TSTP Solution File: NUM523+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM523+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:06:23 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 213
% Syntax : Number of formulae : 691 ( 92 unt; 0 def)
% Number of atoms : 2702 ( 616 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3453 (1442 ~;1570 |; 194 &)
% ( 182 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 174 ( 172 usr; 166 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 790 ( 770 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2348,plain,
$false,
inference(avatar_sat_refutation,[],[f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f307,f316,f320,f324,f329,f333,f337,f341,f345,f349,f353,f373,f392,f396,f415,f420,f425,f431,f435,f439,f443,f447,f451,f455,f459,f463,f528,f534,f538,f542,f546,f550,f554,f561,f565,f569,f573,f577,f581,f588,f625,f629,f633,f637,f647,f684,f688,f692,f714,f720,f728,f732,f736,f740,f744,f795,f799,f803,f807,f811,f815,f819,f828,f881,f893,f897,f915,f919,f933,f941,f946,f951,f956,f961,f966,f971,f976,f981,f986,f991,f1000,f1005,f1010,f1015,f1020,f1025,f1030,f1035,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1469,f1473,f1510,f1514,f1518,f1522,f1526,f1530,f1549,f1626,f1630,f1634,f1638,f1642,f1646,f1746,f1751,f1812,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f1845,f1849,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1966,f1970,f2116,f2120,f2124,f2128,f2132,f2136,f2140,f2144,f2149,f2153,f2157,f2161,f2165,f2169,f2336,f2347]) ).
fof(f2347,plain,
( ~ spl6_4
| ~ spl6_6
| ~ spl6_3
| spl6_2
| ~ spl6_1
| ~ spl6_76 ),
inference(avatar_split_clause,[],[f2346,f817,f236,f240,f245,f260,f250]) ).
fof(f250,plain,
( spl6_4
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f260,plain,
( spl6_6
<=> aNaturalNumber0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f245,plain,
( spl6_3
<=> isPrime0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f240,plain,
( spl6_2
<=> doDivides0(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f236,plain,
( spl6_1
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f817,plain,
( spl6_76
<=> ! [X2,X0,X1] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_76])]) ).
fof(f2346,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ spl6_1
| ~ spl6_76 ),
inference(duplicate_literal_removal,[],[f2337]) ).
fof(f2337,plain,
( doDivides0(xp,xn)
| doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ spl6_1
| ~ spl6_76 ),
inference(resolution,[],[f237,f818]) ).
fof(f818,plain,
( ! [X2,X0,X1] :
( ~ doDivides0(X2,sdtasdt0(X0,X1))
| doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_76 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f237,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f2336,plain,
( ~ spl6_6
| ~ spl6_129
| ~ spl6_128
| spl6_1
| ~ spl6_29
| ~ spl6_52 ),
inference(avatar_split_clause,[],[f615,f575,f412,f236,f1739,f1743,f260]) ).
fof(f1743,plain,
( spl6_129
<=> aNaturalNumber0(sdtasdt0(xn,xn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_129])]) ).
fof(f1739,plain,
( spl6_128
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_128])]) ).
fof(f412,plain,
( spl6_29
<=> sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
fof(f575,plain,
( spl6_52
<=> ! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_52])]) ).
fof(f615,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ spl6_29
| ~ spl6_52 ),
inference(superposition,[],[f576,f414]) ).
fof(f414,plain,
( sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn)
| ~ spl6_29 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f576,plain,
( ! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) )
| ~ spl6_52 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f2169,plain,
( spl6_165
| ~ spl6_15
| ~ spl6_58 ),
inference(avatar_split_clause,[],[f672,f635,f305,f2167]) ).
fof(f2167,plain,
( spl6_165
<=> ! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sdtsldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_165])]) ).
fof(f305,plain,
( spl6_15
<=> ! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f635,plain,
( spl6_58
<=> ! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_58])]) ).
fof(f672,plain,
( ! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sdtsldt0(X1,X0)) )
| ~ spl6_15
| ~ spl6_58 ),
inference(resolution,[],[f636,f306]) ).
fof(f306,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sP1(X0) )
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f636,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_58 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f2165,plain,
( spl6_164
| ~ spl6_30
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f670,f631,f418,f2163]) ).
fof(f2163,plain,
( spl6_164
<=> ! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_164])]) ).
fof(f418,plain,
( spl6_30
<=> ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_30])]) ).
fof(f631,plain,
( spl6_57
<=> ! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_57])]) ).
fof(f670,plain,
( ! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) )
| ~ spl6_30
| ~ spl6_57 ),
inference(duplicate_literal_removal,[],[f661]) ).
fof(f661,plain,
( ! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_30
| ~ spl6_57 ),
inference(resolution,[],[f632,f419]) ).
fof(f419,plain,
( ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_30 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f632,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_57 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f2161,plain,
( spl6_163
| ~ spl6_30
| ~ spl6_56 ),
inference(avatar_split_clause,[],[f658,f627,f418,f2159]) ).
fof(f2159,plain,
( spl6_163
<=> ! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_163])]) ).
fof(f627,plain,
( spl6_56
<=> ! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_56])]) ).
fof(f658,plain,
( ! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) )
| ~ spl6_30
| ~ spl6_56 ),
inference(duplicate_literal_removal,[],[f649]) ).
fof(f649,plain,
( ! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_30
| ~ spl6_56 ),
inference(resolution,[],[f628,f419]) ).
fof(f628,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_56 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f2157,plain,
( spl6_162
| ~ spl6_21
| ~ spl6_40 ),
inference(avatar_split_clause,[],[f518,f461,f335,f2155]) ).
fof(f2155,plain,
( spl6_162
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sdtmndt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_162])]) ).
fof(f335,plain,
( spl6_21
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f461,plain,
( spl6_40
<=> ! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_40])]) ).
fof(f518,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sdtmndt0(X1,X0)) )
| ~ spl6_21
| ~ spl6_40 ),
inference(resolution,[],[f462,f336]) ).
fof(f336,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f462,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_40 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f2153,plain,
( spl6_161
| ~ spl6_20
| ~ spl6_40 ),
inference(avatar_split_clause,[],[f517,f461,f331,f2151]) ).
fof(f2151,plain,
( spl6_161
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sdtmndt0(X1,X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_161])]) ).
fof(f331,plain,
( spl6_20
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sdtmndt0(X1,X0),sz00) )
| ~ spl6_20
| ~ spl6_40 ),
inference(resolution,[],[f462,f332]) ).
fof(f332,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f2149,plain,
( spl6_9
| ~ spl6_160
| ~ spl6_17
| ~ spl6_59 ),
inference(avatar_split_clause,[],[f772,f644,f318,f2146,f275]) ).
fof(f275,plain,
( spl6_9
<=> sP0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f2146,plain,
( spl6_160
<=> isPrime0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_160])]) ).
fof(f318,plain,
( spl6_17
<=> ! [X0] :
( sP0(X0)
| ~ isPrime0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f644,plain,
( spl6_59
<=> sP1(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_59])]) ).
fof(f772,plain,
( ~ isPrime0(sz10)
| sP0(sz10)
| ~ spl6_17
| ~ spl6_59 ),
inference(resolution,[],[f646,f319]) ).
fof(f319,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0)
| sP0(X0) )
| ~ spl6_17 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f646,plain,
( sP1(sz10)
| ~ spl6_59 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f2144,plain,
( spl6_159
| ~ spl6_21
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f509,f457,f335,f2142]) ).
fof(f2142,plain,
( spl6_159
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_159])]) ).
fof(f457,plain,
( spl6_39
<=> ! [X0,X1] :
( aNaturalNumber0(sK5(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_39])]) ).
fof(f509,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK5(X0,X1)) )
| ~ spl6_21
| ~ spl6_39 ),
inference(resolution,[],[f458,f336]) ).
fof(f458,plain,
( ! [X0,X1] :
( aNaturalNumber0(sK5(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_39 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f2140,plain,
( spl6_158
| ~ spl6_20
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f508,f457,f331,f2138]) ).
fof(f2138,plain,
( spl6_158
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK5(X0,X1),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_158])]) ).
fof(f508,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK5(X0,X1),sz00) )
| ~ spl6_20
| ~ spl6_39 ),
inference(resolution,[],[f458,f332]) ).
fof(f2136,plain,
( spl6_157
| ~ spl6_21
| ~ spl6_38 ),
inference(avatar_split_clause,[],[f500,f453,f335,f2134]) ).
fof(f2134,plain,
( spl6_157
<=> ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_157])]) ).
fof(f453,plain,
( spl6_38
<=> ! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_38])]) ).
fof(f500,plain,
( ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK4(X0,X1)) )
| ~ spl6_21
| ~ spl6_38 ),
inference(resolution,[],[f454,f336]) ).
fof(f454,plain,
( ! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_38 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f2132,plain,
( spl6_156
| ~ spl6_20
| ~ spl6_38 ),
inference(avatar_split_clause,[],[f499,f453,f331,f2130]) ).
fof(f2130,plain,
( spl6_156
<=> ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK4(X0,X1),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_156])]) ).
fof(f499,plain,
( ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK4(X0,X1),sz00) )
| ~ spl6_20
| ~ spl6_38 ),
inference(resolution,[],[f454,f332]) ).
fof(f2128,plain,
( spl6_155
| ~ spl6_21
| ~ spl6_34 ),
inference(avatar_split_clause,[],[f475,f437,f335,f2126]) ).
fof(f2126,plain,
( spl6_155
<=> ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_155])]) ).
fof(f437,plain,
( spl6_34
<=> ! [X0] :
( aNaturalNumber0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_34])]) ).
fof(f475,plain,
( ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK3(X0)) )
| ~ spl6_21
| ~ spl6_34 ),
inference(resolution,[],[f438,f336]) ).
fof(f438,plain,
( ! [X0] :
( aNaturalNumber0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_34 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f2124,plain,
( spl6_154
| ~ spl6_20
| ~ spl6_34 ),
inference(avatar_split_clause,[],[f474,f437,f331,f2122]) ).
fof(f2122,plain,
( spl6_154
<=> ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK3(X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_154])]) ).
fof(f474,plain,
( ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sK3(X0),sz00) )
| ~ spl6_20
| ~ spl6_34 ),
inference(resolution,[],[f438,f332]) ).
fof(f2120,plain,
( spl6_153
| ~ spl6_21
| ~ spl6_33 ),
inference(avatar_split_clause,[],[f468,f433,f335,f2118]) ).
fof(f2118,plain,
( spl6_153
<=> ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sz00 = sdtasdt0(sz00,sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_153])]) ).
fof(f433,plain,
( spl6_33
<=> ! [X0] :
( sP0(X0)
| aNaturalNumber0(sK2(X0))
| sz10 = X0
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_33])]) ).
fof(f468,plain,
( ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sz00 = sdtasdt0(sz00,sK2(X0)) )
| ~ spl6_21
| ~ spl6_33 ),
inference(resolution,[],[f434,f336]) ).
fof(f434,plain,
( ! [X0] :
( aNaturalNumber0(sK2(X0))
| sP0(X0)
| sz10 = X0
| sz00 = X0 )
| ~ spl6_33 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f2116,plain,
( spl6_152
| ~ spl6_20
| ~ spl6_33 ),
inference(avatar_split_clause,[],[f467,f433,f331,f2114]) ).
fof(f2114,plain,
( spl6_152
<=> ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sz00 = sdtasdt0(sK2(X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_152])]) ).
fof(f467,plain,
( ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sz00 = sdtasdt0(sK2(X0),sz00) )
| ~ spl6_20
| ~ spl6_33 ),
inference(resolution,[],[f434,f332]) ).
fof(f1970,plain,
( ~ spl6_8
| spl6_151
| ~ spl6_32
| ~ spl6_51 ),
inference(avatar_split_clause,[],[f608,f571,f429,f1968,f270]) ).
fof(f270,plain,
( spl6_8
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f1968,plain,
( spl6_151
<=> ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_151])]) ).
fof(f429,plain,
( spl6_32
<=> ! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_32])]) ).
fof(f571,plain,
( spl6_51
<=> ! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_51])]) ).
fof(f608,plain,
( ! [X0] :
( sz10 = X0
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| ~ spl6_32
| ~ spl6_51 ),
inference(duplicate_literal_removal,[],[f607]) ).
fof(f607,plain,
( ! [X0] :
( sz10 = X0
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_32
| ~ spl6_51 ),
inference(resolution,[],[f572,f430]) ).
fof(f430,plain,
( ! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_32 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f572,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_51 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f1966,plain,
( spl6_150
| ~ spl6_30
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f597,f563,f418,f1964]) ).
fof(f1964,plain,
( spl6_150
<=> ! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_150])]) ).
fof(f563,plain,
( spl6_49
<=> ! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_49])]) ).
fof(f597,plain,
( ! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0) )
| ~ spl6_30
| ~ spl6_49 ),
inference(duplicate_literal_removal,[],[f590]) ).
fof(f590,plain,
( ! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_30
| ~ spl6_49 ),
inference(resolution,[],[f564,f419]) ).
fof(f564,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| iLess0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_49 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f1960,plain,
( ~ spl6_8
| spl6_149
| ~ spl6_32
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f594,f563,f429,f1958,f270]) ).
fof(f1958,plain,
( spl6_149
<=> ! [X0] :
( iLess0(sz10,X0)
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_149])]) ).
fof(f594,plain,
( ! [X0] :
( iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| sz00 = X0 )
| ~ spl6_32
| ~ spl6_49 ),
inference(duplicate_literal_removal,[],[f593]) ).
fof(f593,plain,
( ! [X0] :
( iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_32
| ~ spl6_49 ),
inference(resolution,[],[f564,f430]) ).
fof(f1956,plain,
( spl6_148
| ~ spl6_25
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f410,f394,f351,f1954]) ).
fof(f1954,plain,
( spl6_148
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sz10,sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_148])]) ).
fof(f351,plain,
( spl6_25
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f394,plain,
( spl6_28
<=> ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sz10,sdtasdt0(X1,X0)) )
| ~ spl6_25
| ~ spl6_28 ),
inference(resolution,[],[f395,f352]) ).
fof(f352,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f395,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_28 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f1952,plain,
( spl6_147
| ~ spl6_24
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f409,f394,f347,f1950]) ).
fof(f1950,plain,
( spl6_147
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sdtasdt0(X1,X0),sz10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_147])]) ).
fof(f347,plain,
( spl6_24
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f409,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sdtasdt0(X1,X0),sz10) )
| ~ spl6_24
| ~ spl6_28 ),
inference(resolution,[],[f395,f348]) ).
fof(f348,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 )
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f1948,plain,
( spl6_146
| ~ spl6_23
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f408,f394,f343,f1946]) ).
fof(f1946,plain,
( spl6_146
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sz00,sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_146])]) ).
fof(f343,plain,
( spl6_23
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f408,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sz00,sdtasdt0(X1,X0)) )
| ~ spl6_23
| ~ spl6_28 ),
inference(resolution,[],[f395,f344]) ).
fof(f344,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f1944,plain,
( spl6_145
| ~ spl6_22
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f407,f394,f339,f1942]) ).
fof(f1942,plain,
( spl6_145
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sdtasdt0(X1,X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_145])]) ).
fof(f339,plain,
( spl6_22
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f407,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sdtasdt0(X1,X0),sz00) )
| ~ spl6_22
| ~ spl6_28 ),
inference(resolution,[],[f395,f340]) ).
fof(f340,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f1940,plain,
( spl6_144
| ~ spl6_25
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f403,f390,f351,f1938]) ).
fof(f1938,plain,
( spl6_144
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sz10,sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_144])]) ).
fof(f390,plain,
( spl6_27
<=> ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sz10,sdtpldt0(X1,X0)) )
| ~ spl6_25
| ~ spl6_27 ),
inference(resolution,[],[f391,f352]) ).
fof(f391,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_27 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f1936,plain,
( spl6_143
| ~ spl6_24
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f402,f390,f347,f1934]) ).
fof(f1934,plain,
( spl6_143
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sdtpldt0(X1,X0),sz10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_143])]) ).
fof(f402,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sdtpldt0(X1,X0),sz10) )
| ~ spl6_24
| ~ spl6_27 ),
inference(resolution,[],[f391,f348]) ).
fof(f1932,plain,
( spl6_142
| ~ spl6_23
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f401,f390,f343,f1930]) ).
fof(f1930,plain,
( spl6_142
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sz00,sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_142])]) ).
fof(f401,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sz00,sdtpldt0(X1,X0)) )
| ~ spl6_23
| ~ spl6_27 ),
inference(resolution,[],[f391,f344]) ).
fof(f1928,plain,
( spl6_141
| ~ spl6_22
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f400,f390,f339,f1926]) ).
fof(f1926,plain,
( spl6_141
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sdtpldt0(X1,X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_141])]) ).
fof(f400,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sdtpldt0(X1,X0),sz00) )
| ~ spl6_22
| ~ spl6_27 ),
inference(resolution,[],[f391,f340]) ).
fof(f1924,plain,
( spl6_140
| ~ spl6_15
| ~ spl6_129 ),
inference(avatar_split_clause,[],[f1781,f1743,f305,f1921]) ).
fof(f1921,plain,
( spl6_140
<=> sP1(sdtasdt0(xn,xn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_140])]) ).
fof(f1781,plain,
( sP1(sdtasdt0(xn,xn))
| ~ spl6_15
| ~ spl6_129 ),
inference(resolution,[],[f1745,f306]) ).
fof(f1745,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl6_129 ),
inference(avatar_component_clause,[],[f1743]) ).
fof(f1849,plain,
( spl6_139
| ~ spl6_15
| ~ spl6_40 ),
inference(avatar_split_clause,[],[f516,f461,f305,f1847]) ).
fof(f1847,plain,
( spl6_139
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sdtmndt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_139])]) ).
fof(f516,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sdtmndt0(X1,X0)) )
| ~ spl6_15
| ~ spl6_40 ),
inference(resolution,[],[f462,f306]) ).
fof(f1845,plain,
( spl6_138
| ~ spl6_15
| ~ spl6_128 ),
inference(avatar_split_clause,[],[f1752,f1739,f305,f1842]) ).
fof(f1842,plain,
( spl6_138
<=> sP1(sdtasdt0(xm,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_138])]) ).
fof(f1752,plain,
( sP1(sdtasdt0(xm,xm))
| ~ spl6_15
| ~ spl6_128 ),
inference(resolution,[],[f1740,f306]) ).
fof(f1740,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl6_128 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f1840,plain,
( spl6_137
| ~ spl6_15
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f507,f457,f305,f1838]) ).
fof(f1838,plain,
( spl6_137
<=> ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_137])]) ).
fof(f507,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sK5(X0,X1)) )
| ~ spl6_15
| ~ spl6_39 ),
inference(resolution,[],[f458,f306]) ).
fof(f1836,plain,
( spl6_136
| ~ spl6_15
| ~ spl6_38 ),
inference(avatar_split_clause,[],[f498,f453,f305,f1834]) ).
fof(f1834,plain,
( spl6_136
<=> ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_136])]) ).
fof(f498,plain,
( ! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(sK4(X0,X1)) )
| ~ spl6_15
| ~ spl6_38 ),
inference(resolution,[],[f454,f306]) ).
fof(f1832,plain,
( spl6_135
| ~ spl6_15
| ~ spl6_34 ),
inference(avatar_split_clause,[],[f473,f437,f305,f1830]) ).
fof(f1830,plain,
( spl6_135
<=> ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sP1(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_135])]) ).
fof(f473,plain,
( ! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sP1(sK3(X0)) )
| ~ spl6_15
| ~ spl6_34 ),
inference(resolution,[],[f438,f306]) ).
fof(f1828,plain,
( spl6_134
| ~ spl6_15
| ~ spl6_33 ),
inference(avatar_split_clause,[],[f466,f433,f305,f1826]) ).
fof(f1826,plain,
( spl6_134
<=> ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sP1(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_134])]) ).
fof(f466,plain,
( ! [X0] :
( sP0(X0)
| sz10 = X0
| sz00 = X0
| sP1(sK2(X0)) )
| ~ spl6_15
| ~ spl6_33 ),
inference(resolution,[],[f434,f306]) ).
fof(f1824,plain,
( spl6_133
| ~ spl6_21
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f406,f394,f335,f1822]) ).
fof(f1822,plain,
( spl6_133
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_133])]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtasdt0(X1,X0)) )
| ~ spl6_21
| ~ spl6_28 ),
inference(resolution,[],[f395,f336]) ).
fof(f1820,plain,
( spl6_132
| ~ spl6_20
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f405,f394,f331,f1818]) ).
fof(f1818,plain,
( spl6_132
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtasdt0(X1,X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_132])]) ).
fof(f405,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtasdt0(X1,X0),sz00) )
| ~ spl6_20
| ~ spl6_28 ),
inference(resolution,[],[f395,f332]) ).
fof(f1816,plain,
( spl6_131
| ~ spl6_21
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f399,f390,f335,f1814]) ).
fof(f1814,plain,
( spl6_131
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_131])]) ).
fof(f399,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtpldt0(X1,X0)) )
| ~ spl6_21
| ~ spl6_27 ),
inference(resolution,[],[f391,f336]) ).
fof(f1812,plain,
( spl6_130
| ~ spl6_20
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f398,f390,f331,f1810]) ).
fof(f1810,plain,
( spl6_130
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtpldt0(X1,X0),sz00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_130])]) ).
fof(f398,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtpldt0(X1,X0),sz00) )
| ~ spl6_20
| ~ spl6_27 ),
inference(resolution,[],[f391,f332]) ).
fof(f1751,plain,
( ~ spl6_5
| ~ spl6_28
| spl6_128 ),
inference(avatar_split_clause,[],[f1748,f1739,f394,f255]) ).
fof(f255,plain,
( spl6_5
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f1748,plain,
( ~ aNaturalNumber0(xm)
| ~ spl6_28
| spl6_128 ),
inference(duplicate_literal_removal,[],[f1747]) ).
fof(f1747,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ spl6_28
| spl6_128 ),
inference(resolution,[],[f1741,f395]) ).
fof(f1741,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl6_128 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f1746,plain,
( ~ spl6_6
| ~ spl6_128
| spl6_129
| ~ spl6_28
| ~ spl6_29 ),
inference(avatar_split_clause,[],[f416,f412,f394,f1743,f1739,f260]) ).
fof(f416,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ spl6_28
| ~ spl6_29 ),
inference(superposition,[],[f395,f414]) ).
fof(f1646,plain,
( spl6_127
| ~ spl6_16
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f671,f631,f314,f1644]) ).
fof(f1644,plain,
( spl6_127
<=> ! [X0] :
( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_127])]) ).
fof(f314,plain,
( spl6_16
<=> ! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f671,plain,
( ! [X0] :
( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_16
| ~ spl6_57 ),
inference(duplicate_literal_removal,[],[f660]) ).
fof(f660,plain,
( ! [X0] :
( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_16
| ~ spl6_57 ),
inference(resolution,[],[f632,f315]) ).
fof(f315,plain,
( ! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f1642,plain,
( spl6_126
| ~ spl6_16
| ~ spl6_56 ),
inference(avatar_split_clause,[],[f659,f627,f314,f1640]) ).
fof(f1640,plain,
( spl6_126
<=> ! [X0] :
( sdtpldt0(X0,sK5(X0,X0)) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_126])]) ).
fof(f659,plain,
( ! [X0] :
( sdtpldt0(X0,sK5(X0,X0)) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl6_16
| ~ spl6_56 ),
inference(duplicate_literal_removal,[],[f648]) ).
fof(f648,plain,
( ! [X0] :
( sdtpldt0(X0,sK5(X0,X0)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_16
| ~ spl6_56 ),
inference(resolution,[],[f628,f315]) ).
fof(f1638,plain,
( spl6_125
| ~ spl6_8
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f490,f449,f270,f1636]) ).
fof(f1636,plain,
( spl6_125
<=> ! [X0] :
( sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_125])]) ).
fof(f449,plain,
( spl6_37
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_37])]) ).
fof(f490,plain,
( ! [X0] :
( sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_8
| ~ spl6_37 ),
inference(resolution,[],[f450,f272]) ).
fof(f272,plain,
( aNaturalNumber0(sz10)
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_37 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1634,plain,
( spl6_124
| ~ spl6_7
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f489,f449,f265,f1632]) ).
fof(f1632,plain,
( spl6_124
<=> ! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_124])]) ).
fof(f265,plain,
( spl6_7
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f489,plain,
( ! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_7
| ~ spl6_37 ),
inference(resolution,[],[f450,f267]) ).
fof(f267,plain,
( aNaturalNumber0(sz00)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f1630,plain,
( spl6_123
| ~ spl6_8
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f481,f445,f270,f1628]) ).
fof(f1628,plain,
( spl6_123
<=> ! [X0] :
( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_123])]) ).
fof(f445,plain,
( spl6_36
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_36])]) ).
fof(f481,plain,
( ! [X0] :
( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_8
| ~ spl6_36 ),
inference(resolution,[],[f446,f272]) ).
fof(f446,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1626,plain,
( spl6_122
| ~ spl6_7
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f480,f445,f265,f1624]) ).
fof(f1624,plain,
( spl6_122
<=> ! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_122])]) ).
fof(f480,plain,
( ! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_7
| ~ spl6_36 ),
inference(resolution,[],[f446,f267]) ).
fof(f1549,plain,
( spl6_10
| ~ spl6_121
| ~ spl6_17
| ~ spl6_54 ),
inference(avatar_split_clause,[],[f716,f585,f318,f1546,f280]) ).
fof(f280,plain,
( spl6_10
<=> sP0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f1546,plain,
( spl6_121
<=> isPrime0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_121])]) ).
fof(f585,plain,
( spl6_54
<=> sP1(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_54])]) ).
fof(f716,plain,
( ~ isPrime0(sz00)
| sP0(sz00)
| ~ spl6_17
| ~ spl6_54 ),
inference(resolution,[],[f587,f319]) ).
fof(f587,plain,
( sP1(sz00)
| ~ spl6_54 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f1530,plain,
( spl6_120
| ~ spl6_6
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f495,f449,f260,f1528]) ).
fof(f1528,plain,
( spl6_120
<=> ! [X0] :
( sdtasdt0(X0,xp) = sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_120])]) ).
fof(f495,plain,
( ! [X0] :
( sdtasdt0(X0,xp) = sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_6
| ~ spl6_37 ),
inference(resolution,[],[f450,f262]) ).
fof(f262,plain,
( aNaturalNumber0(xp)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1526,plain,
( spl6_119
| ~ spl6_5
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f494,f449,f255,f1524]) ).
fof(f1524,plain,
( spl6_119
<=> ! [X0] :
( sdtasdt0(X0,xm) = sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_119])]) ).
fof(f494,plain,
( ! [X0] :
( sdtasdt0(X0,xm) = sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_5
| ~ spl6_37 ),
inference(resolution,[],[f450,f257]) ).
fof(f257,plain,
( aNaturalNumber0(xm)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f1522,plain,
( spl6_118
| ~ spl6_4
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f493,f449,f250,f1520]) ).
fof(f1520,plain,
( spl6_118
<=> ! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_118])]) ).
fof(f493,plain,
( ! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_4
| ~ spl6_37 ),
inference(resolution,[],[f450,f252]) ).
fof(f252,plain,
( aNaturalNumber0(xn)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f1518,plain,
( spl6_117
| ~ spl6_6
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f486,f445,f260,f1516]) ).
fof(f1516,plain,
( spl6_117
<=> ! [X0] :
( sdtpldt0(X0,xp) = sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_117])]) ).
fof(f486,plain,
( ! [X0] :
( sdtpldt0(X0,xp) = sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_6
| ~ spl6_36 ),
inference(resolution,[],[f446,f262]) ).
fof(f1514,plain,
( spl6_116
| ~ spl6_5
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f485,f445,f255,f1512]) ).
fof(f1512,plain,
( spl6_116
<=> ! [X0] :
( sdtpldt0(X0,xm) = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_116])]) ).
fof(f485,plain,
( ! [X0] :
( sdtpldt0(X0,xm) = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_5
| ~ spl6_36 ),
inference(resolution,[],[f446,f257]) ).
fof(f1510,plain,
( spl6_115
| ~ spl6_4
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f484,f445,f250,f1508]) ).
fof(f1508,plain,
( spl6_115
<=> ! [X0] :
( sdtpldt0(X0,xn) = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_115])]) ).
fof(f484,plain,
( ! [X0] :
( sdtpldt0(X0,xn) = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_4
| ~ spl6_36 ),
inference(resolution,[],[f446,f252]) ).
fof(f1473,plain,
( spl6_114
| ~ spl6_15
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f404,f394,f305,f1471]) ).
fof(f1471,plain,
( spl6_114
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_114])]) ).
fof(f404,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtasdt0(X1,X0)) )
| ~ spl6_15
| ~ spl6_28 ),
inference(resolution,[],[f395,f306]) ).
fof(f1469,plain,
( spl6_113
| ~ spl6_15
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f397,f390,f305,f1467]) ).
fof(f1467,plain,
( spl6_113
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_113])]) ).
fof(f397,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtpldt0(X1,X0)) )
| ~ spl6_15
| ~ spl6_27 ),
inference(resolution,[],[f391,f306]) ).
fof(f1336,plain,
( spl6_112
| ~ spl6_8
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f380,f347,f270,f1333]) ).
fof(f1333,plain,
( spl6_112
<=> sz10 = sdtasdt0(sz10,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_112])]) ).
fof(f380,plain,
( sz10 = sdtasdt0(sz10,sz10)
| ~ spl6_8
| ~ spl6_24 ),
inference(resolution,[],[f348,f272]) ).
fof(f1331,plain,
( spl6_111
| ~ spl6_8
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f375,f343,f270,f1328]) ).
fof(f1328,plain,
( spl6_111
<=> sz10 = sdtpldt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_111])]) ).
fof(f375,plain,
( sz10 = sdtpldt0(sz00,sz10)
| ~ spl6_8
| ~ spl6_23 ),
inference(resolution,[],[f344,f272]) ).
fof(f1326,plain,
( spl6_110
| ~ spl6_3
| ~ spl6_17
| ~ spl6_31 ),
inference(avatar_split_clause,[],[f556,f422,f318,f245,f1323]) ).
fof(f1323,plain,
( spl6_110
<=> sP0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_110])]) ).
fof(f422,plain,
( spl6_31
<=> sP1(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_31])]) ).
fof(f556,plain,
( ~ isPrime0(xp)
| sP0(xp)
| ~ spl6_17
| ~ spl6_31 ),
inference(resolution,[],[f424,f319]) ).
fof(f424,plain,
( sP1(xp)
| ~ spl6_31 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f1321,plain,
( spl6_109
| ~ spl6_8
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f365,f339,f270,f1318]) ).
fof(f1318,plain,
( spl6_109
<=> sz10 = sdtpldt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_109])]) ).
fof(f365,plain,
( sz10 = sdtpldt0(sz10,sz00)
| ~ spl6_8
| ~ spl6_22 ),
inference(resolution,[],[f340,f272]) ).
fof(f1316,plain,
( spl6_108
| ~ spl6_7
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f364,f339,f265,f1313]) ).
fof(f1313,plain,
( spl6_108
<=> sz00 = sdtpldt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_108])]) ).
fof(f364,plain,
( sz00 = sdtpldt0(sz00,sz00)
| ~ spl6_7
| ~ spl6_22 ),
inference(resolution,[],[f340,f267]) ).
fof(f1311,plain,
( spl6_107
| ~ spl6_8
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f360,f335,f270,f1308]) ).
fof(f1308,plain,
( spl6_107
<=> sz00 = sdtasdt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_107])]) ).
fof(f360,plain,
( sz00 = sdtasdt0(sz00,sz10)
| ~ spl6_8
| ~ spl6_21 ),
inference(resolution,[],[f336,f272]) ).
fof(f1306,plain,
( spl6_106
| ~ spl6_8
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f355,f331,f270,f1303]) ).
fof(f1303,plain,
( spl6_106
<=> sz00 = sdtasdt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_106])]) ).
fof(f355,plain,
( sz00 = sdtasdt0(sz10,sz00)
| ~ spl6_8
| ~ spl6_20 ),
inference(resolution,[],[f332,f272]) ).
fof(f1301,plain,
( spl6_105
| ~ spl6_7
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f354,f331,f265,f1298]) ).
fof(f1298,plain,
( spl6_105
<=> sz00 = sdtasdt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_105])]) ).
fof(f354,plain,
( sz00 = sdtasdt0(sz00,sz00)
| ~ spl6_7
| ~ spl6_20 ),
inference(resolution,[],[f332,f267]) ).
fof(f1035,plain,
( spl6_104
| ~ spl6_6
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f388,f351,f260,f1032]) ).
fof(f1032,plain,
( spl6_104
<=> xp = sdtasdt0(sz10,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_104])]) ).
fof(f388,plain,
( xp = sdtasdt0(sz10,xp)
| ~ spl6_6
| ~ spl6_25 ),
inference(resolution,[],[f352,f262]) ).
fof(f1030,plain,
( spl6_103
| ~ spl6_5
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f387,f351,f255,f1027]) ).
fof(f1027,plain,
( spl6_103
<=> xm = sdtasdt0(sz10,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_103])]) ).
fof(f387,plain,
( xm = sdtasdt0(sz10,xm)
| ~ spl6_5
| ~ spl6_25 ),
inference(resolution,[],[f352,f257]) ).
fof(f1025,plain,
( spl6_102
| ~ spl6_4
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f386,f351,f250,f1022]) ).
fof(f1022,plain,
( spl6_102
<=> xn = sdtasdt0(sz10,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_102])]) ).
fof(f386,plain,
( xn = sdtasdt0(sz10,xn)
| ~ spl6_4
| ~ spl6_25 ),
inference(resolution,[],[f352,f252]) ).
fof(f1020,plain,
( spl6_101
| ~ spl6_6
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f383,f347,f260,f1017]) ).
fof(f1017,plain,
( spl6_101
<=> xp = sdtasdt0(xp,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_101])]) ).
fof(f383,plain,
( xp = sdtasdt0(xp,sz10)
| ~ spl6_6
| ~ spl6_24 ),
inference(resolution,[],[f348,f262]) ).
fof(f1015,plain,
( spl6_100
| ~ spl6_5
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f382,f347,f255,f1012]) ).
fof(f1012,plain,
( spl6_100
<=> xm = sdtasdt0(xm,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_100])]) ).
fof(f382,plain,
( xm = sdtasdt0(xm,sz10)
| ~ spl6_5
| ~ spl6_24 ),
inference(resolution,[],[f348,f257]) ).
fof(f1010,plain,
( spl6_99
| ~ spl6_4
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f381,f347,f250,f1007]) ).
fof(f1007,plain,
( spl6_99
<=> xn = sdtasdt0(xn,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_99])]) ).
fof(f381,plain,
( xn = sdtasdt0(xn,sz10)
| ~ spl6_4
| ~ spl6_24 ),
inference(resolution,[],[f348,f252]) ).
fof(f1005,plain,
( spl6_98
| ~ spl6_6
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f378,f343,f260,f1002]) ).
fof(f1002,plain,
( spl6_98
<=> xp = sdtpldt0(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_98])]) ).
fof(f378,plain,
( xp = sdtpldt0(sz00,xp)
| ~ spl6_6
| ~ spl6_23 ),
inference(resolution,[],[f344,f262]) ).
fof(f1000,plain,
( spl6_96
| ~ spl6_97
| ~ spl6_18
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f529,f370,f322,f997,f993]) ).
fof(f993,plain,
( spl6_96
<=> isPrime0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_96])]) ).
fof(f997,plain,
( spl6_97
<=> sP0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_97])]) ).
fof(f322,plain,
( spl6_18
<=> ! [X0] :
( isPrime0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f370,plain,
( spl6_26
<=> sP1(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f529,plain,
( ~ sP0(xm)
| isPrime0(xm)
| ~ spl6_18
| ~ spl6_26 ),
inference(resolution,[],[f372,f323]) ).
fof(f323,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| isPrime0(X0) )
| ~ spl6_18 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f372,plain,
( sP1(xm)
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f991,plain,
( spl6_95
| ~ spl6_5
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f377,f343,f255,f988]) ).
fof(f988,plain,
( spl6_95
<=> xm = sdtpldt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_95])]) ).
fof(f377,plain,
( xm = sdtpldt0(sz00,xm)
| ~ spl6_5
| ~ spl6_23 ),
inference(resolution,[],[f344,f257]) ).
fof(f986,plain,
( spl6_94
| ~ spl6_4
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f376,f343,f250,f983]) ).
fof(f983,plain,
( spl6_94
<=> xn = sdtpldt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_94])]) ).
fof(f376,plain,
( xn = sdtpldt0(sz00,xn)
| ~ spl6_4
| ~ spl6_23 ),
inference(resolution,[],[f344,f252]) ).
fof(f981,plain,
( spl6_93
| ~ spl6_6
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f368,f339,f260,f978]) ).
fof(f978,plain,
( spl6_93
<=> xp = sdtpldt0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_93])]) ).
fof(f368,plain,
( xp = sdtpldt0(xp,sz00)
| ~ spl6_6
| ~ spl6_22 ),
inference(resolution,[],[f340,f262]) ).
fof(f976,plain,
( spl6_92
| ~ spl6_5
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f367,f339,f255,f973]) ).
fof(f973,plain,
( spl6_92
<=> xm = sdtpldt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_92])]) ).
fof(f367,plain,
( xm = sdtpldt0(xm,sz00)
| ~ spl6_5
| ~ spl6_22 ),
inference(resolution,[],[f340,f257]) ).
fof(f971,plain,
( spl6_91
| ~ spl6_4
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f366,f339,f250,f968]) ).
fof(f968,plain,
( spl6_91
<=> xn = sdtpldt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_91])]) ).
fof(f366,plain,
( xn = sdtpldt0(xn,sz00)
| ~ spl6_4
| ~ spl6_22 ),
inference(resolution,[],[f340,f252]) ).
fof(f966,plain,
( spl6_90
| ~ spl6_6
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f363,f335,f260,f963]) ).
fof(f963,plain,
( spl6_90
<=> sz00 = sdtasdt0(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_90])]) ).
fof(f363,plain,
( sz00 = sdtasdt0(sz00,xp)
| ~ spl6_6
| ~ spl6_21 ),
inference(resolution,[],[f336,f262]) ).
fof(f961,plain,
( spl6_89
| ~ spl6_5
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f362,f335,f255,f958]) ).
fof(f958,plain,
( spl6_89
<=> sz00 = sdtasdt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_89])]) ).
fof(f362,plain,
( sz00 = sdtasdt0(sz00,xm)
| ~ spl6_5
| ~ spl6_21 ),
inference(resolution,[],[f336,f257]) ).
fof(f956,plain,
( spl6_88
| ~ spl6_4
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f361,f335,f250,f953]) ).
fof(f953,plain,
( spl6_88
<=> sz00 = sdtasdt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_88])]) ).
fof(f361,plain,
( sz00 = sdtasdt0(sz00,xn)
| ~ spl6_4
| ~ spl6_21 ),
inference(resolution,[],[f336,f252]) ).
fof(f951,plain,
( spl6_87
| ~ spl6_6
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f358,f331,f260,f948]) ).
fof(f948,plain,
( spl6_87
<=> sz00 = sdtasdt0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_87])]) ).
fof(f358,plain,
( sz00 = sdtasdt0(xp,sz00)
| ~ spl6_6
| ~ spl6_20 ),
inference(resolution,[],[f332,f262]) ).
fof(f946,plain,
( spl6_86
| ~ spl6_5
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f357,f331,f255,f943]) ).
fof(f943,plain,
( spl6_86
<=> sz00 = sdtasdt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_86])]) ).
fof(f357,plain,
( sz00 = sdtasdt0(xm,sz00)
| ~ spl6_5
| ~ spl6_20 ),
inference(resolution,[],[f332,f257]) ).
fof(f941,plain,
( spl6_85
| ~ spl6_4
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f356,f331,f250,f938]) ).
fof(f938,plain,
( spl6_85
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_85])]) ).
fof(f356,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl6_4
| ~ spl6_20 ),
inference(resolution,[],[f332,f252]) ).
fof(f933,plain,
spl6_84,
inference(avatar_split_clause,[],[f149,f931]) ).
fof(f931,plain,
( spl6_84
<=> ! [X2,X0,X1] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_84])]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( sz00 != X2
& sz00 != X1
& sz00 != X0
& aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X2,sdtasdt0(X1,X1)) = sdtasdt0(X0,X0)
=> ( iLess0(X0,xn)
=> ~ isPrime0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
fof(f919,plain,
spl6_83,
inference(avatar_split_clause,[],[f229,f917]) ).
fof(f917,plain,
( spl6_83
<=> ! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_83])]) ).
fof(f229,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f198]) ).
fof(f198,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f915,plain,
spl6_82,
inference(avatar_split_clause,[],[f195,f913]) ).
fof(f913,plain,
( spl6_82
<=> ! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_82])]) ).
fof(f195,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(f897,plain,
spl6_81,
inference(avatar_split_clause,[],[f215,f895]) ).
fof(f895,plain,
( spl6_81
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_81])]) ).
fof(f215,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& sz00 != X0 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f893,plain,
spl6_80,
inference(avatar_split_clause,[],[f213,f891]) ).
fof(f891,plain,
( spl6_80
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_80])]) ).
fof(f213,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f881,plain,
spl6_79,
inference(avatar_split_clause,[],[f226,f879]) ).
fof(f879,plain,
( spl6_79
<=> ! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_79])]) ).
fof(f226,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f186]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f828,plain,
( spl6_77
| ~ spl6_78
| ~ spl6_18
| ~ spl6_19 ),
inference(avatar_split_clause,[],[f464,f326,f322,f825,f821]) ).
fof(f821,plain,
( spl6_77
<=> isPrime0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_77])]) ).
fof(f825,plain,
( spl6_78
<=> sP0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_78])]) ).
fof(f326,plain,
( spl6_19
<=> sP1(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f464,plain,
( ~ sP0(xn)
| isPrime0(xn)
| ~ spl6_18
| ~ spl6_19 ),
inference(resolution,[],[f328,f323]) ).
fof(f328,plain,
( sP1(xn)
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f819,plain,
spl6_76,
inference(avatar_split_clause,[],[f211,f817]) ).
fof(f211,plain,
! [X2,X0,X1] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
fof(f815,plain,
spl6_75,
inference(avatar_split_clause,[],[f210,f813]) ).
fof(f813,plain,
( spl6_75
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_75])]) ).
fof(f210,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f811,plain,
spl6_74,
inference(avatar_split_clause,[],[f209,f809]) ).
fof(f809,plain,
( spl6_74
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_74])]) ).
fof(f209,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f807,plain,
spl6_73,
inference(avatar_split_clause,[],[f194,f805]) ).
fof(f805,plain,
( spl6_73
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_73])]) ).
fof(f194,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f803,plain,
spl6_72,
inference(avatar_split_clause,[],[f192,f801]) ).
fof(f801,plain,
( spl6_72
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_72])]) ).
fof(f192,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f799,plain,
spl6_71,
inference(avatar_split_clause,[],[f163,f797]) ).
fof(f797,plain,
( spl6_71
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_71])]) ).
fof(f163,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f795,plain,
spl6_70,
inference(avatar_split_clause,[],[f162,f793]) ).
fof(f793,plain,
( spl6_70
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_70])]) ).
fof(f162,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f744,plain,
spl6_69,
inference(avatar_split_clause,[],[f230,f742]) ).
fof(f742,plain,
( spl6_69
<=> ! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_69])]) ).
fof(f230,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f197]) ).
fof(f197,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f740,plain,
spl6_68,
inference(avatar_split_clause,[],[f218,f738]) ).
fof(f738,plain,
( spl6_68
<=> ! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_68])]) ).
fof(f218,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(f736,plain,
spl6_67,
inference(avatar_split_clause,[],[f217,f734]) ).
fof(f734,plain,
( spl6_67
<=> ! [X2,X0,X1] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_67])]) ).
fof(f217,plain,
! [X2,X0,X1] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(f732,plain,
spl6_66,
inference(avatar_split_clause,[],[f208,f730]) ).
fof(f730,plain,
( spl6_66
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_66])]) ).
fof(f208,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f728,plain,
spl6_65,
inference(avatar_split_clause,[],[f207,f726]) ).
fof(f726,plain,
( spl6_65
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_65])]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f720,plain,
spl6_64,
inference(avatar_split_clause,[],[f221,f718]) ).
fof(f718,plain,
( spl6_64
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_64])]) ).
fof(f221,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f714,plain,
spl6_63,
inference(avatar_split_clause,[],[f220,f712]) ).
fof(f712,plain,
( spl6_63
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_63])]) ).
fof(f220,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f692,plain,
spl6_62,
inference(avatar_split_clause,[],[f219,f690]) ).
fof(f690,plain,
( spl6_62
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_62])]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f688,plain,
spl6_61,
inference(avatar_split_clause,[],[f216,f686]) ).
fof(f686,plain,
( spl6_61
<=> ! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_61])]) ).
fof(f216,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f684,plain,
spl6_60,
inference(avatar_split_clause,[],[f189,f682]) ).
fof(f682,plain,
( spl6_60
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_60])]) ).
fof(f189,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f647,plain,
( spl6_59
| ~ spl6_8
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f309,f305,f270,f644]) ).
fof(f309,plain,
( sP1(sz10)
| ~ spl6_8
| ~ spl6_15 ),
inference(resolution,[],[f306,f272]) ).
fof(f637,plain,
spl6_58,
inference(avatar_split_clause,[],[f231,f635]) ).
fof(f231,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f196]) ).
fof(f196,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f633,plain,
spl6_57,
inference(avatar_split_clause,[],[f227,f631]) ).
fof(f227,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f629,plain,
spl6_56,
inference(avatar_split_clause,[],[f205,f627]) ).
fof(f205,plain,
! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK5(X0,X1)) = X1
& aNaturalNumber0(sK5(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f137,f138]) ).
fof(f138,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK5(X0,X1)) = X1
& aNaturalNumber0(sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f625,plain,
spl6_55,
inference(avatar_split_clause,[],[f202,f623]) ).
fof(f623,plain,
( spl6_55
<=> ! [X0,X1] :
( sdtasdt0(X0,sK4(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_55])]) ).
fof(f202,plain,
! [X0,X1] :
( sdtasdt0(X0,sK4(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f133,f134]) ).
fof(f134,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f588,plain,
( spl6_54
| ~ spl6_7
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f308,f305,f265,f585]) ).
fof(f308,plain,
( sP1(sz00)
| ~ spl6_7
| ~ spl6_15 ),
inference(resolution,[],[f306,f267]) ).
fof(f581,plain,
spl6_53,
inference(avatar_split_clause,[],[f233,f579]) ).
fof(f579,plain,
( spl6_53
<=> ! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_53])]) ).
fof(f233,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f577,plain,
spl6_52,
inference(avatar_split_clause,[],[f232,f575]) ).
fof(f232,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f203]) ).
fof(f203,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f573,plain,
spl6_51,
inference(avatar_split_clause,[],[f200,f571]) ).
fof(f200,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f569,plain,
spl6_50,
inference(avatar_split_clause,[],[f199,f567]) ).
fof(f567,plain,
( spl6_50
<=> ! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_50])]) ).
fof(f199,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sz00 != X1
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(f565,plain,
spl6_49,
inference(avatar_split_clause,[],[f190,f563]) ).
fof(f190,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f561,plain,
spl6_48,
inference(avatar_split_clause,[],[f168,f559]) ).
fof(f559,plain,
( spl6_48
<=> ! [X2,X0] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_48])]) ).
fof(f168,plain,
! [X2,X0] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( sP0(X0)
| ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f123,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP0(X0) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP0(X0) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( sP0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f554,plain,
spl6_47,
inference(avatar_split_clause,[],[f188,f552]) ).
fof(f552,plain,
( spl6_47
<=> ! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_47])]) ).
fof(f188,plain,
! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f550,plain,
spl6_46,
inference(avatar_split_clause,[],[f187,f548]) ).
fof(f548,plain,
( spl6_46
<=> ! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_46])]) ).
fof(f187,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f546,plain,
spl6_45,
inference(avatar_split_clause,[],[f183,f544]) ).
fof(f544,plain,
( spl6_45
<=> ! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_45])]) ).
fof(f183,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f542,plain,
spl6_44,
inference(avatar_split_clause,[],[f175,f540]) ).
fof(f540,plain,
( spl6_44
<=> ! [X0] :
( doDivides0(sK3(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_44])]) ).
fof(f175,plain,
! [X0] :
( doDivides0(sK3(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( isPrime0(sK3(X0))
& doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0)) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f62,f126]) ).
fof(f126,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK3(X0))
& doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f538,plain,
spl6_43,
inference(avatar_split_clause,[],[f172,f536]) ).
fof(f536,plain,
( spl6_43
<=> ! [X0] :
( sP0(X0)
| sK2(X0) != X0
| sz10 = X0
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_43])]) ).
fof(f172,plain,
! [X0] :
( sP0(X0)
| sK2(X0) != X0
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f534,plain,
spl6_42,
inference(avatar_split_clause,[],[f171,f532]) ).
fof(f532,plain,
( spl6_42
<=> ! [X0] :
( sP0(X0)
| sz10 != sK2(X0)
| sz10 = X0
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_42])]) ).
fof(f171,plain,
! [X0] :
( sP0(X0)
| sz10 != sK2(X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f528,plain,
spl6_41,
inference(avatar_split_clause,[],[f170,f526]) ).
fof(f526,plain,
( spl6_41
<=> ! [X0] :
( sP0(X0)
| doDivides0(sK2(X0),X0)
| sz10 = X0
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_41])]) ).
fof(f170,plain,
! [X0] :
( sP0(X0)
| doDivides0(sK2(X0),X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f463,plain,
spl6_40,
inference(avatar_split_clause,[],[f228,f461]) ).
fof(f228,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f459,plain,
spl6_39,
inference(avatar_split_clause,[],[f204,f457]) ).
fof(f204,plain,
! [X0,X1] :
( aNaturalNumber0(sK5(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f455,plain,
spl6_38,
inference(avatar_split_clause,[],[f201,f453]) ).
fof(f201,plain,
! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f451,plain,
spl6_37,
inference(avatar_split_clause,[],[f180,f449]) ).
fof(f180,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f447,plain,
spl6_36,
inference(avatar_split_clause,[],[f179,f445]) ).
fof(f179,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f443,plain,
spl6_35,
inference(avatar_split_clause,[],[f176,f441]) ).
fof(f441,plain,
( spl6_35
<=> ! [X0] :
( isPrime0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_35])]) ).
fof(f176,plain,
! [X0] :
( isPrime0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f439,plain,
spl6_34,
inference(avatar_split_clause,[],[f174,f437]) ).
fof(f174,plain,
! [X0] :
( aNaturalNumber0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f435,plain,
spl6_33,
inference(avatar_split_clause,[],[f169,f433]) ).
fof(f169,plain,
! [X0] :
( sP0(X0)
| aNaturalNumber0(sK2(X0))
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f431,plain,
spl6_32,
inference(avatar_split_clause,[],[f161,f429]) ).
fof(f161,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f425,plain,
( spl6_31
| ~ spl6_6
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f312,f305,f260,f422]) ).
fof(f312,plain,
( sP1(xp)
| ~ spl6_6
| ~ spl6_15 ),
inference(resolution,[],[f306,f262]) ).
fof(f420,plain,
spl6_30,
inference(avatar_split_clause,[],[f182,f418]) ).
fof(f182,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f415,plain,
spl6_29,
inference(avatar_split_clause,[],[f142,f412]) ).
fof(f142,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(f396,plain,
spl6_28,
inference(avatar_split_clause,[],[f178,f394]) ).
fof(f178,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f392,plain,
spl6_27,
inference(avatar_split_clause,[],[f177,f390]) ).
fof(f177,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f373,plain,
( spl6_26
| ~ spl6_5
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f311,f305,f255,f370]) ).
fof(f311,plain,
( sP1(xm)
| ~ spl6_5
| ~ spl6_15 ),
inference(resolution,[],[f306,f257]) ).
fof(f353,plain,
spl6_25,
inference(avatar_split_clause,[],[f159,f351]) ).
fof(f159,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f349,plain,
spl6_24,
inference(avatar_split_clause,[],[f158,f347]) ).
fof(f158,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f345,plain,
spl6_23,
inference(avatar_split_clause,[],[f157,f343]) ).
fof(f157,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f341,plain,
spl6_22,
inference(avatar_split_clause,[],[f156,f339]) ).
fof(f156,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f337,plain,
spl6_21,
inference(avatar_split_clause,[],[f155,f335]) ).
fof(f155,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f333,plain,
spl6_20,
inference(avatar_split_clause,[],[f154,f331]) ).
fof(f154,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f329,plain,
( spl6_19
| ~ spl6_4
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f310,f305,f250,f326]) ).
fof(f310,plain,
( sP1(xn)
| ~ spl6_4
| ~ spl6_15 ),
inference(resolution,[],[f306,f252]) ).
fof(f324,plain,
spl6_18,
inference(avatar_split_clause,[],[f165,f322]) ).
fof(f165,plain,
! [X0] :
( isPrime0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ( ( isPrime0(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ isPrime0(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ( isPrime0(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f320,plain,
spl6_17,
inference(avatar_split_clause,[],[f164,f318]) ).
fof(f164,plain,
! [X0] :
( sP0(X0)
| ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f316,plain,
spl6_16,
inference(avatar_split_clause,[],[f153,f314]) ).
fof(f153,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
fof(f307,plain,
spl6_15,
inference(avatar_split_clause,[],[f173,f305]) ).
fof(f173,plain,
! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f60,f118,f117]) ).
fof(f60,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f303,plain,
~ spl6_14,
inference(avatar_split_clause,[],[f152,f300]) ).
fof(f300,plain,
( spl6_14
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f152,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f298,plain,
~ spl6_13,
inference(avatar_split_clause,[],[f148,f295]) ).
fof(f295,plain,
( spl6_13
<=> sz00 = xp ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f148,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
( sz00 != xp
& sz00 != xm
& sz00 != xn
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(f293,plain,
~ spl6_12,
inference(avatar_split_clause,[],[f147,f290]) ).
fof(f290,plain,
( spl6_12
<=> sz00 = xm ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f147,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f288,plain,
~ spl6_11,
inference(avatar_split_clause,[],[f146,f285]) ).
fof(f285,plain,
( spl6_11
<=> sz00 = xn ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f146,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f283,plain,
~ spl6_10,
inference(avatar_split_clause,[],[f224,f280]) ).
fof(f224,plain,
~ sP0(sz00),
inference(equality_resolution,[],[f166]) ).
fof(f166,plain,
! [X0] :
( sz00 != X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f278,plain,
~ spl6_9,
inference(avatar_split_clause,[],[f223,f275]) ).
fof(f223,plain,
~ sP0(sz10),
inference(equality_resolution,[],[f167]) ).
fof(f167,plain,
! [X0] :
( sz10 != X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f273,plain,
spl6_8,
inference(avatar_split_clause,[],[f151,f270]) ).
fof(f151,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f268,plain,
spl6_7,
inference(avatar_split_clause,[],[f150,f265]) ).
fof(f150,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f263,plain,
spl6_6,
inference(avatar_split_clause,[],[f145,f260]) ).
fof(f145,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f258,plain,
spl6_5,
inference(avatar_split_clause,[],[f144,f255]) ).
fof(f144,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f253,plain,
spl6_4,
inference(avatar_split_clause,[],[f143,f250]) ).
fof(f143,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f248,plain,
spl6_3,
inference(avatar_split_clause,[],[f141,f245]) ).
fof(f141,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(f243,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f140,f240,f236]) ).
fof(f140,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM523+1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 05:38:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (28767)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (28770)WARNING: value z3 for option sas not known
% 0.14/0.40 % (28771)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (28768)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (28769)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (28772)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)
% 0.14/0.40 % (28774)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)
% 0.14/0.40 % (28770)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)
% 0.14/0.40 % (28773)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)
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [1]
% 0.14/0.41 TRYING [2]
% 0.14/0.41 TRYING [3]
% 0.14/0.41 TRYING [3]
% 0.21/0.42 TRYING [4]
% 0.21/0.42 TRYING [4]
% 0.21/0.47 TRYING [1]
% 0.21/0.47 TRYING [2]
% 0.21/0.47 TRYING [3]
% 0.21/0.48 % (28772)First to succeed.
% 0.21/0.48 TRYING [4]
% 0.21/0.48 TRYING [5]
% 0.21/0.49 % (28772)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28767"
% 0.21/0.49 % (28772)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (28772)------------------------------
% 0.21/0.50 % (28772)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.50 % (28772)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (28772)Memory used [KB]: 2288
% 0.21/0.50 % (28772)Time elapsed: 0.095 s
% 0.21/0.50 % (28772)Instructions burned: 152 (million)
% 0.21/0.50 % (28767)Success in time 0.127 s
%------------------------------------------------------------------------------