TSTP Solution File: RNG049+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG049+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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:55:28 EDT 2024
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 224
% Syntax : Number of formulae : 744 ( 75 unt; 0 def)
% Number of atoms : 2896 ( 501 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3914 (1762 ~;1796 |; 123 &)
% ( 187 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 192 ( 190 usr; 183 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 981 ( 973 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1964,plain,
$false,
inference(avatar_sat_refutation,[],[f184,f189,f194,f199,f204,f208,f214,f218,f222,f226,f230,f234,f239,f243,f251,f256,f262,f266,f270,f274,f278,f282,f286,f290,f297,f304,f308,f312,f316,f320,f324,f328,f348,f352,f360,f364,f377,f381,f385,f389,f394,f401,f405,f409,f413,f417,f424,f427,f446,f491,f495,f499,f503,f509,f525,f529,f533,f548,f558,f562,f576,f580,f588,f607,f612,f622,f631,f638,f642,f657,f661,f665,f695,f699,f703,f707,f724,f728,f745,f749,f768,f773,f777,f781,f785,f803,f814,f818,f822,f826,f830,f834,f895,f903,f907,f911,f915,f919,f928,f932,f936,f940,f987,f996,f1008,f1012,f1016,f1020,f1024,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1116,f1121,f1126,f1137,f1148,f1152,f1156,f1160,f1164,f1168,f1201,f1205,f1209,f1213,f1220,f1287,f1299,f1311,f1370,f1380,f1389,f1401,f1425,f1429,f1433,f1456,f1471,f1475,f1480,f1508,f1528,f1552,f1556,f1560,f1564,f1611,f1617,f1628,f1632,f1655,f1659,f1663,f1695,f1701,f1705,f1709,f1713,f1744,f1754,f1760,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1807,f1814,f1823,f1827,f1866,f1941,f1960,f1963]) ).
fof(f1963,plain,
( ~ spl5_118
| ~ spl5_133
| ~ spl5_18
| ~ spl5_38
| spl5_1
| ~ spl5_52
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f549,f545,f493,f181,f374,f259,f1280,f1110]) ).
fof(f1110,plain,
( spl5_118
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_118])]) ).
fof(f1280,plain,
( spl5_133
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_133])]) ).
fof(f259,plain,
( spl5_18
<=> sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f374,plain,
( spl5_38
<=> sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
fof(f181,plain,
( spl5_1
<=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f493,plain,
( spl5_52
<=> ! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).
fof(f545,plain,
( spl5_59
<=> sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).
fof(f549,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_52
| ~ spl5_59 ),
inference(superposition,[],[f494,f547]) ).
fof(f547,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ spl5_59 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f494,plain,
( ! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_52 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f1960,plain,
( ~ spl5_133
| ~ spl5_4
| ~ spl5_181
| spl5_182
| ~ spl5_38
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f480,f415,f374,f1957,f1953,f196,f1280]) ).
fof(f196,plain,
( spl5_4
<=> aScalar0(sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f1953,plain,
( spl5_181
<=> sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_181])]) ).
fof(f1957,plain,
( spl5_182
<=> sz0z00 = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_182])]) ).
fof(f415,plain,
( spl5_47
<=> ! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).
fof(f480,plain,
( sz0z00 = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ spl5_38
| ~ spl5_47 ),
inference(resolution,[],[f416,f376]) ).
fof(f376,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ spl5_38 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_47 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f1941,plain,
( ~ spl5_4
| ~ spl5_133
| spl5_180
| ~ spl5_38
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f512,f501,f374,f1939,f1280,f196]) ).
fof(f1939,plain,
( spl5_180
<=> ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_180])]) ).
fof(f501,plain,
( spl5_54
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).
fof(f512,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(X0,sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_38
| ~ spl5_54 ),
inference(resolution,[],[f502,f376]) ).
fof(f502,plain,
( ! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_54 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f1866,plain,
( ~ spl5_2
| ~ spl5_101
| ~ spl5_31
| spl5_154 ),
inference(avatar_split_clause,[],[f1612,f1608,f318,f925,f186]) ).
fof(f186,plain,
( spl5_2
<=> aVector0(xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f925,plain,
( spl5_101
<=> aNaturalNumber0(aDimensionOf0(xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).
fof(f318,plain,
( spl5_31
<=> ! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
fof(f1608,plain,
( spl5_154
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_154])]) ).
fof(f1612,plain,
( ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs)
| ~ spl5_31
| spl5_154 ),
inference(resolution,[],[f1610,f319]) ).
fof(f319,plain,
( ! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) )
| ~ spl5_31 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f1610,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| spl5_154 ),
inference(avatar_component_clause,[],[f1608]) ).
fof(f1827,plain,
( spl5_179
| ~ spl5_4
| ~ spl5_55
| ~ spl5_93 ),
inference(avatar_split_clause,[],[f891,f832,f506,f196,f1825]) ).
fof(f1825,plain,
( spl5_179
<=> ! [X0] :
( sdtasdt0(X0,sz0z00) = sdtasdt0(sdtasdt0(X0,sz0z00),sz0z00)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_179])]) ).
fof(f506,plain,
( spl5_55
<=> sz0z00 = sdtasdt0(sz0z00,sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).
fof(f832,plain,
( spl5_93
<=> ! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sz0z00) = sdtasdt0(X0,sdtasdt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).
fof(f891,plain,
( ! [X0] :
( sdtasdt0(X0,sz0z00) = sdtasdt0(sdtasdt0(X0,sz0z00),sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_55
| ~ spl5_93 ),
inference(forward_demodulation,[],[f885,f508]) ).
fof(f508,plain,
( sz0z00 = sdtasdt0(sz0z00,sz0z00)
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f885,plain,
( ! [X0] :
( sdtasdt0(sdtasdt0(X0,sz0z00),sz0z00) = sdtasdt0(X0,sdtasdt0(sz0z00,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_93 ),
inference(resolution,[],[f833,f198]) ).
fof(f198,plain,
( aScalar0(sz0z00)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f833,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(sdtasdt0(X0,X1),sz0z00) = sdtasdt0(X0,sdtasdt0(X1,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_93 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f1823,plain,
( spl5_178
| ~ spl5_4
| ~ spl5_42
| ~ spl5_92 ),
inference(avatar_split_clause,[],[f884,f828,f391,f196,f1821]) ).
fof(f1821,plain,
( spl5_178
<=> ! [X0] :
( sdtpldt0(X0,sz0z00) = sdtpldt0(sdtpldt0(X0,sz0z00),sz0z00)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_178])]) ).
fof(f391,plain,
( spl5_42
<=> sz0z00 = sdtpldt0(sz0z00,sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f828,plain,
( spl5_92
<=> ! [X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,sdtpldt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).
fof(f884,plain,
( ! [X0] :
( sdtpldt0(X0,sz0z00) = sdtpldt0(sdtpldt0(X0,sz0z00),sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_42
| ~ spl5_92 ),
inference(forward_demodulation,[],[f878,f393]) ).
fof(f393,plain,
( sz0z00 = sdtpldt0(sz0z00,sz0z00)
| ~ spl5_42 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f878,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(X0,sz0z00),sz0z00) = sdtpldt0(X0,sdtpldt0(sz0z00,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_92 ),
inference(resolution,[],[f829,f198]) ).
fof(f829,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,sdtpldt0(X1,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_92 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f1814,plain,
( ~ spl5_3
| ~ spl5_14
| ~ spl5_176 ),
inference(avatar_split_clause,[],[f1813,f1800,f241,f191]) ).
fof(f191,plain,
( spl5_3
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f241,plain,
( spl5_14
<=> ! [X0] :
( sz00 != szszuzczcdt0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f1800,plain,
( spl5_176
<=> sz00 = szszuzczcdt0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_176])]) ).
fof(f1813,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl5_14
| ~ spl5_176 ),
inference(trivial_inequality_removal,[],[f1810]) ).
fof(f1810,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sz00)
| ~ spl5_14
| ~ spl5_176 ),
inference(superposition,[],[f242,f1802]) ).
fof(f1802,plain,
( sz00 = szszuzczcdt0(sz00)
| ~ spl5_176 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f242,plain,
( ! [X0] :
( sz00 != szszuzczcdt0(X0)
| ~ aNaturalNumber0(X0) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f1807,plain,
( spl5_176
| spl5_177
| ~ spl5_3
| ~ spl5_83 ),
inference(avatar_split_clause,[],[f786,f771,f191,f1804,f1800]) ).
fof(f1804,plain,
( spl5_177
<=> szszuzczcdt0(sz00) = szszuzczcdt0(sK4(szszuzczcdt0(sz00))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_177])]) ).
fof(f771,plain,
( spl5_83
<=> ! [X0] :
( sz00 = szszuzczcdt0(X0)
| szszuzczcdt0(X0) = szszuzczcdt0(sK4(szszuzczcdt0(X0)))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).
fof(f786,plain,
( szszuzczcdt0(sz00) = szszuzczcdt0(sK4(szszuzczcdt0(sz00)))
| sz00 = szszuzczcdt0(sz00)
| ~ spl5_3
| ~ spl5_83 ),
inference(resolution,[],[f772,f193]) ).
fof(f193,plain,
( aNaturalNumber0(sz00)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f772,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) = szszuzczcdt0(sK4(szszuzczcdt0(X0)))
| sz00 = szszuzczcdt0(X0) )
| ~ spl5_83 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f1798,plain,
( spl5_175
| ~ spl5_11
| ~ spl5_76 ),
inference(avatar_split_clause,[],[f718,f701,f228,f1796]) ).
fof(f1796,plain,
( spl5_175
<=> ! [X0] :
( sdtasdt0(sz0z00,smndt0(X0)) = sdtasdt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_175])]) ).
fof(f228,plain,
( spl5_11
<=> ! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f701,plain,
( spl5_76
<=> ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sz0z00) = sdtasdt0(sz0z00,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).
fof(f718,plain,
( ! [X0] :
( sdtasdt0(sz0z00,smndt0(X0)) = sdtasdt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_11
| ~ spl5_76 ),
inference(resolution,[],[f702,f229]) ).
fof(f229,plain,
( ! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f702,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sz0z00) = sdtasdt0(sz0z00,X0) )
| ~ spl5_76 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f1794,plain,
( spl5_174
| ~ spl5_11
| ~ spl5_75 ),
inference(avatar_split_clause,[],[f712,f697,f228,f1792]) ).
fof(f1792,plain,
( spl5_174
<=> ! [X0] :
( sdtpldt0(sz0z00,smndt0(X0)) = sdtpldt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_174])]) ).
fof(f697,plain,
( spl5_75
<=> ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sz0z00) = sdtpldt0(sz0z00,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).
fof(f712,plain,
( ! [X0] :
( sdtpldt0(sz0z00,smndt0(X0)) = sdtpldt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_11
| ~ spl5_75 ),
inference(resolution,[],[f698,f229]) ).
fof(f698,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sz0z00) = sdtpldt0(sz0z00,X0) )
| ~ spl5_75 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f1790,plain,
( spl5_173
| ~ spl5_24
| ~ spl5_73 ),
inference(avatar_split_clause,[],[f686,f663,f284,f1788]) ).
fof(f1788,plain,
( spl5_173
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtasdt0(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_173])]) ).
fof(f284,plain,
( spl5_24
<=> ! [X0] :
( sz0z00 = sdtasdt0(sz0z00,X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f663,plain,
( spl5_73
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sP2(sdtasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).
fof(f686,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtasdt0(X0,X1)) )
| ~ spl5_24
| ~ spl5_73 ),
inference(resolution,[],[f664,f285]) ).
fof(f285,plain,
( ! [X0] :
( ~ sP2(X0)
| sz0z00 = sdtasdt0(sz0z00,X0) )
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f664,plain,
( ! [X0,X1] :
( sP2(sdtasdt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_73 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f1786,plain,
( spl5_172
| ~ spl5_23
| ~ spl5_73 ),
inference(avatar_split_clause,[],[f685,f663,f280,f1784]) ).
fof(f1784,plain,
( spl5_172
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sdtasdt0(X0,X1),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_172])]) ).
fof(f280,plain,
( spl5_23
<=> ! [X0] :
( sz0z00 = sdtasdt0(X0,sz0z00)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f685,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sdtasdt0(X0,X1),sz0z00) )
| ~ spl5_23
| ~ spl5_73 ),
inference(resolution,[],[f664,f281]) ).
fof(f281,plain,
( ! [X0] :
( ~ sP2(X0)
| sz0z00 = sdtasdt0(X0,sz0z00) )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f1782,plain,
( spl5_171
| ~ spl5_24
| ~ spl5_72 ),
inference(avatar_split_clause,[],[f676,f659,f284,f1780]) ).
fof(f1780,plain,
( spl5_171
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtpldt0(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_171])]) ).
fof(f659,plain,
( spl5_72
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sP2(sdtpldt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).
fof(f676,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtpldt0(X0,X1)) )
| ~ spl5_24
| ~ spl5_72 ),
inference(resolution,[],[f660,f285]) ).
fof(f660,plain,
( ! [X0,X1] :
( sP2(sdtpldt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_72 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1778,plain,
( spl5_170
| ~ spl5_23
| ~ spl5_72 ),
inference(avatar_split_clause,[],[f675,f659,f280,f1776]) ).
fof(f1776,plain,
( spl5_170
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sdtpldt0(X0,X1),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_170])]) ).
fof(f675,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(sdtpldt0(X0,X1),sz0z00) )
| ~ spl5_23
| ~ spl5_72 ),
inference(resolution,[],[f660,f281]) ).
fof(f1774,plain,
( spl5_169
| ~ spl5_24
| ~ spl5_71 ),
inference(avatar_split_clause,[],[f669,f655,f284,f1772]) ).
fof(f1772,plain,
( spl5_169
<=> ! [X0,X1] :
( ~ aVector0(X0)
| ~ aNaturalNumber0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtlbdtrb0(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_169])]) ).
fof(f655,plain,
( spl5_71
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aVector0(X1)
| sP2(sdtlbdtrb0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).
fof(f669,plain,
( ! [X0,X1] :
( ~ aVector0(X0)
| ~ aNaturalNumber0(X1)
| sz0z00 = sdtasdt0(sz0z00,sdtlbdtrb0(X0,X1)) )
| ~ spl5_24
| ~ spl5_71 ),
inference(resolution,[],[f656,f285]) ).
fof(f656,plain,
( ! [X0,X1] :
( sP2(sdtlbdtrb0(X1,X0))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_71 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f1770,plain,
( spl5_168
| ~ spl5_23
| ~ spl5_71 ),
inference(avatar_split_clause,[],[f668,f655,f280,f1768]) ).
fof(f1768,plain,
( spl5_168
<=> ! [X0,X1] :
( ~ aVector0(X0)
| ~ aNaturalNumber0(X1)
| sz0z00 = sdtasdt0(sdtlbdtrb0(X0,X1),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_168])]) ).
fof(f668,plain,
( ! [X0,X1] :
( ~ aVector0(X0)
| ~ aNaturalNumber0(X1)
| sz0z00 = sdtasdt0(sdtlbdtrb0(X0,X1),sz0z00) )
| ~ spl5_23
| ~ spl5_71 ),
inference(resolution,[],[f656,f281]) ).
fof(f1760,plain,
( spl5_167
| ~ spl5_76
| ~ spl5_134 ),
inference(avatar_split_clause,[],[f1324,f1284,f701,f1757]) ).
fof(f1757,plain,
( spl5_167
<=> sdtasdt0(sdtasasdt0(xs,xs),sz0z00) = sdtasdt0(sz0z00,sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_167])]) ).
fof(f1284,plain,
( spl5_134
<=> aScalar0(sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_134])]) ).
fof(f1324,plain,
( sdtasdt0(sdtasasdt0(xs,xs),sz0z00) = sdtasdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ spl5_76
| ~ spl5_134 ),
inference(resolution,[],[f1286,f702]) ).
fof(f1286,plain,
( aScalar0(sdtasasdt0(xs,xs))
| ~ spl5_134 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f1754,plain,
( spl5_166
| ~ spl5_75
| ~ spl5_134 ),
inference(avatar_split_clause,[],[f1323,f1284,f697,f1751]) ).
fof(f1751,plain,
( spl5_166
<=> sdtpldt0(sdtasasdt0(xs,xs),sz0z00) = sdtpldt0(sz0z00,sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_166])]) ).
fof(f1323,plain,
( sdtpldt0(sdtasasdt0(xs,xs),sz0z00) = sdtpldt0(sz0z00,sdtasasdt0(xs,xs))
| ~ spl5_75
| ~ spl5_134 ),
inference(resolution,[],[f1286,f698]) ).
fof(f1744,plain,
( spl5_5
| spl5_165
| ~ spl5_2
| ~ spl5_84 ),
inference(avatar_split_clause,[],[f790,f775,f186,f1741,f201]) ).
fof(f201,plain,
( spl5_5
<=> sz00 = aDimensionOf0(xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f1741,plain,
( spl5_165
<=> aDimensionOf0(xs) = szszuzczcdt0(sK4(aDimensionOf0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_165])]) ).
fof(f775,plain,
( spl5_84
<=> ! [X0] :
( sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(sK4(aDimensionOf0(X0)))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).
fof(f790,plain,
( aDimensionOf0(xs) = szszuzczcdt0(sK4(aDimensionOf0(xs)))
| sz00 = aDimensionOf0(xs)
| ~ spl5_2
| ~ spl5_84 ),
inference(resolution,[],[f776,f188]) ).
fof(f188,plain,
( aVector0(xs)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f776,plain,
( ! [X0] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(sK4(aDimensionOf0(X0)))
| sz00 = aDimensionOf0(X0) )
| ~ spl5_84 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f1713,plain,
( spl5_164
| ~ spl5_26
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f356,f302,f295,f1711]) ).
fof(f1711,plain,
( spl5_164
<=> ! [X0] :
( ~ sP1(X0)
| sz00 = aDimensionOf0(sziznziztdt0(X0))
| sP1(sziznziztdt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_164])]) ).
fof(f295,plain,
( spl5_26
<=> ! [X0] :
( ~ sP1(X0)
| aVector0(sziznziztdt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
fof(f302,plain,
( spl5_27
<=> ! [X0] :
( sP1(X0)
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
fof(f356,plain,
( ! [X0] :
( ~ sP1(X0)
| sz00 = aDimensionOf0(sziznziztdt0(X0))
| sP1(sziznziztdt0(X0)) )
| ~ spl5_26
| ~ spl5_27 ),
inference(resolution,[],[f296,f303]) ).
fof(f303,plain,
( ! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sP1(X0) )
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f296,plain,
( ! [X0] :
( aVector0(sziznziztdt0(X0))
| ~ sP1(X0) )
| ~ spl5_26 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f1709,plain,
( spl5_163
| ~ spl5_19
| ~ spl5_29 ),
inference(avatar_split_clause,[],[f340,f310,f264,f1707]) ).
fof(f1707,plain,
( spl5_163
<=> ! [X0] :
( sz0z00 = sdtpldt0(smndt0(smndt0(X0)),smndt0(X0))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_163])]) ).
fof(f264,plain,
( spl5_19
<=> ! [X0] :
( ~ aScalar0(X0)
| sP2(smndt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f310,plain,
( spl5_29
<=> ! [X0] :
( sz0z00 = sdtpldt0(smndt0(X0),X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
fof(f340,plain,
( ! [X0] :
( sz0z00 = sdtpldt0(smndt0(smndt0(X0)),smndt0(X0))
| ~ aScalar0(X0) )
| ~ spl5_19
| ~ spl5_29 ),
inference(resolution,[],[f311,f265]) ).
fof(f265,plain,
( ! [X0] :
( sP2(smndt0(X0))
| ~ aScalar0(X0) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f311,plain,
( ! [X0] :
( ~ sP2(X0)
| sz0z00 = sdtpldt0(smndt0(X0),X0) )
| ~ spl5_29 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f1705,plain,
( spl5_162
| ~ spl5_19
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f337,f306,f264,f1703]) ).
fof(f1703,plain,
( spl5_162
<=> ! [X0] :
( sz0z00 = sdtpldt0(smndt0(X0),smndt0(smndt0(X0)))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_162])]) ).
fof(f306,plain,
( spl5_28
<=> ! [X0] :
( sz0z00 = sdtpldt0(X0,smndt0(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
fof(f337,plain,
( ! [X0] :
( sz0z00 = sdtpldt0(smndt0(X0),smndt0(smndt0(X0)))
| ~ aScalar0(X0) )
| ~ spl5_19
| ~ spl5_28 ),
inference(resolution,[],[f307,f265]) ).
fof(f307,plain,
( ! [X0] :
( ~ sP2(X0)
| sz0z00 = sdtpldt0(X0,smndt0(X0)) )
| ~ spl5_28 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f1701,plain,
( ~ spl5_121
| ~ spl5_8
| spl5_100 ),
inference(avatar_split_clause,[],[f1633,f921,f216,f1123]) ).
fof(f1123,plain,
( spl5_121
<=> aVector0(sziznziztdt0(xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_121])]) ).
fof(f216,plain,
( spl5_8
<=> ! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f921,plain,
( spl5_100
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_100])]) ).
fof(f1633,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ spl5_8
| spl5_100 ),
inference(resolution,[],[f923,f217]) ).
fof(f217,plain,
( ! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f923,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| spl5_100 ),
inference(avatar_component_clause,[],[f921]) ).
fof(f1695,plain,
( spl5_161
| ~ spl5_69
| ~ spl5_82 ),
inference(avatar_split_clause,[],[f769,f766,f635,f1693]) ).
fof(f1693,plain,
( spl5_161
<=> ! [X0] :
( sdtlbdtrb0(xs,X0) = sdtlbdtrb0(sziznziztdt0(xs),X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_161])]) ).
fof(f635,plain,
( spl5_69
<=> sP1(xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).
fof(f766,plain,
( spl5_82
<=> ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(X1,X0) = sdtlbdtrb0(sziznziztdt0(X1),X0)
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).
fof(f769,plain,
( ! [X0] :
( sdtlbdtrb0(xs,X0) = sdtlbdtrb0(sziznziztdt0(xs),X0)
| ~ aNaturalNumber0(X0) )
| ~ spl5_69
| ~ spl5_82 ),
inference(resolution,[],[f767,f637]) ).
fof(f637,plain,
( sP1(xs)
| ~ spl5_69 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f767,plain,
( ! [X0,X1] :
( ~ sP1(X1)
| sdtlbdtrb0(X1,X0) = sdtlbdtrb0(sziznziztdt0(X1),X0)
| ~ aNaturalNumber0(X0) )
| ~ spl5_82 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f1663,plain,
( spl5_160
| ~ spl5_19
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f334,f272,f264,f1661]) ).
fof(f1661,plain,
( spl5_160
<=> ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = sdtpldt0(smndt0(X0),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_160])]) ).
fof(f272,plain,
( spl5_21
<=> ! [X0] :
( sdtpldt0(X0,sz0z00) = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f334,plain,
( ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = sdtpldt0(smndt0(X0),sz0z00) )
| ~ spl5_19
| ~ spl5_21 ),
inference(resolution,[],[f265,f273]) ).
fof(f273,plain,
( ! [X0] :
( ~ sP2(X0)
| sdtpldt0(X0,sz0z00) = X0 )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f1659,plain,
( spl5_159
| ~ spl5_19
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f333,f276,f264,f1657]) ).
fof(f1657,plain,
( spl5_159
<=> ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = sdtpldt0(sz0z00,smndt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_159])]) ).
fof(f276,plain,
( spl5_22
<=> ! [X0] :
( sdtpldt0(sz0z00,X0) = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f333,plain,
( ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = sdtpldt0(sz0z00,smndt0(X0)) )
| ~ spl5_19
| ~ spl5_22 ),
inference(resolution,[],[f265,f277]) ).
fof(f277,plain,
( ! [X0] :
( ~ sP2(X0)
| sdtpldt0(sz0z00,X0) = X0 )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f1655,plain,
( spl5_158
| ~ spl5_19
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f330,f288,f264,f1653]) ).
fof(f1653,plain,
( spl5_158
<=> ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = smndt0(smndt0(smndt0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_158])]) ).
fof(f288,plain,
( spl5_25
<=> ! [X0] :
( smndt0(smndt0(X0)) = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
fof(f330,plain,
( ! [X0] :
( ~ aScalar0(X0)
| smndt0(X0) = smndt0(smndt0(smndt0(X0))) )
| ~ spl5_19
| ~ spl5_25 ),
inference(resolution,[],[f265,f289]) ).
fof(f289,plain,
( ! [X0] :
( ~ sP2(X0)
| smndt0(smndt0(X0)) = X0 )
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f1632,plain,
( spl5_157
| ~ spl5_19
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f332,f280,f264,f1630]) ).
fof(f1630,plain,
( spl5_157
<=> ! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(smndt0(X0),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_157])]) ).
fof(f332,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(smndt0(X0),sz0z00) )
| ~ spl5_19
| ~ spl5_23 ),
inference(resolution,[],[f265,f281]) ).
fof(f1628,plain,
( spl5_156
| ~ spl5_19
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f331,f284,f264,f1626]) ).
fof(f1626,plain,
( spl5_156
<=> ! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(sz0z00,smndt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_156])]) ).
fof(f331,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(sz0z00,smndt0(X0)) )
| ~ spl5_19
| ~ spl5_24 ),
inference(resolution,[],[f265,f285]) ).
fof(f1617,plain,
( spl5_155
| ~ spl5_6
| ~ spl5_118 ),
inference(avatar_split_clause,[],[f1221,f1110,f206,f1614]) ).
fof(f1614,plain,
( spl5_155
<=> sP2(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_155])]) ).
fof(f206,plain,
( spl5_6
<=> ! [X0] :
( sP2(X0)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f1221,plain,
( sP2(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_6
| ~ spl5_118 ),
inference(resolution,[],[f1111,f207]) ).
fof(f207,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sP2(X0) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f1111,plain,
( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_118 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1611,plain,
( ~ spl5_154
| ~ spl5_33
| spl5_133 ),
inference(avatar_split_clause,[],[f1290,f1280,f326,f1608]) ).
fof(f326,plain,
( spl5_33
<=> ! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
fof(f1290,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ spl5_33
| spl5_133 ),
inference(duplicate_literal_removal,[],[f1289]) ).
fof(f1289,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ spl5_33
| spl5_133 ),
inference(resolution,[],[f1282,f327]) ).
fof(f327,plain,
( ! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f1282,plain,
( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| spl5_133 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1564,plain,
( spl5_153
| ~ spl5_31
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f627,f620,f318,f1562]) ).
fof(f1562,plain,
( spl5_153
<=> ! [X4,X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtlbdtrb0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtlbdtrb0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtlbdtrb0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X4)
| ~ aVector0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_153])]) ).
fof(f620,plain,
( spl5_67
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).
fof(f627,plain,
( ! [X2,X3,X0,X1,X4] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtlbdtrb0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtlbdtrb0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtlbdtrb0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X4)
| ~ aVector0(X3) )
| ~ spl5_31
| ~ spl5_67 ),
inference(resolution,[],[f621,f319]) ).
fof(f621,plain,
( ! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_67 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f1560,plain,
( spl5_152
| ~ spl5_33
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f625,f620,f326,f1558]) ).
fof(f1558,plain,
( spl5_152
<=> ! [X4,X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtasdt0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtasdt0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtasdt0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X4)
| ~ aScalar0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_152])]) ).
fof(f625,plain,
( ! [X2,X3,X0,X1,X4] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtasdt0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtasdt0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtasdt0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X4)
| ~ aScalar0(X3) )
| ~ spl5_33
| ~ spl5_67 ),
inference(resolution,[],[f621,f327]) ).
fof(f1556,plain,
( spl5_151
| ~ spl5_32
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f624,f620,f322,f1554]) ).
fof(f1554,plain,
( spl5_151
<=> ! [X4,X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtpldt0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtpldt0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtpldt0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X4)
| ~ aScalar0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_151])]) ).
fof(f322,plain,
( spl5_32
<=> ! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
fof(f624,plain,
( ! [X2,X3,X0,X1,X4] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sdtpldt0(X3,X4))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sdtpldt0(X3,X4))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtpldt0(X3,X4))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X4)
| ~ aScalar0(X3) )
| ~ spl5_32
| ~ spl5_67 ),
inference(resolution,[],[f621,f323]) ).
fof(f323,plain,
( ! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_32 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f1552,plain,
( spl5_150
| ~ spl5_47
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f614,f610,f415,f1550]) ).
fof(f1550,plain,
( spl5_150
<=> ! [X0,X3,X2,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtasdt0(X3,X1) = sdtasdt0(X2,X0)
| ~ sdtlseqdt0(sdtasdt0(X3,X1),sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_150])]) ).
fof(f610,plain,
( spl5_66
<=> ! [X0,X3,X2,X1] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).
fof(f614,plain,
( ! [X2,X3,X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtasdt0(X3,X1) = sdtasdt0(X2,X0)
| ~ sdtlseqdt0(sdtasdt0(X3,X1),sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X3,X1)) )
| ~ spl5_47
| ~ spl5_66 ),
inference(resolution,[],[f611,f416]) ).
fof(f611,plain,
( ! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_66 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f1528,plain,
( spl5_149
| ~ spl5_54
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f613,f610,f501,f1526]) ).
fof(f1526,plain,
( spl5_149
<=> ! [X4,X0,X3,X2,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtlseqdt0(X4,sdtasdt0(X3,X1))
| ~ sdtlseqdt0(X4,sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X3,X1))
| ~ aScalar0(sdtasdt0(X2,X0))
| ~ aScalar0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_149])]) ).
fof(f613,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtlseqdt0(X4,sdtasdt0(X3,X1))
| ~ sdtlseqdt0(X4,sdtasdt0(X2,X0))
| ~ aScalar0(sdtasdt0(X3,X1))
| ~ aScalar0(sdtasdt0(X2,X0))
| ~ aScalar0(X4) )
| ~ spl5_54
| ~ spl5_66 ),
inference(resolution,[],[f611,f502]) ).
fof(f1508,plain,
( spl5_148
| ~ spl5_47
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f590,f586,f415,f1506]) ).
fof(f1506,plain,
( spl5_148
<=> ! [X0,X3,X2,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtpldt0(X3,X1) = sdtpldt0(X2,X0)
| ~ sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_148])]) ).
fof(f586,plain,
( spl5_64
<=> ! [X0,X3,X2,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).
fof(f590,plain,
( ! [X2,X3,X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtpldt0(X3,X1) = sdtpldt0(X2,X0)
| ~ sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X3,X1)) )
| ~ spl5_47
| ~ spl5_64 ),
inference(resolution,[],[f587,f416]) ).
fof(f587,plain,
( ! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_64 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1480,plain,
( spl5_147
| ~ spl5_6
| ~ spl5_134 ),
inference(avatar_split_clause,[],[f1312,f1284,f206,f1477]) ).
fof(f1477,plain,
( spl5_147
<=> sP2(sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_147])]) ).
fof(f1312,plain,
( sP2(sdtasasdt0(xs,xs))
| ~ spl5_6
| ~ spl5_134 ),
inference(resolution,[],[f1286,f207]) ).
fof(f1475,plain,
( spl5_146
| ~ spl5_11
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f626,f620,f228,f1473]) ).
fof(f1473,plain,
( spl5_146
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,smndt0(X3))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,smndt0(X3))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X3))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_146])]) ).
fof(f626,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,smndt0(X3))) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,smndt0(X3))),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X3))))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3) )
| ~ spl5_11
| ~ spl5_67 ),
inference(resolution,[],[f621,f229]) ).
fof(f1471,plain,
( spl5_145
| ~ spl5_54
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f589,f586,f501,f1469]) ).
fof(f1469,plain,
( spl5_145
<=> ! [X4,X0,X3,X2,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtlseqdt0(X4,sdtpldt0(X3,X1))
| ~ sdtlseqdt0(X4,sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X3,X1))
| ~ aScalar0(sdtpldt0(X2,X0))
| ~ aScalar0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_145])]) ).
fof(f589,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| sdtlseqdt0(X4,sdtpldt0(X3,X1))
| ~ sdtlseqdt0(X4,sdtpldt0(X2,X0))
| ~ aScalar0(sdtpldt0(X3,X1))
| ~ aScalar0(sdtpldt0(X2,X0))
| ~ aScalar0(X4) )
| ~ spl5_54
| ~ spl5_64 ),
inference(resolution,[],[f587,f502]) ).
fof(f1456,plain,
( spl5_144
| ~ spl5_4
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f623,f620,f196,f1454]) ).
fof(f1454,plain,
( spl5_144
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sz0z00)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sz0z00)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sz0z00)))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_144])]) ).
fof(f623,plain,
( ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,sz0z00)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,sz0z00)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,sz0z00)))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_67 ),
inference(resolution,[],[f621,f198]) ).
fof(f1433,plain,
( spl5_143
| ~ spl5_31
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f572,f560,f318,f1431]) ).
fof(f1431,plain,
( spl5_143
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtlbdtrb0(X2,X3)),sdtasdt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_143])]) ).
fof(f560,plain,
( spl5_61
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).
fof(f572,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtlbdtrb0(X2,X3)),sdtasdt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) )
| ~ spl5_31
| ~ spl5_61 ),
inference(resolution,[],[f561,f319]) ).
fof(f561,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X2)
| sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_61 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f1429,plain,
( spl5_142
| ~ spl5_33
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f570,f560,f326,f1427]) ).
fof(f1427,plain,
( spl5_142
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtasdt0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtasdt0(X2,X3)),sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_142])]) ).
fof(f570,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtasdt0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtasdt0(X2,X3)),sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_33
| ~ spl5_61 ),
inference(resolution,[],[f561,f327]) ).
fof(f1425,plain,
( spl5_141
| ~ spl5_32
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f569,f560,f322,f1423]) ).
fof(f1423,plain,
( spl5_141
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtpldt0(X2,X3)),sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_141])]) ).
fof(f569,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X0,sdtpldt0(X2,X3)),sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_32
| ~ spl5_61 ),
inference(resolution,[],[f561,f323]) ).
fof(f1401,plain,
( ~ spl5_4
| spl5_140
| ~ spl5_52
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f515,f501,f493,f1399,f196]) ).
fof(f1399,plain,
( spl5_140
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X0)
| ~ aScalar0(sdtpldt0(X1,X2))
| ~ sdtlseqdt0(X0,sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_140])]) ).
fof(f515,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(X0,sz0z00)
| ~ aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_52
| ~ spl5_54 ),
inference(resolution,[],[f502,f494]) ).
fof(f1389,plain,
( ~ spl5_4
| spl5_139
| ~ spl5_53
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f514,f501,f497,f1387,f196]) ).
fof(f1387,plain,
( spl5_139
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X1,X2))
| ~ sdtlseqdt0(X0,sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_139])]) ).
fof(f497,plain,
( spl5_53
<=> ! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(X0,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(X0,sz0z00)
| ~ aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_53
| ~ spl5_54 ),
inference(resolution,[],[f502,f498]) ).
fof(f498,plain,
( ! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_53 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f1380,plain,
( ~ spl5_4
| spl5_138
| ~ spl5_47
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f510,f497,f415,f1378,f196]) ).
fof(f1378,plain,
( spl5_138
<=> ! [X0,X1] :
( ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtasdt0(X1,X0))
| ~ sdtlseqdt0(sdtasdt0(X1,X0),sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| sz0z00 = sdtasdt0(X1,X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_138])]) ).
fof(f510,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtasdt0(X1,X0)
| ~ sdtlseqdt0(sdtasdt0(X1,X0),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(X1,X0)) )
| ~ spl5_47
| ~ spl5_53 ),
inference(resolution,[],[f498,f416]) ).
fof(f1370,plain,
( ~ spl5_4
| spl5_137
| ~ spl5_47
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f504,f493,f415,f1368,f196]) ).
fof(f1368,plain,
( spl5_137
<=> ! [X0,X1] :
( ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(X1,X0))
| ~ sdtlseqdt0(sdtpldt0(X1,X0),sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| sz0z00 = sdtpldt0(X1,X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_137])]) ).
fof(f504,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| sz0z00 = sdtpldt0(X1,X0)
| ~ sdtlseqdt0(sdtpldt0(X1,X0),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtpldt0(X1,X0)) )
| ~ spl5_47
| ~ spl5_52 ),
inference(resolution,[],[f494,f416]) ).
fof(f1311,plain,
( ~ spl5_2
| ~ spl5_70
| spl5_134 ),
inference(avatar_split_clause,[],[f1288,f1284,f640,f186]) ).
fof(f640,plain,
( spl5_70
<=> ! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).
fof(f1288,plain,
( ~ aVector0(xs)
| ~ spl5_70
| spl5_134 ),
inference(resolution,[],[f1285,f641]) ).
fof(f641,plain,
( ! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) )
| ~ spl5_70 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f1285,plain,
( ~ aScalar0(sdtasasdt0(xs,xs))
| spl5_134 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f1299,plain,
( ~ spl5_118
| ~ spl5_4
| ~ spl5_135
| spl5_136
| ~ spl5_18
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f479,f415,f259,f1296,f1292,f196,f1110]) ).
fof(f1292,plain,
( spl5_135
<=> sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_135])]) ).
fof(f1296,plain,
( spl5_136
<=> sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_136])]) ).
fof(f479,plain,
( sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))
| ~ sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_18
| ~ spl5_47 ),
inference(resolution,[],[f416,f261]) ).
fof(f261,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f1287,plain,
( ~ spl5_118
| ~ spl5_133
| spl5_134
| ~ spl5_32
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f550,f545,f322,f1284,f1280,f1110]) ).
fof(f550,plain,
( aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ spl5_32
| ~ spl5_59 ),
inference(superposition,[],[f323,f547]) ).
fof(f1220,plain,
( ~ spl5_69
| ~ spl5_26
| spl5_121 ),
inference(avatar_split_clause,[],[f1175,f1123,f295,f635]) ).
fof(f1175,plain,
( ~ sP1(xs)
| ~ spl5_26
| spl5_121 ),
inference(resolution,[],[f1125,f296]) ).
fof(f1125,plain,
( ~ aVector0(sziznziztdt0(xs))
| spl5_121 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1213,plain,
( spl5_132
| ~ spl5_68 ),
inference(avatar_split_clause,[],[f633,f629,f1211]) ).
fof(f1211,plain,
( spl5_132
<=> ! [X0] :
( sz00 = aDimensionOf0(X0)
| sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0))))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_132])]) ).
fof(f629,plain,
( spl5_68
<=> ! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).
fof(f633,plain,
( ! [X0] :
( sz00 = aDimensionOf0(X0)
| sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0))))
| ~ aVector0(X0) )
| ~ spl5_68 ),
inference(duplicate_literal_removal,[],[f632]) ).
fof(f632,plain,
( ! [X0] :
( sz00 = aDimensionOf0(X0)
| sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0))))
| ~ aVector0(X0)
| ~ aVector0(X0) )
| ~ spl5_68 ),
inference(equality_resolution,[],[f630]) ).
fof(f630,plain,
( ! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| ~ aVector0(X1)
| ~ aVector0(X0) )
| ~ spl5_68 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f1209,plain,
( spl5_131
| ~ spl5_31
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f567,f556,f318,f1207]) ).
fof(f1207,plain,
( spl5_131
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtlbdtrb0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_131])]) ).
fof(f556,plain,
( spl5_60
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).
fof(f567,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtlbdtrb0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) )
| ~ spl5_31
| ~ spl5_60 ),
inference(resolution,[],[f557,f319]) ).
fof(f557,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X2)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_60 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f1205,plain,
( spl5_130
| ~ spl5_33
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f565,f556,f326,f1203]) ).
fof(f1203,plain,
( spl5_130
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtasdt0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_130])]) ).
fof(f565,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtasdt0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_33
| ~ spl5_60 ),
inference(resolution,[],[f557,f327]) ).
fof(f1201,plain,
( spl5_129
| ~ spl5_32
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f564,f556,f322,f1199]) ).
fof(f1199,plain,
( spl5_129
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_129])]) ).
fof(f564,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(X2,X3))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_32
| ~ spl5_60 ),
inference(resolution,[],[f557,f323]) ).
fof(f1168,plain,
( spl5_128
| ~ spl5_31
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f543,f527,f318,f1166]) ).
fof(f1166,plain,
( spl5_128
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_128])]) ).
fof(f527,plain,
( spl5_57
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).
fof(f543,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) )
| ~ spl5_31
| ~ spl5_57 ),
inference(resolution,[],[f528,f319]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X2)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_57 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f1164,plain,
( spl5_127
| ~ spl5_33
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f541,f527,f326,f1162]) ).
fof(f1162,plain,
( spl5_127
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_127])]) ).
fof(f541,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_33
| ~ spl5_57 ),
inference(resolution,[],[f528,f327]) ).
fof(f1160,plain,
( spl5_126
| ~ spl5_32
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f540,f527,f322,f1158]) ).
fof(f1158,plain,
( spl5_126
<=> ! [X0,X3,X2,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_126])]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(X2,X3)) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_32
| ~ spl5_57 ),
inference(resolution,[],[f528,f323]) ).
fof(f1156,plain,
( spl5_125
| ~ spl5_31
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f538,f523,f318,f1154]) ).
fof(f1154,plain,
( spl5_125
<=> ! [X0,X3,X2,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_125])]) ).
fof(f523,plain,
( spl5_56
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).
fof(f538,plain,
( ! [X2,X3,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtlbdtrb0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtlbdtrb0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X3)
| ~ aVector0(X2) )
| ~ spl5_31
| ~ spl5_56 ),
inference(resolution,[],[f524,f319]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X2)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f1152,plain,
( spl5_124
| ~ spl5_33
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f536,f523,f326,f1150]) ).
fof(f1150,plain,
( spl5_124
<=> ! [X0,X3,X2,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtasdt0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_124])]) ).
fof(f536,plain,
( ! [X2,X3,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtasdt0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_33
| ~ spl5_56 ),
inference(resolution,[],[f524,f327]) ).
fof(f1148,plain,
( spl5_123
| ~ spl5_32
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f535,f523,f322,f1146]) ).
fof(f1146,plain,
( spl5_123
<=> ! [X0,X3,X2,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_123])]) ).
fof(f535,plain,
( ! [X2,X3,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X3)
| ~ aScalar0(X2) )
| ~ spl5_32
| ~ spl5_56 ),
inference(resolution,[],[f524,f323]) ).
fof(f1137,plain,
( spl5_122
| ~ spl5_11
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f571,f560,f228,f1135]) ).
fof(f1135,plain,
( spl5_122
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),smndt0(X2)) = sdtpldt0(sdtasdt0(X0,smndt0(X2)),sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_122])]) ).
fof(f571,plain,
( ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),smndt0(X2)) = sdtpldt0(sdtasdt0(X0,smndt0(X2)),sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl5_11
| ~ spl5_61 ),
inference(resolution,[],[f561,f229]) ).
fof(f1126,plain,
( ~ spl5_121
| ~ spl5_70
| spl5_118 ),
inference(avatar_split_clause,[],[f1117,f1110,f640,f1123]) ).
fof(f1117,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ spl5_70
| spl5_118 ),
inference(resolution,[],[f1112,f641]) ).
fof(f1112,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| spl5_118 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1121,plain,
( spl5_120
| ~ spl5_11
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f566,f556,f228,f1119]) ).
fof(f1119,plain,
( spl5_120
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,smndt0(X2))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_120])]) ).
fof(f566,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,smndt0(X2))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl5_11
| ~ spl5_60 ),
inference(resolution,[],[f557,f229]) ).
fof(f1116,plain,
( ~ spl5_4
| ~ spl5_118
| spl5_119
| ~ spl5_18
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f511,f501,f259,f1114,f1110,f196]) ).
fof(f1114,plain,
( spl5_119
<=> ! [X0] :
( sdtlseqdt0(X0,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_119])]) ).
fof(f511,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(X0,sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_18
| ~ spl5_54 ),
inference(resolution,[],[f502,f261]) ).
fof(f1049,plain,
( spl5_117
| ~ spl5_11
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f542,f527,f228,f1047]) ).
fof(f1047,plain,
( spl5_117
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),smndt0(X2)) = sdtasdt0(X0,sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_117])]) ).
fof(f542,plain,
( ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),smndt0(X2)) = sdtasdt0(X0,sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl5_11
| ~ spl5_57 ),
inference(resolution,[],[f528,f229]) ).
fof(f1045,plain,
( spl5_116
| ~ spl5_11
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f537,f523,f228,f1043]) ).
fof(f1043,plain,
( spl5_116
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),smndt0(X2)) = sdtpldt0(X0,sdtpldt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_116])]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),smndt0(X2)) = sdtpldt0(X0,sdtpldt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl5_11
| ~ spl5_56 ),
inference(resolution,[],[f524,f229]) ).
fof(f1041,plain,
( spl5_115
| ~ spl5_31
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f478,f411,f318,f1039]) ).
fof(f1039,plain,
( spl5_115
<=> ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtlbdtrb0(X1,X2))) = sdtasdt0(smndt0(X0),sdtlbdtrb0(X1,X2))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_115])]) ).
fof(f411,plain,
( spl5_46
<=> ! [X0,X1] :
( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).
fof(f478,plain,
( ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtlbdtrb0(X1,X2))) = sdtasdt0(smndt0(X0),sdtlbdtrb0(X1,X2))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) )
| ~ spl5_31
| ~ spl5_46 ),
inference(resolution,[],[f412,f319]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X0) )
| ~ spl5_46 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f1037,plain,
( spl5_114
| ~ spl5_33
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f476,f411,f326,f1035]) ).
fof(f1035,plain,
( spl5_114
<=> ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtasdt0(X1,X2))) = sdtasdt0(smndt0(X0),sdtasdt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_114])]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtasdt0(X1,X2))) = sdtasdt0(smndt0(X0),sdtasdt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_33
| ~ spl5_46 ),
inference(resolution,[],[f412,f327]) ).
fof(f1033,plain,
( spl5_113
| ~ spl5_32
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f475,f411,f322,f1031]) ).
fof(f1031,plain,
( spl5_113
<=> ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtpldt0(X1,X2))) = sdtasdt0(smndt0(X0),sdtpldt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_113])]) ).
fof(f475,plain,
( ! [X2,X0,X1] :
( smndt0(sdtasdt0(X0,sdtpldt0(X1,X2))) = sdtasdt0(smndt0(X0),sdtpldt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_32
| ~ spl5_46 ),
inference(resolution,[],[f412,f323]) ).
fof(f1029,plain,
( spl5_112
| ~ spl5_31
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f472,f407,f318,f1027]) ).
fof(f1027,plain,
( spl5_112
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtlbdtrb0(X1,X2))) = smndt0(sdtasdt0(X0,sdtlbdtrb0(X1,X2)))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_112])]) ).
fof(f407,plain,
( spl5_45
<=> ! [X0,X1] :
( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtlbdtrb0(X1,X2))) = smndt0(sdtasdt0(X0,sdtlbdtrb0(X1,X2)))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) )
| ~ spl5_31
| ~ spl5_45 ),
inference(resolution,[],[f408,f319]) ).
fof(f408,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X0) )
| ~ spl5_45 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f1025,plain,
( ~ spl5_2
| ~ spl5_8
| spl5_101 ),
inference(avatar_split_clause,[],[f976,f925,f216,f186]) ).
fof(f976,plain,
( ~ aVector0(xs)
| ~ spl5_8
| spl5_101 ),
inference(resolution,[],[f926,f217]) ).
fof(f926,plain,
( ~ aNaturalNumber0(aDimensionOf0(xs))
| spl5_101 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f1024,plain,
( spl5_111
| ~ spl5_33
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f470,f407,f326,f1022]) ).
fof(f1022,plain,
( spl5_111
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtasdt0(X1,X2))) = smndt0(sdtasdt0(X0,sdtasdt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_111])]) ).
fof(f470,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtasdt0(X1,X2))) = smndt0(sdtasdt0(X0,sdtasdt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_33
| ~ spl5_45 ),
inference(resolution,[],[f408,f327]) ).
fof(f1020,plain,
( spl5_110
| ~ spl5_32
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f469,f407,f322,f1018]) ).
fof(f1018,plain,
( spl5_110
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtpldt0(X1,X2))) = smndt0(sdtasdt0(X0,sdtpldt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_110])]) ).
fof(f469,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,smndt0(sdtpldt0(X1,X2))) = smndt0(sdtasdt0(X0,sdtpldt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_32
| ~ spl5_45 ),
inference(resolution,[],[f408,f323]) ).
fof(f1016,plain,
( spl5_109
| ~ spl5_31
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f466,f403,f318,f1014]) ).
fof(f1014,plain,
( spl5_109
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtlbdtrb0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtlbdtrb0(X1,X2)))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).
fof(f403,plain,
( spl5_44
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
fof(f466,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,sdtlbdtrb0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtlbdtrb0(X1,X2)))
| ~ aScalar0(X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) )
| ~ spl5_31
| ~ spl5_44 ),
inference(resolution,[],[f404,f319]) ).
fof(f404,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
| ~ aScalar0(X0) )
| ~ spl5_44 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f1012,plain,
( spl5_108
| ~ spl5_33
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f464,f403,f326,f1010]) ).
fof(f1010,plain,
( spl5_108
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtasdt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_108])]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtasdt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_33
| ~ spl5_44 ),
inference(resolution,[],[f404,f327]) ).
fof(f1008,plain,
( spl5_107
| ~ spl5_32
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f463,f403,f322,f1006]) ).
fof(f1006,plain,
( spl5_107
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtpldt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_107])]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtasdt0(smndt0(X0),smndt0(sdtpldt0(X1,X2)))
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_32
| ~ spl5_44 ),
inference(resolution,[],[f404,f323]) ).
fof(f996,plain,
( ~ spl5_4
| spl5_106
| ~ spl5_20
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f513,f501,f268,f994,f196]) ).
fof(f994,plain,
( spl5_106
<=> ! [X0,X1] :
( sdtlseqdt0(X0,sdtasdt0(X1,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X1,X1))
| ~ sdtlseqdt0(X0,sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_106])]) ).
fof(f268,plain,
( spl5_20
<=> ! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f513,plain,
( ! [X0,X1] :
( sdtlseqdt0(X0,sdtasdt0(X1,X1))
| ~ sdtlseqdt0(X0,sz0z00)
| ~ aScalar0(sdtasdt0(X1,X1))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl5_20
| ~ spl5_54 ),
inference(resolution,[],[f502,f269]) ).
fof(f269,plain,
( ! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f987,plain,
( ~ spl5_4
| spl5_105
| ~ spl5_20
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f481,f415,f268,f985,f196]) ).
fof(f985,plain,
( spl5_105
<=> ! [X0] :
( sz0z00 = sdtasdt0(X0,X0)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasdt0(X0,X0),sz0z00) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_105])]) ).
fof(f481,plain,
( ! [X0] :
( sz0z00 = sdtasdt0(X0,X0)
| ~ sdtlseqdt0(sdtasdt0(X0,X0),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ aScalar0(X0) )
| ~ spl5_20
| ~ spl5_47 ),
inference(resolution,[],[f416,f269]) ).
fof(f940,plain,
( spl5_104
| ~ spl5_4
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f568,f560,f196,f938]) ).
fof(f938,plain,
( spl5_104
<=> ! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(sdtasdt0(X0,sz0z00),sdtasdt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_104])]) ).
fof(f568,plain,
( ! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(sdtasdt0(X0,sz0z00),sdtasdt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_61 ),
inference(resolution,[],[f561,f198]) ).
fof(f936,plain,
( spl5_103
| ~ spl5_4
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f563,f556,f196,f934]) ).
fof(f934,plain,
( spl5_103
<=> ! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sz0z00)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_103])]) ).
fof(f563,plain,
( ! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sz0z00)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_60 ),
inference(resolution,[],[f557,f198]) ).
fof(f932,plain,
( spl5_102
| ~ spl5_31
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f451,f444,f318,f930]) ).
fof(f930,plain,
( spl5_102
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtlbdtrb0(X1,X2)) = sdtasdt0(sdtlbdtrb0(X1,X2),X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_102])]) ).
fof(f444,plain,
( spl5_50
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).
fof(f451,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtlbdtrb0(X1,X2)) = sdtasdt0(sdtlbdtrb0(X1,X2),X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) )
| ~ spl5_31
| ~ spl5_50 ),
inference(resolution,[],[f445,f319]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ spl5_50 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f928,plain,
( ~ spl5_100
| spl5_101
| ~ spl5_10
| ~ spl5_87 ),
inference(avatar_split_clause,[],[f864,f800,f224,f925,f921]) ).
fof(f224,plain,
( spl5_10
<=> ! [X0] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f800,plain,
( spl5_87
<=> aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).
fof(f864,plain,
( aNaturalNumber0(aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl5_10
| ~ spl5_87 ),
inference(superposition,[],[f225,f802]) ).
fof(f802,plain,
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl5_87 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f225,plain,
( ! [X0] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f919,plain,
( spl5_99
| ~ spl5_33
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f449,f444,f326,f917]) ).
fof(f917,plain,
( spl5_99
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_99])]) ).
fof(f449,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_33
| ~ spl5_50 ),
inference(resolution,[],[f445,f327]) ).
fof(f915,plain,
( spl5_98
| ~ spl5_32
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f448,f444,f322,f913]) ).
fof(f913,plain,
( spl5_98
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtasdt0(sdtpldt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_98])]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtasdt0(sdtpldt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_32
| ~ spl5_50 ),
inference(resolution,[],[f445,f323]) ).
fof(f911,plain,
( spl5_97
| ~ spl5_31
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f442,f422,f318,f909]) ).
fof(f909,plain,
( spl5_97
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtlbdtrb0(X1,X2)) = sdtpldt0(sdtlbdtrb0(X1,X2),X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).
fof(f422,plain,
( spl5_49
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtlbdtrb0(X1,X2)) = sdtpldt0(sdtlbdtrb0(X1,X2),X0)
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) )
| ~ spl5_31
| ~ spl5_49 ),
inference(resolution,[],[f423,f319]) ).
fof(f423,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ spl5_49 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f907,plain,
( spl5_96
| ~ spl5_33
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f440,f422,f326,f905]) ).
fof(f905,plain,
( spl5_96
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtasdt0(X1,X2)) = sdtpldt0(sdtasdt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).
fof(f440,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtasdt0(X1,X2)) = sdtpldt0(sdtasdt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_33
| ~ spl5_49 ),
inference(resolution,[],[f423,f327]) ).
fof(f903,plain,
( spl5_95
| ~ spl5_32
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f439,f422,f322,f901]) ).
fof(f901,plain,
( spl5_95
<=> ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).
fof(f439,plain,
( ! [X2,X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1) )
| ~ spl5_32
| ~ spl5_49 ),
inference(resolution,[],[f423,f323]) ).
fof(f895,plain,
( spl5_94
| ~ spl5_30
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f368,f358,f314,f893]) ).
fof(f893,plain,
( spl5_94
<=> ! [X0] :
( sz00 = sK4(X0)
| sK4(X0) = szszuzczcdt0(sK4(sK4(X0)))
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).
fof(f314,plain,
( spl5_30
<=> ! [X0] :
( aNaturalNumber0(sK4(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
fof(f358,plain,
( spl5_36
<=> ! [X0] :
( szszuzczcdt0(sK4(X0)) = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
fof(f368,plain,
( ! [X0] :
( sz00 = sK4(X0)
| sK4(X0) = szszuzczcdt0(sK4(sK4(X0)))
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_30
| ~ spl5_36 ),
inference(resolution,[],[f359,f315]) ).
fof(f315,plain,
( ! [X0] :
( aNaturalNumber0(sK4(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f359,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| szszuzczcdt0(sK4(X0)) = X0 )
| ~ spl5_36 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f834,plain,
( spl5_93
| ~ spl5_4
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f539,f527,f196,f832]) ).
fof(f539,plain,
( ! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sz0z00) = sdtasdt0(X0,sdtasdt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_57 ),
inference(resolution,[],[f528,f198]) ).
fof(f830,plain,
( spl5_92
| ~ spl5_4
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f534,f523,f196,f828]) ).
fof(f534,plain,
( ! [X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,sdtpldt0(X1,sz0z00))
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_56 ),
inference(resolution,[],[f524,f198]) ).
fof(f826,plain,
( spl5_91
| ~ spl5_37
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f520,f501,f362,f824]) ).
fof(f824,plain,
( spl5_91
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).
fof(f362,plain,
( spl5_37
<=> ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f520,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X2) )
| ~ spl5_37
| ~ spl5_54 ),
inference(duplicate_literal_removal,[],[f517]) ).
fof(f517,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) )
| ~ spl5_37
| ~ spl5_54 ),
inference(resolution,[],[f502,f363]) ).
fof(f363,plain,
( ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) )
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f822,plain,
( spl5_90
| ~ spl5_11
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f477,f411,f228,f820]) ).
fof(f820,plain,
( spl5_90
<=> ! [X0,X1] :
( sdtasdt0(smndt0(X0),smndt0(X1)) = smndt0(sdtasdt0(X0,smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).
fof(f477,plain,
( ! [X0,X1] :
( sdtasdt0(smndt0(X0),smndt0(X1)) = smndt0(sdtasdt0(X0,smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl5_11
| ~ spl5_46 ),
inference(resolution,[],[f412,f229]) ).
fof(f818,plain,
( spl5_89
| ~ spl5_11
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f471,f407,f228,f816]) ).
fof(f816,plain,
( spl5_89
<=> ! [X0,X1] :
( sdtasdt0(X0,smndt0(smndt0(X1))) = smndt0(sdtasdt0(X0,smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).
fof(f471,plain,
( ! [X0,X1] :
( sdtasdt0(X0,smndt0(smndt0(X1))) = smndt0(sdtasdt0(X0,smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl5_11
| ~ spl5_45 ),
inference(resolution,[],[f408,f229]) ).
fof(f814,plain,
( spl5_88
| ~ spl5_11
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f465,f403,f228,f812]) ).
fof(f812,plain,
( spl5_88
<=> ! [X0,X1] :
( sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X0),smndt0(smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).
fof(f465,plain,
( ! [X0,X1] :
( sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X0),smndt0(smndt0(X1)))
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl5_11
| ~ spl5_44 ),
inference(resolution,[],[f404,f229]) ).
fof(f803,plain,
( spl5_87
| ~ spl5_69
| ~ spl5_74 ),
inference(avatar_split_clause,[],[f708,f693,f635,f800]) ).
fof(f693,plain,
( spl5_74
<=> ! [X0] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).
fof(f708,plain,
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl5_69
| ~ spl5_74 ),
inference(resolution,[],[f694,f637]) ).
fof(f694,plain,
( ! [X0] :
( ~ sP1(X0)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) )
| ~ spl5_74 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f785,plain,
( spl5_86
| ~ spl5_11
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f450,f444,f228,f783]) ).
fof(f783,plain,
( spl5_86
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X1),X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X1),X0)
| ~ aScalar0(X1) )
| ~ spl5_11
| ~ spl5_50 ),
inference(resolution,[],[f445,f229]) ).
fof(f781,plain,
( spl5_85
| ~ spl5_11
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f441,f422,f228,f779]) ).
fof(f779,plain,
( spl5_85
<=> ! [X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,smndt0(X1)) = sdtpldt0(smndt0(X1),X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| sdtpldt0(X0,smndt0(X1)) = sdtpldt0(smndt0(X1),X0)
| ~ aScalar0(X1) )
| ~ spl5_11
| ~ spl5_49 ),
inference(resolution,[],[f423,f229]) ).
fof(f777,plain,
( spl5_84
| ~ spl5_8
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f367,f358,f216,f775]) ).
fof(f367,plain,
( ! [X0] :
( sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(sK4(aDimensionOf0(X0)))
| ~ aVector0(X0) )
| ~ spl5_8
| ~ spl5_36 ),
inference(resolution,[],[f359,f217]) ).
fof(f773,plain,
( spl5_83
| ~ spl5_10
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f366,f358,f224,f771]) ).
fof(f366,plain,
( ! [X0] :
( sz00 = szszuzczcdt0(X0)
| szszuzczcdt0(X0) = szszuzczcdt0(sK4(szszuzczcdt0(X0)))
| ~ aNaturalNumber0(X0) )
| ~ spl5_10
| ~ spl5_36 ),
inference(resolution,[],[f359,f225]) ).
fof(f768,plain,
( spl5_82
| ~ spl5_17
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f395,f383,f254,f766]) ).
fof(f254,plain,
( spl5_17
<=> ! [X0] :
( sP0(X0,sziznziztdt0(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f383,plain,
( spl5_40
<=> ! [X0,X1,X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
fof(f395,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(X1,X0) = sdtlbdtrb0(sziznziztdt0(X1),X0)
| ~ sP1(X1) )
| ~ spl5_17
| ~ spl5_40 ),
inference(resolution,[],[f384,f255]) ).
fof(f255,plain,
( ! [X0] :
( sP0(X0,sziznziztdt0(X0))
| ~ sP1(X0) )
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f384,plain,
( ! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f749,plain,
( spl5_81
| ~ spl5_65 ),
inference(avatar_split_clause,[],[f608,f605,f747]) ).
fof(f747,plain,
( spl5_81
<=> ! [X0] :
( sP0(X0,X0)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X0))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).
fof(f605,plain,
( spl5_65
<=> ! [X0,X1] :
( sP0(X0,X1)
| sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).
fof(f608,plain,
( ! [X0] :
( sP0(X0,X0)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X0))
| ~ aVector0(X0) )
| ~ spl5_65 ),
inference(equality_resolution,[],[f606]) ).
fof(f606,plain,
( ! [X0,X1] :
( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
| sP0(X0,X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) )
| ~ spl5_65 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f745,plain,
( spl5_80
| ~ spl5_4
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f474,f411,f196,f743]) ).
fof(f743,plain,
( spl5_80
<=> ! [X0] :
( sdtasdt0(smndt0(X0),sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).
fof(f474,plain,
( ! [X0] :
( sdtasdt0(smndt0(X0),sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_46 ),
inference(resolution,[],[f412,f198]) ).
fof(f728,plain,
( spl5_79
| ~ spl5_4
| ~ spl5_16
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f473,f407,f248,f196,f726]) ).
fof(f726,plain,
( spl5_79
<=> ! [X0] :
( sdtasdt0(X0,sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).
fof(f248,plain,
( spl5_16
<=> sz0z00 = smndt0(sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f473,plain,
( ! [X0] :
( sdtasdt0(X0,sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_16
| ~ spl5_45 ),
inference(forward_demodulation,[],[f468,f250]) ).
fof(f250,plain,
( sz0z00 = smndt0(sz0z00)
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f468,plain,
( ! [X0] :
( sdtasdt0(X0,smndt0(sz0z00)) = smndt0(sdtasdt0(X0,sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_45 ),
inference(resolution,[],[f408,f198]) ).
fof(f724,plain,
( spl5_78
| ~ spl5_4
| ~ spl5_16
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f467,f403,f248,f196,f722]) ).
fof(f722,plain,
( spl5_78
<=> ! [X0] :
( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).
fof(f467,plain,
( ! [X0] :
( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),sz0z00)
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_16
| ~ spl5_44 ),
inference(forward_demodulation,[],[f462,f250]) ).
fof(f462,plain,
( ! [X0] :
( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),smndt0(sz0z00))
| ~ aScalar0(X0) )
| ~ spl5_4
| ~ spl5_44 ),
inference(resolution,[],[f404,f198]) ).
fof(f707,plain,
( spl5_77
| ~ spl5_6
| ~ spl5_70 ),
inference(avatar_split_clause,[],[f643,f640,f206,f705]) ).
fof(f705,plain,
( spl5_77
<=> ! [X0] :
( ~ aVector0(X0)
| sP2(sdtasasdt0(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).
fof(f643,plain,
( ! [X0] :
( ~ aVector0(X0)
| sP2(sdtasasdt0(X0,X0)) )
| ~ spl5_6
| ~ spl5_70 ),
inference(resolution,[],[f641,f207]) ).
fof(f703,plain,
( spl5_76
| ~ spl5_4
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f447,f444,f196,f701]) ).
fof(f447,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sz0z00) = sdtasdt0(sz0z00,X0) )
| ~ spl5_4
| ~ spl5_50 ),
inference(resolution,[],[f445,f198]) ).
fof(f699,plain,
( spl5_75
| ~ spl5_4
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f438,f422,f196,f697]) ).
fof(f438,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sz0z00) = sdtpldt0(sz0z00,X0) )
| ~ spl5_4
| ~ spl5_49 ),
inference(resolution,[],[f423,f198]) ).
fof(f695,plain,
( spl5_74
| ~ spl5_17
| ~ spl5_35 ),
inference(avatar_split_clause,[],[f355,f350,f254,f693]) ).
fof(f350,plain,
( spl5_35
<=> ! [X0,X1] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
fof(f355,plain,
( ! [X0] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
| ~ sP1(X0) )
| ~ spl5_17
| ~ spl5_35 ),
inference(resolution,[],[f351,f255]) ).
fof(f351,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1)) )
| ~ spl5_35 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f665,plain,
( spl5_73
| ~ spl5_6
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f344,f326,f206,f663]) ).
fof(f344,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sP2(sdtasdt0(X1,X0)) )
| ~ spl5_6
| ~ spl5_33 ),
inference(resolution,[],[f327,f207]) ).
fof(f661,plain,
( spl5_72
| ~ spl5_6
| ~ spl5_32 ),
inference(avatar_split_clause,[],[f343,f322,f206,f659]) ).
fof(f343,plain,
( ! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sP2(sdtpldt0(X1,X0)) )
| ~ spl5_6
| ~ spl5_32 ),
inference(resolution,[],[f323,f207]) ).
fof(f657,plain,
( spl5_71
| ~ spl5_6
| ~ spl5_31 ),
inference(avatar_split_clause,[],[f342,f318,f206,f655]) ).
fof(f342,plain,
( ! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aVector0(X1)
| sP2(sdtlbdtrb0(X1,X0)) )
| ~ spl5_6
| ~ spl5_31 ),
inference(resolution,[],[f319,f207]) ).
fof(f642,plain,
( spl5_70
| ~ spl5_43 ),
inference(avatar_split_clause,[],[f453,f399,f640]) ).
fof(f399,plain,
( spl5_43
<=> ! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f453,plain,
( ! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) )
| ~ spl5_43 ),
inference(duplicate_literal_removal,[],[f452]) ).
fof(f452,plain,
( ! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ aVector0(X0) )
| ~ spl5_43 ),
inference(equality_resolution,[],[f400]) ).
fof(f400,plain,
( ! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1))
| ~ aVector0(X1)
| ~ aVector0(X0) )
| ~ spl5_43 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f638,plain,
( spl5_69
| spl5_5
| ~ spl5_2
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f329,f302,f186,f201,f635]) ).
fof(f329,plain,
( sz00 = aDimensionOf0(xs)
| sP1(xs)
| ~ spl5_2
| ~ spl5_27 ),
inference(resolution,[],[f303,f188]) ).
fof(f631,plain,
spl5_68,
inference(avatar_split_clause,[],[f154,f629]) ).
fof(f154,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( sz00 != aDimensionOf0(X1)
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(f622,plain,
spl5_67,
inference(avatar_split_clause,[],[f175,f620]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(f612,plain,
spl5_66,
inference(avatar_split_clause,[],[f177,f610]) ).
fof(f177,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
fof(f607,plain,
spl5_65,
inference(avatar_split_clause,[],[f133,f605]) ).
fof(f133,plain,
! [X0,X1] :
( sP0(X0,X1)
| sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
& aNaturalNumber0(sK3(X0,X1)) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) )
& ( ( ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f111,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) )
=> ( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
& aNaturalNumber0(sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) )
& ( ( ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) )
& ( ( ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) )
& ( ( ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f588,plain,
spl5_64,
inference(avatar_split_clause,[],[f176,f586]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(f580,plain,
spl5_63,
inference(avatar_split_clause,[],[f165,f578]) ).
fof(f578,plain,
( spl5_63
<=> ! [X0,X1] :
( X0 = X1
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).
fof(f165,plain,
! [X0,X1] :
( X0 = X1
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( X0 = X1
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = X1
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtasdt0(X0,X0) = sdtasdt0(X1,X1)
& sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
fof(f576,plain,
spl5_62,
inference(avatar_split_clause,[],[f153,f574]) ).
fof(f574,plain,
( spl5_62
<=> ! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).
fof(f153,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( sz00 != aDimensionOf0(X1)
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
fof(f562,plain,
spl5_61,
inference(avatar_split_clause,[],[f173,f560]) ).
fof(f173,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(f558,plain,
spl5_60,
inference(avatar_split_clause,[],[f172,f556]) ).
fof(f172,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f548,plain,
spl5_59,
inference(avatar_split_clause,[],[f120,f545]) ).
fof(f120,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1568) ).
fof(f533,plain,
spl5_58,
inference(avatar_split_clause,[],[f179,f531]) ).
fof(f531,plain,
( spl5_58
<=> ! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X1)
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).
fof(f179,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(inner_rewriting,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( sz00 = aDimensionOf0(X1)
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sz0z00 = sdtasasdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f529,plain,
spl5_57,
inference(avatar_split_clause,[],[f170,f527]) ).
fof(f170,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(f525,plain,
spl5_56,
inference(avatar_split_clause,[],[f168,f523]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f509,plain,
( spl5_55
| ~ spl5_7
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f293,f280,f211,f506]) ).
fof(f211,plain,
( spl5_7
<=> sP2(sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f293,plain,
( sz0z00 = sdtasdt0(sz0z00,sz0z00)
| ~ spl5_7
| ~ spl5_23 ),
inference(resolution,[],[f281,f213]) ).
fof(f213,plain,
( sP2(sz0z00)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f503,plain,
spl5_54,
inference(avatar_split_clause,[],[f174,f501]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
fof(f499,plain,
spl5_53,
inference(avatar_split_clause,[],[f167,f497]) ).
fof(f167,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(f495,plain,
spl5_52,
inference(avatar_split_clause,[],[f166,f493]) ).
fof(f166,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f491,plain,
spl5_51,
inference(avatar_split_clause,[],[f132,f489]) ).
fof(f489,plain,
( spl5_51
<=> ! [X0,X1] :
( sP0(X0,X1)
| aNaturalNumber0(sK3(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).
fof(f132,plain,
! [X0,X1] :
( sP0(X0,X1)
| aNaturalNumber0(sK3(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f446,plain,
( spl5_48
| spl5_50 ),
inference(avatar_split_clause,[],[f171,f444,f419]) ).
fof(f419,plain,
( spl5_48
<=> ! [X2] : ~ aScalar0(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).
fof(f171,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f427,plain,
( ~ spl5_4
| ~ spl5_48 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f425,plain,
( $false
| ~ spl5_4
| ~ spl5_48 ),
inference(resolution,[],[f420,f198]) ).
fof(f420,plain,
( ! [X2] : ~ aScalar0(X2)
| ~ spl5_48 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f424,plain,
( spl5_48
| spl5_49 ),
inference(avatar_split_clause,[],[f169,f422,f419]) ).
fof(f169,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f417,plain,
spl5_47,
inference(avatar_split_clause,[],[f164,f415]) ).
fof(f164,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(f413,plain,
spl5_46,
inference(avatar_split_clause,[],[f162,f411]) ).
fof(f162,plain,
! [X0,X1] :
( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(f409,plain,
spl5_45,
inference(avatar_split_clause,[],[f161,f407]) ).
fof(f161,plain,
! [X0,X1] :
( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f405,plain,
spl5_44,
inference(avatar_split_clause,[],[f160,f403]) ).
fof(f160,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
fof(f401,plain,
spl5_43,
inference(avatar_split_clause,[],[f152,f399]) ).
fof(f152,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(f394,plain,
( spl5_42
| ~ spl5_7
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f291,f272,f211,f391]) ).
fof(f291,plain,
( sz0z00 = sdtpldt0(sz0z00,sz0z00)
| ~ spl5_7
| ~ spl5_21 ),
inference(resolution,[],[f273,f213]) ).
fof(f389,plain,
spl5_41,
inference(avatar_split_clause,[],[f157,f387]) ).
fof(f387,plain,
( spl5_41
<=> ! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
fof(f157,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f385,plain,
spl5_40,
inference(avatar_split_clause,[],[f131,f383]) ).
fof(f131,plain,
! [X3,X0,X1] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f381,plain,
spl5_39,
inference(avatar_split_clause,[],[f123,f379]) ).
fof(f379,plain,
( spl5_39
<=> ! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
fof(f123,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( aVector0(X0)
=> ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1516) ).
fof(f377,plain,
spl5_38,
inference(avatar_split_clause,[],[f122,f374]) ).
fof(f122,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
fof(f364,plain,
spl5_37,
inference(avatar_split_clause,[],[f163,f362]) ).
fof(f163,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
fof(f360,plain,
spl5_36,
inference(avatar_split_clause,[],[f151,f358]) ).
fof(f151,plain,
! [X0] :
( szszuzczcdt0(sK4(X0)) = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ( szszuzczcdt0(sK4(X0)) = X0
& aNaturalNumber0(sK4(X0)) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f62,f115]) ).
fof(f115,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(sK4(X0)) = X0
& aNaturalNumber0(sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).
fof(f352,plain,
spl5_35,
inference(avatar_split_clause,[],[f130,f350]) ).
fof(f130,plain,
! [X0,X1] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f348,plain,
spl5_34,
inference(avatar_split_clause,[],[f128,f346]) ).
fof(f346,plain,
( spl5_34
<=> ! [X0,X1] :
( sziznziztdt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f128,plain,
! [X0,X1] :
( sziznziztdt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( sziznziztdt0(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| sziznziztdt0(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( sziznziztdt0(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f328,plain,
spl5_33,
inference(avatar_split_clause,[],[f159,f326]) ).
fof(f159,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f324,plain,
spl5_32,
inference(avatar_split_clause,[],[f158,f322]) ).
fof(f158,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(f320,plain,
spl5_31,
inference(avatar_split_clause,[],[f156,f318]) ).
fof(f156,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aVector0(X0) )
=> aScalar0(sdtlbdtrb0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(f316,plain,
spl5_30,
inference(avatar_split_clause,[],[f150,f314]) ).
fof(f150,plain,
! [X0] :
( aNaturalNumber0(sK4(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f312,plain,
spl5_29,
inference(avatar_split_clause,[],[f146,f310]) ).
fof(f146,plain,
! [X0] :
( sz0z00 = sdtpldt0(smndt0(X0),X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f308,plain,
spl5_28,
inference(avatar_split_clause,[],[f145,f306]) ).
fof(f145,plain,
! [X0] :
( sz0z00 = sdtpldt0(X0,smndt0(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f304,plain,
spl5_27,
inference(avatar_split_clause,[],[f134,f302]) ).
fof(f134,plain,
! [X0] :
( sP1(X0)
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( sP1(X0)
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(definition_folding,[],[f54,f104,f103]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( sziznziztdt0(X0) = X1
<=> ( ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( sziznziztdt0(X0) = X1
<=> ( ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( aVector0(X0)
=> ( sz00 != aDimensionOf0(X0)
=> ! [X1] :
( sziznziztdt0(X0) = X1
<=> ( ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
& aVector0(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(f297,plain,
( spl5_26
| ~ spl5_9
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f257,f254,f220,f295]) ).
fof(f220,plain,
( spl5_9
<=> ! [X0,X1] :
( aVector0(X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f257,plain,
( ! [X0] :
( ~ sP1(X0)
| aVector0(sziznziztdt0(X0)) )
| ~ spl5_9
| ~ spl5_17 ),
inference(resolution,[],[f255,f221]) ).
fof(f221,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| aVector0(X1) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f290,plain,
spl5_25,
inference(avatar_split_clause,[],[f147,f288]) ).
fof(f147,plain,
! [X0] :
( smndt0(smndt0(X0)) = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f286,plain,
spl5_24,
inference(avatar_split_clause,[],[f144,f284]) ).
fof(f144,plain,
! [X0] :
( sz0z00 = sdtasdt0(sz0z00,X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f282,plain,
spl5_23,
inference(avatar_split_clause,[],[f143,f280]) ).
fof(f143,plain,
! [X0] :
( sz0z00 = sdtasdt0(X0,sz0z00)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f278,plain,
spl5_22,
inference(avatar_split_clause,[],[f142,f276]) ).
fof(f142,plain,
! [X0] :
( sdtpldt0(sz0z00,X0) = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f274,plain,
spl5_21,
inference(avatar_split_clause,[],[f141,f272]) ).
fof(f141,plain,
! [X0] :
( sdtpldt0(X0,sz0z00) = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f270,plain,
spl5_20,
inference(avatar_split_clause,[],[f140,f268]) ).
fof(f140,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(f266,plain,
( spl5_19
| ~ spl5_6
| ~ spl5_11 ),
inference(avatar_split_clause,[],[f235,f228,f206,f264]) ).
fof(f235,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sP2(smndt0(X0)) )
| ~ spl5_6
| ~ spl5_11 ),
inference(resolution,[],[f229,f207]) ).
fof(f262,plain,
spl5_18,
inference(avatar_split_clause,[],[f121,f259]) ).
fof(f121,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(cnf_transformation,[],[f41]) ).
fof(f256,plain,
spl5_17,
inference(avatar_split_clause,[],[f178,f254]) ).
fof(f178,plain,
! [X0] :
( sP0(X0,sziznziztdt0(X0))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( sP0(X0,X1)
| sziznziztdt0(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f251,plain,
( spl5_15
| spl5_16 ),
inference(avatar_split_clause,[],[f148,f248,f245]) ).
fof(f245,plain,
( spl5_15
<=> ! [X0] : ~ sP2(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f148,plain,
! [X0] :
( sz0z00 = smndt0(sz0z00)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f243,plain,
spl5_14,
inference(avatar_split_clause,[],[f137,f241]) ).
fof(f137,plain,
! [X0] :
( sz00 != szszuzczcdt0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ( sz00 != szszuzczcdt0(X0)
& aNaturalNumber0(szszuzczcdt0(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != szszuzczcdt0(X0)
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
fof(f239,plain,
spl5_13,
inference(avatar_split_clause,[],[f135,f237]) ).
fof(f237,plain,
( spl5_13
<=> ! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f135,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f234,plain,
spl5_12,
inference(avatar_split_clause,[],[f139,f232]) ).
fof(f232,plain,
( spl5_12
<=> ! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f139,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
fof(f230,plain,
spl5_11,
inference(avatar_split_clause,[],[f138,f228]) ).
fof(f138,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(f226,plain,
spl5_10,
inference(avatar_split_clause,[],[f136,f224]) ).
fof(f136,plain,
! [X0] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f222,plain,
spl5_9,
inference(avatar_split_clause,[],[f129,f220]) ).
fof(f129,plain,
! [X0,X1] :
( aVector0(X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f218,plain,
spl5_8,
inference(avatar_split_clause,[],[f126,f216]) ).
fof(f126,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f214,plain,
( spl5_7
| ~ spl5_4
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f209,f206,f196,f211]) ).
fof(f209,plain,
( sP2(sz0z00)
| ~ spl5_4
| ~ spl5_6 ),
inference(resolution,[],[f207,f198]) ).
fof(f208,plain,
spl5_6,
inference(avatar_split_clause,[],[f149,f206]) ).
fof(f149,plain,
! [X0] :
( sP2(X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( sP2(X0)
| ~ aScalar0(X0) ),
inference(definition_folding,[],[f60,f106]) ).
fof(f60,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(f204,plain,
~ spl5_5,
inference(avatar_split_clause,[],[f119,f201]) ).
fof(f119,plain,
sz00 != aDimensionOf0(xs),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
sz00 != aDimensionOf0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
fof(f199,plain,
spl5_4,
inference(avatar_split_clause,[],[f125,f196]) ).
fof(f125,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f194,plain,
spl5_3,
inference(avatar_split_clause,[],[f124,f191]) ).
fof(f124,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNat) ).
fof(f189,plain,
spl5_2,
inference(avatar_split_clause,[],[f118,f186]) ).
fof(f118,plain,
aVector0(xs),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
fof(f184,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f117,f181]) ).
fof(f117,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(flattening,[],[f43]) ).
fof(f43,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG049+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
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:18:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.22/0.36 % (12992)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (12997)WARNING: value z3 for option sas not known
% 0.22/0.38 % (12995)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (12999)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)
% 0.22/0.38 % (12997)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)
% 0.22/0.38 % (13001)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)
% 0.22/0.38 % (13000)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)
% 0.22/0.38 % (12996)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (12998)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [3]
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.44 TRYING [3]
% 0.22/0.45 TRYING [4]
% 0.22/0.46 % (12999)First to succeed.
% 0.22/0.46 TRYING [4]
% 0.22/0.47 % (12999)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12992"
% 0.22/0.47 % (12999)Refutation found. Thanks to Tanya!
% 0.22/0.47 % SZS status Theorem for theBenchmark
% 0.22/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.48 % (12999)------------------------------
% 0.22/0.48 % (12999)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.48 % (12999)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (12999)Memory used [KB]: 2144
% 0.22/0.48 % (12999)Time elapsed: 0.088 s
% 0.22/0.48 % (12999)Instructions burned: 139 (million)
% 0.22/0.48 % (12992)Success in time 0.109 s
%------------------------------------------------------------------------------