TSTP Solution File: RNG099+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG099+2 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:52:22 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 233
% Syntax : Number of formulae : 726 ( 109 unt; 0 def)
% Number of atoms : 2420 ( 308 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2883 (1189 ~;1205 |; 218 &)
% ( 212 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 197 ( 195 usr; 187 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 9 con; 0-3 aty)
% Number of variables : 802 ( 745 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2023,plain,
$false,
inference(avatar_sat_refutation,[],[f214,f219,f224,f229,f234,f239,f244,f249,f253,f257,f261,f266,f271,f276,f280,f284,f291,f295,f300,f305,f309,f313,f320,f329,f333,f337,f341,f345,f349,f353,f357,f361,f365,f406,f410,f414,f418,f422,f426,f430,f434,f438,f442,f452,f491,f503,f516,f520,f524,f545,f550,f554,f562,f566,f570,f574,f593,f597,f612,f616,f620,f644,f657,f661,f669,f673,f677,f684,f692,f696,f700,f704,f718,f723,f727,f731,f735,f764,f768,f772,f776,f780,f784,f788,f808,f833,f837,f841,f858,f863,f867,f889,f893,f897,f913,f918,f923,f928,f933,f938,f943,f948,f953,f958,f963,f968,f1029,f1034,f1039,f1044,f1049,f1054,f1059,f1102,f1107,f1112,f1117,f1137,f1166,f1171,f1176,f1181,f1218,f1240,f1261,f1282,f1304,f1309,f1314,f1319,f1324,f1329,f1334,f1339,f1366,f1396,f1401,f1406,f1411,f1416,f1420,f1462,f1467,f1471,f1475,f1479,f1483,f1487,f1491,f1510,f1533,f1542,f1546,f1551,f1555,f1559,f1563,f1567,f1634,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1715,f1817,f1824,f1829,f1832,f1871,f1875,f1915,f1920,f1978,f1979,f2021,f2022]) ).
fof(f2022,plain,
( ~ spl17_24
| ~ spl17_20
| ~ spl17_15
| ~ spl17_19 ),
inference(avatar_split_clause,[],[f314,f297,f278,f302,f322]) ).
fof(f322,plain,
( spl17_24
<=> aElement0(xw) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f302,plain,
( spl17_20
<=> aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f278,plain,
( spl17_15
<=> ! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f297,plain,
( spl17_19
<=> aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f314,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ aElement0(xw)
| ~ spl17_15
| ~ spl17_19 ),
inference(resolution,[],[f299,f279]) ).
fof(f279,plain,
( ! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) )
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f299,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f2021,plain,
( ~ spl17_24
| ~ spl17_186
| ~ spl17_11
| ~ spl17_20 ),
inference(avatar_split_clause,[],[f316,f302,f259,f2018,f322]) ).
fof(f2018,plain,
( spl17_186
<=> sdteqdtlpzmzozddtrp0(xw,xy,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_186])]) ).
fof(f259,plain,
( spl17_11
<=> ! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f316,plain,
( ~ sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aElement0(xw)
| ~ spl17_11
| ~ spl17_20 ),
inference(resolution,[],[f304,f260]) ).
fof(f260,plain,
( ! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ aElement0(X0) )
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f304,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f1979,plain,
( ~ spl17_45
| ~ spl17_6
| ~ spl17_42
| spl17_179 ),
inference(avatar_split_clause,[],[f1831,f1826,f432,f236,f449]) ).
fof(f449,plain,
( spl17_45
<=> aElement0(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f236,plain,
( spl17_6
<=> aElement0(xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f432,plain,
( spl17_42
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f1826,plain,
( spl17_179
<=> aElement0(sdtasdt0(xa,xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_179])]) ).
fof(f1831,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| ~ spl17_42
| spl17_179 ),
inference(resolution,[],[f1828,f433]) ).
fof(f433,plain,
( ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl17_42 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f1828,plain,
( ~ aElement0(sdtasdt0(xa,xy))
| spl17_179 ),
inference(avatar_component_clause,[],[f1826]) ).
fof(f1978,plain,
( ~ spl17_3
| spl17_185
| ~ spl17_27
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f558,f552,f335,f1976,f221]) ).
fof(f221,plain,
( spl17_3
<=> aSet0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f1976,plain,
( spl17_185
<=> ! [X0,X1] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1))
| ~ aElementOf0(X1,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_185])]) ).
fof(f335,plain,
( spl17_27
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f552,plain,
( spl17_53
<=> ! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xJ)
| aElement0(sdtasdt0(X0,X1))
| ~ aSet0(xJ) )
| ~ spl17_27
| ~ spl17_53 ),
inference(resolution,[],[f553,f336]) ).
fof(f336,plain,
( ! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) )
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f553,plain,
( ! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) )
| ~ spl17_53 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f1920,plain,
( ~ spl17_1
| spl17_184
| ~ spl17_27
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f556,f543,f335,f1918,f211]) ).
fof(f211,plain,
( spl17_1
<=> aSet0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f1918,plain,
( spl17_184
<=> ! [X0,X1] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1))
| ~ aElementOf0(X1,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_184])]) ).
fof(f543,plain,
( spl17_51
<=> ! [X4,X3] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f556,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xI)
| aElement0(sdtasdt0(X0,X1))
| ~ aSet0(xI) )
| ~ spl17_27
| ~ spl17_51 ),
inference(resolution,[],[f544,f336]) ).
fof(f544,plain,
( ! [X3,X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) )
| ~ spl17_51 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f1915,plain,
( ~ spl17_182
| spl17_183
| ~ spl17_26
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f458,f412,f331,f1913,f1909]) ).
fof(f1909,plain,
( spl17_182
<=> aIdeal0(sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_182])]) ).
fof(f1913,plain,
( spl17_183
<=> ! [X0] :
( sP0(sdtpldt1(xI,xJ),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_183])]) ).
fof(f331,plain,
( spl17_26
<=> ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f412,plain,
( spl17_37
<=> ! [X2,X0] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f458,plain,
( ! [X0] :
( sP0(sdtpldt1(xI,xJ),X0)
| ~ aIdeal0(sdtpldt1(xI,xJ))
| ~ aElement0(X0) )
| ~ spl17_26
| ~ spl17_37 ),
inference(resolution,[],[f413,f332]) ).
fof(f332,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f413,plain,
( ! [X2,X0] :
( ~ aElementOf0(X2,X0)
| sP0(X0,X2)
| ~ aIdeal0(X0) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f1875,plain,
( spl17_181
| ~ spl17_18
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f455,f408,f293,f1873]) ).
fof(f1873,plain,
( spl17_181
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(smndt0(X0)),smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_181])]) ).
fof(f293,plain,
( spl17_18
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f408,plain,
( spl17_36
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f455,plain,
( ! [X0] :
( sz00 = sdtpldt0(smndt0(smndt0(X0)),smndt0(X0))
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_36 ),
inference(resolution,[],[f409,f294]) ).
fof(f294,plain,
( ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f409,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1871,plain,
( spl17_180
| ~ spl17_18
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f445,f404,f293,f1869]) ).
fof(f1869,plain,
( spl17_180
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),smndt0(smndt0(X0)))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_180])]) ).
fof(f404,plain,
( spl17_35
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f445,plain,
( ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),smndt0(smndt0(X0)))
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_35 ),
inference(resolution,[],[f405,f294]) ).
fof(f405,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f1832,plain,
( ~ spl17_52
| ~ spl17_5
| ~ spl17_42
| spl17_178 ),
inference(avatar_split_clause,[],[f1830,f1821,f432,f231,f547]) ).
fof(f547,plain,
( spl17_52
<=> aElement0(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f231,plain,
( spl17_5
<=> aElement0(xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f1821,plain,
( spl17_178
<=> aElement0(sdtasdt0(xb,xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_178])]) ).
fof(f1830,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| ~ spl17_42
| spl17_178 ),
inference(resolution,[],[f1823,f433]) ).
fof(f1823,plain,
( ~ aElement0(sdtasdt0(xb,xx))
| spl17_178 ),
inference(avatar_component_clause,[],[f1821]) ).
fof(f1829,plain,
( ~ spl17_179
| ~ spl17_45
| ~ spl17_163
| spl17_176 ),
inference(avatar_split_clause,[],[f1819,f1810,f1557,f449,f1826]) ).
fof(f1557,plain,
( spl17_163
<=> ! [X0] :
( sdtasdt0(X0,xy) = sdtasdt0(xy,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_163])]) ).
fof(f1810,plain,
( spl17_176
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_176])]) ).
fof(f1819,plain,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ spl17_45
| ~ spl17_163
| spl17_176 ),
inference(forward_demodulation,[],[f1812,f1594]) ).
fof(f1594,plain,
( sdtasdt0(xy,xa) = sdtasdt0(xa,xy)
| ~ spl17_45
| ~ spl17_163 ),
inference(resolution,[],[f1558,f451]) ).
fof(f451,plain,
( aElement0(xa)
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1558,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xy) = sdtasdt0(xy,X0) )
| ~ spl17_163 ),
inference(avatar_component_clause,[],[f1557]) ).
fof(f1812,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| spl17_176 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f1824,plain,
( ~ spl17_178
| ~ spl17_52
| ~ spl17_162
| spl17_177 ),
inference(avatar_split_clause,[],[f1818,f1814,f1553,f547,f1821]) ).
fof(f1553,plain,
( spl17_162
<=> ! [X0] :
( sdtasdt0(X0,xx) = sdtasdt0(xx,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_162])]) ).
fof(f1814,plain,
( spl17_177
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_177])]) ).
fof(f1818,plain,
( ~ aElement0(sdtasdt0(xb,xx))
| ~ spl17_52
| ~ spl17_162
| spl17_177 ),
inference(forward_demodulation,[],[f1816,f1579]) ).
fof(f1579,plain,
( sdtasdt0(xx,xb) = sdtasdt0(xb,xx)
| ~ spl17_52
| ~ spl17_162 ),
inference(resolution,[],[f1554,f549]) ).
fof(f549,plain,
( aElement0(xb)
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f1554,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0) )
| ~ spl17_162 ),
inference(avatar_component_clause,[],[f1553]) ).
fof(f1816,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| spl17_177 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f1817,plain,
( ~ spl17_176
| ~ spl17_177
| spl17_24
| ~ spl17_43
| ~ spl17_46 ),
inference(avatar_split_clause,[],[f504,f488,f436,f322,f1814,f1810]) ).
fof(f436,plain,
( spl17_43
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f488,plain,
( spl17_46
<=> xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f504,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa))
| ~ spl17_43
| ~ spl17_46 ),
inference(superposition,[],[f437,f490]) ).
fof(f490,plain,
( xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f437,plain,
( ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl17_43 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f1715,plain,
( spl17_175
| ~ spl17_8
| ~ spl17_125
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1710,f1645,f1173,f246,f1712]) ).
fof(f1712,plain,
( spl17_175
<=> sz00 = smndt0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_175])]) ).
fof(f246,plain,
( spl17_8
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f1173,plain,
( spl17_125
<=> sz00 = sdtpldt0(smndt0(sz00),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).
fof(f1645,plain,
( spl17_169
<=> ! [X0] :
( smndt0(X0) = sdtpldt0(smndt0(X0),sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_169])]) ).
fof(f1710,plain,
( sz00 = smndt0(sz00)
| ~ spl17_8
| ~ spl17_125
| ~ spl17_169 ),
inference(forward_demodulation,[],[f1696,f1175]) ).
fof(f1175,plain,
( sz00 = sdtpldt0(smndt0(sz00),sz00)
| ~ spl17_125 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f1696,plain,
( smndt0(sz00) = sdtpldt0(smndt0(sz00),sz00)
| ~ spl17_8
| ~ spl17_169 ),
inference(resolution,[],[f1646,f248]) ).
fof(f248,plain,
( aElement0(sz00)
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f1646,plain,
( ! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtpldt0(smndt0(X0),sz00) )
| ~ spl17_169 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f1667,plain,
( spl17_174
| ~ spl17_7
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f646,f618,f241,f1665]) ).
fof(f1665,plain,
( spl17_174
<=> ! [X0] :
( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_174])]) ).
fof(f241,plain,
( spl17_7
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f618,plain,
( spl17_62
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f646,plain,
( ! [X0] :
( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0)
| ~ aElement0(X0) )
| ~ spl17_7
| ~ spl17_62 ),
inference(resolution,[],[f619,f243]) ).
fof(f243,plain,
( aElement0(sz10)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f619,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0) )
| ~ spl17_62 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f1663,plain,
( spl17_173
| ~ spl17_8
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f645,f618,f246,f1661]) ).
fof(f1661,plain,
( spl17_173
<=> ! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_173])]) ).
fof(f645,plain,
( ! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0)
| ~ aElement0(X0) )
| ~ spl17_8
| ~ spl17_62 ),
inference(resolution,[],[f619,f248]) ).
fof(f1659,plain,
( spl17_172
| ~ spl17_7
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f629,f614,f241,f1657]) ).
fof(f1657,plain,
( spl17_172
<=> ! [X0] :
( sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_172])]) ).
fof(f614,plain,
( spl17_61
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f629,plain,
( ! [X0] :
( sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0)
| ~ aElement0(X0) )
| ~ spl17_7
| ~ spl17_61 ),
inference(resolution,[],[f615,f243]) ).
fof(f615,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0) )
| ~ spl17_61 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f1655,plain,
( spl17_171
| ~ spl17_8
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f628,f614,f246,f1653]) ).
fof(f1653,plain,
( spl17_171
<=> ! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_171])]) ).
fof(f628,plain,
( ! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0)
| ~ aElement0(X0) )
| ~ spl17_8
| ~ spl17_61 ),
inference(resolution,[],[f615,f248]) ).
fof(f1651,plain,
( spl17_170
| ~ spl17_18
| ~ spl17_33 ),
inference(avatar_split_clause,[],[f400,f359,f293,f1649]) ).
fof(f1649,plain,
( spl17_170
<=> ! [X0] :
( smndt0(X0) = sdtpldt0(sz00,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_170])]) ).
fof(f359,plain,
( spl17_33
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f400,plain,
( ! [X0] :
( smndt0(X0) = sdtpldt0(sz00,smndt0(X0))
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_33 ),
inference(resolution,[],[f360,f294]) ).
fof(f360,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 )
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f1647,plain,
( spl17_169
| ~ spl17_18
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f395,f355,f293,f1645]) ).
fof(f355,plain,
( spl17_32
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f395,plain,
( ! [X0] :
( smndt0(X0) = sdtpldt0(smndt0(X0),sz00)
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_32 ),
inference(resolution,[],[f356,f294]) ).
fof(f356,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f1643,plain,
( spl17_168
| ~ spl17_18
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f390,f351,f293,f1641]) ).
fof(f1641,plain,
( spl17_168
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(sz10,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_168])]) ).
fof(f351,plain,
( spl17_31
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f390,plain,
( ! [X0] :
( smndt0(X0) = sdtasdt0(sz10,smndt0(X0))
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_31 ),
inference(resolution,[],[f352,f294]) ).
fof(f352,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(sz10,X0) = X0 )
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f1639,plain,
( spl17_167
| ~ spl17_30
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f494,f449,f347,f1636]) ).
fof(f1636,plain,
( spl17_167
<=> xa = sdtasdt0(xa,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_167])]) ).
fof(f347,plain,
( spl17_30
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f494,plain,
( xa = sdtasdt0(xa,sz10)
| ~ spl17_30
| ~ spl17_45 ),
inference(resolution,[],[f451,f348]) ).
fof(f348,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 )
| ~ spl17_30 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f1634,plain,
( spl17_166
| ~ spl17_18
| ~ spl17_30 ),
inference(avatar_split_clause,[],[f385,f347,f293,f1632]) ).
fof(f1632,plain,
( spl17_166
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(X0),sz10)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_166])]) ).
fof(f385,plain,
( ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(X0),sz10)
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_30 ),
inference(resolution,[],[f348,f294]) ).
fof(f1567,plain,
( spl17_165
| ~ spl17_6
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f651,f618,f236,f1565]) ).
fof(f1565,plain,
( spl17_165
<=> ! [X0] :
( sdtpldt0(X0,xy) = sdtpldt0(xy,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_165])]) ).
fof(f651,plain,
( ! [X0] :
( sdtpldt0(X0,xy) = sdtpldt0(xy,X0)
| ~ aElement0(X0) )
| ~ spl17_6
| ~ spl17_62 ),
inference(resolution,[],[f619,f238]) ).
fof(f238,plain,
( aElement0(xy)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f1563,plain,
( spl17_164
| ~ spl17_5
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f650,f618,f231,f1561]) ).
fof(f1561,plain,
( spl17_164
<=> ! [X0] :
( sdtpldt0(X0,xx) = sdtpldt0(xx,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_164])]) ).
fof(f650,plain,
( ! [X0] :
( sdtpldt0(X0,xx) = sdtpldt0(xx,X0)
| ~ aElement0(X0) )
| ~ spl17_5
| ~ spl17_62 ),
inference(resolution,[],[f619,f233]) ).
fof(f233,plain,
( aElement0(xx)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f1559,plain,
( spl17_163
| ~ spl17_6
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f634,f614,f236,f1557]) ).
fof(f634,plain,
( ! [X0] :
( sdtasdt0(X0,xy) = sdtasdt0(xy,X0)
| ~ aElement0(X0) )
| ~ spl17_6
| ~ spl17_61 ),
inference(resolution,[],[f615,f238]) ).
fof(f1555,plain,
( spl17_162
| ~ spl17_5
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f633,f614,f231,f1553]) ).
fof(f633,plain,
( ! [X0] :
( sdtasdt0(X0,xx) = sdtasdt0(xx,X0)
| ~ aElement0(X0) )
| ~ spl17_5
| ~ spl17_61 ),
inference(resolution,[],[f615,f233]) ).
fof(f1551,plain,
( spl17_161
| ~ spl17_29
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f493,f449,f343,f1548]) ).
fof(f1548,plain,
( spl17_161
<=> sz00 = sdtasdt0(sz00,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_161])]) ).
fof(f343,plain,
( spl17_29
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f493,plain,
( sz00 = sdtasdt0(sz00,xa)
| ~ spl17_29
| ~ spl17_45 ),
inference(resolution,[],[f451,f344]) ).
fof(f344,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl17_29 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f1546,plain,
( spl17_160
| ~ spl17_17
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f626,f610,f288,f1544]) ).
fof(f1544,plain,
( spl17_160
<=> ! [X0] :
( aElementOf0(sz10,X0)
| ~ aElementOf0(xb,X0)
| ~ sP0(X0,xa) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_160])]) ).
fof(f288,plain,
( spl17_17
<=> sz10 = sdtpldt0(xa,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f610,plain,
( spl17_60
<=> ! [X5,X0,X1] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f626,plain,
( ! [X0] :
( aElementOf0(sz10,X0)
| ~ aElementOf0(xb,X0)
| ~ sP0(X0,xa) )
| ~ spl17_17
| ~ spl17_60 ),
inference(superposition,[],[f611,f290]) ).
fof(f290,plain,
( sz10 = sdtpldt0(xa,xb)
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f611,plain,
( ! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP0(X0,X1) )
| ~ spl17_60 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f1542,plain,
( ~ spl17_158
| ~ spl17_13
| spl17_159
| ~ spl17_17
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f607,f595,f288,f1539,f268,f1535]) ).
fof(f1535,plain,
( spl17_158
<=> aElementOf0(xa,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_158])]) ).
fof(f268,plain,
( spl17_13
<=> aElementOf0(xb,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f1539,plain,
( spl17_159
<=> aElementOf0(sz10,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_159])]) ).
fof(f595,plain,
( spl17_59
<=> ! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f607,plain,
( aElementOf0(sz10,xJ)
| ~ aElementOf0(xb,xJ)
| ~ aElementOf0(xa,xJ)
| ~ spl17_17
| ~ spl17_59 ),
inference(superposition,[],[f596,f290]) ).
fof(f596,plain,
( ! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) )
| ~ spl17_59 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f1533,plain,
( ~ spl17_12
| ~ spl17_156
| spl17_157
| ~ spl17_17
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f601,f591,f288,f1530,f1526,f263]) ).
fof(f263,plain,
( spl17_12
<=> aElementOf0(xa,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f1526,plain,
( spl17_156
<=> aElementOf0(xb,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_156])]) ).
fof(f1530,plain,
( spl17_157
<=> aElementOf0(sz10,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_157])]) ).
fof(f591,plain,
( spl17_58
<=> ! [X5,X3] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f601,plain,
( aElementOf0(sz10,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(xa,xI)
| ~ spl17_17
| ~ spl17_58 ),
inference(superposition,[],[f592,f290]) ).
fof(f592,plain,
( ! [X3,X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) )
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f1510,plain,
( spl17_155
| ~ spl17_28
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f492,f449,f339,f1507]) ).
fof(f1507,plain,
( spl17_155
<=> sz00 = sdtasdt0(xa,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_155])]) ).
fof(f339,plain,
( spl17_28
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f492,plain,
( sz00 = sdtasdt0(xa,sz00)
| ~ spl17_28
| ~ spl17_45 ),
inference(resolution,[],[f451,f340]) ).
fof(f340,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f1491,plain,
( spl17_154
| ~ spl17_16
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f469,f428,f282,f1489]) ).
fof(f1489,plain,
( spl17_154
<=> ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtpldt1(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_154])]) ).
fof(f282,plain,
( spl17_16
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f428,plain,
( spl17_41
<=> ! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f469,plain,
( ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtpldt1(X1,X0)) )
| ~ spl17_16
| ~ spl17_41 ),
inference(resolution,[],[f429,f283]) ).
fof(f283,plain,
( ! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) )
| ~ spl17_16 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f429,plain,
( ! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) )
| ~ spl17_41 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f1487,plain,
( spl17_153
| ~ spl17_16
| ~ spl17_40 ),
inference(avatar_split_clause,[],[f468,f424,f282,f1485]) ).
fof(f1485,plain,
( spl17_153
<=> ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtasasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_153])]) ).
fof(f424,plain,
( spl17_40
<=> ! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f468,plain,
( ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtasasdt0(X1,X0)) )
| ~ spl17_16
| ~ spl17_40 ),
inference(resolution,[],[f425,f283]) ).
fof(f425,plain,
( ! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) )
| ~ spl17_40 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f1483,plain,
( spl17_152
| ~ spl17_18
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f380,f343,f293,f1481]) ).
fof(f1481,plain,
( spl17_152
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_152])]) ).
fof(f380,plain,
( ! [X0] :
( sz00 = sdtasdt0(sz00,smndt0(X0))
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_29 ),
inference(resolution,[],[f344,f294]) ).
fof(f1479,plain,
( spl17_151
| ~ spl17_18
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f375,f339,f293,f1477]) ).
fof(f1477,plain,
( spl17_151
<=> ! [X0] :
( sz00 = sdtasdt0(smndt0(X0),sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_151])]) ).
fof(f375,plain,
( ! [X0] :
( sz00 = sdtasdt0(smndt0(X0),sz00)
| ~ aElement0(X0) )
| ~ spl17_18
| ~ spl17_28 ),
inference(resolution,[],[f340,f294]) ).
fof(f1475,plain,
( ~ spl17_4
| spl17_150
| ~ spl17_22
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f464,f412,f311,f1473,f226]) ).
fof(f226,plain,
( spl17_4
<=> aIdeal0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f1473,plain,
( spl17_150
<=> ! [X0] :
( sP0(xJ,sK5(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_150])]) ).
fof(f311,plain,
( spl17_22
<=> ! [X0] :
( aElementOf0(sK5(X0),xJ)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f464,plain,
( ! [X0] :
( sP0(xJ,sK5(X0))
| ~ aIdeal0(xJ)
| ~ aElement0(X0) )
| ~ spl17_22
| ~ spl17_37 ),
inference(resolution,[],[f413,f312]) ).
fof(f312,plain,
( ! [X0] :
( aElementOf0(sK5(X0),xJ)
| ~ aElement0(X0) )
| ~ spl17_22 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f1471,plain,
( ~ spl17_2
| spl17_149
| ~ spl17_21
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f463,f412,f307,f1469,f216]) ).
fof(f216,plain,
( spl17_2
<=> aIdeal0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f1469,plain,
( spl17_149
<=> ! [X0] :
( sP0(xI,sK4(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_149])]) ).
fof(f307,plain,
( spl17_21
<=> ! [X0] :
( aElementOf0(sK4(X0),xI)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f463,plain,
( ! [X0] :
( sP0(xI,sK4(X0))
| ~ aIdeal0(xI)
| ~ aElement0(X0) )
| ~ spl17_21
| ~ spl17_37 ),
inference(resolution,[],[f413,f308]) ).
fof(f308,plain,
( ! [X0] :
( aElementOf0(sK4(X0),xI)
| ~ aElement0(X0) )
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f1467,plain,
( ~ spl17_2
| spl17_148
| ~ spl17_20
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f460,f412,f302,f1464,f216]) ).
fof(f1464,plain,
( spl17_148
<=> sP0(xI,sdtpldt0(xw,smndt0(xx))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_148])]) ).
fof(f460,plain,
( sP0(xI,sdtpldt0(xw,smndt0(xx)))
| ~ aIdeal0(xI)
| ~ spl17_20
| ~ spl17_37 ),
inference(resolution,[],[f413,f304]) ).
fof(f1462,plain,
( ~ spl17_4
| spl17_147
| ~ spl17_19
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f459,f412,f297,f1459,f226]) ).
fof(f1459,plain,
( spl17_147
<=> sP0(xJ,sdtpldt0(xw,smndt0(xy))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_147])]) ).
fof(f459,plain,
( sP0(xJ,sdtpldt0(xw,smndt0(xy)))
| ~ aIdeal0(xJ)
| ~ spl17_19
| ~ spl17_37 ),
inference(resolution,[],[f413,f299]) ).
fof(f1420,plain,
( spl17_146
| ~ spl17_23
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f541,f522,f318,f1418]) ).
fof(f1418,plain,
( spl17_146
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| aSet0(sdtasasdt0(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_146])]) ).
fof(f318,plain,
( spl17_23
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f522,plain,
( spl17_50
<=> ! [X0,X1] :
( sP1(X1,X0,sdtasasdt0(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f541,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| aSet0(sdtasasdt0(X0,X1)) )
| ~ spl17_23
| ~ spl17_50 ),
inference(resolution,[],[f523,f319]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| aSet0(X2) )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f523,plain,
( ! [X0,X1] :
( sP1(X1,X0,sdtasasdt0(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f1416,plain,
( spl17_145
| ~ spl17_7
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f534,f518,f241,f1413]) ).
fof(f1413,plain,
( spl17_145
<=> smndt0(sz10) = sdtasdt0(sz10,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_145])]) ).
fof(f518,plain,
( spl17_49
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f534,plain,
( smndt0(sz10) = sdtasdt0(sz10,smndt0(sz10))
| ~ spl17_7
| ~ spl17_49 ),
inference(resolution,[],[f519,f243]) ).
fof(f519,plain,
( ! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) )
| ~ spl17_49 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f1411,plain,
( spl17_144
| ~ spl17_8
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f533,f518,f246,f1408]) ).
fof(f1408,plain,
( spl17_144
<=> smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_144])]) ).
fof(f533,plain,
( smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10))
| ~ spl17_8
| ~ spl17_49 ),
inference(resolution,[],[f519,f248]) ).
fof(f1406,plain,
( spl17_143
| ~ spl17_7
| ~ spl17_48 ),
inference(avatar_split_clause,[],[f526,f514,f241,f1403]) ).
fof(f1403,plain,
( spl17_143
<=> smndt0(sz10) = sdtasdt0(smndt0(sz10),sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_143])]) ).
fof(f514,plain,
( spl17_48
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f526,plain,
( smndt0(sz10) = sdtasdt0(smndt0(sz10),sz10)
| ~ spl17_7
| ~ spl17_48 ),
inference(resolution,[],[f515,f243]) ).
fof(f515,plain,
( ! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ spl17_48 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f1401,plain,
( spl17_142
| ~ spl17_8
| ~ spl17_48 ),
inference(avatar_split_clause,[],[f525,f514,f246,f1398]) ).
fof(f1398,plain,
( spl17_142
<=> smndt0(sz00) = sdtasdt0(smndt0(sz10),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_142])]) ).
fof(f525,plain,
( smndt0(sz00) = sdtasdt0(smndt0(sz10),sz00)
| ~ spl17_8
| ~ spl17_48 ),
inference(resolution,[],[f515,f248]) ).
fof(f1396,plain,
( spl17_141
| ~ spl17_27
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f467,f416,f335,f1394]) ).
fof(f1394,plain,
( spl17_141
<=> ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_141])]) ).
fof(f416,plain,
( spl17_38
<=> ! [X0] :
( aIdeal0(X0)
| aElementOf0(sK8(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f467,plain,
( ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK8(X0)) )
| ~ spl17_27
| ~ spl17_38 ),
inference(duplicate_literal_removal,[],[f466]) ).
fof(f466,plain,
( ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK8(X0))
| ~ aSet0(X0) )
| ~ spl17_27
| ~ spl17_38 ),
inference(resolution,[],[f417,f336]) ).
fof(f417,plain,
( ! [X0] :
( aElementOf0(sK8(X0),X0)
| aIdeal0(X0)
| ~ aSet0(X0) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f1366,plain,
( ~ spl17_6
| ~ spl17_139
| ~ spl17_140
| ~ spl17_10
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f1139,f1104,f255,f1363,f1359,f236]) ).
fof(f1359,plain,
( spl17_139
<=> sdteqdtlpzmzozddtrp0(xy,xx,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_139])]) ).
fof(f1363,plain,
( spl17_140
<=> aElementOf0(sz00,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_140])]) ).
fof(f255,plain,
( spl17_10
<=> ! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f1104,plain,
( spl17_118
<=> sz00 = sdtpldt0(xy,smndt0(xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
fof(f1139,plain,
( ~ aElementOf0(sz00,xJ)
| ~ sdteqdtlpzmzozddtrp0(xy,xx,xI)
| ~ aElement0(xy)
| ~ spl17_10
| ~ spl17_118 ),
inference(superposition,[],[f256,f1106]) ).
fof(f1106,plain,
( sz00 = sdtpldt0(xy,smndt0(xy))
| ~ spl17_118 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f256,plain,
( ! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) )
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f1339,plain,
( spl17_138
| ~ spl17_6
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f539,f518,f236,f1336]) ).
fof(f1336,plain,
( spl17_138
<=> smndt0(xy) = sdtasdt0(xy,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_138])]) ).
fof(f539,plain,
( smndt0(xy) = sdtasdt0(xy,smndt0(sz10))
| ~ spl17_6
| ~ spl17_49 ),
inference(resolution,[],[f519,f238]) ).
fof(f1334,plain,
( spl17_137
| ~ spl17_5
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f538,f518,f231,f1331]) ).
fof(f1331,plain,
( spl17_137
<=> smndt0(xx) = sdtasdt0(xx,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_137])]) ).
fof(f538,plain,
( smndt0(xx) = sdtasdt0(xx,smndt0(sz10))
| ~ spl17_5
| ~ spl17_49 ),
inference(resolution,[],[f519,f233]) ).
fof(f1329,plain,
( spl17_136
| ~ spl17_6
| ~ spl17_48 ),
inference(avatar_split_clause,[],[f531,f514,f236,f1326]) ).
fof(f1326,plain,
( spl17_136
<=> smndt0(xy) = sdtasdt0(smndt0(sz10),xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_136])]) ).
fof(f531,plain,
( smndt0(xy) = sdtasdt0(smndt0(sz10),xy)
| ~ spl17_6
| ~ spl17_48 ),
inference(resolution,[],[f515,f238]) ).
fof(f1324,plain,
( spl17_135
| ~ spl17_5
| ~ spl17_48 ),
inference(avatar_split_clause,[],[f530,f514,f231,f1321]) ).
fof(f1321,plain,
( spl17_135
<=> smndt0(xx) = sdtasdt0(smndt0(sz10),xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_135])]) ).
fof(f530,plain,
( smndt0(xx) = sdtasdt0(smndt0(sz10),xx)
| ~ spl17_5
| ~ spl17_48 ),
inference(resolution,[],[f515,f233]) ).
fof(f1319,plain,
( spl17_134
| ~ spl17_6
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f511,f501,f236,f1316]) ).
fof(f1316,plain,
( spl17_134
<=> xy = sdtpldt0(sK4(xy),sK5(xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_134])]) ).
fof(f501,plain,
( spl17_47
<=> ! [X0] :
( sdtpldt0(sK4(X0),sK5(X0)) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f511,plain,
( xy = sdtpldt0(sK4(xy),sK5(xy))
| ~ spl17_6
| ~ spl17_47 ),
inference(resolution,[],[f502,f238]) ).
fof(f502,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sK4(X0),sK5(X0)) = X0 )
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f1314,plain,
( spl17_133
| ~ spl17_5
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f510,f501,f231,f1311]) ).
fof(f1311,plain,
( spl17_133
<=> xx = sdtpldt0(sK4(xx),sK5(xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_133])]) ).
fof(f510,plain,
( xx = sdtpldt0(sK4(xx),sK5(xx))
| ~ spl17_5
| ~ spl17_47 ),
inference(resolution,[],[f502,f233]) ).
fof(f1309,plain,
( spl17_132
| ~ spl17_7
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f506,f501,f241,f1306]) ).
fof(f1306,plain,
( spl17_132
<=> sz10 = sdtpldt0(sK4(sz10),sK5(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_132])]) ).
fof(f506,plain,
( sz10 = sdtpldt0(sK4(sz10),sK5(sz10))
| ~ spl17_7
| ~ spl17_47 ),
inference(resolution,[],[f502,f243]) ).
fof(f1304,plain,
( spl17_131
| ~ spl17_8
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f505,f501,f246,f1301]) ).
fof(f1301,plain,
( spl17_131
<=> sz00 = sdtpldt0(sK4(sz00),sK5(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_131])]) ).
fof(f505,plain,
( sz00 = sdtpldt0(sK4(sz00),sK5(sz00))
| ~ spl17_8
| ~ spl17_47 ),
inference(resolution,[],[f502,f248]) ).
fof(f1282,plain,
( ~ spl17_3
| spl17_130
| ~ spl17_22
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f372,f335,f311,f1280,f221]) ).
fof(f1280,plain,
( spl17_130
<=> ! [X0] :
( aElement0(sK5(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_130])]) ).
fof(f372,plain,
( ! [X0] :
( aElement0(sK5(X0))
| ~ aSet0(xJ)
| ~ aElement0(X0) )
| ~ spl17_22
| ~ spl17_27 ),
inference(resolution,[],[f336,f312]) ).
fof(f1261,plain,
( ~ spl17_1
| spl17_129
| ~ spl17_21
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f371,f335,f307,f1259,f211]) ).
fof(f1259,plain,
( spl17_129
<=> ! [X0] :
( aElement0(sK4(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_129])]) ).
fof(f371,plain,
( ! [X0] :
( aElement0(sK4(X0))
| ~ aSet0(xI)
| ~ aElement0(X0) )
| ~ spl17_21
| ~ spl17_27 ),
inference(resolution,[],[f336,f308]) ).
fof(f1240,plain,
( ~ spl17_1
| spl17_128
| ~ spl17_20
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f368,f335,f302,f1237,f211]) ).
fof(f1237,plain,
( spl17_128
<=> aElement0(sdtpldt0(xw,smndt0(xx))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_128])]) ).
fof(f368,plain,
( aElement0(sdtpldt0(xw,smndt0(xx)))
| ~ aSet0(xI)
| ~ spl17_20
| ~ spl17_27 ),
inference(resolution,[],[f336,f304]) ).
fof(f1218,plain,
( ~ spl17_3
| spl17_127
| ~ spl17_19
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f367,f335,f297,f1215,f221]) ).
fof(f1215,plain,
( spl17_127
<=> aElement0(sdtpldt0(xw,smndt0(xy))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_127])]) ).
fof(f367,plain,
( aElement0(sdtpldt0(xw,smndt0(xy)))
| ~ aSet0(xJ)
| ~ spl17_19
| ~ spl17_27 ),
inference(resolution,[],[f336,f299]) ).
fof(f1181,plain,
( spl17_126
| ~ spl17_7
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f454,f408,f241,f1178]) ).
fof(f1178,plain,
( spl17_126
<=> sz00 = sdtpldt0(smndt0(sz10),sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_126])]) ).
fof(f454,plain,
( sz00 = sdtpldt0(smndt0(sz10),sz10)
| ~ spl17_7
| ~ spl17_36 ),
inference(resolution,[],[f409,f243]) ).
fof(f1176,plain,
( spl17_125
| ~ spl17_8
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f453,f408,f246,f1173]) ).
fof(f453,plain,
( sz00 = sdtpldt0(smndt0(sz00),sz00)
| ~ spl17_8
| ~ spl17_36 ),
inference(resolution,[],[f409,f248]) ).
fof(f1171,plain,
( spl17_124
| ~ spl17_7
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f444,f404,f241,f1168]) ).
fof(f1168,plain,
( spl17_124
<=> sz00 = sdtpldt0(sz10,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
fof(f444,plain,
( sz00 = sdtpldt0(sz10,smndt0(sz10))
| ~ spl17_7
| ~ spl17_35 ),
inference(resolution,[],[f405,f243]) ).
fof(f1166,plain,
( spl17_123
| ~ spl17_8
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f443,f404,f246,f1163]) ).
fof(f1163,plain,
( spl17_123
<=> sz00 = sdtpldt0(sz00,smndt0(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
fof(f443,plain,
( sz00 = sdtpldt0(sz00,smndt0(sz00))
| ~ spl17_8
| ~ spl17_35 ),
inference(resolution,[],[f405,f248]) ).
fof(f1137,plain,
( ~ spl17_5
| ~ spl17_121
| ~ spl17_122
| ~ spl17_11
| ~ spl17_117 ),
inference(avatar_split_clause,[],[f1118,f1099,f259,f1134,f1130,f231]) ).
fof(f1130,plain,
( spl17_121
<=> sdteqdtlpzmzozddtrp0(xx,xy,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
fof(f1134,plain,
( spl17_122
<=> aElementOf0(sz00,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
fof(f1099,plain,
( spl17_117
<=> sz00 = sdtpldt0(xx,smndt0(xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
fof(f1118,plain,
( ~ aElementOf0(sz00,xI)
| ~ sdteqdtlpzmzozddtrp0(xx,xy,xJ)
| ~ aElement0(xx)
| ~ spl17_11
| ~ spl17_117 ),
inference(superposition,[],[f260,f1101]) ).
fof(f1101,plain,
( sz00 = sdtpldt0(xx,smndt0(xx))
| ~ spl17_117 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1117,plain,
( spl17_120
| ~ spl17_6
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f457,f408,f236,f1114]) ).
fof(f1114,plain,
( spl17_120
<=> sz00 = sdtpldt0(smndt0(xy),xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
fof(f457,plain,
( sz00 = sdtpldt0(smndt0(xy),xy)
| ~ spl17_6
| ~ spl17_36 ),
inference(resolution,[],[f409,f238]) ).
fof(f1112,plain,
( spl17_119
| ~ spl17_5
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f456,f408,f231,f1109]) ).
fof(f1109,plain,
( spl17_119
<=> sz00 = sdtpldt0(smndt0(xx),xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
fof(f456,plain,
( sz00 = sdtpldt0(smndt0(xx),xx)
| ~ spl17_5
| ~ spl17_36 ),
inference(resolution,[],[f409,f233]) ).
fof(f1107,plain,
( spl17_118
| ~ spl17_6
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f447,f404,f236,f1104]) ).
fof(f447,plain,
( sz00 = sdtpldt0(xy,smndt0(xy))
| ~ spl17_6
| ~ spl17_35 ),
inference(resolution,[],[f405,f238]) ).
fof(f1102,plain,
( spl17_117
| ~ spl17_5
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f446,f404,f231,f1099]) ).
fof(f446,plain,
( sz00 = sdtpldt0(xx,smndt0(xx))
| ~ spl17_5
| ~ spl17_35 ),
inference(resolution,[],[f405,f233]) ).
fof(f1059,plain,
( spl17_116
| ~ spl17_7
| ~ spl17_33 ),
inference(avatar_split_clause,[],[f399,f359,f241,f1056]) ).
fof(f1056,plain,
( spl17_116
<=> sz10 = sdtpldt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
fof(f399,plain,
( sz10 = sdtpldt0(sz00,sz10)
| ~ spl17_7
| ~ spl17_33 ),
inference(resolution,[],[f360,f243]) ).
fof(f1054,plain,
( spl17_115
| ~ spl17_7
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f394,f355,f241,f1051]) ).
fof(f1051,plain,
( spl17_115
<=> sz10 = sdtpldt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
fof(f394,plain,
( sz10 = sdtpldt0(sz10,sz00)
| ~ spl17_7
| ~ spl17_32 ),
inference(resolution,[],[f356,f243]) ).
fof(f1049,plain,
( spl17_114
| ~ spl17_8
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f393,f355,f246,f1046]) ).
fof(f1046,plain,
( spl17_114
<=> sz00 = sdtpldt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
fof(f393,plain,
( sz00 = sdtpldt0(sz00,sz00)
| ~ spl17_8
| ~ spl17_32 ),
inference(resolution,[],[f356,f248]) ).
fof(f1044,plain,
( spl17_113
| ~ spl17_7
| ~ spl17_30 ),
inference(avatar_split_clause,[],[f384,f347,f241,f1041]) ).
fof(f1041,plain,
( spl17_113
<=> sz10 = sdtasdt0(sz10,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
fof(f384,plain,
( sz10 = sdtasdt0(sz10,sz10)
| ~ spl17_7
| ~ spl17_30 ),
inference(resolution,[],[f348,f243]) ).
fof(f1039,plain,
( spl17_112
| ~ spl17_7
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f379,f343,f241,f1036]) ).
fof(f1036,plain,
( spl17_112
<=> sz00 = sdtasdt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
fof(f379,plain,
( sz00 = sdtasdt0(sz00,sz10)
| ~ spl17_7
| ~ spl17_29 ),
inference(resolution,[],[f344,f243]) ).
fof(f1034,plain,
( spl17_111
| ~ spl17_7
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f374,f339,f241,f1031]) ).
fof(f1031,plain,
( spl17_111
<=> sz00 = sdtasdt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
fof(f374,plain,
( sz00 = sdtasdt0(sz10,sz00)
| ~ spl17_7
| ~ spl17_28 ),
inference(resolution,[],[f340,f243]) ).
fof(f1029,plain,
( spl17_110
| ~ spl17_8
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f373,f339,f246,f1026]) ).
fof(f1026,plain,
( spl17_110
<=> sz00 = sdtasdt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
fof(f373,plain,
( sz00 = sdtasdt0(sz00,sz00)
| ~ spl17_8
| ~ spl17_28 ),
inference(resolution,[],[f340,f248]) ).
fof(f968,plain,
( ~ spl17_4
| spl17_109
| ~ spl17_13
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f462,f412,f268,f965,f226]) ).
fof(f965,plain,
( spl17_109
<=> sP0(xJ,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
fof(f462,plain,
( sP0(xJ,xb)
| ~ aIdeal0(xJ)
| ~ spl17_13
| ~ spl17_37 ),
inference(resolution,[],[f413,f270]) ).
fof(f270,plain,
( aElementOf0(xb,xJ)
| ~ spl17_13 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f963,plain,
( ~ spl17_2
| spl17_108
| ~ spl17_12
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f461,f412,f263,f960,f216]) ).
fof(f960,plain,
( spl17_108
<=> sP0(xI,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
fof(f461,plain,
( sP0(xI,xa)
| ~ aIdeal0(xI)
| ~ spl17_12
| ~ spl17_37 ),
inference(resolution,[],[f413,f265]) ).
fof(f265,plain,
( aElementOf0(xa,xI)
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f958,plain,
( spl17_107
| ~ spl17_6
| ~ spl17_33 ),
inference(avatar_split_clause,[],[f402,f359,f236,f955]) ).
fof(f955,plain,
( spl17_107
<=> xy = sdtpldt0(sz00,xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f402,plain,
( xy = sdtpldt0(sz00,xy)
| ~ spl17_6
| ~ spl17_33 ),
inference(resolution,[],[f360,f238]) ).
fof(f953,plain,
( spl17_106
| ~ spl17_5
| ~ spl17_33 ),
inference(avatar_split_clause,[],[f401,f359,f231,f950]) ).
fof(f950,plain,
( spl17_106
<=> xx = sdtpldt0(sz00,xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
fof(f401,plain,
( xx = sdtpldt0(sz00,xx)
| ~ spl17_5
| ~ spl17_33 ),
inference(resolution,[],[f360,f233]) ).
fof(f948,plain,
( spl17_105
| ~ spl17_6
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f397,f355,f236,f945]) ).
fof(f945,plain,
( spl17_105
<=> xy = sdtpldt0(xy,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f397,plain,
( xy = sdtpldt0(xy,sz00)
| ~ spl17_6
| ~ spl17_32 ),
inference(resolution,[],[f356,f238]) ).
fof(f943,plain,
( spl17_104
| ~ spl17_5
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f396,f355,f231,f940]) ).
fof(f940,plain,
( spl17_104
<=> xx = sdtpldt0(xx,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
fof(f396,plain,
( xx = sdtpldt0(xx,sz00)
| ~ spl17_5
| ~ spl17_32 ),
inference(resolution,[],[f356,f233]) ).
fof(f938,plain,
( spl17_103
| ~ spl17_6
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f392,f351,f236,f935]) ).
fof(f935,plain,
( spl17_103
<=> xy = sdtasdt0(sz10,xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f392,plain,
( xy = sdtasdt0(sz10,xy)
| ~ spl17_6
| ~ spl17_31 ),
inference(resolution,[],[f352,f238]) ).
fof(f933,plain,
( spl17_102
| ~ spl17_5
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f391,f351,f231,f930]) ).
fof(f930,plain,
( spl17_102
<=> xx = sdtasdt0(sz10,xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).
fof(f391,plain,
( xx = sdtasdt0(sz10,xx)
| ~ spl17_5
| ~ spl17_31 ),
inference(resolution,[],[f352,f233]) ).
fof(f928,plain,
( spl17_101
| ~ spl17_6
| ~ spl17_30 ),
inference(avatar_split_clause,[],[f387,f347,f236,f925]) ).
fof(f925,plain,
( spl17_101
<=> xy = sdtasdt0(xy,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
fof(f387,plain,
( xy = sdtasdt0(xy,sz10)
| ~ spl17_6
| ~ spl17_30 ),
inference(resolution,[],[f348,f238]) ).
fof(f923,plain,
( spl17_100
| ~ spl17_5
| ~ spl17_30 ),
inference(avatar_split_clause,[],[f386,f347,f231,f920]) ).
fof(f920,plain,
( spl17_100
<=> xx = sdtasdt0(xx,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).
fof(f386,plain,
( xx = sdtasdt0(xx,sz10)
| ~ spl17_5
| ~ spl17_30 ),
inference(resolution,[],[f348,f233]) ).
fof(f918,plain,
( spl17_99
| ~ spl17_6
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f382,f343,f236,f915]) ).
fof(f915,plain,
( spl17_99
<=> sz00 = sdtasdt0(sz00,xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
fof(f382,plain,
( sz00 = sdtasdt0(sz00,xy)
| ~ spl17_6
| ~ spl17_29 ),
inference(resolution,[],[f344,f238]) ).
fof(f913,plain,
( spl17_98
| ~ spl17_5
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f381,f343,f231,f910]) ).
fof(f910,plain,
( spl17_98
<=> sz00 = sdtasdt0(sz00,xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).
fof(f381,plain,
( sz00 = sdtasdt0(sz00,xx)
| ~ spl17_5
| ~ spl17_29 ),
inference(resolution,[],[f344,f233]) ).
fof(f897,plain,
spl17_97,
inference(avatar_split_clause,[],[f189,f895]) ).
fof(f895,plain,
( spl17_97
<=> ! [X4,X0,X5,X2,X1] :
( sP3(X0,X1,X2)
| sdtpldt0(X4,X5) != sK12(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
fof(f189,plain,
! [X2,X0,X1,X4,X5] :
( sP3(X0,X1,X2)
| sdtpldt0(X4,X5) != sK12(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != sK12(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK12(X0,X1,X2),X2) )
& ( ( sK12(X0,X1,X2) = sdtpldt0(sK13(X0,X1,X2),sK14(X0,X1,X2))
& aElementOf0(sK14(X0,X1,X2),X0)
& aElementOf0(sK13(X0,X1,X2),X1) )
| aElementOf0(sK12(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ( sdtpldt0(sK15(X0,X1,X8),sK16(X0,X1,X8)) = X8
& aElementOf0(sK16(X0,X1,X8),X0)
& aElementOf0(sK15(X0,X1,X8),X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16])],[f111,f114,f113,f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X5,X4] :
( sdtpldt0(X4,X5) != sK12(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK12(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK12(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(sK12(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK12(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
=> ( sK12(X0,X1,X2) = sdtpldt0(sK13(X0,X1,X2),sK14(X0,X1,X2))
& aElementOf0(sK14(X0,X1,X2),X0)
& aElementOf0(sK13(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
=> ( sdtpldt0(sK15(X0,X1,X8),sK16(X0,X1,X8)) = X8
& aElementOf0(sK16(X0,X1,X8),X0)
& aElementOf0(sK15(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X1,X0,X2] :
( ( sP3(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) ) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f893,plain,
spl17_96,
inference(avatar_split_clause,[],[f188,f891]) ).
fof(f891,plain,
( spl17_96
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| sK12(X0,X1,X2) = sdtpldt0(sK13(X0,X1,X2),sK14(X0,X1,X2))
| aElementOf0(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
fof(f188,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| sK12(X0,X1,X2) = sdtpldt0(sK13(X0,X1,X2),sK14(X0,X1,X2))
| aElementOf0(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f889,plain,
spl17_95,
inference(avatar_split_clause,[],[f180,f887]) ).
fof(f887,plain,
( spl17_95
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ aElementOf0(sK11(X0,X1,X2),X0)
| ~ aElementOf0(sK11(X0,X1,X2),X1)
| ~ aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ aElementOf0(sK11(X0,X1,X2),X0)
| ~ aElementOf0(sK11(X0,X1,X2),X1)
| ~ aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ aElementOf0(sK11(X0,X1,X2),X0)
| ~ aElementOf0(sK11(X0,X1,X2),X1)
| ~ aElementOf0(sK11(X0,X1,X2),X2) )
& ( ( aElementOf0(sK11(X0,X1,X2),X0)
& aElementOf0(sK11(X0,X1,X2),X1) )
| aElementOf0(sK11(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK11(X0,X1,X2),X0)
| ~ aElementOf0(sK11(X0,X1,X2),X1)
| ~ aElementOf0(sK11(X0,X1,X2),X2) )
& ( ( aElementOf0(sK11(X0,X1,X2),X0)
& aElementOf0(sK11(X0,X1,X2),X1) )
| aElementOf0(sK11(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f867,plain,
spl17_94,
inference(avatar_split_clause,[],[f205,f865]) ).
fof(f865,plain,
( spl17_94
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
fof(f205,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f863,plain,
( spl17_93
| ~ spl17_6
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f377,f339,f236,f860]) ).
fof(f860,plain,
( spl17_93
<=> sz00 = sdtasdt0(xy,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
fof(f377,plain,
( sz00 = sdtasdt0(xy,sz00)
| ~ spl17_6
| ~ spl17_28 ),
inference(resolution,[],[f340,f238]) ).
fof(f858,plain,
spl17_92,
inference(avatar_split_clause,[],[f204,f856]) ).
fof(f856,plain,
( spl17_92
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
fof(f204,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f841,plain,
spl17_91,
inference(avatar_split_clause,[],[f184,f839]) ).
fof(f839,plain,
( spl17_91
<=> ! [X0,X8,X2,X1] :
( sdtpldt0(sK15(X0,X1,X8),sK16(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
fof(f184,plain,
! [X2,X0,X1,X8] :
( sdtpldt0(sK15(X0,X1,X8),sK16(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f837,plain,
spl17_90,
inference(avatar_split_clause,[],[f179,f835]) ).
fof(f835,plain,
( spl17_90
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| aElementOf0(sK11(X0,X1,X2),X0)
| aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| aElementOf0(sK11(X0,X1,X2),X0)
| aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f833,plain,
spl17_89,
inference(avatar_split_clause,[],[f178,f831]) ).
fof(f831,plain,
( spl17_89
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| aElementOf0(sK11(X0,X1,X2),X1)
| aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| aElementOf0(sK11(X0,X1,X2),X1)
| aElementOf0(sK11(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f808,plain,
( spl17_88
| ~ spl17_5
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f376,f339,f231,f805]) ).
fof(f805,plain,
( spl17_88
<=> sz00 = sdtasdt0(xx,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
fof(f376,plain,
( sz00 = sdtasdt0(xx,sz00)
| ~ spl17_5
| ~ spl17_28 ),
inference(resolution,[],[f340,f233]) ).
fof(f788,plain,
spl17_87,
inference(avatar_split_clause,[],[f203,f786]) ).
fof(f786,plain,
( spl17_87
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
fof(f203,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f784,plain,
spl17_86,
inference(avatar_split_clause,[],[f202,f782]) ).
fof(f782,plain,
( spl17_86
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f202,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f780,plain,
spl17_85,
inference(avatar_split_clause,[],[f171,f778]) ).
fof(f778,plain,
( spl17_85
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK9(X0,X1),X0)
| ~ aElementOf0(sK10(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK9(X0,X1),X0)
| ~ aElementOf0(sK10(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( X0 = X1
| ( ~ aElementOf0(sK9(X0,X1),X0)
& aElementOf0(sK9(X0,X1),X1) )
| ( ~ aElementOf0(sK10(X0,X1),X1)
& aElementOf0(sK10(X0,X1),X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f54,f102,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK9(X0,X1),X0)
& aElementOf0(sK9(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sK10(X0,X1),X1)
& aElementOf0(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(X3,X1) ) )
=> X0 = X1 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,X1) ) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
fof(f776,plain,
spl17_84,
inference(avatar_split_clause,[],[f170,f774]) ).
fof(f774,plain,
( spl17_84
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK9(X0,X1),X0)
| aElementOf0(sK10(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f170,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK9(X0,X1),X0)
| aElementOf0(sK10(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f772,plain,
spl17_83,
inference(avatar_split_clause,[],[f169,f770]) ).
fof(f770,plain,
( spl17_83
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK9(X0,X1),X1)
| ~ aElementOf0(sK10(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f169,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK9(X0,X1),X1)
| ~ aElementOf0(sK10(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f768,plain,
spl17_82,
inference(avatar_split_clause,[],[f168,f766]) ).
fof(f766,plain,
( spl17_82
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK9(X0,X1),X1)
| aElementOf0(sK10(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f168,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK9(X0,X1),X1)
| aElementOf0(sK10(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f764,plain,
spl17_81,
inference(avatar_split_clause,[],[f163,f762]) ).
fof(f762,plain,
( spl17_81
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
| ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f163,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
| ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
& aElement0(sK6(X0,X1)) )
| ( ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0)
& aElementOf0(sK7(X0,X1),X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f92,f94,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
& aElement0(sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0)
& aElementOf0(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f735,plain,
spl17_80,
inference(avatar_split_clause,[],[f201,f733]) ).
fof(f733,plain,
( spl17_80
<=> ! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f201,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
& ( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( aIdeal0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMod) ).
fof(f731,plain,
spl17_79,
inference(avatar_split_clause,[],[f200,f729]) ).
fof(f729,plain,
( spl17_79
<=> ! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f200,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f727,plain,
spl17_78,
inference(avatar_split_clause,[],[f187,f725]) ).
fof(f725,plain,
( spl17_78
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK14(X0,X1,X2),X0)
| aElementOf0(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f187,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK14(X0,X1,X2),X0)
| aElementOf0(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f723,plain,
spl17_77,
inference(avatar_split_clause,[],[f186,f721]) ).
fof(f721,plain,
( spl17_77
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK13(X0,X1,X2),X1)
| aElementOf0(sK12(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK13(X0,X1,X2),X1)
| aElementOf0(sK12(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f718,plain,
( spl17_75
| ~ spl17_76
| ~ spl17_10
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f604,f595,f255,f715,f712]) ).
fof(f712,plain,
( spl17_75
<=> ! [X0] :
( ~ aElementOf0(X0,xJ)
| ~ aElement0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f715,plain,
( spl17_76
<=> aElementOf0(smndt0(xy),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f604,plain,
( ! [X0] :
( ~ aElementOf0(smndt0(xy),xJ)
| ~ aElementOf0(X0,xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) )
| ~ spl17_10
| ~ spl17_59 ),
inference(resolution,[],[f596,f256]) ).
fof(f704,plain,
spl17_74,
inference(avatar_split_clause,[],[f207,f702]) ).
fof(f702,plain,
( spl17_74
<=> ! [X10,X0,X9,X2,X1] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f207,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP3(X0,X1,X2) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f700,plain,
spl17_73,
inference(avatar_split_clause,[],[f199,f698]) ).
fof(f698,plain,
( spl17_73
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f199,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(f696,plain,
spl17_72,
inference(avatar_split_clause,[],[f192,f694]) ).
fof(f694,plain,
( spl17_72
<=> ! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f192,plain,
! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP3(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f58,f86]) ).
fof(f58,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(f692,plain,
spl17_71,
inference(avatar_split_clause,[],[f162,f690]) ).
fof(f690,plain,
( spl17_71
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
| aElementOf0(sK7(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f162,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ aElementOf0(sdtasdt0(sK6(X0,X1),X1),X0)
| aElementOf0(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f684,plain,
spl17_70,
inference(avatar_split_clause,[],[f161,f682]) ).
fof(f682,plain,
( spl17_70
<=> ! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK6(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f161,plain,
! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK6(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK7(X0,X1)),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f677,plain,
spl17_69,
inference(avatar_split_clause,[],[f183,f675]) ).
fof(f675,plain,
( spl17_69
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK16(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f183,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK16(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f673,plain,
spl17_68,
inference(avatar_split_clause,[],[f182,f671]) ).
fof(f671,plain,
( spl17_68
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK15(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f182,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK15(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f669,plain,
spl17_67,
inference(avatar_split_clause,[],[f177,f667]) ).
fof(f667,plain,
( spl17_67
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f177,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f661,plain,
spl17_66,
inference(avatar_split_clause,[],[f173,f659]) ).
fof(f659,plain,
( spl17_66
<=> ! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f173,plain,
! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP1(X1,X0,X2) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f657,plain,
spl17_65,
inference(avatar_split_clause,[],[f160,f655]) ).
fof(f655,plain,
( spl17_65
<=> ! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK6(X0,X1))
| aElementOf0(sK7(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f160,plain,
! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK6(X0,X1))
| aElementOf0(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f644,plain,
( spl17_63
| ~ spl17_64
| ~ spl17_11
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f598,f591,f259,f641,f638]) ).
fof(f638,plain,
( spl17_63
<=> ! [X0] :
( ~ aElementOf0(X0,xI)
| ~ aElement0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f641,plain,
( spl17_64
<=> aElementOf0(smndt0(xx),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f598,plain,
( ! [X0] :
( ~ aElementOf0(smndt0(xx),xI)
| ~ aElementOf0(X0,xI)
| ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ aElement0(X0) )
| ~ spl17_11
| ~ spl17_58 ),
inference(resolution,[],[f592,f260]) ).
fof(f620,plain,
spl17_62,
inference(avatar_split_clause,[],[f198,f618]) ).
fof(f198,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f616,plain,
spl17_61,
inference(avatar_split_clause,[],[f197,f614]) ).
fof(f197,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f612,plain,
spl17_60,
inference(avatar_split_clause,[],[f158,f610]) ).
fof(f158,plain,
! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f597,plain,
spl17_59,
inference(avatar_split_clause,[],[f131,f595]) ).
fof(f131,plain,
! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
( aIdeal0(xJ)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1) )
& ! [X2] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ) ) )
| ~ aElementOf0(X0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI) ) )
| ~ aElementOf0(X3,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X0,X2),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,xI)
=> ( ! [X4] :
( aElement0(X4)
=> aElementOf0(sdtasdt0(X4,X3),xI) )
& ! [X5] :
( aElementOf0(X5,xI)
=> aElementOf0(sdtpldt0(X3,X5),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(f593,plain,
spl17_58,
inference(avatar_split_clause,[],[f127,f591]) ).
fof(f127,plain,
! [X3,X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f43]) ).
fof(f574,plain,
spl17_57,
inference(avatar_split_clause,[],[f208,f572]) ).
fof(f572,plain,
( spl17_57
<=> ! [X0,X1] :
( sP3(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f208,plain,
! [X0,X1] :
( sP3(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f191]) ).
fof(f191,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f570,plain,
spl17_56,
inference(avatar_split_clause,[],[f176,f568]) ).
fof(f568,plain,
( spl17_56
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f176,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f566,plain,
spl17_55,
inference(avatar_split_clause,[],[f175,f564]) ).
fof(f564,plain,
( spl17_55
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f175,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f562,plain,
spl17_54,
inference(avatar_split_clause,[],[f159,f560]) ).
fof(f560,plain,
( spl17_54
<=> ! [X4,X0,X1] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f159,plain,
! [X0,X1,X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f554,plain,
spl17_53,
inference(avatar_split_clause,[],[f132,f552]) ).
fof(f132,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f43]) ).
fof(f550,plain,
( ~ spl17_3
| spl17_52
| ~ spl17_13
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f370,f335,f268,f547,f221]) ).
fof(f370,plain,
( aElement0(xb)
| ~ aSet0(xJ)
| ~ spl17_13
| ~ spl17_27 ),
inference(resolution,[],[f336,f270]) ).
fof(f545,plain,
spl17_51,
inference(avatar_split_clause,[],[f128,f543]) ).
fof(f128,plain,
! [X3,X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f43]) ).
fof(f524,plain,
spl17_50,
inference(avatar_split_clause,[],[f206,f522]) ).
fof(f206,plain,
! [X0,X1] :
( sP1(X1,X0,sdtasasdt0(X0,X1))
| ~ sP2(X0,X1) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f520,plain,
spl17_49,
inference(avatar_split_clause,[],[f157,f518]) ).
fof(f157,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f516,plain,
spl17_48,
inference(avatar_split_clause,[],[f156,f514]) ).
fof(f156,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f503,plain,
spl17_47,
inference(avatar_split_clause,[],[f141,f501]) ).
fof(f141,plain,
! [X0] :
( sdtpldt0(sK4(X0),sK5(X0)) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( aElementOf0(X0,sdtpldt1(xI,xJ))
& sdtpldt0(sK4(X0),sK5(X0)) = X0
& aElementOf0(sK5(X0),xJ)
& aElementOf0(sK4(X0),xI) )
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f44,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,xJ)
& aElementOf0(X1,xI) )
=> ( sdtpldt0(sK4(X0),sK5(X0)) = X0
& aElementOf0(sK5(X0),xJ)
& aElementOf0(sK4(X0),xI) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ( aElementOf0(X0,sdtpldt1(xI,xJ))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,xJ)
& aElementOf0(X1,xI) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( aElement0(X0)
=> ( aElementOf0(X0,sdtpldt1(xI,xJ))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,xJ)
& aElementOf0(X1,xI) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205_03) ).
fof(f491,plain,
spl17_46,
inference(avatar_split_clause,[],[f125,f488]) ).
fof(f125,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(f452,plain,
( ~ spl17_1
| spl17_45
| ~ spl17_12
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f369,f335,f263,f449,f211]) ).
fof(f369,plain,
( aElement0(xa)
| ~ aSet0(xI)
| ~ spl17_12
| ~ spl17_27 ),
inference(resolution,[],[f336,f265]) ).
fof(f442,plain,
spl17_44,
inference(avatar_split_clause,[],[f209,f440]) ).
fof(f440,plain,
( spl17_44
<=> ! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f209,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f190]) ).
fof(f190,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f438,plain,
spl17_43,
inference(avatar_split_clause,[],[f196,f436]) ).
fof(f196,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f434,plain,
spl17_42,
inference(avatar_split_clause,[],[f195,f432]) ).
fof(f195,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f430,plain,
spl17_41,
inference(avatar_split_clause,[],[f194,f428]) ).
fof(f194,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> aIdeal0(sdtpldt1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).
fof(f426,plain,
spl17_40,
inference(avatar_split_clause,[],[f193,f424]) ).
fof(f193,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> aIdeal0(sdtasasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).
fof(f422,plain,
spl17_39,
inference(avatar_split_clause,[],[f167,f420]) ).
fof(f420,plain,
( spl17_39
<=> ! [X0] :
( aIdeal0(X0)
| ~ sP0(X0,sK8(X0))
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f167,plain,
! [X0] :
( aIdeal0(X0)
| ~ sP0(X0,sK8(X0))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ~ sP0(X0,sK8(X0))
& aElementOf0(sK8(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f98,f99]) ).
fof(f99,plain,
! [X0] :
( ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
=> ( ~ sP0(X0,sK8(X0))
& aElementOf0(sK8(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(definition_folding,[],[f52,f81]) ).
fof(f52,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f418,plain,
spl17_38,
inference(avatar_split_clause,[],[f166,f416]) ).
fof(f166,plain,
! [X0] :
( aIdeal0(X0)
| aElementOf0(sK8(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f414,plain,
spl17_37,
inference(avatar_split_clause,[],[f165,f412]) ).
fof(f165,plain,
! [X2,X0] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f410,plain,
spl17_36,
inference(avatar_split_clause,[],[f155,f408]) ).
fof(f155,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(f406,plain,
spl17_35,
inference(avatar_split_clause,[],[f154,f404]) ).
fof(f154,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f365,plain,
spl17_34,
inference(avatar_split_clause,[],[f181,f363]) ).
fof(f363,plain,
( spl17_34
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f181,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f56,f84,f83]) ).
fof(f56,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
fof(f361,plain,
spl17_33,
inference(avatar_split_clause,[],[f153,f359]) ).
fof(f153,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f357,plain,
spl17_32,
inference(avatar_split_clause,[],[f152,f355]) ).
fof(f152,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f353,plain,
spl17_31,
inference(avatar_split_clause,[],[f151,f351]) ).
fof(f151,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f349,plain,
spl17_30,
inference(avatar_split_clause,[],[f150,f347]) ).
fof(f150,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f345,plain,
spl17_29,
inference(avatar_split_clause,[],[f149,f343]) ).
fof(f149,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f341,plain,
spl17_28,
inference(avatar_split_clause,[],[f148,f339]) ).
fof(f148,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f337,plain,
spl17_27,
inference(avatar_split_clause,[],[f146,f335]) ).
fof(f146,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f333,plain,
spl17_26,
inference(avatar_split_clause,[],[f142,f331]) ).
fof(f142,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f329,plain,
( ~ spl17_24
| ~ spl17_25
| ~ spl17_10
| ~ spl17_19 ),
inference(avatar_split_clause,[],[f315,f297,f255,f326,f322]) ).
fof(f326,plain,
( spl17_25
<=> sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f315,plain,
( ~ sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aElement0(xw)
| ~ spl17_10
| ~ spl17_19 ),
inference(resolution,[],[f299,f256]) ).
fof(f320,plain,
spl17_23,
inference(avatar_split_clause,[],[f174,f318]) ).
fof(f174,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f313,plain,
spl17_22,
inference(avatar_split_clause,[],[f140,f311]) ).
fof(f140,plain,
! [X0] :
( aElementOf0(sK5(X0),xJ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f309,plain,
spl17_21,
inference(avatar_split_clause,[],[f139,f307]) ).
fof(f139,plain,
! [X0] :
( aElementOf0(sK4(X0),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f305,plain,
spl17_20,
inference(avatar_split_clause,[],[f124,f302]) ).
fof(f124,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1332) ).
fof(f300,plain,
spl17_19,
inference(avatar_split_clause,[],[f123,f297]) ).
fof(f123,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(f295,plain,
spl17_18,
inference(avatar_split_clause,[],[f147,f293]) ).
fof(f147,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(f291,plain,
spl17_17,
inference(avatar_split_clause,[],[f138,f288]) ).
fof(f138,plain,
sz10 = sdtpldt0(xa,xb),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
( sz10 = sdtpldt0(xa,xb)
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
fof(f284,plain,
spl17_16,
inference(avatar_split_clause,[],[f164,f282]) ).
fof(f164,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f280,plain,
spl17_15,
inference(avatar_split_clause,[],[f119,f278]) ).
fof(f119,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
& ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
| ( ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
& ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f276,plain,
~ spl17_14,
inference(avatar_split_clause,[],[f145,f273]) ).
fof(f273,plain,
( spl17_14
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f145,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f271,plain,
spl17_13,
inference(avatar_split_clause,[],[f137,f268]) ).
fof(f137,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f31]) ).
fof(f266,plain,
spl17_12,
inference(avatar_split_clause,[],[f136,f263]) ).
fof(f136,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f31]) ).
fof(f261,plain,
spl17_11,
inference(avatar_split_clause,[],[f121,f259]) ).
fof(f121,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f257,plain,
spl17_10,
inference(avatar_split_clause,[],[f120,f255]) ).
fof(f120,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f253,plain,
spl17_9,
inference(avatar_split_clause,[],[f122,f251]) ).
fof(f251,plain,
( spl17_9
<=> ! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f122,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f249,plain,
spl17_8,
inference(avatar_split_clause,[],[f144,f246]) ).
fof(f144,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f244,plain,
spl17_7,
inference(avatar_split_clause,[],[f143,f241]) ).
fof(f143,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f239,plain,
spl17_6,
inference(avatar_split_clause,[],[f135,f236]) ).
fof(f135,plain,
aElement0(xy),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(f234,plain,
spl17_5,
inference(avatar_split_clause,[],[f134,f231]) ).
fof(f134,plain,
aElement0(xx),
inference(cnf_transformation,[],[f30]) ).
fof(f229,plain,
spl17_4,
inference(avatar_split_clause,[],[f133,f226]) ).
fof(f133,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f43]) ).
fof(f224,plain,
spl17_3,
inference(avatar_split_clause,[],[f130,f221]) ).
fof(f130,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f43]) ).
fof(f219,plain,
spl17_2,
inference(avatar_split_clause,[],[f129,f216]) ).
fof(f129,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f43]) ).
fof(f214,plain,
spl17_1,
inference(avatar_split_clause,[],[f126,f211]) ).
fof(f126,plain,
aSet0(xI),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 02:23:28 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (22538)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (22541)WARNING: value z3 for option sas not known
% 0.14/0.38 % (22545)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (22544)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (22543)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (22540)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (22542)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (22541)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (22539)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.40 TRYING [3]
% 0.20/0.42 % (22543)First to succeed.
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.43 % (22543)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43 % (22543)------------------------------
% 0.20/0.43 % (22543)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.43 % (22543)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (22543)Memory used [KB]: 1901
% 0.20/0.43 % (22543)Time elapsed: 0.051 s
% 0.20/0.43 % (22543)Instructions burned: 92 (million)
% 0.20/0.43 % (22543)------------------------------
% 0.20/0.43 % (22543)------------------------------
% 0.20/0.43 % (22538)Success in time 0.069 s
%------------------------------------------------------------------------------