TSTP Solution File: NUM489+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:26:39 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 170
% Syntax : Number of formulae : 533 ( 98 unt; 0 def)
% Number of atoms : 1967 ( 480 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 2418 ( 984 ~;1047 |; 186 &)
% ( 138 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 130 ( 128 usr; 122 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 614 ( 594 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1546,plain,
$false,
inference(avatar_sat_refutation,[],[f238,f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f302,f312,f317,f321,f326,f330,f334,f338,f342,f346,f350,f354,f358,f363,f397,f401,f420,f424,f430,f434,f438,f442,f446,f450,f454,f458,f464,f530,f534,f538,f542,f546,f550,f554,f560,f564,f568,f572,f576,f580,f585,f629,f633,f637,f641,f646,f694,f698,f702,f728,f732,f740,f744,f748,f752,f756,f808,f812,f816,f820,f824,f828,f837,f881,f893,f897,f911,f915,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f998,f1003,f1008,f1013,f1018,f1023,f1028,f1294,f1299,f1304,f1309,f1314,f1319,f1324,f1329,f1461,f1465,f1501,f1505,f1509,f1513,f1517,f1521,f1526,f1544,f1545]) ).
fof(f1545,plain,
( ~ spl6_5
| ~ spl6_3
| spl6_1
| ~ spl6_10
| ~ spl6_15
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f681,f635,f309,f280,f235,f245,f255]) ).
fof(f255,plain,
( spl6_5
<=> aNaturalNumber0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f245,plain,
( spl6_3
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f235,plain,
( spl6_1
<=> xn = sdtpldt0(xp,xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f280,plain,
( spl6_10
<=> sdtlseqdt0(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f309,plain,
( spl6_15
<=> xr = sdtmndt0(xn,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f635,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(f681,plain,
( xn = sdtpldt0(xp,xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl6_10
| ~ spl6_15
| ~ spl6_57 ),
inference(forward_demodulation,[],[f673,f311]) ).
fof(f311,plain,
( xr = sdtmndt0(xn,xp)
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f673,plain,
( xn = sdtpldt0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl6_10
| ~ spl6_57 ),
inference(resolution,[],[f636,f282]) ).
fof(f282,plain,
( sdtlseqdt0(xp,xn)
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f636,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_57 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f1544,plain,
( spl6_121
| ~ spl6_14
| ~ spl6_120 ),
inference(avatar_split_clause,[],[f1527,f1523,f300,f1541]) ).
fof(f1541,plain,
( spl6_121
<=> sP1(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_121])]) ).
fof(f300,plain,
( spl6_14
<=> ! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f1523,plain,
( spl6_120
<=> aNaturalNumber0(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_120])]) ).
fof(f1527,plain,
( sP1(xr)
| ~ spl6_14
| ~ spl6_120 ),
inference(resolution,[],[f1525,f301]) ).
fof(f301,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sP1(X0) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f1525,plain,
( aNaturalNumber0(xr)
| ~ spl6_120 ),
inference(avatar_component_clause,[],[f1523]) ).
fof(f1526,plain,
( ~ spl6_5
| ~ spl6_3
| ~ spl6_10
| spl6_120
| ~ spl6_15
| ~ spl6_40 ),
inference(avatar_split_clause,[],[f524,f462,f309,f1523,f280,f245,f255]) ).
fof(f462,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(f524,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl6_15
| ~ spl6_40 ),
inference(superposition,[],[f463,f311]) ).
fof(f463,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_40 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f1521,plain,
( spl6_119
| ~ spl6_5
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f494,f448,f255,f1519]) ).
fof(f1519,plain,
( spl6_119
<=> ! [X0] :
( sdtasdt0(X0,xp) = sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_119])]) ).
fof(f448,plain,
( spl6_37
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_37])]) ).
fof(f494,plain,
( ! [X0] :
( sdtasdt0(X0,xp) = sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_5
| ~ spl6_37 ),
inference(resolution,[],[f449,f257]) ).
fof(f257,plain,
( aNaturalNumber0(xp)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_37 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f1517,plain,
( spl6_118
| ~ spl6_4
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f493,f448,f250,f1515]) ).
fof(f1515,plain,
( spl6_118
<=> ! [X0] :
( sdtasdt0(X0,xm) = sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_118])]) ).
fof(f250,plain,
( spl6_4
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f493,plain,
( ! [X0] :
( sdtasdt0(X0,xm) = sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_4
| ~ spl6_37 ),
inference(resolution,[],[f449,f252]) ).
fof(f252,plain,
( aNaturalNumber0(xm)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f1513,plain,
( spl6_117
| ~ spl6_3
| ~ spl6_37 ),
inference(avatar_split_clause,[],[f492,f448,f245,f1511]) ).
fof(f1511,plain,
( spl6_117
<=> ! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_117])]) ).
fof(f492,plain,
( ! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_3
| ~ spl6_37 ),
inference(resolution,[],[f449,f247]) ).
fof(f247,plain,
( aNaturalNumber0(xn)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f1509,plain,
( spl6_116
| ~ spl6_5
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f485,f444,f255,f1507]) ).
fof(f1507,plain,
( spl6_116
<=> ! [X0] :
( sdtpldt0(X0,xp) = sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_116])]) ).
fof(f444,plain,
( spl6_36
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_36])]) ).
fof(f485,plain,
( ! [X0] :
( sdtpldt0(X0,xp) = sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_5
| ~ spl6_36 ),
inference(resolution,[],[f445,f257]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f1505,plain,
( spl6_115
| ~ spl6_4
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f484,f444,f250,f1503]) ).
fof(f1503,plain,
( spl6_115
<=> ! [X0] :
( sdtpldt0(X0,xm) = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_115])]) ).
fof(f484,plain,
( ! [X0] :
( sdtpldt0(X0,xm) = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_4
| ~ spl6_36 ),
inference(resolution,[],[f445,f252]) ).
fof(f1501,plain,
( spl6_114
| ~ spl6_3
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f483,f444,f245,f1499]) ).
fof(f1499,plain,
( spl6_114
<=> ! [X0] :
( sdtpldt0(X0,xn) = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_114])]) ).
fof(f483,plain,
( ! [X0] :
( sdtpldt0(X0,xn) = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl6_3
| ~ spl6_36 ),
inference(resolution,[],[f445,f247]) ).
fof(f1465,plain,
( spl6_113
| ~ spl6_14
| ~ spl6_29 ),
inference(avatar_split_clause,[],[f409,f399,f300,f1463]) ).
fof(f1463,plain,
( spl6_113
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_113])]) ).
fof(f399,plain,
( spl6_29
<=> ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
fof(f409,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtasdt0(X1,X0)) )
| ~ spl6_14
| ~ spl6_29 ),
inference(resolution,[],[f400,f301]) ).
fof(f400,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_29 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f1461,plain,
( spl6_112
| ~ spl6_14
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f402,f395,f300,f1459]) ).
fof(f1459,plain,
( spl6_112
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_112])]) ).
fof(f395,plain,
( spl6_28
<=> ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
fof(f402,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(sdtpldt0(X1,X0)) )
| ~ spl6_14
| ~ spl6_28 ),
inference(resolution,[],[f396,f301]) ).
fof(f396,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl6_28 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f1329,plain,
( spl6_111
| ~ spl6_7
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f385,f352,f265,f1326]) ).
fof(f1326,plain,
( spl6_111
<=> sz10 = sdtasdt0(sz10,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_111])]) ).
fof(f265,plain,
( spl6_7
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f352,plain,
( spl6_25
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f385,plain,
( sz10 = sdtasdt0(sz10,sz10)
| ~ spl6_7
| ~ spl6_25 ),
inference(resolution,[],[f353,f267]) ).
fof(f267,plain,
( aNaturalNumber0(sz10)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f353,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f1324,plain,
( spl6_110
| ~ spl6_2
| ~ spl6_19
| ~ spl6_30 ),
inference(avatar_split_clause,[],[f556,f417,f328,f240,f1321]) ).
fof(f1321,plain,
( spl6_110
<=> sP0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_110])]) ).
fof(f240,plain,
( spl6_2
<=> isPrime0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f328,plain,
( spl6_19
<=> ! [X0] :
( sP0(X0)
| ~ isPrime0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f417,plain,
( spl6_30
<=> sP1(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_30])]) ).
fof(f556,plain,
( ~ isPrime0(xp)
| sP0(xp)
| ~ spl6_19
| ~ spl6_30 ),
inference(resolution,[],[f419,f329]) ).
fof(f329,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0)
| sP0(X0) )
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f419,plain,
( sP1(xp)
| ~ spl6_30 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f1319,plain,
( spl6_109
| ~ spl6_7
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f380,f348,f265,f1316]) ).
fof(f1316,plain,
( spl6_109
<=> sz10 = sdtpldt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_109])]) ).
fof(f348,plain,
( spl6_24
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f380,plain,
( sz10 = sdtpldt0(sz00,sz10)
| ~ spl6_7
| ~ spl6_24 ),
inference(resolution,[],[f349,f267]) ).
fof(f349,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 )
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f1314,plain,
( spl6_108
| ~ spl6_7
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f375,f344,f265,f1311]) ).
fof(f1311,plain,
( spl6_108
<=> sz10 = sdtpldt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_108])]) ).
fof(f344,plain,
( spl6_23
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f375,plain,
( sz10 = sdtpldt0(sz10,sz00)
| ~ spl6_7
| ~ spl6_23 ),
inference(resolution,[],[f345,f267]) ).
fof(f345,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f1309,plain,
( spl6_107
| ~ spl6_6
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f374,f344,f260,f1306]) ).
fof(f1306,plain,
( spl6_107
<=> sz00 = sdtpldt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_107])]) ).
fof(f260,plain,
( spl6_6
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f374,plain,
( sz00 = sdtpldt0(sz00,sz00)
| ~ spl6_6
| ~ spl6_23 ),
inference(resolution,[],[f345,f262]) ).
fof(f262,plain,
( aNaturalNumber0(sz00)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1304,plain,
( spl6_106
| ~ spl6_7
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f370,f340,f265,f1301]) ).
fof(f1301,plain,
( spl6_106
<=> sz00 = sdtasdt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_106])]) ).
fof(f340,plain,
( spl6_22
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f370,plain,
( sz00 = sdtasdt0(sz00,sz10)
| ~ spl6_7
| ~ spl6_22 ),
inference(resolution,[],[f341,f267]) ).
fof(f341,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f1299,plain,
( spl6_105
| ~ spl6_7
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f365,f336,f265,f1296]) ).
fof(f1296,plain,
( spl6_105
<=> sz00 = sdtasdt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_105])]) ).
fof(f336,plain,
( spl6_21
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f365,plain,
( sz00 = sdtasdt0(sz10,sz00)
| ~ spl6_7
| ~ spl6_21 ),
inference(resolution,[],[f337,f267]) ).
fof(f337,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f1294,plain,
( spl6_104
| ~ spl6_6
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f364,f336,f260,f1291]) ).
fof(f1291,plain,
( spl6_104
<=> sz00 = sdtasdt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_104])]) ).
fof(f364,plain,
( sz00 = sdtasdt0(sz00,sz00)
| ~ spl6_6
| ~ spl6_21 ),
inference(resolution,[],[f337,f262]) ).
fof(f1028,plain,
( spl6_103
| ~ spl6_5
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f393,f356,f255,f1025]) ).
fof(f1025,plain,
( spl6_103
<=> xp = sdtasdt0(sz10,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_103])]) ).
fof(f356,plain,
( spl6_26
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f393,plain,
( xp = sdtasdt0(sz10,xp)
| ~ spl6_5
| ~ spl6_26 ),
inference(resolution,[],[f357,f257]) ).
fof(f357,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 )
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f1023,plain,
( spl6_102
| ~ spl6_4
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f392,f356,f250,f1020]) ).
fof(f1020,plain,
( spl6_102
<=> xm = sdtasdt0(sz10,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_102])]) ).
fof(f392,plain,
( xm = sdtasdt0(sz10,xm)
| ~ spl6_4
| ~ spl6_26 ),
inference(resolution,[],[f357,f252]) ).
fof(f1018,plain,
( spl6_101
| ~ spl6_3
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f391,f356,f245,f1015]) ).
fof(f1015,plain,
( spl6_101
<=> xn = sdtasdt0(sz10,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_101])]) ).
fof(f391,plain,
( xn = sdtasdt0(sz10,xn)
| ~ spl6_3
| ~ spl6_26 ),
inference(resolution,[],[f357,f247]) ).
fof(f1013,plain,
( spl6_100
| ~ spl6_5
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f388,f352,f255,f1010]) ).
fof(f1010,plain,
( spl6_100
<=> xp = sdtasdt0(xp,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_100])]) ).
fof(f388,plain,
( xp = sdtasdt0(xp,sz10)
| ~ spl6_5
| ~ spl6_25 ),
inference(resolution,[],[f353,f257]) ).
fof(f1008,plain,
( spl6_99
| ~ spl6_4
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f387,f352,f250,f1005]) ).
fof(f1005,plain,
( spl6_99
<=> xm = sdtasdt0(xm,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_99])]) ).
fof(f387,plain,
( xm = sdtasdt0(xm,sz10)
| ~ spl6_4
| ~ spl6_25 ),
inference(resolution,[],[f353,f252]) ).
fof(f1003,plain,
( spl6_98
| ~ spl6_3
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f386,f352,f245,f1000]) ).
fof(f1000,plain,
( spl6_98
<=> xn = sdtasdt0(xn,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_98])]) ).
fof(f386,plain,
( xn = sdtasdt0(xn,sz10)
| ~ spl6_3
| ~ spl6_25 ),
inference(resolution,[],[f353,f247]) ).
fof(f998,plain,
( spl6_96
| ~ spl6_97
| ~ spl6_20
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f525,f360,f332,f995,f991]) ).
fof(f991,plain,
( spl6_96
<=> isPrime0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_96])]) ).
fof(f995,plain,
( spl6_97
<=> sP0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_97])]) ).
fof(f332,plain,
( spl6_20
<=> ! [X0] :
( isPrime0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f360,plain,
( spl6_27
<=> sP1(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f525,plain,
( ~ sP0(xm)
| isPrime0(xm)
| ~ spl6_20
| ~ spl6_27 ),
inference(resolution,[],[f362,f333]) ).
fof(f333,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| isPrime0(X0) )
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f362,plain,
( sP1(xm)
| ~ spl6_27 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f989,plain,
( spl6_95
| ~ spl6_5
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f383,f348,f255,f986]) ).
fof(f986,plain,
( spl6_95
<=> xp = sdtpldt0(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_95])]) ).
fof(f383,plain,
( xp = sdtpldt0(sz00,xp)
| ~ spl6_5
| ~ spl6_24 ),
inference(resolution,[],[f349,f257]) ).
fof(f984,plain,
( spl6_94
| ~ spl6_4
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f382,f348,f250,f981]) ).
fof(f981,plain,
( spl6_94
<=> xm = sdtpldt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_94])]) ).
fof(f382,plain,
( xm = sdtpldt0(sz00,xm)
| ~ spl6_4
| ~ spl6_24 ),
inference(resolution,[],[f349,f252]) ).
fof(f979,plain,
( spl6_93
| ~ spl6_3
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f381,f348,f245,f976]) ).
fof(f976,plain,
( spl6_93
<=> xn = sdtpldt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_93])]) ).
fof(f381,plain,
( xn = sdtpldt0(sz00,xn)
| ~ spl6_3
| ~ spl6_24 ),
inference(resolution,[],[f349,f247]) ).
fof(f974,plain,
( spl6_92
| ~ spl6_5
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f378,f344,f255,f971]) ).
fof(f971,plain,
( spl6_92
<=> xp = sdtpldt0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_92])]) ).
fof(f378,plain,
( xp = sdtpldt0(xp,sz00)
| ~ spl6_5
| ~ spl6_23 ),
inference(resolution,[],[f345,f257]) ).
fof(f969,plain,
( spl6_91
| ~ spl6_4
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f377,f344,f250,f966]) ).
fof(f966,plain,
( spl6_91
<=> xm = sdtpldt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_91])]) ).
fof(f377,plain,
( xm = sdtpldt0(xm,sz00)
| ~ spl6_4
| ~ spl6_23 ),
inference(resolution,[],[f345,f252]) ).
fof(f964,plain,
( spl6_90
| ~ spl6_3
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f376,f344,f245,f961]) ).
fof(f961,plain,
( spl6_90
<=> xn = sdtpldt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_90])]) ).
fof(f376,plain,
( xn = sdtpldt0(xn,sz00)
| ~ spl6_3
| ~ spl6_23 ),
inference(resolution,[],[f345,f247]) ).
fof(f959,plain,
( spl6_89
| ~ spl6_5
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f373,f340,f255,f956]) ).
fof(f956,plain,
( spl6_89
<=> sz00 = sdtasdt0(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_89])]) ).
fof(f373,plain,
( sz00 = sdtasdt0(sz00,xp)
| ~ spl6_5
| ~ spl6_22 ),
inference(resolution,[],[f341,f257]) ).
fof(f954,plain,
( spl6_88
| ~ spl6_4
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f372,f340,f250,f951]) ).
fof(f951,plain,
( spl6_88
<=> sz00 = sdtasdt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_88])]) ).
fof(f372,plain,
( sz00 = sdtasdt0(sz00,xm)
| ~ spl6_4
| ~ spl6_22 ),
inference(resolution,[],[f341,f252]) ).
fof(f949,plain,
( spl6_87
| ~ spl6_3
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f371,f340,f245,f946]) ).
fof(f946,plain,
( spl6_87
<=> sz00 = sdtasdt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_87])]) ).
fof(f371,plain,
( sz00 = sdtasdt0(sz00,xn)
| ~ spl6_3
| ~ spl6_22 ),
inference(resolution,[],[f341,f247]) ).
fof(f944,plain,
( spl6_86
| ~ spl6_5
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f368,f336,f255,f941]) ).
fof(f941,plain,
( spl6_86
<=> sz00 = sdtasdt0(xp,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_86])]) ).
fof(f368,plain,
( sz00 = sdtasdt0(xp,sz00)
| ~ spl6_5
| ~ spl6_21 ),
inference(resolution,[],[f337,f257]) ).
fof(f939,plain,
( spl6_85
| ~ spl6_4
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f367,f336,f250,f936]) ).
fof(f936,plain,
( spl6_85
<=> sz00 = sdtasdt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_85])]) ).
fof(f367,plain,
( sz00 = sdtasdt0(xm,sz00)
| ~ spl6_4
| ~ spl6_21 ),
inference(resolution,[],[f337,f252]) ).
fof(f934,plain,
( spl6_84
| ~ spl6_3
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f366,f336,f245,f931]) ).
fof(f931,plain,
( spl6_84
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_84])]) ).
fof(f366,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl6_3
| ~ spl6_21 ),
inference(resolution,[],[f337,f247]) ).
fof(f929,plain,
spl6_83,
inference(avatar_split_clause,[],[f149,f927]) ).
fof(f927,plain,
( spl6_83
<=> ! [X2,X0,X1] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_83])]) ).
fof(f149,plain,
! [X2,X0,X1] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f915,plain,
spl6_82,
inference(avatar_split_clause,[],[f228,f913]) ).
fof(f913,plain,
( spl6_82
<=> ! [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_82])]) ).
fof(f228,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,[],[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(flattening,[],[f129]) ).
fof(f129,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,[],[f89]) ).
fof(f89,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f911,plain,
spl6_81,
inference(avatar_split_clause,[],[f195,f909]) ).
fof(f909,plain,
( spl6_81
<=> ! [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_81])]) ).
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,[],[f87]) ).
fof(f87,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f897,plain,
spl6_80,
inference(avatar_split_clause,[],[f214,f895]) ).
fof(f895,plain,
( spl6_80
<=> ! [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_80])]) ).
fof(f214,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,[],[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(flattening,[],[f104]) ).
fof(f104,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/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f893,plain,
spl6_79,
inference(avatar_split_clause,[],[f212,f891]) ).
fof(f891,plain,
( spl6_79
<=> ! [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_79])]) ).
fof(f212,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,[],[f105]) ).
fof(f881,plain,
spl6_78,
inference(avatar_split_clause,[],[f225,f879]) ).
fof(f879,plain,
( spl6_78
<=> ! [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_78])]) ).
fof(f225,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,[],[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(flattening,[],[f127]) ).
fof(f127,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,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[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(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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f837,plain,
( spl6_76
| ~ spl6_77
| ~ spl6_18
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f459,f332,f323,f834,f830]) ).
fof(f830,plain,
( spl6_76
<=> isPrime0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_76])]) ).
fof(f834,plain,
( spl6_77
<=> sP0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_77])]) ).
fof(f323,plain,
( spl6_18
<=> sP1(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f459,plain,
( ~ sP0(xn)
| isPrime0(xn)
| ~ spl6_18
| ~ spl6_20 ),
inference(resolution,[],[f325,f333]) ).
fof(f325,plain,
( sP1(xn)
| ~ spl6_18 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f828,plain,
spl6_75,
inference(avatar_split_clause,[],[f210,f826]) ).
fof(f826,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,[],[f103]) ).
fof(f103,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f824,plain,
spl6_74,
inference(avatar_split_clause,[],[f209,f822]) ).
fof(f822,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,[],[f103]) ).
fof(f820,plain,
spl6_73,
inference(avatar_split_clause,[],[f194,f818]) ).
fof(f818,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,[],[f85]) ).
fof(f85,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f816,plain,
spl6_72,
inference(avatar_split_clause,[],[f192,f814]) ).
fof(f814,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,[],[f85]) ).
fof(f812,plain,
spl6_71,
inference(avatar_split_clause,[],[f163,f810]) ).
fof(f810,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,[],[f59]) ).
fof(f59,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f808,plain,
spl6_70,
inference(avatar_split_clause,[],[f162,f806]) ).
fof(f806,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,[],[f59]) ).
fof(f756,plain,
spl6_69,
inference(avatar_split_clause,[],[f229,f754]) ).
fof(f754,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(f229,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,[],[f130]) ).
fof(f752,plain,
spl6_68,
inference(avatar_split_clause,[],[f217,f750]) ).
fof(f750,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(f217,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f110]) ).
fof(f110,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/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(f748,plain,
spl6_67,
inference(avatar_split_clause,[],[f216,f746]) ).
fof(f746,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(f216,plain,
! [X2,X0,X1] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f108]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
fof(f744,plain,
spl6_66,
inference(avatar_split_clause,[],[f208,f742]) ).
fof(f742,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,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f740,plain,
spl6_65,
inference(avatar_split_clause,[],[f207,f738]) ).
fof(f738,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,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f732,plain,
spl6_64,
inference(avatar_split_clause,[],[f220,f730]) ).
fof(f730,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(f220,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f114]) ).
fof(f114,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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f728,plain,
spl6_63,
inference(avatar_split_clause,[],[f219,f726]) ).
fof(f726,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(f219,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f702,plain,
spl6_62,
inference(avatar_split_clause,[],[f218,f700]) ).
fof(f700,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(f218,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,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/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f698,plain,
spl6_61,
inference(avatar_split_clause,[],[f215,f696]) ).
fof(f696,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(f215,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f694,plain,
spl6_60,
inference(avatar_split_clause,[],[f189,f692]) ).
fof(f692,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,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,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/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(f646,plain,
( spl6_59
| ~ spl6_7
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f304,f300,f265,f643]) ).
fof(f643,plain,
( spl6_59
<=> sP1(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_59])]) ).
fof(f304,plain,
( sP1(sz10)
| ~ spl6_7
| ~ spl6_14 ),
inference(resolution,[],[f301,f267]) ).
fof(f641,plain,
spl6_58,
inference(avatar_split_clause,[],[f230,f639]) ).
fof(f639,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(f230,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,[],[f130]) ).
fof(f637,plain,
spl6_57,
inference(avatar_split_clause,[],[f226,f635]) ).
fof(f226,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,[],[f128]) ).
fof(f633,plain,
spl6_56,
inference(avatar_split_clause,[],[f205,f631]) ).
fof(f631,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(f205,plain,
! [X0,X1] :
( sdtpldt0(X0,sK5(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,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])],[f136,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK5(X0,X1)) = X1
& aNaturalNumber0(sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f136,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,[],[f135]) ).
fof(f135,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,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,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/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f629,plain,
spl6_55,
inference(avatar_split_clause,[],[f202,f627]) ).
fof(f627,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,[],[f134]) ).
fof(f134,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])],[f132,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,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,[],[f131]) ).
fof(f131,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,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f94]) ).
fof(f94,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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f585,plain,
( spl6_54
| ~ spl6_6
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f303,f300,f260,f582]) ).
fof(f582,plain,
( spl6_54
<=> sP1(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_54])]) ).
fof(f303,plain,
( sP1(sz00)
| ~ spl6_6
| ~ spl6_14 ),
inference(resolution,[],[f301,f262]) ).
fof(f580,plain,
spl6_53,
inference(avatar_split_clause,[],[f232,f578]) ).
fof(f578,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(f232,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,[],[f138]) ).
fof(f576,plain,
spl6_52,
inference(avatar_split_clause,[],[f231,f574]) ).
fof(f574,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(f231,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,[],[f134]) ).
fof(f572,plain,
spl6_51,
inference(avatar_split_clause,[],[f200,f570]) ).
fof(f570,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(f200,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,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/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f568,plain,
spl6_50,
inference(avatar_split_clause,[],[f199,f566]) ).
fof(f566,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,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,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/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(f564,plain,
spl6_49,
inference(avatar_split_clause,[],[f190,f562]) ).
fof(f562,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(f190,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,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/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f560,plain,
spl6_48,
inference(avatar_split_clause,[],[f168,f558]) ).
fof(f558,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,[],[f124]) ).
fof(f124,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])],[f122,f123]) ).
fof(f123,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(f122,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,[],[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(flattening,[],[f120]) ).
fof(f120,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,[],[f116]) ).
fof(f116,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,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,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/sandbox2/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,[],[f79]) ).
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,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,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/sandbox2/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,[],[f126]) ).
fof(f126,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])],[f63,f125]) ).
fof(f125,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK3(X0))
& doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,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/sandbox2/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,[],[f124]) ).
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,[],[f124]) ).
fof(f530,plain,
spl6_41,
inference(avatar_split_clause,[],[f170,f528]) ).
fof(f528,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,[],[f124]) ).
fof(f464,plain,
spl6_40,
inference(avatar_split_clause,[],[f227,f462]) ).
fof(f227,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,[],[f128]) ).
fof(f458,plain,
spl6_39,
inference(avatar_split_clause,[],[f204,f456]) ).
fof(f456,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(f204,plain,
! [X0,X1] :
( aNaturalNumber0(sK5(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f454,plain,
spl6_38,
inference(avatar_split_clause,[],[f201,f452]) ).
fof(f452,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(f201,plain,
! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f450,plain,
spl6_37,
inference(avatar_split_clause,[],[f180,f448]) ).
fof(f180,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,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/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f446,plain,
spl6_36,
inference(avatar_split_clause,[],[f179,f444]) ).
fof(f179,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,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/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f442,plain,
spl6_35,
inference(avatar_split_clause,[],[f176,f440]) ).
fof(f440,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,[],[f126]) ).
fof(f438,plain,
spl6_34,
inference(avatar_split_clause,[],[f174,f436]) ).
fof(f436,plain,
( spl6_34
<=> ! [X0] :
( aNaturalNumber0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_34])]) ).
fof(f174,plain,
! [X0] :
( aNaturalNumber0(sK3(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f434,plain,
spl6_33,
inference(avatar_split_clause,[],[f169,f432]) ).
fof(f432,plain,
( spl6_33
<=> ! [X0] :
( sP0(X0)
| aNaturalNumber0(sK2(X0))
| sz10 = X0
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_33])]) ).
fof(f169,plain,
! [X0] :
( sP0(X0)
| aNaturalNumber0(sK2(X0))
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f430,plain,
spl6_32,
inference(avatar_split_clause,[],[f161,f428]) ).
fof(f428,plain,
( spl6_32
<=> ! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_32])]) ).
fof(f161,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,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/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(f424,plain,
spl6_31,
inference(avatar_split_clause,[],[f182,f422]) ).
fof(f422,plain,
( spl6_31
<=> ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_31])]) ).
fof(f182,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f420,plain,
( spl6_30
| ~ spl6_5
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f307,f300,f255,f417]) ).
fof(f307,plain,
( sP1(xp)
| ~ spl6_5
| ~ spl6_14 ),
inference(resolution,[],[f301,f257]) ).
fof(f401,plain,
spl6_29,
inference(avatar_split_clause,[],[f178,f399]) ).
fof(f178,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,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/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f397,plain,
spl6_28,
inference(avatar_split_clause,[],[f177,f395]) ).
fof(f177,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,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/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f363,plain,
( spl6_27
| ~ spl6_4
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f306,f300,f250,f360]) ).
fof(f306,plain,
( sP1(xm)
| ~ spl6_4
| ~ spl6_14 ),
inference(resolution,[],[f301,f252]) ).
fof(f358,plain,
spl6_26,
inference(avatar_split_clause,[],[f159,f356]) ).
fof(f159,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,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/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f354,plain,
spl6_25,
inference(avatar_split_clause,[],[f158,f352]) ).
fof(f158,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f350,plain,
spl6_24,
inference(avatar_split_clause,[],[f157,f348]) ).
fof(f157,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,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/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f346,plain,
spl6_23,
inference(avatar_split_clause,[],[f156,f344]) ).
fof(f156,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f342,plain,
spl6_22,
inference(avatar_split_clause,[],[f155,f340]) ).
fof(f155,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,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/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f338,plain,
spl6_21,
inference(avatar_split_clause,[],[f154,f336]) ).
fof(f154,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f334,plain,
spl6_20,
inference(avatar_split_clause,[],[f165,f332]) ).
fof(f165,plain,
! [X0] :
( isPrime0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ( ( isPrime0(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ isPrime0(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ( isPrime0(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f330,plain,
spl6_19,
inference(avatar_split_clause,[],[f164,f328]) ).
fof(f164,plain,
! [X0] :
( sP0(X0)
| ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f326,plain,
( spl6_18
| ~ spl6_3
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f305,f300,f245,f323]) ).
fof(f305,plain,
( sP1(xn)
| ~ spl6_3
| ~ spl6_14 ),
inference(resolution,[],[f301,f247]) ).
fof(f321,plain,
spl6_17,
inference(avatar_split_clause,[],[f153,f319]) ).
fof(f319,plain,
( spl6_17
<=> ! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f153,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f317,plain,
spl6_16,
inference(avatar_split_clause,[],[f143,f314]) ).
fof(f314,plain,
( spl6_16
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f143,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f312,plain,
spl6_15,
inference(avatar_split_clause,[],[f141,f309]) ).
fof(f141,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f302,plain,
spl6_14,
inference(avatar_split_clause,[],[f173,f300]) ).
fof(f173,plain,
! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( sP1(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f61,f117,f116]) ).
fof(f61,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f298,plain,
~ spl6_13,
inference(avatar_split_clause,[],[f152,f295]) ).
fof(f295,plain,
( spl6_13
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f152,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f293,plain,
spl6_12,
inference(avatar_split_clause,[],[f148,f290]) ).
fof(f290,plain,
( spl6_12
<=> sdtlseqdt0(xr,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f148,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
( sdtlseqdt0(xr,xn)
& xn != xr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(f288,plain,
~ spl6_11,
inference(avatar_split_clause,[],[f147,f285]) ).
fof(f285,plain,
( spl6_11
<=> xn = xr ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f147,plain,
xn != xr,
inference(cnf_transformation,[],[f44]) ).
fof(f283,plain,
spl6_10,
inference(avatar_split_clause,[],[f140,f280]) ).
fof(f140,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f278,plain,
~ spl6_9,
inference(avatar_split_clause,[],[f223,f275]) ).
fof(f275,plain,
( spl6_9
<=> sP0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f223,plain,
~ sP0(sz00),
inference(equality_resolution,[],[f166]) ).
fof(f166,plain,
! [X0] :
( sz00 != X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f273,plain,
~ spl6_8,
inference(avatar_split_clause,[],[f222,f270]) ).
fof(f270,plain,
( spl6_8
<=> sP0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f222,plain,
~ sP0(sz10),
inference(equality_resolution,[],[f167]) ).
fof(f167,plain,
! [X0] :
( sz10 != X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f268,plain,
spl6_7,
inference(avatar_split_clause,[],[f151,f265]) ).
fof(f151,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f263,plain,
spl6_6,
inference(avatar_split_clause,[],[f150,f260]) ).
fof(f150,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f258,plain,
spl6_5,
inference(avatar_split_clause,[],[f146,f255]) ).
fof(f146,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f253,plain,
spl6_4,
inference(avatar_split_clause,[],[f145,f250]) ).
fof(f145,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f248,plain,
spl6_3,
inference(avatar_split_clause,[],[f144,f245]) ).
fof(f144,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f243,plain,
spl6_2,
inference(avatar_split_clause,[],[f142,f240]) ).
fof(f142,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f238,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f139,f235]) ).
fof(f139,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
xn != sdtpldt0(xp,xr),
inference(flattening,[],[f46]) ).
fof(f46,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n019.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 Apr 29 23:59:59 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.21/0.36 % (22486)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (22489)WARNING: value z3 for option sas not known
% 0.21/0.38 % (22488)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (22487)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (22490)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (22489)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)
% 0.21/0.38 % (22491)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)
% 0.21/0.38 % (22493)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)
% 0.21/0.38 % (22492)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [3]
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.41 TRYING [4]
% 0.21/0.42 TRYING [4]
% 0.21/0.42 % (22491)First to succeed.
% 0.21/0.43 % (22491)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (22491)------------------------------
% 0.21/0.44 % (22491)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.44 % (22491)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (22491)Memory used [KB]: 1690
% 0.21/0.44 % (22491)Time elapsed: 0.048 s
% 0.21/0.44 % (22491)Instructions burned: 79 (million)
% 0.21/0.44 % (22491)------------------------------
% 0.21/0.44 % (22491)------------------------------
% 0.21/0.44 % (22486)Success in time 0.06 s
%------------------------------------------------------------------------------