5686,plain,
( spl0_252
| ~ spl0_16
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f687,f666,f92,f5684]) ).
fof(f5684,plain,
( spl0_252
<=> ! [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_252])]) ).
fof(f666,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(f687,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,[],[f667,f93]) ).
fof(f667,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,[],[f666]) ).
fof(f5682,plain,
( spl0_251
| ~ spl0_17
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f684,f666,f102,f5680]) ).
fof(f5680,plain,
( spl0_251
<=> ! [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_251])]) ).
fof(f684,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,[],[f667,f103]) ).
fof(f5678,plain,
( spl0_250
| ~ spl0_55
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f683,f666,f427,f5676]) ).
fof(f5676,plain,
( spl0_250
<=> ! [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_250])]) ).
fof(f683,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,[],[f667,f428]) ).
fof(f5674,plain,
( spl0_249
| ~ spl0_68
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f681,f666,f597,f5672]) ).
fof(f5672,plain,
( spl0_249
<=> ! [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_249])]) ).
fof(f681,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,[],[f667,f598]) ).
fof(f5670,plain,
( spl0_248
| ~ spl0_47
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f662,f633,f314,f5668]) ).
fof(f5668,plain,
( spl0_248
<=> ! [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_248])]) ).
fof(f314,plain,
( spl0_47
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f633,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(f662,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,[],[f634,f315]) ).
fof(f315,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f634,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,[],[f633]) ).
fof(f5666,plain,
( spl0_247
| ~ spl0_29
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f653,f633,f185,f5664]) ).
fof(f5664,plain,
( spl0_247
<=> ! [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_247])]) ).
fof(f185,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(f653,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,[],[f634,f186]) ).
fof(f186,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f5662,plain,
( ~ spl0_246
| spl0_2
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f3611,f3171,f22,f5659]) ).
fof(f5659,plain,
( spl0_246
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(r,not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f3171,plain,
( spl0_163
<=> ! [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_163])]) ).
fof(f3611,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(r,not(q))))
| spl0_2
| ~ spl0_163 ),
inference(resolution,[],[f3172,f24]) ).
fof(f3172,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X3,or(X2,X1))))
| ~ theorem(or(X0,or(X1,X2))) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f3171]) ).
fof(f5657,plain,
( spl0_245
| ~ spl0_30
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f652,f633,f189,f5655]) ).
fof(f5655,plain,
( spl0_245
<=> ! [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_245])]) ).
fof(f189,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(f652,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,[],[f634,f190]) ).
fof(f190,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f5653,plain,
( spl0_244
| ~ spl0_10
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f643,f633,f60,f5651]) ).
fof(f5651,plain,
( spl0_244
<=> ! [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_244])]) ).
fof(f60,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f643,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,[],[f634,f61]) ).
fof(f61,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f5649,plain,
( spl0_243
| ~ spl0_12
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f639,f633,f71,f5647]) ).
fof(f5647,plain,
( spl0_243
<=> ! [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_243])]) ).
fof(f71,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(f639,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,[],[f634,f72]) ).
fof(f72,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f5645,plain,
( spl0_242
| ~ spl0_50
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f628,f597,f329,f5643]) ).
fof(f5643,plain,
( spl0_242
<=> ! [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_242])]) ).
fof(f329,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(f628,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,[],[f598,f330]) ).
fof(f330,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f5641,plain,
( spl0_241
| ~ spl0_32
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f618,f597,f218,f5639]) ).
fof(f5639,plain,
( spl0_241
<=> ! [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_241])]) ).
fof(f218,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(f618,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,[],[f598,f219]) ).
fof(f219,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f5637,plain,
( spl0_240
| ~ spl0_60
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f616,f597,f487,f5635]) ).
fof(f5635,plain,
( spl0_240
<=> ! [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_240])]) ).
fof(f487,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(f616,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,[],[f598,f488]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f5633,plain,
( spl0_239
| ~ spl0_62
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f610,f597,f495,f5631]) ).
fof(f495,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(f610,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,[],[f598,f496]) ).
fof(f496,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f5629,plain,
( spl0_238
| ~ spl0_48
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f608,f597,f321,f5627]) ).
fof(f5627,plain,
( spl0_238
<=> ! [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_238])]) ).
fof(f321,plain,
( spl0_48
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f608,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,[],[f598,f322]) ).
fof(f322,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f5625,plain,
( spl0_237
| ~ spl0_59
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f605,f597,f483,f5623]) ).
fof(f5623,plain,
( spl0_237
<=> ! [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_237])]) ).
fof(f483,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(f605,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,[],[f598,f484]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f5621,plain,
( spl0_236
| ~ spl0_19
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f604,f597,f117,f5619]) ).
fof(f5619,plain,
( spl0_236
<=> ! [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_236])]) ).
fof(f117,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(f604,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,[],[f598,f118]) ).
fof(f118,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f5611,plain,
( spl0_235
| ~ spl0_54
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f594,f547,f377,f5609]) ).
fof(f5609,plain,
( spl0_235
<=> ! [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_235])]) ).
fof(f377,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(f547,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(f594,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,[],[f548,f378]) ).
fof(f378,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,X1))
| ~ theorem(not(X2)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f548,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,[],[f547]) ).
fof(f5607,plain,
( spl0_234
| ~ spl0_54
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f589,f543,f377,f5605]) ).
fof(f5605,plain,
( spl0_234
<=> ! [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_234])]) ).
fof(f543,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(f589,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,[],[f544,f378]) ).
fof(f544,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,[],[f543]) ).
fof(f5603,plain,
( spl0_233
| ~ spl0_31
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f586,f543,f193,f5601]) ).
fof(f5601,plain,
( spl0_233
<=> ! [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_233])]) ).
fof(f193,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(f586,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,[],[f544,f194]) ).
fof(f194,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f5599,plain,
( spl0_232
| ~ spl0_12
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f563,f539,f71,f5597]) ).
fof(f5597,plain,
( spl0_232
<=> ! [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_232])]) ).
fof(f539,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(f563,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,[],[f540,f72]) ).
fof(f540,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,[],[f539]) ).
fof(f5595,plain,
( spl0_231
| ~ spl0_54
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f553,f535,f377,f5593]) ).
fof(f5593,plain,
( spl0_231
<=> ! [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_231])]) ).
fof(f535,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(f553,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,[],[f536,f378]) ).
fof(f536,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f5591,plain,
( spl0_230
| ~ spl0_31
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f551,f535,f193,f5589]) ).
fof(f5589,plain,
( spl0_230
<=> ! [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_230])]) ).
fof(f551,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,[],[f536,f194]) ).
fof(f5587,plain,
( spl0_229
| ~ spl0_17
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f519,f491,f102,f5585]) ).
fof(f5585,plain,
( spl0_229
<=> ! [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_229])]) ).
fof(f491,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(f519,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,[],[f492,f103]) ).
fof(f492,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X2,X0)),X1),X2))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f5583,plain,
( spl0_228
| ~ spl0_55
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f518,f491,f427,f5581]) ).
fof(f5581,plain,
( spl0_228
<=> ! [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_228])]) ).
fof(f518,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,[],[f492,f428]) ).
fof(f5579,plain,
( spl0_227
| ~ spl0_15
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f511,f487,f85,f5577]) ).
fof(f5577,plain,
( spl0_227
<=> ! [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_227])]) ).
fof(f85,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f511,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,[],[f488,f86]) ).
fof(f86,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f5575,plain,
( spl0_226
| ~ spl0_31
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f476,f460,f193,f5573]) ).
fof(f5573,plain,
( spl0_226
<=> ! [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_226])]) ).
fof(f460,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(f476,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,[],[f461,f194]) ).
fof(f461,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f5565,plain,
( spl0_225
| ~ spl0_34
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f422,f377,f231,f5563]) ).
fof(f5563,plain,
( spl0_225
<=> ! [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_225])]) ).
fof(f231,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(f422,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,[],[f378,f232]) ).
fof(f232,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,[],[f231]) ).
fof(f5561,plain,
( spl0_224
| ~ spl0_14
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f407,f377,f80,f5559]) ).
fof(f5559,plain,
( spl0_224
<=> ! [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_224])]) ).
fof(f80,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(f407,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,[],[f378,f81]) ).
fof(f81,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,[],[f80]) ).
fof(f5557,plain,
( spl0_223
| ~ spl0_36
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f406,f377,f240,f5555]) ).
fof(f5555,plain,
( spl0_223
<=> ! [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_223])]) ).
fof(f240,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(f406,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,[],[f378,f241]) ).
fof(f241,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,[],[f240]) ).
fof(f5246,plain,
( ~ spl0_222
| spl0_39
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1532,f1464,f263,f5243]) ).
fof(f5243,plain,
( spl0_222
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f263,plain,
( spl0_39
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(q),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1464,plain,
( spl0_100
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1532,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),not(q)))
| spl0_39
| ~ spl0_100 ),
inference(resolution,[],[f1465,f265]) ).
fof(f265,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(q),r)))
| spl0_39 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1464]) ).
fof(f4958,plain,
( ~ spl0_221
| spl0_2
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1531,f1464,f22,f4955]) ).
fof(f4955,plain,
( spl0_221
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1531,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),not(p)))
| spl0_2
| ~ spl0_100 ),
inference(resolution,[],[f1465,f24]) ).
fof(f4891,plain,
( spl0_220
| ~ spl0_47
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f626,f597,f314,f4889]) ).
fof(f4889,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(f626,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,[],[f598,f315]) ).
fof(f4887,plain,
( spl0_219
| ~ spl0_51
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f593,f543,f333,f4885]) ).
fof(f4885,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(f333,plain,
( spl0_51
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f593,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,[],[f544,f334]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f4883,plain,
( spl0_218
| ~ spl0_15
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f588,f543,f85,f4881]) ).
fof(f4881,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(f588,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,[],[f544,f86]) ).
fof(f4879,plain,
( spl0_217
| ~ spl0_27
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f581,f539,f171,f4877]) ).
fof(f4877,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(f171,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(f581,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,[],[f540,f172]) ).
fof(f172,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f4875,plain,
( spl0_216
| ~ spl0_54
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f527,f495,f377,f4873]) ).
fof(f4873,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(f527,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,[],[f496,f378]) ).
fof(f4871,plain,
( spl0_215
| ~ spl0_31
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f522,f495,f193,f4869]) ).
fof(f4869,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(f522,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,[],[f496,f194]) ).
fof(f4867,plain,
( spl0_214
| ~ spl0_54
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f516,f491,f377,f4865]) ).
fof(f4865,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(f516,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,[],[f492,f378]) ).
fof(f4863,plain,
( spl0_213
| ~ spl0_54
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f512,f487,f377,f4861]) ).
fof(f4861,plain,
( spl0_213
<=> ! [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_213])]) ).
fof(f512,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,[],[f488,f378]) ).
fof(f4859,plain,
( spl0_212
| ~ spl0_53
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f506,f487,f373,f4857]) ).
fof(f4857,plain,
( spl0_212
<=> ! [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_212])]) ).
fof(f373,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(f506,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,[],[f488,f374]) ).
fof(f374,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f4855,plain,
( spl0_211
| ~ spl0_54
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f504,f483,f377,f4853]) ).
fof(f4853,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f504,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,[],[f484,f378]) ).
fof(f4851,plain,
( spl0_210
| ~ spl0_31
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f499,f483,f193,f4849]) ).
fof(f4849,plain,
( spl0_210
<=> ! [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_210])]) ).
fof(f499,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,[],[f484,f194]) ).
fof(f4847,plain,
( spl0_209
| ~ spl0_51
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f474,f456,f333,f4845]) ).
fof(f4845,plain,
( spl0_209
<=> ! [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_209])]) ).
fof(f456,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,
( ! [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,[],[f457,f334]) ).
fof(f457,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f4843,plain,
( spl0_208
| ~ spl0_17
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f467,f452,f102,f4841]) ).
fof(f4841,plain,
( spl0_208
<=> ! [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_208])]) ).
fof(f452,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(f467,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,[],[f453,f103]) ).
fof(f453,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f4839,plain,
( spl0_207
| ~ spl0_55
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f466,f452,f427,f4837]) ).
fof(f4837,plain,
( spl0_207
<=> ! [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_207])]) ).
fof(f466,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,[],[f453,f428]) ).
fof(f4835,plain,
( spl0_206
| ~ spl0_33
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f420,f377,f222,f4833]) ).
fof(f4833,plain,
( spl0_206
<=> ! [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_206])]) ).
fof(f222,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(f420,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,[],[f378,f223]) ).
fof(f223,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),not(or(X2,X0))))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f4831,plain,
( spl0_205
| ~ spl0_32
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f415,f377,f218,f4829]) ).
fof(f4829,plain,
( spl0_205
<=> ! [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_205])]) ).
fof(f415,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,[],[f378,f219]) ).
fof(f4827,plain,
( spl0_204
| ~ spl0_19
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f405,f377,f117,f4825]) ).
fof(f4825,plain,
( spl0_204
<=> ! [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_204])]) ).
fof(f405,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,[],[f378,f118]) ).
fof(f4823,plain,
( spl0_203
| ~ spl0_32
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f396,f373,f218,f4821]) ).
fof(f4821,plain,
( spl0_203
<=> ! [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_203])]) ).
fof(f396,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,[],[f374,f219]) ).
fof(f4819,plain,
( ~ spl0_202
| spl0_2
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f4435,f4310,f22,f4816]) ).
fof(f4816,plain,
( spl0_202
<=> theorem(not(or(not(p),or(not(or(not(p),q)),r)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f4310,plain,
( spl0_188
<=> ! [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_188])]) ).
fof(f4435,plain,
( ~ theorem(not(or(not(p),or(not(or(not(p),q)),r))))
| spl0_2
| ~ spl0_188 ),
inference(resolution,[],[f4311,f24]) ).
fof(f4311,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(X1,X2))),X3))
| ~ theorem(not(or(X1,or(X0,X2)))) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f4310]) ).
fof(f4814,plain,
( spl0_201
| ~ spl0_30
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f394,f373,f189,f4812]) ).
fof(f4812,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(f394,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,[],[f374,f190]) ).
fof(f4362,plain,
( spl0_200
| ~ spl0_53
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f585,f543,f373,f4360]) ).
fof(f4360,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(f585,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,[],[f544,f374]) ).
fof(f4358,plain,
( spl0_199
| ~ spl0_26
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f575,f539,f163,f4356]) ).
fof(f4356,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(f163,plain,
( spl0_26
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f575,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,[],[f540,f164]) ).
fof(f164,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f4354,plain,
( spl0_198
| ~ spl0_53
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f550,f535,f373,f4352]) ).
fof(f4352,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f550,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,[],[f536,f374]) ).
fof(f4348,plain,
( spl0_197
| ~ spl0_51
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f520,f491,f333,f4346]) ).
fof(f4346,plain,
( spl0_197
<=> ! [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_197])]) ).
fof(f520,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,[],[f492,f334]) ).
fof(f4344,plain,
( spl0_196
| ~ spl0_54
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f479,f460,f377,f4342]) ).
fof(f4342,plain,
( spl0_196
<=> ! [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_196])]) ).
fof(f479,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,[],[f461,f378]) ).
fof(f4340,plain,
( spl0_195
| ~ spl0_15
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f478,f460,f85,f4338]) ).
fof(f4338,plain,
( spl0_195
<=> ! [X0] :
( ~ theorem(or(not(or(not(X0),not(X0))),X0))
| theorem(not(or(not(X0),not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f478,plain,
( ! [X0] :
( ~ theorem(or(not(or(not(X0),not(X0))),X0))
| theorem(not(or(not(X0),not(X0)))) )
| ~ spl0_15
| ~ spl0_58 ),
inference(resolution,[],[f461,f86]) ).
fof(f4336,plain,
( spl0_194
| ~ spl0_53
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f475,f460,f373,f4334]) ).
fof(f4334,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f475,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,[],[f461,f374]) ).
fof(f4332,plain,
( spl0_193
| ~ spl0_54
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f470,f456,f377,f4330]) ).
fof(f4330,plain,
( spl0_193
<=> ! [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_193])]) ).
fof(f470,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,[],[f457,f378]) ).
fof(f4328,plain,
( spl0_192
| ~ spl0_54
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f464,f452,f377,f4326]) ).
fof(f4326,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f464,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,[],[f453,f378]) ).
fof(f4324,plain,
( spl0_191
| ~ spl0_28
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f421,f377,f181,f4322]) ).
fof(f4322,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f181,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(f421,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,[],[f378,f182]) ).
fof(f182,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f4320,plain,
( spl0_190
| ~ spl0_29
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f414,f377,f185,f4318]) ).
fof(f4318,plain,
( spl0_190
<=> ! [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_190])]) ).
fof(f414,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,[],[f378,f186]) ).
fof(f4316,plain,
( spl0_189
| ~ spl0_30
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f413,f377,f189,f4314]) ).
fof(f4314,plain,
( spl0_189
<=> ! [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_189])]) ).
fof(f413,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,[],[f378,f190]) ).
fof(f4312,plain,
( spl0_188
| ~ spl0_12
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f404,f377,f71,f4310]) ).
fof(f404,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,[],[f378,f72]) ).
fof(f4308,plain,
( ~ spl0_187
| ~ spl0_100
| spl0_169 ),
inference(avatar_split_clause,[],[f3731,f3479,f1464,f4305]) ).
fof(f4305,plain,
( spl0_187
<=> theorem(or(not(q),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f3479,plain,
( spl0_169
<=> theorem(or(not(q),or(not(p),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f3731,plain,
( ~ theorem(or(not(q),not(p)))
| ~ spl0_100
| spl0_169 ),
inference(resolution,[],[f3481,f1465]) ).
fof(f3481,plain,
( ~ theorem(or(not(q),or(not(p),r)))
| spl0_169 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f4303,plain,
( spl0_186
| ~ spl0_29
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f395,f373,f185,f4301]) ).
fof(f4301,plain,
( spl0_186
<=> ! [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_186])]) ).
fof(f395,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,[],[f374,f186]) ).
fof(f4299,plain,
( spl0_185
| ~ spl0_14
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f388,f373,f80,f4297]) ).
fof(f4297,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f388,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,[],[f374,f81]) ).
fof(f4295,plain,
( spl0_184
| ~ spl0_36
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f387,f373,f240,f4293]) ).
fof(f4293,plain,
( spl0_184
<=> ! [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_184])]) ).
fof(f387,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,[],[f374,f241]) ).
fof(f3813,plain,
( spl0_183
| ~ spl0_14
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f609,f597,f80,f3811]) ).
fof(f3811,plain,
( spl0_183
<=> ! [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_183])]) ).
fof(f609,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,[],[f598,f81]) ).
fof(f3809,plain,
( spl0_182
| ~ spl0_36
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f606,f597,f240,f3807]) ).
fof(f3807,plain,
( spl0_182
<=> ! [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_182])]) ).
fof(f606,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,[],[f598,f241]) ).
fof(f3805,plain,
( spl0_181
| ~ spl0_16
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f590,f543,f92,f3803]) ).
fof(f3803,plain,
( spl0_181
<=> ! [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_181])]) ).
fof(f590,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,[],[f544,f93]) ).
fof(f3801,plain,
( spl0_180
| ~ spl0_22
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f572,f539,f139,f3799]) ).
fof(f3799,plain,
( spl0_180
<=> ! [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_180])]) ).
fof(f139,plain,
( spl0_22
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f572,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,[],[f540,f140]) ).
fof(f140,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f3797,plain,
( ~ spl0_179
| ~ spl0_93
| spl0_169 ),
inference(avatar_split_clause,[],[f3732,f3479,f1433,f3794]) ).
fof(f3794,plain,
( spl0_179
<=> theorem(or(r,not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1433,plain,
( spl0_93
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f3732,plain,
( ~ theorem(or(r,not(p)))
| ~ spl0_93
| spl0_169 ),
inference(resolution,[],[f3481,f1434]) ).
fof(f1434,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f3792,plain,
( spl0_178
| ~ spl0_48
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f561,f539,f321,f3790]) ).
fof(f3790,plain,
( spl0_178
<=> ! [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_178])]) ).
fof(f561,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,[],[f540,f322]) ).
fof(f3788,plain,
( spl0_177
| ~ spl0_16
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f554,f535,f92,f3786]) ).
fof(f3786,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(or(not(X0),X1),or(not(X0),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(or(not(X0),X1),or(not(X0),X1))))) )
| ~ spl0_16
| ~ spl0_64 ),
inference(resolution,[],[f536,f93]) ).
fof(f3784,plain,
( spl0_176
| ~ spl0_6
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f508,f487,f41,f3782]) ).
fof(f3782,plain,
( spl0_176
<=> ! [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_176])]) ).
fof(f41,plain,
( spl0_6
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f508,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,[],[f488,f42]) ).
fof(f42,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f3780,plain,
( spl0_175
| ~ spl0_53
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f498,f483,f373,f3778]) ).
fof(f3778,plain,
( spl0_175
<=> ! [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_175])]) ).
fof(f498,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,[],[f484,f374]) ).
fof(f3776,plain,
( spl0_174
| ~ spl0_51
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f468,f452,f333,f3774]) ).
fof(f3774,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f468,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,[],[f453,f334]) ).
fof(f3772,plain,
( spl0_173
| ~ spl0_14
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f438,f427,f80,f3770]) ).
fof(f3770,plain,
( spl0_173
<=> ! [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_173])]) ).
fof(f438,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,[],[f428,f81]) ).
fof(f3768,plain,
( spl0_172
| ~ spl0_36
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f435,f427,f240,f3766]) ).
fof(f3766,plain,
( spl0_172
<=> ! [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_172])]) ).
fof(f435,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,[],[f428,f241]) ).
fof(f3764,plain,
( spl0_171
| ~ spl0_19
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f386,f373,f117,f3762]) ).
fof(f3762,plain,
( spl0_171
<=> ! [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_171])]) ).
fof(f386,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,[],[f374,f118]) ).
fof(f3760,plain,
( spl0_170
| ~ spl0_33
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f340,f325,f222,f3758]) ).
fof(f3758,plain,
( spl0_170
<=> ! [X0,X1] :
( theorem(or(X0,not(or(X0,X1))))
| ~ theorem(or(not(X1),not(or(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f325,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f340,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(X0,X1))))
| ~ theorem(or(not(X1),not(or(X0,X1)))) )
| ~ spl0_33
| ~ spl0_49 ),
inference(resolution,[],[f326,f223]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f3482,plain,
( ~ spl0_169
| spl0_2
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f3285,f3102,f22,f3479]) ).
fof(f3102,plain,
( spl0_146
<=> ! [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_146])]) ).
fof(f3285,plain,
( ~ theorem(or(not(q),or(not(p),r)))
| spl0_2
| ~ spl0_146 ),
inference(resolution,[],[f3103,f24]) ).
fof(f3103,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f3102]) ).
fof(f3264,plain,
( ~ spl0_168
| spl0_2
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f2480,f2362,f22,f3261]) ).
fof(f3261,plain,
( spl0_168
<=> theorem(not(or(or(not(p),r),not(or(not(p),q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f2362,plain,
( spl0_115
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2480,plain,
( ~ theorem(not(or(or(not(p),r),not(or(not(p),q)))))
| spl0_2
| ~ spl0_115 ),
inference(resolution,[],[f2363,f24]) ).
fof(f2363,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f3189,plain,
( spl0_167
| ~ spl0_26
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f650,f633,f163,f3187]) ).
fof(f3187,plain,
( spl0_167
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f650,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_26
| ~ spl0_69 ),
inference(resolution,[],[f634,f164]) ).
fof(f3185,plain,
( spl0_166
| ~ spl0_11
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f638,f633,f66,f3183]) ).
fof(f3183,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f66,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f638,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) )
| ~ spl0_11
| ~ spl0_69 ),
inference(resolution,[],[f634,f67]) ).
fof(f67,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f3181,plain,
( spl0_165
| ~ spl0_27
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f620,f597,f171,f3179]) ).
fof(f620,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,[],[f598,f172]) ).
fof(f3177,plain,
( spl0_164
| ~ spl0_6
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f587,f543,f41,f3175]) ).
fof(f3175,plain,
( spl0_164
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) )
| ~ spl0_6
| ~ spl0_66 ),
inference(resolution,[],[f544,f42]) ).
fof(f3173,plain,
( spl0_163
| ~ spl0_11
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f562,f539,f66,f3171]) ).
fof(f562,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,[],[f540,f67]) ).
fof(f3169,plain,
( spl0_162
| ~ spl0_6
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f552,f535,f41,f3167]) ).
fof(f3167,plain,
( spl0_162
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f552,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) )
| ~ spl0_6
| ~ spl0_64 ),
inference(resolution,[],[f536,f42]) ).
fof(f3165,plain,
( spl0_161
| ~ spl0_16
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f528,f495,f92,f3163]) ).
fof(f3163,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) )
| ~ spl0_16
| ~ spl0_62 ),
inference(resolution,[],[f496,f93]) ).
fof(f3161,plain,
( spl0_160
| ~ spl0_17
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f525,f495,f102,f3159]) ).
fof(f3159,plain,
( spl0_160
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) )
| ~ spl0_17
| ~ spl0_62 ),
inference(resolution,[],[f496,f103]) ).
fof(f3157,plain,
( spl0_159
| ~ spl0_55
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f524,f495,f427,f3155]) ).
fof(f3155,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) )
| ~ spl0_55
| ~ spl0_62 ),
inference(resolution,[],[f496,f428]) ).
fof(f3153,plain,
( spl0_158
| ~ spl0_16
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f513,f487,f92,f3151]) ).
fof(f3151,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f513,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) )
| ~ spl0_16
| ~ spl0_60 ),
inference(resolution,[],[f488,f93]) ).
fof(f3149,plain,
( spl0_157
| ~ spl0_17
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f510,f487,f102,f3147]) ).
fof(f3147,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f510,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) )
| ~ spl0_17
| ~ spl0_60 ),
inference(resolution,[],[f488,f103]) ).
fof(f3145,plain,
( spl0_156
| ~ spl0_55
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f509,f487,f427,f3143]) ).
fof(f3143,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f509,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) )
| ~ spl0_55
| ~ spl0_60 ),
inference(resolution,[],[f488,f428]) ).
fof(f3141,plain,
( spl0_155
| ~ spl0_16
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f505,f483,f92,f3139]) ).
fof(f3139,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f505,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) )
| ~ spl0_16
| ~ spl0_59 ),
inference(resolution,[],[f484,f93]) ).
fof(f3137,plain,
( spl0_154
| ~ spl0_17
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f502,f483,f102,f3135]) ).
fof(f3135,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f502,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) )
| ~ spl0_17
| ~ spl0_59 ),
inference(resolution,[],[f484,f103]) ).
fof(f3133,plain,
( spl0_153
| ~ spl0_55
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f501,f483,f427,f3131]) ).
fof(f3131,plain,
( spl0_153
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) )
| ~ spl0_55
| ~ spl0_59 ),
inference(resolution,[],[f484,f428]) ).
fof(f3129,plain,
( spl0_152
| ~ spl0_6
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f477,f460,f41,f3127]) ).
fof(f3127,plain,
( spl0_152
<=> ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f477,plain,
( ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_58 ),
inference(resolution,[],[f461,f42]) ).
fof(f3125,plain,
( spl0_151
| ~ spl0_50
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f450,f427,f329,f3123]) ).
fof(f3123,plain,
( spl0_151
<=> ! [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_151])]) ).
fof(f450,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,[],[f428,f330]) ).
fof(f3121,plain,
( ~ spl0_150
| spl0_76
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f2483,f2362,f726,f3118]) ).
fof(f3118,plain,
( spl0_150
<=> theorem(not(or(r,not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f726,plain,
( spl0_76
<=> theorem(or(not(or(not(p),r)),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f2483,plain,
( ~ theorem(not(or(r,not(p))))
| spl0_76
| ~ spl0_115 ),
inference(resolution,[],[f2363,f728]) ).
fof(f728,plain,
( ~ theorem(or(not(or(not(p),r)),r))
| spl0_76 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f3116,plain,
( spl0_149
| ~ spl0_32
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f443,f427,f218,f3114]) ).
fof(f3114,plain,
( spl0_149
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f443,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) )
| ~ spl0_32
| ~ spl0_55 ),
inference(resolution,[],[f428,f219]) ).
fof(f3112,plain,
( spl0_148
| ~ spl0_48
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f437,f427,f321,f3110]) ).
fof(f3110,plain,
( spl0_148
<=> ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f437,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_55 ),
inference(resolution,[],[f428,f322]) ).
fof(f3108,plain,
( spl0_147
| ~ spl0_19
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f434,f427,f117,f3106]) ).
fof(f3106,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f434,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19
| ~ spl0_55 ),
inference(resolution,[],[f428,f118]) ).
fof(f3104,plain,
( spl0_146
| ~ spl0_12
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f385,f373,f71,f3102]) ).
fof(f385,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,[],[f374,f72]) ).
fof(f3100,plain,
( spl0_145
| ~ spl0_17
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f351,f329,f102,f3098]) ).
fof(f3098,plain,
( spl0_145
<=> ! [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_145])]) ).
fof(f351,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,[],[f330,f103]) ).
fof(f3096,plain,
( spl0_144
| ~ spl0_27
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f347,f325,f171,f3094]) ).
fof(f3094,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f347,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) )
| ~ spl0_27
| ~ spl0_49 ),
inference(resolution,[],[f326,f172]) ).
fof(f3092,plain,
( spl0_143
| ~ spl0_17
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f339,f321,f102,f3090]) ).
fof(f3090,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f339,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) )
| ~ spl0_17
| ~ spl0_48 ),
inference(resolution,[],[f322,f103]) ).
fof(f2674,plain,
( spl0_142
| ~ spl0_26
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f615,f597,f163,f2672]) ).
fof(f2672,plain,
( spl0_142
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f615,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2))))
| ~ spl0_26
| ~ spl0_68 ),
inference(resolution,[],[f598,f164]) ).
fof(f2670,plain,
( spl0_141
| ~ spl0_29
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f613,f597,f185,f2668]) ).
fof(f2668,plain,
( spl0_141
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f613,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2))))
| ~ spl0_29
| ~ spl0_68 ),
inference(resolution,[],[f598,f186]) ).
fof(f2666,plain,
( spl0_140
| ~ spl0_11
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f602,f597,f66,f2664]) ).
fof(f2664,plain,
( spl0_140
<=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f602,plain,
( ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1))))
| ~ spl0_11
| ~ spl0_68 ),
inference(resolution,[],[f598,f67]) ).
fof(f2662,plain,
( spl0_139
| ~ spl0_6
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f500,f483,f41,f2660]) ).
fof(f2660,plain,
( spl0_139
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f500,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) )
| ~ spl0_6
| ~ spl0_59 ),
inference(resolution,[],[f484,f42]) ).
fof(f2658,plain,
( spl0_138
| ~ spl0_16
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f480,f460,f92,f2656]) ).
fof(f2656,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f480,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) )
| ~ spl0_16
| ~ spl0_58 ),
inference(resolution,[],[f461,f93]) ).
fof(f2654,plain,
( spl0_137
| ~ spl0_47
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f449,f427,f314,f2652]) ).
fof(f2652,plain,
( spl0_137
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f449,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1)))
| ~ spl0_47
| ~ spl0_55 ),
inference(resolution,[],[f428,f315]) ).
fof(f2650,plain,
( ~ spl0_136
| spl0_76
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f2525,f2387,f726,f2647]) ).
fof(f2647,plain,
( spl0_136
<=> theorem(or(r,p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2387,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2525,plain,
( ~ theorem(or(r,p))
| spl0_76
| ~ spl0_121 ),
inference(resolution,[],[f2388,f728]) ).
fof(f2388,plain,
( ! [X0,X1] :
( theorem(or(not(or(not(X1),X0)),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f2645,plain,
( spl0_135
| ~ spl0_29
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f442,f427,f185,f2643]) ).
fof(f2643,plain,
( spl0_135
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f442,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2))))))
| ~ spl0_29
| ~ spl0_55 ),
inference(resolution,[],[f428,f186]) ).
fof(f2641,plain,
( spl0_134
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f441,f427,f189,f2639]) ).
fof(f2639,plain,
( spl0_134
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f441,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1))))))
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f428,f190]) ).
fof(f2637,plain,
( spl0_133
| ~ spl0_10
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f436,f427,f60,f2635]) ).
fof(f2635,plain,
( spl0_133
<=> ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f436,plain,
( ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0)))
| ~ spl0_10
| ~ spl0_55 ),
inference(resolution,[],[f428,f61]) ).
fof(f2633,plain,
( spl0_132
| ~ spl0_12
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f433,f427,f71,f2631]) ).
fof(f2631,plain,
( spl0_132
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f433,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1)))
| ~ spl0_12
| ~ spl0_55 ),
inference(resolution,[],[f428,f72]) ).
fof(f2629,plain,
( spl0_131
| ~ spl0_50
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f425,f377,f329,f2627]) ).
fof(f2627,plain,
( spl0_131
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f425,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) )
| ~ spl0_50
| ~ spl0_54 ),
inference(resolution,[],[f378,f330]) ).
fof(f2625,plain,
( spl0_130
| ~ spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f417,f377,f171,f2623]) ).
fof(f2623,plain,
( spl0_130
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f417,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) )
| ~ spl0_27
| ~ spl0_54 ),
inference(resolution,[],[f378,f172]) ).
fof(f2621,plain,
( spl0_129
| ~ spl0_48
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f402,f377,f321,f2619]) ).
fof(f2619,plain,
( spl0_129
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f402,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) )
| ~ spl0_48
| ~ spl0_54 ),
inference(resolution,[],[f378,f322]) ).
fof(f2617,plain,
( spl0_128
| ~ spl0_27
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f398,f373,f171,f2615]) ).
fof(f2615,plain,
( spl0_128
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f398,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_53 ),
inference(resolution,[],[f374,f172]) ).
fof(f2613,plain,
( spl0_127
| ~ spl0_12
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f355,f333,f71,f2611]) ).
fof(f2611,plain,
( spl0_127
<=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f355,plain,
( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
| ~ spl0_12
| ~ spl0_51 ),
inference(resolution,[],[f334,f72]) ).
fof(f2609,plain,
( spl0_126
| ~ spl0_31
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f336,f321,f193,f2607]) ).
fof(f2607,plain,
( spl0_126
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f336,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) )
| ~ spl0_31
| ~ spl0_48 ),
inference(resolution,[],[f322,f194]) ).
fof(f2605,plain,
( ~ spl0_125
| ~ spl0_99
| spl0_116 ),
inference(avatar_split_clause,[],[f2461,f2366,f1460,f2602]) ).
fof(f2602,plain,
( spl0_125
<=> theorem(not(not(r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1460,plain,
( spl0_99
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2366,plain,
( spl0_116
<=> theorem(or(or(not(q),r),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f2461,plain,
( ~ theorem(not(not(r)))
| ~ spl0_99
| spl0_116 ),
inference(resolution,[],[f2368,f1461]) ).
fof(f1461,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1460]) ).
fof(f2368,plain,
( ~ theorem(or(or(not(q),r),not(p)))
| spl0_116 ),
inference(avatar_component_clause,[],[f2366]) ).
fof(f2600,plain,
( spl0_124
| ~ spl0_17
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f319,f314,f102,f2598]) ).
fof(f2598,plain,
( spl0_124
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f319,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
| ~ spl0_17
| ~ spl0_47 ),
inference(resolution,[],[f315,f103]) ).
fof(f2397,plain,
( spl0_123
| ~ spl0_10
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f560,f539,f60,f2395]) ).
fof(f2395,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f560,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) )
| ~ spl0_10
| ~ spl0_65 ),
inference(resolution,[],[f540,f61]) ).
fof(f2393,plain,
( spl0_122
| ~ spl0_7
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f558,f539,f46,f2391]) ).
fof(f2391,plain,
( spl0_122
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f558,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) )
| ~ spl0_7
| ~ spl0_65 ),
inference(resolution,[],[f540,f47]) ).
fof(f2389,plain,
( spl0_121
| ~ spl0_51
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f526,f495,f333,f2387]) ).
fof(f526,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) )
| ~ spl0_51
| ~ spl0_62 ),
inference(resolution,[],[f496,f334]) ).
fof(f2385,plain,
( spl0_120
| ~ spl0_51
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f503,f483,f333,f2383]) ).
fof(f2383,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f503,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
| ~ spl0_51
| ~ spl0_59 ),
inference(resolution,[],[f484,f334]) ).
fof(f2381,plain,
( spl0_119
| ~ spl0_47
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f424,f377,f314,f2379]) ).
fof(f2379,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f424,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) )
| ~ spl0_47
| ~ spl0_54 ),
inference(resolution,[],[f378,f315]) ).
fof(f2377,plain,
( spl0_118
| ~ spl0_25
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f419,f377,f159,f2375]) ).
fof(f2375,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f159,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f419,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) )
| ~ spl0_25
| ~ spl0_54 ),
inference(resolution,[],[f378,f160]) ).
fof(f160,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f2373,plain,
( spl0_117
| ~ spl0_26
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f412,f377,f163,f2371]) ).
fof(f2371,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f412,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) )
| ~ spl0_26
| ~ spl0_54 ),
inference(resolution,[],[f378,f164]) ).
fof(f2369,plain,
( ~ spl0_116
| spl0_2
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1482,f1433,f22,f2366]) ).
fof(f1482,plain,
( ~ theorem(or(or(not(q),r),not(p)))
| spl0_2
| ~ spl0_93 ),
inference(resolution,[],[f1434,f24]) ).
fof(f2364,plain,
( spl0_115
| ~ spl0_11
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f403,f377,f66,f2362]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_11
| ~ spl0_54 ),
inference(resolution,[],[f378,f67]) ).
fof(f2360,plain,
( spl0_114
| ~ spl0_26
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f393,f373,f163,f2358]) ).
fof(f2358,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f393,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) )
| ~ spl0_26
| ~ spl0_53 ),
inference(resolution,[],[f374,f164]) ).
fof(f2356,plain,
( spl0_113
| ~ spl0_50
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f366,f333,f329,f2354]) ).
fof(f2354,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f366,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) )
| ~ spl0_50
| ~ spl0_51 ),
inference(resolution,[],[f334,f330]) ).
fof(f2352,plain,
( spl0_112
| ~ spl0_48
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f358,f333,f321,f2350]) ).
fof(f2350,plain,
( spl0_112
<=> ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f358,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_48
| ~ spl0_51 ),
inference(resolution,[],[f334,f322]) ).
fof(f2348,plain,
( spl0_111
| ~ spl0_19
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f356,f333,f117,f2346]) ).
fof(f2346,plain,
( spl0_111
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f356,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) )
| ~ spl0_19
| ~ spl0_51 ),
inference(resolution,[],[f334,f118]) ).
fof(f2256,plain,
( spl0_110
| ~ spl0_23
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f614,f597,f143,f2254]) ).
fof(f2254,plain,
( spl0_110
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f143,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f614,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
| ~ spl0_23
| ~ spl0_68 ),
inference(resolution,[],[f598,f144]) ).
fof(f144,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f2252,plain,
( spl0_109
| ~ spl0_7
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f600,f597,f46,f2250]) ).
fof(f2250,plain,
( spl0_109
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f600,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
| ~ spl0_7
| ~ spl0_68 ),
inference(resolution,[],[f598,f47]) ).
fof(f1967,plain,
( ~ spl0_108
| spl0_18
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1533,f1464,f112,f1964]) ).
fof(f1964,plain,
( spl0_108
<=> theorem(or(not(p),not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f112,plain,
( spl0_18
<=> theorem(or(not(p),or(not(q),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1533,plain,
( ~ theorem(or(not(p),not(q)))
| spl0_18
| ~ spl0_100 ),
inference(resolution,[],[f1465,f114]) ).
fof(f114,plain,
( ~ theorem(or(not(p),or(not(q),r)))
| spl0_18 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f1598,plain,
( spl0_2
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1581]) ).
fof(f1581,plain,
( $false
| spl0_2
| ~ spl0_98 ),
inference(resolution,[],[f1457,f24]) ).
fof(f1457,plain,
( ! [X0,X1] : theorem(or(X0,X1))
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1456,plain,
( spl0_98
<=> ! [X0,X1] : theorem(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1597,plain,
( spl0_39
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1582]) ).
fof(f1582,plain,
( $false
| spl0_39
| ~ spl0_98 ),
inference(resolution,[],[f1457,f265]) ).
fof(f1596,plain,
( spl0_63
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1583]) ).
fof(f1583,plain,
( $false
| spl0_63
| ~ spl0_98 ),
inference(resolution,[],[f1457,f532]) ).
fof(f532,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),r))
| spl0_63 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f530,plain,
( spl0_63
<=> theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1595,plain,
( spl0_76
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1584]) ).
fof(f1584,plain,
( $false
| spl0_76
| ~ spl0_98 ),
inference(resolution,[],[f1457,f728]) ).
fof(f1594,plain,
( spl0_18
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1585]) ).
fof(f1585,plain,
( $false
| spl0_18
| ~ spl0_98 ),
inference(resolution,[],[f1457,f114]) ).
fof(f1593,plain,
( spl0_37
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1586]) ).
fof(f1586,plain,
( $false
| spl0_37
| ~ spl0_98 ),
inference(resolution,[],[f1457,f251]) ).
fof(f251,plain,
( ~ theorem(or(not(p),r))
| spl0_37 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f249,plain,
( spl0_37
<=> theorem(or(not(p),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1592,plain,
( spl0_75
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1587]) ).
fof(f1587,plain,
( $false
| spl0_75
| ~ spl0_98 ),
inference(resolution,[],[f1457,f724]) ).
fof(f724,plain,
( ~ theorem(or(not(p),q))
| spl0_75 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f722,plain,
( spl0_75
<=> theorem(or(not(p),q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1591,plain,
( spl0_35
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1588]) ).
fof(f1588,plain,
( $false
| spl0_35
| ~ spl0_98 ),
inference(resolution,[],[f1457,f237]) ).
fof(f237,plain,
( ~ theorem(or(not(q),r))
| spl0_35 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl0_35
<=> theorem(or(not(q),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1578,plain,
( spl0_107
| spl0_98
| ~ spl0_45
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f416,f377,f298,f1456,f1576]) ).
fof(f1576,plain,
( spl0_107
<=> ! [X2,X3] :
( ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f298,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f416,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) )
| ~ spl0_45
| ~ spl0_54 ),
inference(resolution,[],[f378,f299]) ).
fof(f299,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f1574,plain,
( spl0_106
| ~ spl0_22
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f391,f373,f139,f1572]) ).
fof(f1572,plain,
( spl0_106
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f391,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) )
| ~ spl0_22
| ~ spl0_53 ),
inference(resolution,[],[f374,f140]) ).
fof(f1570,plain,
( spl0_105
| ~ spl0_48
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f383,f373,f321,f1568]) ).
fof(f1568,plain,
( spl0_105
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) )
| ~ spl0_48
| ~ spl0_53 ),
inference(resolution,[],[f374,f322]) ).
fof(f1566,plain,
( spl0_104
| ~ spl0_47
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f365,f333,f314,f1564]) ).
fof(f1564,plain,
( spl0_104
<=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f365,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
| ~ spl0_47
| ~ spl0_51 ),
inference(resolution,[],[f334,f315]) ).
fof(f1562,plain,
( spl0_103
| ~ spl0_10
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f357,f333,f60,f1560]) ).
fof(f1560,plain,
( spl0_103
<=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f357,plain,
( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
| ~ spl0_10
| ~ spl0_51 ),
inference(resolution,[],[f334,f61]) ).
fof(f1515,plain,
( ~ spl0_102
| spl0_39
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1483,f1433,f263,f1512]) ).
fof(f1512,plain,
( spl0_102
<=> theorem(or(r,not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1483,plain,
( ~ theorem(or(r,not(q)))
| spl0_39
| ~ spl0_93 ),
inference(resolution,[],[f1434,f265]) ).
fof(f1470,plain,
( spl0_101
| ~ spl0_45
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f619,f597,f298,f1468]) ).
fof(f1468,plain,
( spl0_101
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f619,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) )
| ~ spl0_45
| ~ spl0_68 ),
inference(resolution,[],[f598,f299]) ).
fof(f1466,plain,
( spl0_100
| ~ spl0_27
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f445,f427,f171,f1464]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_27
| ~ spl0_55 ),
inference(resolution,[],[f428,f172]) ).
fof(f1462,plain,
( spl0_99
| ~ spl0_21
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f418,f377,f135,f1460]) ).
fof(f135,plain,
( spl0_21
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_21
| ~ spl0_54 ),
inference(resolution,[],[f378,f136]) ).
fof(f136,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f1458,plain,
( spl0_97
| spl0_98
| ~ spl0_23
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f411,f377,f143,f1456,f1453]) ).
fof(f1453,plain,
( spl0_97
<=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f411,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(X2),X2))) )
| ~ spl0_23
| ~ spl0_54 ),
inference(resolution,[],[f378,f144]) ).
fof(f1451,plain,
( spl0_96
| ~ spl0_22
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f410,f377,f139,f1449]) ).
fof(f1449,plain,
( spl0_96
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f410,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) )
| ~ spl0_22
| ~ spl0_54 ),
inference(resolution,[],[f378,f140]) ).
fof(f1447,plain,
( ~ spl0_41
| spl0_85 ),
inference(avatar_contradiction_clause,[],[f1444]) ).
fof(f1444,plain,
( $false
| ~ spl0_41
| spl0_85 ),
inference(resolution,[],[f1277,f277]) ).
fof(f277,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f276,plain,
( spl0_41
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1277,plain,
( ~ theorem(or(not(r),r))
| spl0_85 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1275,plain,
( spl0_85
<=> theorem(or(not(r),r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1443,plain,
( spl0_95
| ~ spl0_10
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f401,f377,f60,f1441]) ).
fof(f1441,plain,
( spl0_95
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f401,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_10
| ~ spl0_54 ),
inference(resolution,[],[f378,f61]) ).
fof(f1439,plain,
( spl0_94
| ~ spl0_7
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f399,f377,f46,f1437]) ).
fof(f1437,plain,
( spl0_94
<=> ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f399,plain,
( ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) )
| ~ spl0_7
| ~ spl0_54 ),
inference(resolution,[],[f378,f47]) ).
fof(f1435,plain,
( spl0_93
| ~ spl0_11
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f384,f373,f66,f1433]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_11
| ~ spl0_53 ),
inference(resolution,[],[f374,f67]) ).
fof(f1431,plain,
( spl0_92
| ~ spl0_16
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f338,f321,f92,f1429]) ).
fof(f1429,plain,
( spl0_92
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f338,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) )
| ~ spl0_16
| ~ spl0_48 ),
inference(resolution,[],[f322,f93]) ).
fof(f1371,plain,
( spl0_91
| ~ spl0_26
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f440,f427,f163,f1369]) ).
fof(f1369,plain,
( spl0_91
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f440,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_26
| ~ spl0_55 ),
inference(resolution,[],[f428,f164]) ).
fof(f1367,plain,
( spl0_90
| ~ spl0_6
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f337,f321,f41,f1365]) ).
fof(f1365,plain,
( spl0_90
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f337,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_48 ),
inference(resolution,[],[f322,f42]) ).
fof(f1363,plain,
( spl0_89
| ~ spl0_17
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f296,f291,f102,f1361]) ).
fof(f1361,plain,
( spl0_89
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f291,plain,
( spl0_44
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f296,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_44 ),
inference(resolution,[],[f292,f103]) ).
fof(f292,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f1359,plain,
( spl0_88
| ~ spl0_17
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f282,f276,f102,f1357]) ).
fof(f1357,plain,
( spl0_88
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f282,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_41 ),
inference(resolution,[],[f277,f103]) ).
fof(f1308,plain,
( spl0_87
| ~ spl0_7
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f380,f373,f46,f1306]) ).
fof(f1306,plain,
( spl0_87
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_53 ),
inference(resolution,[],[f374,f47]) ).
fof(f1304,plain,
( spl0_86
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f348,f329,f325,f1302]) ).
fof(f1302,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f348,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_49
| ~ spl0_50 ),
inference(resolution,[],[f330,f326]) ).
fof(f1278,plain,
( ~ spl0_84
| ~ spl0_85
| ~ spl0_66
| spl0_76 ),
inference(avatar_split_clause,[],[f1132,f726,f543,f1275,f1271]) ).
fof(f1271,plain,
( spl0_84
<=> theorem(p) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1132,plain,
( ~ theorem(or(not(r),r))
| ~ theorem(p)
| ~ spl0_66
| spl0_76 ),
inference(resolution,[],[f544,f728]) ).
fof(f1025,plain,
( ~ spl0_83
| ~ spl0_20
| spl0_76 ),
inference(avatar_split_clause,[],[f928,f726,f125,f1022]) ).
fof(f1022,plain,
( spl0_83
<=> theorem(not(or(not(p),r))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f125,plain,
( spl0_20
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f928,plain,
( ~ theorem(not(or(not(p),r)))
| ~ spl0_20
| spl0_76 ),
inference(resolution,[],[f728,f126]) ).
fof(f126,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f848,plain,
( ~ spl0_82
| ~ spl0_13
| spl0_75 ),
inference(avatar_split_clause,[],[f841,f722,f75,f845]) ).
fof(f845,plain,
( spl0_82
<=> theorem(q) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f75,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f841,plain,
( ~ theorem(q)
| ~ spl0_13
| spl0_75 ),
inference(resolution,[],[f76,f724]) ).
fof(f76,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f824,plain,
( spl0_2
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f803]) ).
fof(f803,plain,
( $false
| spl0_2
| ~ spl0_42 ),
inference(resolution,[],[f285,f24]) ).
fof(f285,plain,
( ! [X1] : theorem(X1)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl0_42
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f823,plain,
( spl0_39
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f804]) ).
fof(f804,plain,
( $false
| spl0_39
| ~ spl0_42 ),
inference(resolution,[],[f285,f265]) ).
fof(f822,plain,
( ~ spl0_42
| spl0_63 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f805,plain,
( $false
| ~ spl0_42
| spl0_63 ),
inference(resolution,[],[f285,f532]) ).
fof(f821,plain,
( spl0_18
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f806]) ).
fof(f806,plain,
( $false
| spl0_18
| ~ spl0_42 ),
inference(resolution,[],[f285,f114]) ).
fof(f820,plain,
( spl0_37
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f807]) ).
fof(f807,plain,
( $false
| spl0_37
| ~ spl0_42 ),
inference(resolution,[],[f285,f251]) ).
fof(f819,plain,
( ~ spl0_42
| spl0_75 ),
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f808,plain,
( $false
| ~ spl0_42
| spl0_75 ),
inference(resolution,[],[f285,f724]) ).
fof(f818,plain,
( spl0_35
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f809]) ).
fof(f809,plain,
( $false
| spl0_35
| ~ spl0_42 ),
inference(resolution,[],[f285,f237]) ).
fof(f817,plain,
( spl0_38
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f810]) ).
fof(f810,plain,
( $false
| spl0_38
| ~ spl0_42 ),
inference(resolution,[],[f285,f260]) ).
fof(f260,plain,
( ~ theorem(not(or(not(or(not(p),q)),or(not(p),r))))
| spl0_38 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f258,plain,
( spl0_38
<=> theorem(not(or(not(or(not(p),q)),or(not(p),r)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f816,plain,
( spl0_24
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f811]) ).
fof(f811,plain,
( $false
| spl0_24
| ~ spl0_42 ),
inference(resolution,[],[f285,f152]) ).
fof(f152,plain,
( ~ theorem(not(p))
| spl0_24 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl0_24
<=> theorem(not(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f815,plain,
( ~ spl0_42
| spl0_52 ),
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f812,plain,
( $false
| ~ spl0_42
| spl0_52 ),
inference(resolution,[],[f285,f370]) ).
fof(f370,plain,
( ~ theorem(not(q))
| spl0_52 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f368,plain,
( spl0_52
<=> theorem(not(q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f814,plain,
( spl0_40
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f813,plain,
( $false
| spl0_40
| ~ spl0_42 ),
inference(resolution,[],[f285,f273]) ).
fof(f273,plain,
( ~ theorem(r)
| spl0_40 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f271,plain,
( spl0_40
<=> theorem(r) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f802,plain,
( spl0_81
| ~ spl0_43
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f317,f310,f287,f800]) ).
fof(f800,plain,
( spl0_81
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f287,plain,
( spl0_43
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f310,plain,
( spl0_46
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f317,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_43
| ~ spl0_46 ),
inference(resolution,[],[f311,f288]) ).
fof(f288,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f311,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f798,plain,
( spl0_80
| ~ spl0_16
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f308,f298,f92,f796]) ).
fof(f796,plain,
( spl0_80
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f308,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_45 ),
inference(resolution,[],[f299,f93]) ).
fof(f772,plain,
( spl0_79
| ~ spl0_23
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f439,f427,f143,f770]) ).
fof(f770,plain,
( spl0_79
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f439,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_23
| ~ spl0_55 ),
inference(resolution,[],[f428,f144]) ).
fof(f768,plain,
( spl0_78
| ~ spl0_7
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f430,f427,f46,f766]) ).
fof(f766,plain,
( spl0_78
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f430,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_55 ),
inference(resolution,[],[f428,f47]) ).
fof(f758,plain,
( spl0_77
| ~ spl0_16
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f281,f276,f92,f756]) ).
fof(f756,plain,
( spl0_77
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f281,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_41 ),
inference(resolution,[],[f277,f93]) ).
fof(f729,plain,
( ~ spl0_75
| ~ spl0_76
| spl0_63
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f629,f543,f530,f726,f722]) ).
fof(f629,plain,
( ~ theorem(or(not(or(not(p),r)),r))
| ~ theorem(or(not(p),q))
| spl0_63
| ~ spl0_66 ),
inference(resolution,[],[f532,f544]) ).
fof(f720,plain,
( spl0_74
| ~ spl0_31
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f225,f218,f193,f718]) ).
fof(f718,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(f225,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,[],[f219,f194]) ).
fof(f716,plain,
( spl0_73
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f214,f193,f189,f714]) ).
fof(f714,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(f214,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,[],[f194,f190]) ).
fof(f676,plain,
( spl0_72
| ~ spl0_31
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f244,f240,f193,f674]) ).
fof(f244,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,[],[f241,f194]) ).
fof(f672,plain,
( spl0_71
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f215,f193,f185,f670]) ).
fof(f215,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,[],[f194,f186]) ).
fof(f668,plain,
( spl0_70
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f208,f193,f80,f666]) ).
fof(f208,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,[],[f194,f81]) ).
fof(f635,plain,
( spl0_69
| ~ spl0_19
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f207,f193,f117,f633]) ).
fof(f207,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,[],[f194,f118]) ).
fof(f599,plain,
( spl0_68
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f206,f193,f71,f597]) ).
fof(f206,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,[],[f194,f72]) ).
fof(f549,plain,
( spl0_67
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f247,f240,f92,f547]) ).
fof(f247,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,[],[f241,f93]) ).
fof(f545,plain,
( spl0_66
| ~ spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f226,f218,f41,f543]) ).
fof(f226,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,[],[f219,f42]) ).
fof(f541,plain,
( spl0_65
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f216,f193,f171,f539]) ).
fof(f216,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,[],[f194,f172]) ).
fof(f537,plain,
( spl0_64
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f200,f189,f41,f535]) ).
fof(f200,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_30 ),
inference(resolution,[],[f190,f42]) ).
fof(f533,plain,
( ~ spl0_63
| ~ spl0_27
| spl0_39 ),
inference(avatar_split_clause,[],[f267,f263,f171,f530]) ).
fof(f267,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),r))
| ~ spl0_27
| spl0_39 ),
inference(resolution,[],[f265,f172]) ).
fof(f497,plain,
( spl0_62
| ~ spl0_6
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f245,f240,f41,f495]) ).
fof(f245,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_36 ),
inference(resolution,[],[f241,f42]) ).
fof(f493,plain,
( spl0_61
| ~ spl0_16
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f228,f218,f92,f491]) ).
fof(f228,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_32 ),
inference(resolution,[],[f219,f93]) ).
fof(f489,plain,
( spl0_60
| ~ spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f213,f193,f163,f487]) ).
fof(f213,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26
| ~ spl0_31 ),
inference(resolution,[],[f194,f164]) ).
fof(f485,plain,
( spl0_59
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f197,f185,f41,f483]) ).
fof(f197,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f186,f42]) ).
fof(f462,plain,
( spl0_58
| ~ spl0_22
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f211,f193,f139,f460]) ).
fof(f211,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_22
| ~ spl0_31 ),
inference(resolution,[],[f194,f140]) ).
fof(f458,plain,
( spl0_57
| ~ spl0_16
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f202,f189,f92,f456]) ).
fof(f202,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_30 ),
inference(resolution,[],[f190,f93]) ).
fof(f454,plain,
( spl0_56
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f199,f185,f92,f452]) ).
fof(f199,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f186,f93]) ).
fof(f429,plain,
( spl0_55
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f205,f193,f66,f427]) ).
fof(f205,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_31 ),
inference(resolution,[],[f194,f67]) ).
fof(f379,plain,
( spl0_54
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f209,f193,f125,f377]) ).
fof(f209,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_20
| ~ spl0_31 ),
inference(resolution,[],[f194,f126]) ).
fof(f375,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f175,f171,f41,f373]) ).
fof(f175,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_27 ),
inference(resolution,[],[f172,f42]) ).
fof(f371,plain,
( ~ spl0_52
| ~ spl0_20
| spl0_35 ),
inference(avatar_split_clause,[],[f253,f235,f125,f368]) ).
fof(f253,plain,
( ~ theorem(not(q))
| ~ spl0_20
| spl0_35 ),
inference(resolution,[],[f237,f126]) ).
fof(f335,plain,
( spl0_51
| ~ spl0_10
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f204,f193,f60,f333]) ).
fof(f204,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_31 ),
inference(resolution,[],[f194,f61]) ).
fof(f331,plain,
( spl0_50
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f179,f171,f92,f329]) ).
fof(f179,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_27 ),
inference(resolution,[],[f172,f93]) ).
fof(f327,plain,
( spl0_49
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f178,f171,f85,f325]) ).
fof(f178,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f172,f86]) ).
fof(f323,plain,
( spl0_48
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f163,f41,f321]) ).
fof(f167,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f164,f42]) ).
fof(f316,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f169,f163,f92,f314]) ).
fof(f169,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f164,f93]) ).
fof(f312,plain,
( spl0_46
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f147,f139,f41,f310]) ).
fof(f147,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f140,f42]) ).
fof(f300,plain,
( spl0_45
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f133,f125,f102,f298]) ).
fof(f133,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f126,f103]) ).
fof(f293,plain,
( spl0_44
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f143,f92,f291]) ).
fof(f157,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f144,f93]) ).
fof(f289,plain,
( spl0_42
| spl0_43
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f129,f125,f41,f287,f284]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f126,f42]) ).
fof(f278,plain,
( spl0_41
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f156,f143,f85,f276]) ).
fof(f156,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f144,f86]) ).
fof(f274,plain,
( ~ spl0_40
| ~ spl0_13
| spl0_35 ),
inference(avatar_split_clause,[],[f254,f235,f75,f271]) ).
fof(f254,plain,
( ~ theorem(r)
| ~ spl0_13
| spl0_35 ),
inference(resolution,[],[f237,f76]) ).
fof(f266,plain,
( ~ spl0_39
| spl0_2
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f174,f171,f22,f263]) ).
fof(f174,plain,
( ~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(q),r)))
| spl0_2
| ~ spl0_27 ),
inference(resolution,[],[f172,f24]) ).
fof(f261,plain,
( ~ spl0_38
| spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f128,f125,f22,f258]) ).
fof(f128,plain,
( ~ theorem(not(or(not(or(not(p),q)),or(not(p),r))))
| spl0_2
| ~ spl0_20 ),
inference(resolution,[],[f126,f24]) ).
fof(f252,plain,
( ~ spl0_37
| spl0_18
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f176,f171,f112,f249]) ).
fof(f176,plain,
( ~ theorem(or(not(p),r))
| spl0_18
| ~ spl0_27 ),
inference(resolution,[],[f172,f114]) ).
fof(f242,plain,
( spl0_36
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f102,f80,f240]) ).
fof(f109,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,[],[f103,f81]) ).
fof(f238,plain,
( ~ spl0_35
| ~ spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f123,f112,f75,f235]) ).
fof(f123,plain,
( ~ theorem(or(not(q),r))
| ~ spl0_13
| spl0_18 ),
inference(resolution,[],[f114,f76]) ).
fof(f233,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f92,f80,f231]) ).
fof(f99,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,[],[f93,f81]) ).
fof(f224,plain,
( spl0_33
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f117,f92,f222]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) )
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f118,f93]) ).
fof(f220,plain,
( spl0_32
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f117,f102,f218]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) )
| ~ spl0_17
| ~ spl0_19 ),
inference(resolution,[],[f118,f103]) ).
fof(f195,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f120,f117,f41,f193]) ).
fof(f120,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[],[f118,f42]) ).
fof(f191,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f102,f60,f189]) ).
fof(f108,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f103,f61]) ).
fof(f187,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f102,f71,f185]) ).
fof(f107,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f103,f72]) ).
fof(f183,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f92,f71,f181]) ).
fof(f98,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f93,f72]) ).
fof(f173,plain,
( spl0_27
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f102,f75,f171]) ).
fof(f110,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f103,f76]) ).
fof(f165,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f106,f102,f66,f163]) ).
fof(f106,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f103,f67]) ).
fof(f161,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f92,f66,f159]) ).
fof(f97,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f93,f67]) ).
fof(f153,plain,
( ~ spl0_24
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f125,f112,f150]) ).
fof(f130,plain,
( ~ theorem(not(p))
| spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f126,f114]) ).
fof(f145,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f105,f102,f46,f143]) ).
fof(f105,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f103,f47]) ).
fof(f141,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f96,f92,f60,f139]) ).
fof(f96,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f93,f61]) ).
fof(f137,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f95,f92,f46,f135]) ).
fof(f95,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f93,f47]) ).
fof(f127,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f92,f75,f125]) ).
fof(f100,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f93,f76]) ).
fof(f119,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f83,f80,f41,f117]) ).
fof(f83,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f81,f42]) ).
fof(f115,plain,
( ~ spl0_18
| spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f88,f75,f22,f112]) ).
fof(f88,plain,
( ~ theorem(or(not(p),or(not(q),r)))
| spl0_2
| ~ spl0_13 ),
inference(resolution,[],[f76,f24]) ).
fof(f104,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f78,f71,f41,f102]) ).
fof(f78,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_6
| ~ spl0_12 ),
inference(resolution,[],[f72,f42]) ).
fof(f94,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f69,f66,f41,f92]) ).
fof(f69,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f67,f42]) ).
fof(f87,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f64,f60,f41,f85]) ).
fof(f64,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f61,f42]) ).
fof(f82,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f58,f55,f18,f80]) ).
fof(f18,plain,
( spl0_1
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f55,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(f58,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,[],[f56,f19]) ).
fof(f19,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f56,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,[],[f55]) ).
fof(f77,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f63,f46,f41,f75]) ).
fof(f63,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f47,f42]) ).
fof(f73,plain,
( spl0_12
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f53,f50,f18,f71]) ).
fof(f50,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(f53,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f51,f19]) ).
fof(f51,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f68,plain,
( spl0_11
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f44,f37,f18,f66]) ).
fof(f37,plain,
( spl0_5
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f44,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f38,f19]) ).
fof(f38,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f62,plain,
( spl0_10
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f31,f18,f60]) ).
fof(f31,plain,
( spl0_4
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f35,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f32,f19]) ).
fof(f32,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f57,plain,
spl0_9,
inference(avatar_split_clause,[],[f14,f55]) ).
fof(f14,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f52,plain,
spl0_8,
inference(avatar_split_clause,[],[f15,f50]) ).
fof(f15,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/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f48,plain,
( spl0_7
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f34,f27,f18,f46]) ).
fof(f27,plain,
( spl0_3
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f34,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f28,f19]) ).
fof(f28,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f43,plain,
spl0_6,
inference(avatar_split_clause,[],[f16,f41]) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f39,plain,
spl0_5,
inference(avatar_split_clause,[],[f13,f37]) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f33,plain,
spl0_4,
inference(avatar_split_clause,[],[f12,f31]) ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f29,plain,
spl0_3,
inference(avatar_split_clause,[],[f11,f27]) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f25,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f10,f22]) ).
fof(f10,plain,
~ theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r)))),
inference(definition_unfolding,[],[f9,f6,f6,f6,f6,f6,f6]) ).
fof(f9,axiom,
~ theorem(implies(implies(implies(p,q),implies(p,r)),implies(p,implies(q,r)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f20,plain,
spl0_1,
inference(avatar_split_clause,[],[f7,f18]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL231-3 : TPTP v8.1.2. Released v2.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 13:40:34 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.36 % (21181)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (21190)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)
% 0.20/0.37 % (21186)WARNING: value z3 for option sas not known
% 0.20/0.37 % (21184)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (21185)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (21187)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (21186)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)
% 0.20/0.37 % (21189)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)
% 0.20/0.37 % (21188)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)
% 0.20/0.37 TRYING [1]
% 0.20/0.37 TRYING [2]
% 0.20/0.37 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [3]
% 0.20/0.39 TRYING [4]
% 0.20/0.39 TRYING [4]
% 0.20/0.45 TRYING [5]
% 0.20/0.48 TRYING [5]
% 2.22/0.67 TRYING [6]
% 2.97/0.78 TRYING [6]
% 3.48/0.86 % (21188)First to succeed.
% 3.48/0.86 % (21188)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21181"
% 3.48/0.87 % (21188)Refutation found. Thanks to Tanya!
% 3.48/0.87 % SZS status Unsatisfiable for theBenchmark
% 3.48/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/0.87 % (21188)------------------------------
% 3.69/0.87 % (21188)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.69/0.87 % (21188)Termination reason: Refutation
% 3.69/0.87
% 3.69/0.87 % (21188)Memory used [KB]: 4410
% 3.69/0.87 % (21188)Time elapsed: 0.489 s
% 3.69/0.87 % (21188)Instructions burned: 1234 (million)
% 3.69/0.87 % (21181)Success in time 0.5 s
%------------------------------------------------------------------------------