TSTP Solution File: LCL182-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL182-3 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:40:46 EDT 2024
% Result : Unsatisfiable 0.60s 0.58s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 175
% Syntax : Number of formulae : 603 ( 22 unt; 0 def)
% Number of atoms : 1796 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2215 (1022 ~;1027 |; 0 &)
% ( 166 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 170 ( 168 usr; 167 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 952 ( 952 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3667,plain,
$false,
inference(avatar_sat_refutation,[],[f21,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,f182,f186,f190,f194,f219,f223,f232,f237,f241,f251,f256,f262,f270,f277,f281,f288,f298,f302,f312,f316,f320,f324,f359,f363,f367,f419,f444,f448,f452,f477,f481,f485,f489,f524,f528,f533,f537,f541,f592,f625,f658,f662,f666,f706,f710,f744,f750,f754,f780,f784,f794,f795,f796,f797,f798,f799,f800,f801,f802,f812,f1256,f1260,f1273,f1313,f1317,f1321,f1325,f1376,f1389,f1393,f1397,f1401,f1405,f1412,f1416,f1420,f1424,f1428,f1511,f1516,f1520,f1524,f1528,f1532,f1541,f1542,f1543,f1544,f1972,f2181,f2188,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2325,f2493,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2568,f2572,f2576,f2580,f2584,f2588,f2592,f2596,f2600,f2604,f3047,f3051,f3055,f3059,f3063,f3067,f3071,f3075,f3079,f3083,f3087,f3091,f3095,f3099,f3103,f3107,f3127,f3131,f3135,f3139,f3143,f3147,f3151,f3155,f3159,f3178,f3429,f3666]) ).
fof(f3666,plain,
( ~ spl0_40
| spl0_166 ),
inference(avatar_contradiction_clause,[],[f3663]) ).
fof(f3663,plain,
( $false
| ~ spl0_40
| spl0_166 ),
inference(resolution,[],[f3428,f269]) ).
fof(f269,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl0_40
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f3428,plain,
( ~ theorem(or(not(q),not(not(q))))
| spl0_166 ),
inference(avatar_component_clause,[],[f3426]) ).
fof(f3426,plain,
( spl0_166
<=> theorem(or(not(q),not(not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f3429,plain,
( ~ spl0_166
| spl0_1
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f3255,f3061,f18,f3426]) ).
fof(f18,plain,
( spl0_1
<=> theorem(or(not(or(not(p),q)),or(not(not(q)),not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f3061,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f3255,plain,
( ~ theorem(or(not(q),not(not(q))))
| spl0_1
| ~ spl0_144 ),
inference(resolution,[],[f3062,f20]) ).
fof(f20,plain,
( ~ theorem(or(not(or(not(p),q)),or(not(not(q)),not(p))))
| spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f3062,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f3061]) ).
fof(f3178,plain,
( spl0_165
| ~ spl0_21
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f2368,f2283,f135,f3176]) ).
fof(f3176,plain,
( spl0_165
<=> ! [X0,X1] : theorem(or(or(X0,not(X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f135,plain,
( spl0_21
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f2283,plain,
( spl0_111
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2368,plain,
( ! [X0,X1] : theorem(or(or(X0,not(X1)),X1))
| ~ spl0_21
| ~ spl0_111 ),
inference(resolution,[],[f2284,f136]) ).
fof(f136,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f2284,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(or(X2,X2),X1))
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f3159,plain,
( spl0_164
| ~ spl0_26
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f640,f623,f163,f3157]) ).
fof(f3157,plain,
( spl0_164
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
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(f623,plain,
( spl0_68
<=> ! [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_68])]) ).
fof(f640,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_26
| ~ spl0_68 ),
inference(resolution,[],[f624,f164]) ).
fof(f164,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f624,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X3)))
| theorem(or(X0,or(X1,X2)))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f3155,plain,
( spl0_163
| ~ spl0_11
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f628,f623,f66,f3153]) ).
fof(f3153,plain,
( spl0_163
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
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(f628,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) )
| ~ spl0_11
| ~ spl0_68 ),
inference(resolution,[],[f624,f67]) ).
fof(f67,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f3151,plain,
( spl0_162
| ~ spl0_27
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f613,f590,f171,f3149]) ).
fof(f3149,plain,
( spl0_162
<=> ! [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_162])]) ).
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(f590,plain,
( spl0_67
<=> ! [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_67])]) ).
fof(f613,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) )
| ~ spl0_27
| ~ spl0_67 ),
inference(resolution,[],[f591,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(f591,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X2,or(X1,X3))))
| theorem(or(X0,or(X1,or(X2,X3)))) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f3147,plain,
( spl0_161
| ~ spl0_6
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f580,f535,f41,f3145]) ).
fof(f3145,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f535,plain,
( spl0_65
<=> ! [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_65])]) ).
fof(f580,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) )
| ~ spl0_6
| ~ spl0_65 ),
inference(resolution,[],[f536,f42]) ).
fof(f42,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f536,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(or(not(X0),X1))
| ~ theorem(X2) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f3143,plain,
( spl0_160
| ~ spl0_11
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f554,f526,f66,f3141]) ).
fof(f3141,plain,
( spl0_160
<=> ! [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_160])]) ).
fof(f526,plain,
( spl0_63
<=> ! [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_63])]) ).
fof(f554,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X2,X1)))) )
| ~ spl0_11
| ~ spl0_63 ),
inference(resolution,[],[f527,f67]) ).
fof(f527,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X3),X2))
| ~ theorem(or(X0,X3))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f3139,plain,
( spl0_159
| ~ spl0_6
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f544,f522,f41,f3137]) ).
fof(f3137,plain,
( spl0_159
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f522,plain,
( spl0_62
<=> ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) )
| ~ spl0_6
| ~ spl0_62 ),
inference(resolution,[],[f523,f42]) ).
fof(f523,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f3135,plain,
( spl0_158
| ~ spl0_16
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f520,f487,f92,f3133]) ).
fof(f3133,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f92,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f487,plain,
( spl0_61
<=> ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f520,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) )
| ~ spl0_16
| ~ spl0_61 ),
inference(resolution,[],[f488,f93]) ).
fof(f93,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f3131,plain,
( spl0_157
| ~ spl0_17
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f517,f487,f102,f3129]) ).
fof(f3129,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
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(f517,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) )
| ~ spl0_17
| ~ spl0_61 ),
inference(resolution,[],[f488,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(f3127,plain,
( spl0_156
| ~ spl0_54
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f516,f487,f417,f3125]) ).
fof(f3125,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f417,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f516,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) )
| ~ spl0_54
| ~ spl0_61 ),
inference(resolution,[],[f488,f418]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f3107,plain,
( spl0_155
| ~ spl0_16
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f505,f479,f92,f3105]) ).
fof(f3105,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f479,plain,
( spl0_59
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f505,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) )
| ~ spl0_16
| ~ spl0_59 ),
inference(resolution,[],[f480,f93]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f3103,plain,
( spl0_154
| ~ spl0_17
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f502,f479,f102,f3101]) ).
fof(f3101,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f502,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) )
| ~ spl0_17
| ~ spl0_59 ),
inference(resolution,[],[f480,f103]) ).
fof(f3099,plain,
( spl0_153
| ~ spl0_54
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f501,f479,f417,f3097]) ).
fof(f3097,plain,
( spl0_153
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) )
| ~ spl0_54
| ~ spl0_59 ),
inference(resolution,[],[f480,f418]) ).
fof(f3095,plain,
( spl0_152
| ~ spl0_16
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f497,f475,f92,f3093]) ).
fof(f3093,plain,
( spl0_152
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f475,plain,
( spl0_58
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f497,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) )
| ~ spl0_16
| ~ spl0_58 ),
inference(resolution,[],[f476,f93]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f3091,plain,
( spl0_151
| ~ spl0_17
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f494,f475,f102,f3089]) ).
fof(f3089,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f494,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) )
| ~ spl0_17
| ~ spl0_58 ),
inference(resolution,[],[f476,f103]) ).
fof(f3087,plain,
( spl0_150
| ~ spl0_54
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f493,f475,f417,f3085]) ).
fof(f3085,plain,
( spl0_150
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) )
| ~ spl0_54
| ~ spl0_58 ),
inference(resolution,[],[f476,f418]) ).
fof(f3083,plain,
( spl0_149
| ~ spl0_6
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f467,f450,f41,f3081]) ).
fof(f3081,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f450,plain,
( spl0_57
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f467,plain,
( ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_57 ),
inference(resolution,[],[f451,f42]) ).
fof(f451,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f3079,plain,
( spl0_148
| ~ spl0_49
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f440,f417,f318,f3077]) ).
fof(f3077,plain,
( spl0_148
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f318,plain,
( spl0_49
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f440,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) )
| ~ spl0_49
| ~ spl0_54 ),
inference(resolution,[],[f418,f319]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f3075,plain,
( spl0_147
| ~ spl0_32
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f433,f417,f217,f3073]) ).
fof(f3073,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f217,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(f433,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) )
| ~ spl0_32
| ~ spl0_54 ),
inference(resolution,[],[f418,f218]) ).
fof(f218,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f3071,plain,
( spl0_146
| ~ spl0_47
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f427,f417,f310,f3069]) ).
fof(f3069,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f310,plain,
( spl0_47
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f427,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) )
| ~ spl0_47
| ~ spl0_54 ),
inference(resolution,[],[f418,f311]) ).
fof(f311,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f3067,plain,
( spl0_145
| ~ spl0_79
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1456,f1399,f782,f3065]) ).
fof(f3065,plain,
( spl0_145
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f782,plain,
( spl0_79
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1399,plain,
( spl0_92
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1456,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(or(X0,X0)) )
| ~ spl0_79
| ~ spl0_92 ),
inference(resolution,[],[f1400,f783]) ).
fof(f783,plain,
( ! [X0] :
( ~ theorem(or(not(X0),not(X0)))
| ~ theorem(X0) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1400,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f3063,plain,
( spl0_144
| ~ spl0_19
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f424,f417,f117,f3061]) ).
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(f424,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19
| ~ spl0_54 ),
inference(resolution,[],[f418,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(f3059,plain,
( spl0_143
| ~ spl0_12
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f373,f357,f71,f3057]) ).
fof(f3057,plain,
( spl0_143
<=> ! [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_143])]) ).
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(f357,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f373,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) )
| ~ spl0_12
| ~ spl0_51 ),
inference(resolution,[],[f358,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(f358,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f3055,plain,
( spl0_142
| ~ spl0_17
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f340,f318,f102,f3053]) ).
fof(f3053,plain,
( spl0_142
<=> ! [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_142])]) ).
fof(f340,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(or(X0,X1),X2))
| theorem(or(X0,or(or(X3,X2),X1))) )
| ~ spl0_17
| ~ spl0_49 ),
inference(resolution,[],[f319,f103]) ).
fof(f3051,plain,
( spl0_141
| ~ spl0_27
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f336,f314,f171,f3049]) ).
fof(f3049,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f314,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f336,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) )
| ~ spl0_27
| ~ spl0_48 ),
inference(resolution,[],[f315,f172]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f3047,plain,
( spl0_140
| ~ spl0_17
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f328,f310,f102,f3045]) ).
fof(f3045,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) )
| ~ spl0_17
| ~ spl0_47 ),
inference(resolution,[],[f311,f103]) ).
fof(f2604,plain,
( spl0_139
| ~ spl0_26
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f608,f590,f163,f2602]) ).
fof(f2602,plain,
( spl0_139
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f608,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2))))
| ~ spl0_26
| ~ spl0_67 ),
inference(resolution,[],[f591,f164]) ).
fof(f2600,plain,
( spl0_138
| ~ spl0_29
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f606,f590,f184,f2598]) ).
fof(f2598,plain,
( spl0_138
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f184,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(f606,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2))))
| ~ spl0_29
| ~ spl0_67 ),
inference(resolution,[],[f591,f185]) ).
fof(f185,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f2596,plain,
( spl0_137
| ~ spl0_11
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f595,f590,f66,f2594]) ).
fof(f2594,plain,
( spl0_137
<=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f595,plain,
( ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1))))
| ~ spl0_11
| ~ spl0_67 ),
inference(resolution,[],[f591,f67]) ).
fof(f2592,plain,
( spl0_136
| ~ spl0_6
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f492,f475,f41,f2590]) ).
fof(f2590,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f492,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) )
| ~ spl0_6
| ~ spl0_58 ),
inference(resolution,[],[f476,f42]) ).
fof(f2588,plain,
( spl0_135
| ~ spl0_16
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f470,f450,f92,f2586]) ).
fof(f2586,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f470,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) )
| ~ spl0_16
| ~ spl0_57 ),
inference(resolution,[],[f451,f93]) ).
fof(f2584,plain,
( spl0_134
| ~ spl0_46
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f439,f417,f300,f2582]) ).
fof(f2582,plain,
( spl0_134
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f300,plain,
( spl0_46
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f439,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1)))
| ~ spl0_46
| ~ spl0_54 ),
inference(resolution,[],[f418,f301]) ).
fof(f301,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f2580,plain,
( spl0_133
| ~ spl0_29
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f432,f417,f184,f2578]) ).
fof(f2578,plain,
( spl0_133
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f432,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2))))))
| ~ spl0_29
| ~ spl0_54 ),
inference(resolution,[],[f418,f185]) ).
fof(f2576,plain,
( spl0_132
| ~ spl0_30
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f431,f417,f188,f2574]) ).
fof(f2574,plain,
( spl0_132
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f188,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(f431,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1))))))
| ~ spl0_30
| ~ spl0_54 ),
inference(resolution,[],[f418,f189]) ).
fof(f189,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f2572,plain,
( spl0_131
| ~ spl0_10
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f426,f417,f60,f2570]) ).
fof(f2570,plain,
( spl0_131
<=> ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f60,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f426,plain,
( ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0)))
| ~ spl0_10
| ~ spl0_54 ),
inference(resolution,[],[f418,f61]) ).
fof(f61,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f2568,plain,
( spl0_130
| ~ spl0_12
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f423,f417,f71,f2566]) ).
fof(f2566,plain,
( spl0_130
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f423,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1)))
| ~ spl0_12
| ~ spl0_54 ),
inference(resolution,[],[f418,f72]) ).
fof(f2564,plain,
( spl0_129
| ~ spl0_49
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f415,f361,f318,f2562]) ).
fof(f2562,plain,
( spl0_129
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f361,plain,
( spl0_52
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f415,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) )
| ~ spl0_49
| ~ spl0_52 ),
inference(resolution,[],[f362,f319]) ).
fof(f362,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,X1))
| ~ theorem(not(X2)) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f2560,plain,
( spl0_128
| ~ spl0_27
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f407,f361,f171,f2558]) ).
fof(f2558,plain,
( spl0_128
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) )
| ~ spl0_27
| ~ spl0_52 ),
inference(resolution,[],[f362,f172]) ).
fof(f2556,plain,
( spl0_127
| ~ spl0_47
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f391,f361,f310,f2554]) ).
fof(f2554,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f391,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) )
| ~ spl0_47
| ~ spl0_52 ),
inference(resolution,[],[f362,f311]) ).
fof(f2552,plain,
( spl0_126
| ~ spl0_27
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f387,f357,f171,f2550]) ).
fof(f2550,plain,
( spl0_126
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f387,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_51 ),
inference(resolution,[],[f358,f172]) ).
fof(f2548,plain,
( spl0_125
| ~ spl0_12
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f344,f322,f71,f2546]) ).
fof(f2546,plain,
( spl0_125
<=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f322,plain,
( spl0_50
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f344,plain,
( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
| ~ spl0_12
| ~ spl0_50 ),
inference(resolution,[],[f323,f72]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f2544,plain,
( spl0_124
| ~ spl0_31
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f325,f310,f192,f2542]) ).
fof(f2542,plain,
( spl0_124
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f192,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(f325,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) )
| ~ spl0_31
| ~ spl0_47 ),
inference(resolution,[],[f311,f193]) ).
fof(f193,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f2540,plain,
( spl0_123
| ~ spl0_17
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f305,f300,f102,f2538]) ).
fof(f2538,plain,
( spl0_123
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f305,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
| ~ spl0_17
| ~ spl0_46 ),
inference(resolution,[],[f301,f103]) ).
fof(f2493,plain,
( ~ spl0_122
| spl0_1
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f2416,f2295,f18,f2490]) ).
fof(f2490,plain,
( spl0_122
<=> theorem(not(or(q,not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2295,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2416,plain,
( ~ theorem(not(or(q,not(p))))
| spl0_1
| ~ spl0_114 ),
inference(resolution,[],[f2296,f20]) ).
fof(f2296,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f2325,plain,
( spl0_121
| ~ spl0_10
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f552,f526,f60,f2323]) ).
fof(f2323,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f552,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) )
| ~ spl0_10
| ~ spl0_63 ),
inference(resolution,[],[f527,f61]) ).
fof(f2321,plain,
( spl0_120
| ~ spl0_7
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f550,f526,f46,f2319]) ).
fof(f2319,plain,
( spl0_120
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f46,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f550,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) )
| ~ spl0_7
| ~ spl0_63 ),
inference(resolution,[],[f527,f47]) ).
fof(f47,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f2317,plain,
( spl0_119
| ~ spl0_50
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f518,f487,f322,f2315]) ).
fof(f2315,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f518,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) )
| ~ spl0_50
| ~ spl0_61 ),
inference(resolution,[],[f488,f323]) ).
fof(f2313,plain,
( spl0_118
| ~ spl0_50
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f495,f475,f322,f2311]) ).
fof(f2311,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f495,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
| ~ spl0_50
| ~ spl0_58 ),
inference(resolution,[],[f476,f323]) ).
fof(f2309,plain,
( spl0_117
| ~ spl0_46
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f414,f361,f300,f2307]) ).
fof(f2307,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) )
| ~ spl0_46
| ~ spl0_52 ),
inference(resolution,[],[f362,f301]) ).
fof(f2305,plain,
( spl0_116
| ~ spl0_25
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f409,f361,f159,f2303]) ).
fof(f2303,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f159,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) )
| ~ spl0_25
| ~ spl0_52 ),
inference(resolution,[],[f362,f160]) ).
fof(f160,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f2301,plain,
( spl0_115
| ~ spl0_26
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f402,f361,f163,f2299]) ).
fof(f2299,plain,
( spl0_115
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f402,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) )
| ~ spl0_26
| ~ spl0_52 ),
inference(resolution,[],[f362,f164]) ).
fof(f2297,plain,
( spl0_114
| ~ spl0_11
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f392,f361,f66,f2295]) ).
fof(f392,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_11
| ~ spl0_52 ),
inference(resolution,[],[f362,f67]) ).
fof(f2293,plain,
( spl0_113
| ~ spl0_26
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f382,f357,f163,f2291]) ).
fof(f2291,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f382,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) )
| ~ spl0_26
| ~ spl0_51 ),
inference(resolution,[],[f358,f164]) ).
fof(f2289,plain,
( spl0_112
| ~ spl0_16
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f775,f752,f92,f2287]) ).
fof(f2287,plain,
( spl0_112
<=> ! [X0,X1] : theorem(or(or(X0,not(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f752,plain,
( spl0_77
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f775,plain,
( ! [X0,X1] : theorem(or(or(X0,not(X0)),X1))
| ~ spl0_16
| ~ spl0_77 ),
inference(resolution,[],[f753,f93]) ).
fof(f753,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f2285,plain,
( spl0_111
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f355,f322,f318,f2283]) ).
fof(f355,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) )
| ~ spl0_49
| ~ spl0_50 ),
inference(resolution,[],[f323,f319]) ).
fof(f2281,plain,
( spl0_110
| ~ spl0_47
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f347,f322,f310,f2279]) ).
fof(f2279,plain,
( spl0_110
<=> ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f347,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_47
| ~ spl0_50 ),
inference(resolution,[],[f323,f311]) ).
fof(f2277,plain,
( spl0_109
| ~ spl0_19
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f345,f322,f117,f2275]) ).
fof(f2275,plain,
( spl0_109
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f345,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) )
| ~ spl0_19
| ~ spl0_50 ),
inference(resolution,[],[f323,f118]) ).
fof(f2188,plain,
( spl0_108
| ~ spl0_23
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f607,f590,f143,f2186]) ).
fof(f2186,plain,
( spl0_108
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f143,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f607,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
| ~ spl0_23
| ~ spl0_67 ),
inference(resolution,[],[f591,f144]) ).
fof(f144,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f2181,plain,
( spl0_107
| ~ spl0_7
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f593,f590,f46,f2179]) ).
fof(f2179,plain,
( spl0_107
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f593,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
| ~ spl0_7
| ~ spl0_67 ),
inference(resolution,[],[f591,f47]) ).
fof(f1972,plain,
( ~ spl0_106
| spl0_1
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1483,f1418,f18,f1969]) ).
fof(f1969,plain,
( spl0_106
<=> theorem(or(not(or(not(p),q)),not(not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1418,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1483,plain,
( ~ theorem(or(not(or(not(p),q)),not(not(q))))
| spl0_1
| ~ spl0_97 ),
inference(resolution,[],[f1419,f20]) ).
fof(f1419,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f1544,plain,
( spl0_1
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1535]) ).
fof(f1535,plain,
( $false
| spl0_1
| ~ spl0_95 ),
inference(resolution,[],[f1411,f20]) ).
fof(f1411,plain,
( ! [X0,X1] : theorem(or(X0,X1))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1410]) ).
fof(f1410,plain,
( spl0_95
<=> ! [X0,X1] : theorem(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1543,plain,
( spl0_38
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1536]) ).
fof(f1536,plain,
( $false
| spl0_38
| ~ spl0_95 ),
inference(resolution,[],[f1411,f255]) ).
fof(f255,plain,
( ~ theorem(or(not(or(not(p),q)),not(p)))
| spl0_38 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl0_38
<=> theorem(or(not(or(not(p),q)),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1542,plain,
( spl0_18
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1537]) ).
fof(f1537,plain,
( $false
| spl0_18
| ~ spl0_95 ),
inference(resolution,[],[f1411,f114]) ).
fof(f114,plain,
( ~ theorem(or(not(not(q)),not(p)))
| spl0_18 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f112,plain,
( spl0_18
<=> theorem(or(not(not(q)),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1541,plain,
( spl0_75
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f1538]) ).
fof(f1538,plain,
( $false
| spl0_75
| ~ spl0_95 ),
inference(resolution,[],[f1411,f743]) ).
fof(f743,plain,
( ~ theorem(or(not(q),not(p)))
| spl0_75 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f741,plain,
( spl0_75
<=> theorem(or(not(q),not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1532,plain,
( spl0_105
| spl0_95
| ~ spl0_44
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f406,f361,f286,f1410,f1530]) ).
fof(f1530,plain,
( spl0_105
<=> ! [X2,X3] :
( ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f286,plain,
( spl0_44
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) )
| ~ spl0_44
| ~ spl0_52 ),
inference(resolution,[],[f362,f287]) ).
fof(f287,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f1528,plain,
( spl0_104
| ~ spl0_22
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f379,f357,f139,f1526]) ).
fof(f1526,plain,
( spl0_104
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f139,plain,
( spl0_22
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f379,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) )
| ~ spl0_22
| ~ spl0_51 ),
inference(resolution,[],[f358,f140]) ).
fof(f140,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f1524,plain,
( spl0_103
| ~ spl0_47
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f371,f357,f310,f1522]) ).
fof(f1522,plain,
( spl0_103
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f371,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) )
| ~ spl0_47
| ~ spl0_51 ),
inference(resolution,[],[f358,f311]) ).
fof(f1520,plain,
( spl0_102
| ~ spl0_46
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f354,f322,f300,f1518]) ).
fof(f1518,plain,
( spl0_102
<=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f354,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
| ~ spl0_46
| ~ spl0_50 ),
inference(resolution,[],[f323,f301]) ).
fof(f1516,plain,
( ~ spl0_101
| spl0_1
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1440,f1391,f18,f1513]) ).
fof(f1513,plain,
( spl0_101
<=> theorem(or(not(p),not(not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1391,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1440,plain,
( ~ theorem(or(not(p),not(not(q))))
| spl0_1
| ~ spl0_90 ),
inference(resolution,[],[f1392,f20]) ).
fof(f1392,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f1511,plain,
( spl0_100
| ~ spl0_10
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f346,f322,f60,f1509]) ).
fof(f1509,plain,
( spl0_100
<=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f346,plain,
( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
| ~ spl0_10
| ~ spl0_50 ),
inference(resolution,[],[f323,f61]) ).
fof(f1428,plain,
( spl0_99
| ~ spl0_44
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f612,f590,f286,f1426]) ).
fof(f1426,plain,
( spl0_99
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f612,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) )
| ~ spl0_44
| ~ spl0_67 ),
inference(resolution,[],[f591,f287]) ).
fof(f1424,plain,
( spl0_98
| ~ spl0_17
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f772,f752,f102,f1422]) ).
fof(f1422,plain,
( spl0_98
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f772,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X0))))
| ~ spl0_17
| ~ spl0_77 ),
inference(resolution,[],[f753,f103]) ).
fof(f1420,plain,
( spl0_97
| ~ spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f435,f417,f171,f1418]) ).
fof(f435,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_27
| ~ spl0_54 ),
inference(resolution,[],[f418,f172]) ).
fof(f1416,plain,
( spl0_96
| ~ spl0_21
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f408,f361,f135,f1414]) ).
fof(f1414,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_21
| ~ spl0_52 ),
inference(resolution,[],[f362,f136]) ).
fof(f1412,plain,
( spl0_94
| spl0_95
| ~ spl0_23
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f401,f361,f143,f1410,f1407]) ).
fof(f1407,plain,
( spl0_94
<=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(X2),X2))) )
| ~ spl0_23
| ~ spl0_52 ),
inference(resolution,[],[f362,f144]) ).
fof(f1405,plain,
( spl0_93
| ~ spl0_22
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f399,f361,f139,f1403]) ).
fof(f1403,plain,
( spl0_93
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f399,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) )
| ~ spl0_22
| ~ spl0_52 ),
inference(resolution,[],[f362,f140]) ).
fof(f1401,plain,
( spl0_92
| ~ spl0_10
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f390,f361,f60,f1399]) ).
fof(f390,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_10
| ~ spl0_52 ),
inference(resolution,[],[f362,f61]) ).
fof(f1397,plain,
( spl0_91
| ~ spl0_7
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f388,f361,f46,f1395]) ).
fof(f1395,plain,
( spl0_91
<=> ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) )
| ~ spl0_7
| ~ spl0_52 ),
inference(resolution,[],[f362,f47]) ).
fof(f1393,plain,
( spl0_90
| ~ spl0_11
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f372,f357,f66,f1391]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_11
| ~ spl0_51 ),
inference(resolution,[],[f358,f67]) ).
fof(f1389,plain,
( spl0_89
| ~ spl0_16
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f327,f310,f92,f1387]) ).
fof(f1387,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f327,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) )
| ~ spl0_16
| ~ spl0_47 ),
inference(resolution,[],[f311,f93]) ).
fof(f1376,plain,
( spl0_88
| ~ spl0_16
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f765,f748,f92,f1374]) ).
fof(f1374,plain,
( spl0_88
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f748,plain,
( spl0_76
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f765,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X0)))
| ~ spl0_16
| ~ spl0_76 ),
inference(resolution,[],[f749,f93]) ).
fof(f749,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f1325,plain,
( spl0_87
| ~ spl0_26
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f430,f417,f163,f1323]) ).
fof(f1323,plain,
( spl0_87
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f430,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_26
| ~ spl0_54 ),
inference(resolution,[],[f418,f164]) ).
fof(f1321,plain,
( spl0_86
| ~ spl0_6
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f326,f310,f41,f1319]) ).
fof(f1319,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_47 ),
inference(resolution,[],[f311,f42]) ).
fof(f1317,plain,
( spl0_85
| ~ spl0_17
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f284,f279,f102,f1315]) ).
fof(f1315,plain,
( spl0_85
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f279,plain,
( spl0_43
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f284,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_43 ),
inference(resolution,[],[f280,f103]) ).
fof(f280,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f1313,plain,
( spl0_84
| ~ spl0_17
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f266,f260,f102,f1311]) ).
fof(f1311,plain,
( spl0_84
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f260,plain,
( spl0_39
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f266,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_39 ),
inference(resolution,[],[f261,f103]) ).
fof(f261,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1273,plain,
( spl0_83
| ~ spl0_17
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f761,f748,f102,f1271]) ).
fof(f1271,plain,
( spl0_83
<=> ! [X0,X1] : theorem(or(X0,or(not(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f761,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X0),X1)))
| ~ spl0_17
| ~ spl0_76 ),
inference(resolution,[],[f749,f103]) ).
fof(f1260,plain,
( spl0_82
| ~ spl0_7
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f368,f357,f46,f1258]) ).
fof(f1258,plain,
( spl0_82
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_51 ),
inference(resolution,[],[f358,f47]) ).
fof(f1256,plain,
( spl0_81
| ~ spl0_48
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f337,f318,f314,f1254]) ).
fof(f1254,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f337,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_48
| ~ spl0_49 ),
inference(resolution,[],[f319,f315]) ).
fof(f812,plain,
( ~ spl0_80
| ~ spl0_20
| spl0_75 ),
inference(avatar_split_clause,[],[f745,f741,f125,f809]) ).
fof(f809,plain,
( spl0_80
<=> theorem(not(q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f125,plain,
( spl0_20
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f745,plain,
( ~ theorem(not(q))
| ~ spl0_20
| spl0_75 ),
inference(resolution,[],[f743,f126]) ).
fof(f126,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f802,plain,
( spl0_1
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f785]) ).
fof(f785,plain,
( $false
| spl0_1
| ~ spl0_41 ),
inference(resolution,[],[f273,f20]) ).
fof(f273,plain,
( ! [X1] : theorem(X1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f272,plain,
( spl0_41
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f801,plain,
( spl0_38
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f786]) ).
fof(f786,plain,
( $false
| spl0_38
| ~ spl0_41 ),
inference(resolution,[],[f273,f255]) ).
fof(f800,plain,
( spl0_18
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f787]) ).
fof(f787,plain,
( $false
| spl0_18
| ~ spl0_41 ),
inference(resolution,[],[f273,f114]) ).
fof(f799,plain,
( ~ spl0_41
| spl0_75 ),
inference(avatar_contradiction_clause,[],[f788]) ).
fof(f788,plain,
( $false
| ~ spl0_41
| spl0_75 ),
inference(resolution,[],[f273,f743]) ).
fof(f798,plain,
( spl0_37
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f789,plain,
( $false
| spl0_37
| ~ spl0_41 ),
inference(resolution,[],[f273,f250]) ).
fof(f250,plain,
( ~ theorem(not(or(not(p),q)))
| spl0_37 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f248,plain,
( spl0_37
<=> theorem(not(or(not(p),q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f797,plain,
( spl0_35
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f790,plain,
( $false
| spl0_35
| ~ spl0_41 ),
inference(resolution,[],[f273,f236]) ).
fof(f236,plain,
( ~ theorem(not(not(q)))
| spl0_35 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f234,plain,
( spl0_35
<=> theorem(not(not(q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f796,plain,
( spl0_24
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f791,plain,
( $false
| spl0_24
| ~ spl0_41 ),
inference(resolution,[],[f273,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(f795,plain,
( ~ spl0_41
| spl0_74 ),
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f792,plain,
( $false
| ~ spl0_41
| spl0_74 ),
inference(resolution,[],[f273,f739]) ).
fof(f739,plain,
( ~ theorem(p)
| spl0_74 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f737,plain,
( spl0_74
<=> theorem(p) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f794,plain,
( ~ spl0_41
| spl0_64 ),
inference(avatar_contradiction_clause,[],[f793]) ).
fof(f793,plain,
( $false
| ~ spl0_41
| spl0_64 ),
inference(resolution,[],[f273,f532]) ).
fof(f532,plain,
( ~ theorem(q)
| spl0_64 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f530,plain,
( spl0_64
<=> theorem(q) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f784,plain,
( spl0_79
| ~ spl0_42
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f303,f296,f275,f782]) ).
fof(f275,plain,
( spl0_42
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f296,plain,
( spl0_45
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f303,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_42
| ~ spl0_45 ),
inference(resolution,[],[f297,f276]) ).
fof(f276,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f297,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f780,plain,
( spl0_78
| ~ spl0_16
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f294,f286,f92,f778]) ).
fof(f778,plain,
( spl0_78
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f294,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_44 ),
inference(resolution,[],[f287,f93]) ).
fof(f754,plain,
( spl0_77
| ~ spl0_23
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f429,f417,f143,f752]) ).
fof(f429,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_23
| ~ spl0_54 ),
inference(resolution,[],[f418,f144]) ).
fof(f750,plain,
( spl0_76
| ~ spl0_7
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f420,f417,f46,f748]) ).
fof(f420,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_54 ),
inference(resolution,[],[f418,f47]) ).
fof(f744,plain,
( ~ spl0_74
| ~ spl0_75
| spl0_38
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f576,f535,f253,f741,f737]) ).
fof(f576,plain,
( ~ theorem(or(not(q),not(p)))
| ~ theorem(p)
| spl0_38
| ~ spl0_65 ),
inference(resolution,[],[f536,f255]) ).
fof(f710,plain,
( spl0_73
| ~ spl0_31
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f224,f217,f192,f708]) ).
fof(f708,plain,
( spl0_73
<=> ! [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_73])]) ).
fof(f224,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,[],[f218,f193]) ).
fof(f706,plain,
( spl0_72
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f213,f192,f188,f704]) ).
fof(f704,plain,
( spl0_72
<=> ! [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_72])]) ).
fof(f213,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,[],[f193,f189]) ).
fof(f666,plain,
( spl0_71
| ~ spl0_31
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f243,f239,f192,f664]) ).
fof(f664,plain,
( spl0_71
<=> ! [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_71])]) ).
fof(f239,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(f243,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,[],[f240,f193]) ).
fof(f240,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,[],[f239]) ).
fof(f662,plain,
( spl0_70
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f214,f192,f184,f660]) ).
fof(f660,plain,
( spl0_70
<=> ! [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_70])]) ).
fof(f214,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,[],[f193,f185]) ).
fof(f658,plain,
( spl0_69
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f207,f192,f80,f656]) ).
fof(f656,plain,
( spl0_69
<=> ! [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_69])]) ).
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(f207,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,[],[f193,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(f625,plain,
( spl0_68
| ~ spl0_19
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f206,f192,f117,f623]) ).
fof(f206,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,[],[f193,f118]) ).
fof(f592,plain,
( spl0_67
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f205,f192,f71,f590]) ).
fof(f205,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,[],[f193,f72]) ).
fof(f541,plain,
( spl0_66
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f246,f239,f92,f539]) ).
fof(f539,plain,
( spl0_66
<=> ! [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_66])]) ).
fof(f246,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,[],[f240,f93]) ).
fof(f537,plain,
( spl0_65
| ~ spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f225,f217,f41,f535]) ).
fof(f225,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,[],[f218,f42]) ).
fof(f533,plain,
( ~ spl0_64
| spl0_35
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f472,f365,f234,f530]) ).
fof(f365,plain,
( spl0_53
<=> ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f472,plain,
( ~ theorem(q)
| spl0_35
| ~ spl0_53 ),
inference(resolution,[],[f366,f236]) ).
fof(f366,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f528,plain,
( spl0_63
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f215,f192,f171,f526]) ).
fof(f215,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,[],[f193,f172]) ).
fof(f524,plain,
( spl0_62
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f199,f188,f41,f522]) ).
fof(f199,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_30 ),
inference(resolution,[],[f189,f42]) ).
fof(f489,plain,
( spl0_61
| ~ spl0_6
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f244,f239,f41,f487]) ).
fof(f244,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_36 ),
inference(resolution,[],[f240,f42]) ).
fof(f485,plain,
( spl0_60
| ~ spl0_16
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f227,f217,f92,f483]) ).
fof(f483,plain,
( spl0_60
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f227,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_32 ),
inference(resolution,[],[f218,f93]) ).
fof(f481,plain,
( spl0_59
| ~ spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f212,f192,f163,f479]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26
| ~ spl0_31 ),
inference(resolution,[],[f193,f164]) ).
fof(f477,plain,
( spl0_58
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f196,f184,f41,f475]) ).
fof(f196,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f185,f42]) ).
fof(f452,plain,
( spl0_57
| ~ spl0_22
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f210,f192,f139,f450]) ).
fof(f210,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_22
| ~ spl0_31 ),
inference(resolution,[],[f193,f140]) ).
fof(f448,plain,
( spl0_56
| ~ spl0_16
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f201,f188,f92,f446]) ).
fof(f446,plain,
( spl0_56
<=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f201,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_30 ),
inference(resolution,[],[f189,f93]) ).
fof(f444,plain,
( spl0_55
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f198,f184,f92,f442]) ).
fof(f442,plain,
( spl0_55
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f198,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f185,f93]) ).
fof(f419,plain,
( spl0_54
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f204,f192,f66,f417]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_31 ),
inference(resolution,[],[f193,f67]) ).
fof(f367,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f307,f268,f41,f365]) ).
fof(f307,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_40 ),
inference(resolution,[],[f269,f42]) ).
fof(f363,plain,
( spl0_52
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f208,f192,f125,f361]) ).
fof(f208,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_20
| ~ spl0_31 ),
inference(resolution,[],[f193,f126]) ).
fof(f359,plain,
( spl0_51
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f175,f171,f41,f357]) ).
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(f324,plain,
( spl0_50
| ~ spl0_10
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f203,f192,f60,f322]) ).
fof(f203,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_31 ),
inference(resolution,[],[f193,f61]) ).
fof(f320,plain,
( spl0_49
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f178,f171,f92,f318]) ).
fof(f178,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_27 ),
inference(resolution,[],[f172,f93]) ).
fof(f316,plain,
( spl0_48
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f177,f171,f85,f314]) ).
fof(f85,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f172,f86]) ).
fof(f86,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f312,plain,
( spl0_47
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f163,f41,f310]) ).
fof(f167,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f164,f42]) ).
fof(f302,plain,
( spl0_46
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f169,f163,f92,f300]) ).
fof(f169,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f164,f93]) ).
fof(f298,plain,
( spl0_45
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f147,f139,f41,f296]) ).
fof(f147,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f140,f42]) ).
fof(f288,plain,
( spl0_44
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f133,f125,f102,f286]) ).
fof(f133,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f126,f103]) ).
fof(f281,plain,
( spl0_43
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f143,f92,f279]) ).
fof(f157,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f144,f93]) ).
fof(f277,plain,
( spl0_41
| spl0_42
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f129,f125,f41,f275,f272]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f126,f42]) ).
fof(f270,plain,
( spl0_40
| ~ spl0_16
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f265,f260,f92,f268]) ).
fof(f265,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_39 ),
inference(resolution,[],[f261,f93]) ).
fof(f262,plain,
( spl0_39
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f156,f143,f85,f260]) ).
fof(f156,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f144,f86]) ).
fof(f256,plain,
( ~ spl0_38
| spl0_1
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f174,f171,f18,f253]) ).
fof(f174,plain,
( ~ theorem(or(not(or(not(p),q)),not(p)))
| spl0_1
| ~ spl0_27 ),
inference(resolution,[],[f172,f20]) ).
fof(f251,plain,
( ~ spl0_37
| spl0_1
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f128,f125,f18,f248]) ).
fof(f128,plain,
( ~ theorem(not(or(not(p),q)))
| spl0_1
| ~ spl0_20 ),
inference(resolution,[],[f126,f20]) ).
fof(f241,plain,
( spl0_36
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f102,f80,f239]) ).
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(f237,plain,
( ~ spl0_35
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f125,f112,f234]) ).
fof(f130,plain,
( ~ theorem(not(not(q)))
| spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f126,f114]) ).
fof(f232,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f92,f80,f230]) ).
fof(f230,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(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(f223,plain,
( spl0_33
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f117,f92,f221]) ).
fof(f221,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(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(f219,plain,
( spl0_32
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f117,f102,f217]) ).
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(f194,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f120,f117,f41,f192]) ).
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(f190,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f102,f60,f188]) ).
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(f186,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f102,f71,f184]) ).
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(f182,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f92,f71,f180]) ).
fof(f180,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(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(f75,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
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(f76,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f75]) ).
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_13
| spl0_18 ),
inference(avatar_split_clause,[],[f123,f112,f75,f150]) ).
fof(f123,plain,
( ~ theorem(not(p))
| ~ spl0_13
| spl0_18 ),
inference(resolution,[],[f114,f76]) ).
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_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f88,f75,f18,f112]) ).
fof(f88,plain,
( ~ theorem(or(not(not(q)),not(p)))
| spl0_1
| ~ spl0_13 ),
inference(resolution,[],[f76,f20]) ).
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_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f58,f55,f23,f80]) ).
fof(f23,plain,
( spl0_2
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
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_2
| ~ spl0_9 ),
inference(resolution,[],[f56,f24]) ).
fof(f24,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
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_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f53,f50,f23,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_2
| ~ spl0_8 ),
inference(resolution,[],[f51,f24]) ).
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_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f44,f37,f23,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_2
| ~ spl0_5 ),
inference(resolution,[],[f38,f24]) ).
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_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f31,f23,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_2
| ~ spl0_4 ),
inference(resolution,[],[f32,f24]) ).
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/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(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/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f48,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f34,f27,f23,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_2
| ~ spl0_3 ),
inference(resolution,[],[f28,f24]) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f7,f23]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f21,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f18]) ).
fof(f10,plain,
~ theorem(or(not(or(not(p),q)),or(not(not(q)),not(p)))),
inference(definition_unfolding,[],[f9,f6,f6,f6]) ).
fof(f9,axiom,
~ theorem(implies(implies(p,q),implies(not(q),not(p)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.24 % Problem : LCL182-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.25 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.45 % Computer : n008.cluster.edu
% 0.07/0.45 % Model : x86_64 x86_64
% 0.07/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.45 % Memory : 8042.1875MB
% 0.07/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.45 % CPULimit : 300
% 0.07/0.45 % WCLimit : 300
% 0.07/0.45 % DateTime : Mon Apr 29 23:01:27 EDT 2024
% 0.07/0.45 % CPUTime :
% 0.07/0.45 % (18099)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.46 % (18105)WARNING: value z3 for option sas not known
% 0.07/0.46 % (18104)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.46 % (18109)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)
% 0.07/0.46 % (18106)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.46 % (18103)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.46 % (18108)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)
% 0.07/0.46 % (18107)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)
% 0.07/0.46 % (18105)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)
% 0.07/0.46 TRYING [1]
% 0.07/0.46 TRYING [2]
% 0.07/0.46 TRYING [1]
% 0.07/0.46 TRYING [2]
% 0.07/0.47 TRYING [3]
% 0.12/0.47 TRYING [3]
% 0.12/0.47 TRYING [4]
% 0.12/0.47 TRYING [4]
% 0.12/0.50 TRYING [5]
% 0.12/0.51 TRYING [5]
% 0.60/0.58 % (18107)First to succeed.
% 0.60/0.58 % (18107)Refutation found. Thanks to Tanya!
% 0.60/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.60/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.60/0.59 % (18107)------------------------------
% 0.60/0.59 % (18107)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.59 % (18107)Termination reason: Refutation
% 0.60/0.59
% 0.60/0.59 % (18107)Memory used [KB]: 2292
% 0.60/0.59 % (18107)Time elapsed: 0.119 s
% 0.60/0.59 % (18107)Instructions burned: 378 (million)
% 0.60/0.59 % (18107)------------------------------
% 0.60/0.59 % (18107)------------------------------
% 0.60/0.59 % (18099)Success in time 0.129 s
%------------------------------------------------------------------------------