TSTP Solution File: RNG112+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG112+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:57:50 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 274
% Syntax : Number of formulae : 879 ( 134 unt; 0 def)
% Number of atoms : 3157 ( 481 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 3776 (1498 ~;1593 |; 358 &)
% ( 250 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 225 ( 223 usr; 205 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 8 con; 0-4 aty)
% Number of variables : 1146 (1039 !; 107 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2143,plain,
$false,
inference(avatar_sat_refutation,[],[f321,f326,f331,f336,f341,f345,f349,f353,f358,f363,f368,f373,f378,f383,f388,f393,f397,f401,f410,f414,f418,f429,f434,f438,f442,f448,f452,f456,f460,f464,f469,f473,f477,f481,f485,f489,f493,f497,f501,f517,f546,f550,f554,f558,f562,f566,f570,f574,f578,f582,f586,f635,f645,f651,f655,f659,f664,f669,f673,f696,f700,f704,f708,f713,f721,f725,f729,f741,f745,f749,f753,f757,f762,f766,f770,f774,f778,f782,f786,f862,f866,f874,f878,f882,f886,f890,f894,f898,f904,f925,f929,f933,f937,f957,f961,f965,f969,f973,f977,f984,f991,f995,f999,f1003,f1007,f1024,f1028,f1055,f1061,f1065,f1070,f1074,f1078,f1082,f1086,f1090,f1094,f1139,f1143,f1147,f1151,f1156,f1268,f1272,f1276,f1284,f1292,f1320,f1324,f1373,f1378,f1383,f1387,f1404,f1409,f1411,f1440,f1441,f1451,f1457,f1480,f1485,f1486,f1492,f1512,f1518,f1531,f1537,f1550,f1552,f1557,f1563,f1570,f1576,f1583,f1589,f1596,f1597,f1615,f1620,f1625,f1630,f1669,f1711,f1715,f1719,f1724,f1729,f1734,f1739,f1744,f1749,f1754,f1755,f1763,f1776,f1782,f1823,f1870,f1875,f1880,f1885,f1890,f1919,f1924,f1929,f1934,f1967,f1977,f1982,f1988,f1993,f1998,f2003,f2012,f2043,f2048,f2053,f2058,f2063,f2067,f2086,f2133,f2137,f2141,f2142]) ).
fof(f2142,plain,
( ~ spl32_54
| spl32_56
| ~ spl32_7
| ~ spl32_172 ),
inference(avatar_split_clause,[],[f2093,f1769,f347,f642,f632]) ).
fof(f632,plain,
( spl32_54
<=> aElementOf0(sK10,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_54])]) ).
fof(f642,plain,
( spl32_56
<=> sz00 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl32_56])]) ).
fof(f347,plain,
( spl32_7
<=> ! [X0] :
( sz00 != sK9(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_7])]) ).
fof(f1769,plain,
( spl32_172
<=> sz00 = sK9(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_172])]) ).
fof(f2093,plain,
( sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_7
| ~ spl32_172 ),
inference(trivial_inequality_removal,[],[f2091]) ).
fof(f2091,plain,
( sz00 != sz00
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_7
| ~ spl32_172 ),
inference(superposition,[],[f348,f1771]) ).
fof(f1771,plain,
( sz00 = sK9(sK10)
| ~ spl32_172 ),
inference(avatar_component_clause,[],[f1769]) ).
fof(f348,plain,
( ! [X0] :
( sz00 != sK9(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f2141,plain,
( spl32_204
| ~ spl32_18
| ~ spl32_48 ),
inference(avatar_split_clause,[],[f606,f568,f399,f2139]) ).
fof(f2139,plain,
( spl32_204
<=> ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtasasdt0(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_204])]) ).
fof(f399,plain,
( spl32_18
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_18])]) ).
fof(f568,plain,
( spl32_48
<=> ! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_48])]) ).
fof(f606,plain,
( ! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aSet0(sdtasasdt0(X1,X0)) )
| ~ spl32_18
| ~ spl32_48 ),
inference(resolution,[],[f569,f400]) ).
fof(f400,plain,
( ! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) )
| ~ spl32_18 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f569,plain,
( ! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) )
| ~ spl32_48 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f2137,plain,
( spl32_203
| ~ spl32_20
| ~ spl32_30 ),
inference(avatar_split_clause,[],[f520,f458,f412,f2135]) ).
fof(f2135,plain,
( spl32_203
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_203])]) ).
fof(f412,plain,
( spl32_20
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_20])]) ).
fof(f458,plain,
( spl32_30
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_30])]) ).
fof(f520,plain,
( ! [X0] :
( sz00 = sdtasdt0(sz00,smndt0(X0))
| ~ aElement0(X0) )
| ~ spl32_20
| ~ spl32_30 ),
inference(resolution,[],[f459,f413]) ).
fof(f413,plain,
( ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) )
| ~ spl32_20 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f459,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl32_30 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f2133,plain,
( spl32_202
| ~ spl32_20
| ~ spl32_29 ),
inference(avatar_split_clause,[],[f510,f454,f412,f2131]) ).
fof(f2131,plain,
( spl32_202
<=> ! [X0] :
( sz00 = sdtasdt0(smndt0(X0),sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_202])]) ).
fof(f454,plain,
( spl32_29
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_29])]) ).
fof(f510,plain,
( ! [X0] :
( sz00 = sdtasdt0(smndt0(X0),sz00)
| ~ aElement0(X0) )
| ~ spl32_20
| ~ spl32_29 ),
inference(resolution,[],[f455,f413]) ).
fof(f455,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl32_29 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f2086,plain,
( ~ spl32_54
| spl32_56
| ~ spl32_6
| spl32_173 ),
inference(avatar_split_clause,[],[f1777,f1773,f343,f642,f632]) ).
fof(f343,plain,
( spl32_6
<=> ! [X0] :
( aElementOf0(sK9(X0),xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_6])]) ).
fof(f1773,plain,
( spl32_173
<=> aElementOf0(sK9(sK10),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_173])]) ).
fof(f1777,plain,
( sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_6
| spl32_173 ),
inference(resolution,[],[f1775,f344]) ).
fof(f344,plain,
( ! [X0] :
( aElementOf0(sK9(X0),xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_6 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f1775,plain,
( ~ aElementOf0(sK9(sK10),xI)
| spl32_173 ),
inference(avatar_component_clause,[],[f1773]) ).
fof(f2067,plain,
( spl32_201
| ~ spl32_25
| ~ spl32_62 ),
inference(avatar_split_clause,[],[f692,f671,f436,f2065]) ).
fof(f2065,plain,
( spl32_201
<=> ! [X0,X1] :
( ~ sP4(X0,X1)
| aSet0(sdtasasdt0(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_201])]) ).
fof(f436,plain,
( spl32_25
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_25])]) ).
fof(f671,plain,
( spl32_62
<=> ! [X0,X1] :
( sP3(X1,X0,sdtasasdt0(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_62])]) ).
fof(f692,plain,
( ! [X0,X1] :
( ~ sP4(X0,X1)
| aSet0(sdtasasdt0(X0,X1)) )
| ~ spl32_25
| ~ spl32_62 ),
inference(resolution,[],[f672,f437]) ).
fof(f437,plain,
( ! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| aSet0(X2) )
| ~ spl32_25 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f672,plain,
( ! [X0,X1] :
( sP3(X1,X0,sdtasasdt0(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl32_62 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f2063,plain,
( spl32_200
| ~ spl32_4
| ~ spl32_59 ),
inference(avatar_split_clause,[],[f683,f657,f333,f2060]) ).
fof(f2060,plain,
( spl32_200
<=> smndt0(sz10) = sdtasdt0(sz10,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_200])]) ).
fof(f333,plain,
( spl32_4
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_4])]) ).
fof(f657,plain,
( spl32_59
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_59])]) ).
fof(f683,plain,
( smndt0(sz10) = sdtasdt0(sz10,smndt0(sz10))
| ~ spl32_4
| ~ spl32_59 ),
inference(resolution,[],[f658,f335]) ).
fof(f335,plain,
( aElement0(sz10)
| ~ spl32_4 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f658,plain,
( ! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) )
| ~ spl32_59 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f2058,plain,
( spl32_199
| ~ spl32_5
| ~ spl32_59 ),
inference(avatar_split_clause,[],[f682,f657,f338,f2055]) ).
fof(f2055,plain,
( spl32_199
<=> smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_199])]) ).
fof(f338,plain,
( spl32_5
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_5])]) ).
fof(f682,plain,
( smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10))
| ~ spl32_5
| ~ spl32_59 ),
inference(resolution,[],[f658,f340]) ).
fof(f340,plain,
( aElement0(sz00)
| ~ spl32_5 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f2053,plain,
( spl32_198
| ~ spl32_4
| ~ spl32_58 ),
inference(avatar_split_clause,[],[f675,f653,f333,f2050]) ).
fof(f2050,plain,
( spl32_198
<=> smndt0(sz10) = sdtasdt0(smndt0(sz10),sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_198])]) ).
fof(f653,plain,
( spl32_58
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_58])]) ).
fof(f675,plain,
( smndt0(sz10) = sdtasdt0(smndt0(sz10),sz10)
| ~ spl32_4
| ~ spl32_58 ),
inference(resolution,[],[f654,f335]) ).
fof(f654,plain,
( ! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ spl32_58 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f2048,plain,
( spl32_197
| ~ spl32_5
| ~ spl32_58 ),
inference(avatar_split_clause,[],[f674,f653,f338,f2045]) ).
fof(f2045,plain,
( spl32_197
<=> smndt0(sz00) = sdtasdt0(smndt0(sz10),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_197])]) ).
fof(f674,plain,
( smndt0(sz00) = sdtasdt0(smndt0(sz10),sz00)
| ~ spl32_5
| ~ spl32_58 ),
inference(resolution,[],[f654,f340]) ).
fof(f2043,plain,
( spl32_196
| ~ spl32_28
| ~ spl32_46 ),
inference(avatar_split_clause,[],[f605,f560,f450,f2041]) ).
fof(f2041,plain,
( spl32_196
<=> ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_196])]) ).
fof(f450,plain,
( spl32_28
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_28])]) ).
fof(f560,plain,
( spl32_46
<=> ! [X0] :
( aIdeal0(X0)
| aElementOf0(sK17(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_46])]) ).
fof(f605,plain,
( ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK17(X0)) )
| ~ spl32_28
| ~ spl32_46 ),
inference(duplicate_literal_removal,[],[f604]) ).
fof(f604,plain,
( ! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| aElement0(sK17(X0))
| ~ aSet0(X0) )
| ~ spl32_28
| ~ spl32_46 ),
inference(resolution,[],[f561,f451]) ).
fof(f451,plain,
( ! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) )
| ~ spl32_28 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f561,plain,
( ! [X0] :
( aElementOf0(sK17(X0),X0)
| aIdeal0(X0)
| ~ aSet0(X0) )
| ~ spl32_46 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f2012,plain,
( ~ spl32_194
| spl32_195
| ~ spl32_12
| ~ spl32_81 ),
inference(avatar_split_clause,[],[f857,f780,f370,f2009,f2005]) ).
fof(f2005,plain,
( spl32_194
<=> sP8(xa,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_194])]) ).
fof(f2009,plain,
( spl32_195
<=> sP7(xc,xb,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_195])]) ).
fof(f370,plain,
( spl32_12
<=> aGcdOfAnd0(xc,xa,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_12])]) ).
fof(f780,plain,
( spl32_81
<=> ! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_81])]) ).
fof(f857,plain,
( sP7(xc,xb,xa)
| ~ sP8(xa,xb)
| ~ spl32_12
| ~ spl32_81 ),
inference(resolution,[],[f781,f372]) ).
fof(f372,plain,
( aGcdOfAnd0(xc,xa,xb)
| ~ spl32_12 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f781,plain,
( ! [X2,X0,X1] :
( ~ aGcdOfAnd0(X2,X0,X1)
| sP7(X2,X1,X0)
| ~ sP8(X0,X1) )
| ~ spl32_81 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f2003,plain,
( spl32_193
| ~ spl32_3
| ~ spl32_59 ),
inference(avatar_split_clause,[],[f688,f657,f328,f2000]) ).
fof(f2000,plain,
( spl32_193
<=> smndt0(xb) = sdtasdt0(xb,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_193])]) ).
fof(f328,plain,
( spl32_3
<=> aElement0(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_3])]) ).
fof(f688,plain,
( smndt0(xb) = sdtasdt0(xb,smndt0(sz10))
| ~ spl32_3
| ~ spl32_59 ),
inference(resolution,[],[f658,f330]) ).
fof(f330,plain,
( aElement0(xb)
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f1998,plain,
( spl32_192
| ~ spl32_2
| ~ spl32_59 ),
inference(avatar_split_clause,[],[f687,f657,f323,f1995]) ).
fof(f1995,plain,
( spl32_192
<=> smndt0(xa) = sdtasdt0(xa,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_192])]) ).
fof(f323,plain,
( spl32_2
<=> aElement0(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_2])]) ).
fof(f687,plain,
( smndt0(xa) = sdtasdt0(xa,smndt0(sz10))
| ~ spl32_2
| ~ spl32_59 ),
inference(resolution,[],[f658,f325]) ).
fof(f325,plain,
( aElement0(xa)
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1993,plain,
( spl32_191
| ~ spl32_3
| ~ spl32_58 ),
inference(avatar_split_clause,[],[f680,f653,f328,f1990]) ).
fof(f1990,plain,
( spl32_191
<=> smndt0(xb) = sdtasdt0(smndt0(sz10),xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_191])]) ).
fof(f680,plain,
( smndt0(xb) = sdtasdt0(smndt0(sz10),xb)
| ~ spl32_3
| ~ spl32_58 ),
inference(resolution,[],[f654,f330]) ).
fof(f1988,plain,
( spl32_190
| ~ spl32_2
| ~ spl32_58 ),
inference(avatar_split_clause,[],[f679,f653,f323,f1985]) ).
fof(f1985,plain,
( spl32_190
<=> smndt0(xa) = sdtasdt0(smndt0(sz10),xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_190])]) ).
fof(f679,plain,
( smndt0(xa) = sdtasdt0(smndt0(sz10),xa)
| ~ spl32_2
| ~ spl32_58 ),
inference(resolution,[],[f654,f325]) ).
fof(f1982,plain,
( ~ spl32_1
| spl32_189
| ~ spl32_45
| ~ spl32_139 ),
inference(avatar_split_clause,[],[f1761,f1444,f556,f1979,f318]) ).
fof(f318,plain,
( spl32_1
<=> aIdeal0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_1])]) ).
fof(f1979,plain,
( spl32_189
<=> sP2(xI,sK9(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_189])]) ).
fof(f556,plain,
( spl32_45
<=> ! [X2,X0] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_45])]) ).
fof(f1444,plain,
( spl32_139
<=> aElementOf0(sK9(sK11),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_139])]) ).
fof(f1761,plain,
( sP2(xI,sK9(sK11))
| ~ aIdeal0(xI)
| ~ spl32_45
| ~ spl32_139 ),
inference(resolution,[],[f1445,f557]) ).
fof(f557,plain,
( ! [X2,X0] :
( ~ aElementOf0(X2,X0)
| sP2(X0,X2)
| ~ aIdeal0(X0) )
| ~ spl32_45 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f1445,plain,
( aElementOf0(sK9(sK11),xI)
| ~ spl32_139 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f1977,plain,
( ~ spl32_187
| spl32_188
| ~ spl32_15
| ~ spl32_45 ),
inference(avatar_split_clause,[],[f601,f556,f385,f1974,f1970]) ).
fof(f1970,plain,
( spl32_187
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_187])]) ).
fof(f1974,plain,
( spl32_188
<=> sP2(slsdtgt0(xb),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_188])]) ).
fof(f385,plain,
( spl32_15
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_15])]) ).
fof(f601,plain,
( sP2(slsdtgt0(xb),sz00)
| ~ aIdeal0(slsdtgt0(xb))
| ~ spl32_15
| ~ spl32_45 ),
inference(resolution,[],[f557,f387]) ).
fof(f387,plain,
( aElementOf0(sz00,slsdtgt0(xb))
| ~ spl32_15 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f1967,plain,
( ~ spl32_185
| spl32_186
| ~ spl32_13
| ~ spl32_45 ),
inference(avatar_split_clause,[],[f599,f556,f375,f1964,f1960]) ).
fof(f1960,plain,
( spl32_185
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_185])]) ).
fof(f1964,plain,
( spl32_186
<=> sP2(slsdtgt0(xa),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_186])]) ).
fof(f375,plain,
( spl32_13
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_13])]) ).
fof(f599,plain,
( sP2(slsdtgt0(xa),sz00)
| ~ aIdeal0(slsdtgt0(xa))
| ~ spl32_13
| ~ spl32_45 ),
inference(resolution,[],[f557,f377]) ).
fof(f377,plain,
( aElementOf0(sz00,slsdtgt0(xa))
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1934,plain,
( spl32_184
| ~ spl32_4
| ~ spl32_43 ),
inference(avatar_split_clause,[],[f593,f548,f333,f1931]) ).
fof(f1931,plain,
( spl32_184
<=> sz00 = sdtpldt0(smndt0(sz10),sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_184])]) ).
fof(f548,plain,
( spl32_43
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_43])]) ).
fof(f593,plain,
( sz00 = sdtpldt0(smndt0(sz10),sz10)
| ~ spl32_4
| ~ spl32_43 ),
inference(resolution,[],[f549,f335]) ).
fof(f549,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ spl32_43 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f1929,plain,
( spl32_183
| ~ spl32_5
| ~ spl32_43 ),
inference(avatar_split_clause,[],[f592,f548,f338,f1926]) ).
fof(f1926,plain,
( spl32_183
<=> sz00 = sdtpldt0(smndt0(sz00),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_183])]) ).
fof(f592,plain,
( sz00 = sdtpldt0(smndt0(sz00),sz00)
| ~ spl32_5
| ~ spl32_43 ),
inference(resolution,[],[f549,f340]) ).
fof(f1924,plain,
( spl32_182
| ~ spl32_4
| ~ spl32_42 ),
inference(avatar_split_clause,[],[f588,f544,f333,f1921]) ).
fof(f1921,plain,
( spl32_182
<=> sz00 = sdtpldt0(sz10,smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_182])]) ).
fof(f544,plain,
( spl32_42
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_42])]) ).
fof(f588,plain,
( sz00 = sdtpldt0(sz10,smndt0(sz10))
| ~ spl32_4
| ~ spl32_42 ),
inference(resolution,[],[f545,f335]) ).
fof(f545,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ spl32_42 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f1919,plain,
( spl32_181
| ~ spl32_5
| ~ spl32_42 ),
inference(avatar_split_clause,[],[f587,f544,f338,f1916]) ).
fof(f1916,plain,
( spl32_181
<=> sz00 = sdtpldt0(sz00,smndt0(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_181])]) ).
fof(f587,plain,
( sz00 = sdtpldt0(sz00,smndt0(sz00))
| ~ spl32_5
| ~ spl32_42 ),
inference(resolution,[],[f545,f340]) ).
fof(f1890,plain,
( spl32_180
| ~ spl32_3
| ~ spl32_43 ),
inference(avatar_split_clause,[],[f596,f548,f328,f1887]) ).
fof(f1887,plain,
( spl32_180
<=> sz00 = sdtpldt0(smndt0(xb),xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_180])]) ).
fof(f596,plain,
( sz00 = sdtpldt0(smndt0(xb),xb)
| ~ spl32_3
| ~ spl32_43 ),
inference(resolution,[],[f549,f330]) ).
fof(f1885,plain,
( spl32_179
| ~ spl32_2
| ~ spl32_43 ),
inference(avatar_split_clause,[],[f595,f548,f323,f1882]) ).
fof(f1882,plain,
( spl32_179
<=> sz00 = sdtpldt0(smndt0(xa),xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_179])]) ).
fof(f595,plain,
( sz00 = sdtpldt0(smndt0(xa),xa)
| ~ spl32_2
| ~ spl32_43 ),
inference(resolution,[],[f549,f325]) ).
fof(f1880,plain,
( spl32_178
| ~ spl32_3
| ~ spl32_42 ),
inference(avatar_split_clause,[],[f591,f544,f328,f1877]) ).
fof(f1877,plain,
( spl32_178
<=> sz00 = sdtpldt0(xb,smndt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_178])]) ).
fof(f591,plain,
( sz00 = sdtpldt0(xb,smndt0(xb))
| ~ spl32_3
| ~ spl32_42 ),
inference(resolution,[],[f545,f330]) ).
fof(f1875,plain,
( spl32_177
| ~ spl32_2
| ~ spl32_42 ),
inference(avatar_split_clause,[],[f590,f544,f323,f1872]) ).
fof(f1872,plain,
( spl32_177
<=> sz00 = sdtpldt0(xa,smndt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_177])]) ).
fof(f590,plain,
( sz00 = sdtpldt0(xa,smndt0(xa))
| ~ spl32_2
| ~ spl32_42 ),
inference(resolution,[],[f545,f325]) ).
fof(f1870,plain,
( spl32_176
| ~ spl32_17
| ~ spl32_125 ),
inference(avatar_split_clause,[],[f1783,f1153,f395,f1867]) ).
fof(f1867,plain,
( spl32_176
<=> sP1(sK9(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_176])]) ).
fof(f395,plain,
( spl32_17
<=> ! [X0] :
( sP1(X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_17])]) ).
fof(f1153,plain,
( spl32_125
<=> aElement0(sK9(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_125])]) ).
fof(f1783,plain,
( sP1(sK9(sK10))
| ~ spl32_17
| ~ spl32_125 ),
inference(resolution,[],[f1155,f396]) ).
fof(f396,plain,
( ! [X0] :
( ~ aElement0(X0)
| sP1(X0) )
| ~ spl32_17 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f1155,plain,
( aElement0(sK9(sK10))
| ~ spl32_125 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1823,plain,
( ~ spl32_1
| spl32_175
| ~ spl32_45
| ~ spl32_54 ),
inference(avatar_split_clause,[],[f716,f632,f556,f1820,f318]) ).
fof(f1820,plain,
( spl32_175
<=> sP2(xI,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_175])]) ).
fof(f716,plain,
( sP2(xI,sK10)
| ~ aIdeal0(xI)
| ~ spl32_45
| ~ spl32_54 ),
inference(resolution,[],[f634,f557]) ).
fof(f634,plain,
( aElementOf0(sK10,xI)
| ~ spl32_54 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f1782,plain,
( ~ spl32_41
| spl32_174
| ~ spl32_28
| ~ spl32_54 ),
inference(avatar_split_clause,[],[f717,f632,f450,f1779,f514]) ).
fof(f514,plain,
( spl32_41
<=> aSet0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_41])]) ).
fof(f1779,plain,
( spl32_174
<=> aElement0(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_174])]) ).
fof(f717,plain,
( aElement0(sK10)
| ~ aSet0(xI)
| ~ spl32_28
| ~ spl32_54 ),
inference(resolution,[],[f634,f451]) ).
fof(f1776,plain,
( ~ spl32_54
| spl32_56
| spl32_172
| ~ spl32_173
| ~ spl32_8
| ~ spl32_111 ),
inference(avatar_split_clause,[],[f1066,f1053,f351,f1773,f1769,f642,f632]) ).
fof(f351,plain,
( spl32_8
<=> ! [X0] :
( iLess0(sbrdtbr0(sK9(X0)),sbrdtbr0(X0))
| sz00 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_8])]) ).
fof(f1053,plain,
( spl32_111
<=> ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK10))
| ~ aElementOf0(X2,xI)
| sz00 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_111])]) ).
fof(f1066,plain,
( ~ aElementOf0(sK9(sK10),xI)
| sz00 = sK9(sK10)
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_111 ),
inference(resolution,[],[f1054,f352]) ).
fof(f352,plain,
( ! [X0] :
( iLess0(sbrdtbr0(sK9(X0)),sbrdtbr0(X0))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_8 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f1054,plain,
( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK10))
| ~ aElementOf0(X2,xI)
| sz00 = X2 )
| ~ spl32_111 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1763,plain,
( ~ spl32_139
| spl32_140
| spl32_9
| ~ spl32_10
| ~ spl32_8
| ~ spl32_57
| ~ spl32_111 ),
inference(avatar_split_clause,[],[f1758,f1053,f648,f351,f360,f355,f1448,f1444]) ).
fof(f1448,plain,
( spl32_140
<=> sz00 = sK9(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_140])]) ).
fof(f355,plain,
( spl32_9
<=> sz00 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl32_9])]) ).
fof(f360,plain,
( spl32_10
<=> aElementOf0(sK11,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_10])]) ).
fof(f648,plain,
( spl32_57
<=> sK10 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl32_57])]) ).
fof(f1758,plain,
( ~ aElementOf0(sK11,xI)
| sz00 = sK11
| sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| ~ spl32_8
| ~ spl32_57
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1757,f649]) ).
fof(f649,plain,
( sK10 = sK11
| ~ spl32_57 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f1757,plain,
( sz00 = sK11
| sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_57
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1756,f649]) ).
fof(f1756,plain,
( sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_57
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1608,f649]) ).
fof(f1608,plain,
( ~ aElementOf0(sK9(sK11),xI)
| sz00 = sK9(sK10)
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_57
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1066,f649]) ).
fof(f1755,plain,
( ~ spl32_10
| spl32_9
| ~ spl32_7
| ~ spl32_140 ),
inference(avatar_split_clause,[],[f1507,f1448,f347,f355,f360]) ).
fof(f1507,plain,
( sz00 = sK11
| ~ aElementOf0(sK11,xI)
| ~ spl32_7
| ~ spl32_140 ),
inference(trivial_inequality_removal,[],[f1505]) ).
fof(f1505,plain,
( sz00 != sz00
| sz00 = sK11
| ~ aElementOf0(sK11,xI)
| ~ spl32_7
| ~ spl32_140 ),
inference(superposition,[],[f348,f1450]) ).
fof(f1450,plain,
( sz00 = sK9(sK11)
| ~ spl32_140 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1754,plain,
( spl32_171
| ~ spl32_4
| ~ spl32_34 ),
inference(avatar_split_clause,[],[f534,f475,f333,f1751]) ).
fof(f1751,plain,
( spl32_171
<=> sz10 = sdtasdt0(sz10,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_171])]) ).
fof(f475,plain,
( spl32_34
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_34])]) ).
fof(f534,plain,
( sz10 = sdtasdt0(sz10,sz10)
| ~ spl32_4
| ~ spl32_34 ),
inference(resolution,[],[f476,f335]) ).
fof(f476,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 )
| ~ spl32_34 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f1749,plain,
( spl32_170
| ~ spl32_4
| ~ spl32_33 ),
inference(avatar_split_clause,[],[f529,f471,f333,f1746]) ).
fof(f1746,plain,
( spl32_170
<=> sz10 = sdtpldt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_170])]) ).
fof(f471,plain,
( spl32_33
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_33])]) ).
fof(f529,plain,
( sz10 = sdtpldt0(sz00,sz10)
| ~ spl32_4
| ~ spl32_33 ),
inference(resolution,[],[f472,f335]) ).
fof(f472,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 )
| ~ spl32_33 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f1744,plain,
( spl32_169
| ~ spl32_4
| ~ spl32_31 ),
inference(avatar_split_clause,[],[f524,f462,f333,f1741]) ).
fof(f1741,plain,
( spl32_169
<=> sz10 = sdtpldt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_169])]) ).
fof(f462,plain,
( spl32_31
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_31])]) ).
fof(f524,plain,
( sz10 = sdtpldt0(sz10,sz00)
| ~ spl32_4
| ~ spl32_31 ),
inference(resolution,[],[f463,f335]) ).
fof(f463,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl32_31 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f1739,plain,
( spl32_168
| ~ spl32_5
| ~ spl32_31 ),
inference(avatar_split_clause,[],[f523,f462,f338,f1736]) ).
fof(f1736,plain,
( spl32_168
<=> sz00 = sdtpldt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_168])]) ).
fof(f523,plain,
( sz00 = sdtpldt0(sz00,sz00)
| ~ spl32_5
| ~ spl32_31 ),
inference(resolution,[],[f463,f340]) ).
fof(f1734,plain,
( spl32_167
| ~ spl32_4
| ~ spl32_30 ),
inference(avatar_split_clause,[],[f519,f458,f333,f1731]) ).
fof(f1731,plain,
( spl32_167
<=> sz00 = sdtasdt0(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_167])]) ).
fof(f519,plain,
( sz00 = sdtasdt0(sz00,sz10)
| ~ spl32_4
| ~ spl32_30 ),
inference(resolution,[],[f459,f335]) ).
fof(f1729,plain,
( spl32_166
| ~ spl32_4
| ~ spl32_29 ),
inference(avatar_split_clause,[],[f509,f454,f333,f1726]) ).
fof(f1726,plain,
( spl32_166
<=> sz00 = sdtasdt0(sz10,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_166])]) ).
fof(f509,plain,
( sz00 = sdtasdt0(sz10,sz00)
| ~ spl32_4
| ~ spl32_29 ),
inference(resolution,[],[f455,f335]) ).
fof(f1724,plain,
( spl32_165
| ~ spl32_5
| ~ spl32_29 ),
inference(avatar_split_clause,[],[f508,f454,f338,f1721]) ).
fof(f1721,plain,
( spl32_165
<=> sz00 = sdtasdt0(sz00,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_165])]) ).
fof(f508,plain,
( sz00 = sdtasdt0(sz00,sz00)
| ~ spl32_5
| ~ spl32_29 ),
inference(resolution,[],[f455,f340]) ).
fof(f1719,plain,
( spl32_164
| ~ spl32_21
| ~ spl32_26 ),
inference(avatar_split_clause,[],[f443,f440,f416,f1717]) ).
fof(f1717,plain,
( spl32_164
<=> ! [X0] :
( ~ sP1(X0)
| aSet0(slsdtgt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_164])]) ).
fof(f416,plain,
( spl32_21
<=> ! [X0,X1] :
( aSet0(X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_21])]) ).
fof(f440,plain,
( spl32_26
<=> ! [X0] :
( sP0(X0,slsdtgt0(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_26])]) ).
fof(f443,plain,
( ! [X0] :
( ~ sP1(X0)
| aSet0(slsdtgt0(X0)) )
| ~ spl32_21
| ~ spl32_26 ),
inference(resolution,[],[f441,f417]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| aSet0(X1) )
| ~ spl32_21 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f441,plain,
( ! [X0] :
( sP0(X0,slsdtgt0(X0))
| ~ sP1(X0) )
| ~ spl32_26 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f1715,plain,
( spl32_163
| ~ spl32_17
| ~ spl32_20 ),
inference(avatar_split_clause,[],[f420,f412,f395,f1713]) ).
fof(f1713,plain,
( spl32_163
<=> ! [X0] :
( ~ aElement0(X0)
| sP1(smndt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_163])]) ).
fof(f420,plain,
( ! [X0] :
( ~ aElement0(X0)
| sP1(smndt0(X0)) )
| ~ spl32_17
| ~ spl32_20 ),
inference(resolution,[],[f413,f396]) ).
fof(f1711,plain,
( spl32_162
| ~ spl32_18
| ~ spl32_19 ),
inference(avatar_split_clause,[],[f419,f408,f399,f1709]) ).
fof(f1709,plain,
( spl32_162
<=> ! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_162])]) ).
fof(f408,plain,
( spl32_19
<=> ! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_19])]) ).
fof(f419,plain,
( ! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) )
| ~ spl32_18
| ~ spl32_19 ),
inference(resolution,[],[f409,f400]) ).
fof(f409,plain,
( ! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) )
| ~ spl32_19 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1669,plain,
( ~ spl32_1
| spl32_161
| ~ spl32_45
| ~ spl32_144 ),
inference(avatar_split_clause,[],[f1497,f1489,f556,f1666,f318]) ).
fof(f1666,plain,
( spl32_161
<=> sP2(xI,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_161])]) ).
fof(f1489,plain,
( spl32_144
<=> aElementOf0(sz00,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_144])]) ).
fof(f1497,plain,
( sP2(xI,sz00)
| ~ aIdeal0(xI)
| ~ spl32_45
| ~ spl32_144 ),
inference(resolution,[],[f1491,f557]) ).
fof(f1491,plain,
( aElementOf0(sz00,xI)
| ~ spl32_144 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f1630,plain,
( ~ spl32_1
| spl32_160
| ~ spl32_10
| ~ spl32_45 ),
inference(avatar_split_clause,[],[f598,f556,f360,f1627,f318]) ).
fof(f1627,plain,
( spl32_160
<=> sP2(xI,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_160])]) ).
fof(f598,plain,
( sP2(xI,sK11)
| ~ aIdeal0(xI)
| ~ spl32_10
| ~ spl32_45 ),
inference(resolution,[],[f557,f362]) ).
fof(f362,plain,
( aElementOf0(sK11,xI)
| ~ spl32_10 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f1625,plain,
( spl32_159
| ~ spl32_3
| ~ spl32_35 ),
inference(avatar_split_clause,[],[f542,f479,f328,f1622]) ).
fof(f1622,plain,
( spl32_159
<=> xb = sdtasdt0(sz10,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_159])]) ).
fof(f479,plain,
( spl32_35
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_35])]) ).
fof(f542,plain,
( xb = sdtasdt0(sz10,xb)
| ~ spl32_3
| ~ spl32_35 ),
inference(resolution,[],[f480,f330]) ).
fof(f480,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(sz10,X0) = X0 )
| ~ spl32_35 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f1620,plain,
( spl32_158
| ~ spl32_2
| ~ spl32_35 ),
inference(avatar_split_clause,[],[f541,f479,f323,f1617]) ).
fof(f1617,plain,
( spl32_158
<=> xa = sdtasdt0(sz10,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_158])]) ).
fof(f541,plain,
( xa = sdtasdt0(sz10,xa)
| ~ spl32_2
| ~ spl32_35 ),
inference(resolution,[],[f480,f325]) ).
fof(f1615,plain,
( spl32_157
| ~ spl32_3
| ~ spl32_34 ),
inference(avatar_split_clause,[],[f537,f475,f328,f1612]) ).
fof(f1612,plain,
( spl32_157
<=> xb = sdtasdt0(xb,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_157])]) ).
fof(f537,plain,
( xb = sdtasdt0(xb,sz10)
| ~ spl32_3
| ~ spl32_34 ),
inference(resolution,[],[f476,f330]) ).
fof(f1597,plain,
( spl32_9
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144 ),
inference(avatar_split_clause,[],[f1499,f1489,f648,f639,f355]) ).
fof(f639,plain,
( spl32_55
<=> ! [X0] :
( sK10 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_55])]) ).
fof(f1499,plain,
( sz00 = sK11
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144 ),
inference(forward_demodulation,[],[f1495,f649]) ).
fof(f1495,plain,
( sz00 = sK10
| ~ spl32_55
| ~ spl32_144 ),
inference(resolution,[],[f1491,f640]) ).
fof(f640,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sK10 = X0 )
| ~ spl32_55 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f1596,plain,
( spl32_156
| ~ spl32_2
| ~ spl32_34 ),
inference(avatar_split_clause,[],[f536,f475,f323,f1593]) ).
fof(f1593,plain,
( spl32_156
<=> xa = sdtasdt0(xa,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_156])]) ).
fof(f536,plain,
( xa = sdtasdt0(xa,sz10)
| ~ spl32_2
| ~ spl32_34 ),
inference(resolution,[],[f476,f325]) ).
fof(f1589,plain,
( spl32_155
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_154 ),
inference(avatar_split_clause,[],[f1584,f1580,f1489,f648,f639,f1586]) ).
fof(f1586,plain,
( spl32_155
<=> xb = sdtpldt0(sK11,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_155])]) ).
fof(f1580,plain,
( spl32_154
<=> xb = sdtpldt0(sz00,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_154])]) ).
fof(f1584,plain,
( xb = sdtpldt0(sK11,xb)
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_154 ),
inference(forward_demodulation,[],[f1582,f1499]) ).
fof(f1582,plain,
( xb = sdtpldt0(sz00,xb)
| ~ spl32_154 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1583,plain,
( spl32_154
| ~ spl32_3
| ~ spl32_33 ),
inference(avatar_split_clause,[],[f532,f471,f328,f1580]) ).
fof(f532,plain,
( xb = sdtpldt0(sz00,xb)
| ~ spl32_3
| ~ spl32_33 ),
inference(resolution,[],[f472,f330]) ).
fof(f1576,plain,
( spl32_153
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_152 ),
inference(avatar_split_clause,[],[f1571,f1567,f1489,f648,f639,f1573]) ).
fof(f1573,plain,
( spl32_153
<=> xa = sdtpldt0(sK11,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_153])]) ).
fof(f1567,plain,
( spl32_152
<=> xa = sdtpldt0(sz00,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_152])]) ).
fof(f1571,plain,
( xa = sdtpldt0(sK11,xa)
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_152 ),
inference(forward_demodulation,[],[f1569,f1499]) ).
fof(f1569,plain,
( xa = sdtpldt0(sz00,xa)
| ~ spl32_152 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f1570,plain,
( spl32_152
| ~ spl32_2
| ~ spl32_33 ),
inference(avatar_split_clause,[],[f531,f471,f323,f1567]) ).
fof(f531,plain,
( xa = sdtpldt0(sz00,xa)
| ~ spl32_2
| ~ spl32_33 ),
inference(resolution,[],[f472,f325]) ).
fof(f1563,plain,
( spl32_151
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_150 ),
inference(avatar_split_clause,[],[f1558,f1554,f1489,f648,f639,f1560]) ).
fof(f1560,plain,
( spl32_151
<=> xb = sdtpldt0(xb,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_151])]) ).
fof(f1554,plain,
( spl32_150
<=> xb = sdtpldt0(xb,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_150])]) ).
fof(f1558,plain,
( xb = sdtpldt0(xb,sK11)
| ~ spl32_55
| ~ spl32_57
| ~ spl32_144
| ~ spl32_150 ),
inference(forward_demodulation,[],[f1556,f1499]) ).
fof(f1556,plain,
( xb = sdtpldt0(xb,sz00)
| ~ spl32_150 ),
inference(avatar_component_clause,[],[f1554]) ).
fof(f1557,plain,
( spl32_150
| ~ spl32_3
| ~ spl32_31 ),
inference(avatar_split_clause,[],[f527,f462,f328,f1554]) ).
fof(f527,plain,
( xb = sdtpldt0(xb,sz00)
| ~ spl32_3
| ~ spl32_31 ),
inference(resolution,[],[f463,f330]) ).
fof(f1552,plain,
( spl32_9
| ~ spl32_113
| ~ spl32_144 ),
inference(avatar_split_clause,[],[f1494,f1489,f1063,f355]) ).
fof(f1063,plain,
( spl32_113
<=> ! [X0] :
( sK11 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_113])]) ).
fof(f1494,plain,
( sz00 = sK11
| ~ spl32_113
| ~ spl32_144 ),
inference(resolution,[],[f1491,f1064]) ).
fof(f1064,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sK11 = X0 )
| ~ spl32_113 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f1550,plain,
( spl32_149
| ~ spl32_2
| ~ spl32_31 ),
inference(avatar_split_clause,[],[f526,f462,f323,f1547]) ).
fof(f1547,plain,
( spl32_149
<=> xa = sdtpldt0(xa,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_149])]) ).
fof(f526,plain,
( xa = sdtpldt0(xa,sz00)
| ~ spl32_2
| ~ spl32_31 ),
inference(resolution,[],[f463,f325]) ).
fof(f1537,plain,
( spl32_148
| ~ spl32_113
| ~ spl32_144
| ~ spl32_147 ),
inference(avatar_split_clause,[],[f1532,f1528,f1489,f1063,f1534]) ).
fof(f1534,plain,
( spl32_148
<=> sK11 = sdtasdt0(sK11,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_148])]) ).
fof(f1528,plain,
( spl32_147
<=> sz00 = sdtasdt0(sz00,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_147])]) ).
fof(f1532,plain,
( sK11 = sdtasdt0(sK11,xb)
| ~ spl32_113
| ~ spl32_144
| ~ spl32_147 ),
inference(forward_demodulation,[],[f1530,f1494]) ).
fof(f1530,plain,
( sz00 = sdtasdt0(sz00,xb)
| ~ spl32_147 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1531,plain,
( spl32_147
| ~ spl32_3
| ~ spl32_30 ),
inference(avatar_split_clause,[],[f522,f458,f328,f1528]) ).
fof(f522,plain,
( sz00 = sdtasdt0(sz00,xb)
| ~ spl32_3
| ~ spl32_30 ),
inference(resolution,[],[f459,f330]) ).
fof(f1518,plain,
( spl32_146
| ~ spl32_113
| ~ spl32_144
| ~ spl32_145 ),
inference(avatar_split_clause,[],[f1513,f1509,f1489,f1063,f1515]) ).
fof(f1515,plain,
( spl32_146
<=> sK11 = sdtasdt0(sK11,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_146])]) ).
fof(f1509,plain,
( spl32_145
<=> sz00 = sdtasdt0(sz00,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_145])]) ).
fof(f1513,plain,
( sK11 = sdtasdt0(sK11,xa)
| ~ spl32_113
| ~ spl32_144
| ~ spl32_145 ),
inference(forward_demodulation,[],[f1511,f1494]) ).
fof(f1511,plain,
( sz00 = sdtasdt0(sz00,xa)
| ~ spl32_145 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f1512,plain,
( spl32_145
| ~ spl32_2
| ~ spl32_30 ),
inference(avatar_split_clause,[],[f521,f458,f323,f1509]) ).
fof(f521,plain,
( sz00 = sdtasdt0(sz00,xa)
| ~ spl32_2
| ~ spl32_30 ),
inference(resolution,[],[f459,f325]) ).
fof(f1492,plain,
( spl32_144
| ~ spl32_139
| ~ spl32_140 ),
inference(avatar_split_clause,[],[f1487,f1448,f1444,f1489]) ).
fof(f1487,plain,
( aElementOf0(sz00,xI)
| ~ spl32_139
| ~ spl32_140 ),
inference(forward_demodulation,[],[f1445,f1450]) ).
fof(f1486,plain,
( ~ spl32_10
| spl32_9
| ~ spl32_6
| spl32_139 ),
inference(avatar_split_clause,[],[f1452,f1444,f343,f355,f360]) ).
fof(f1452,plain,
( sz00 = sK11
| ~ aElementOf0(sK11,xI)
| ~ spl32_6
| spl32_139 ),
inference(resolution,[],[f1446,f344]) ).
fof(f1446,plain,
( ~ aElementOf0(sK9(sK11),xI)
| spl32_139 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f1485,plain,
( spl32_143
| ~ spl32_3
| ~ spl32_29 ),
inference(avatar_split_clause,[],[f512,f454,f328,f1482]) ).
fof(f1482,plain,
( spl32_143
<=> sz00 = sdtasdt0(xb,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_143])]) ).
fof(f512,plain,
( sz00 = sdtasdt0(xb,sz00)
| ~ spl32_3
| ~ spl32_29 ),
inference(resolution,[],[f455,f330]) ).
fof(f1480,plain,
( spl32_142
| ~ spl32_2
| ~ spl32_29 ),
inference(avatar_split_clause,[],[f511,f454,f323,f1477]) ).
fof(f1477,plain,
( spl32_142
<=> sz00 = sdtasdt0(xa,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_142])]) ).
fof(f511,plain,
( sz00 = sdtasdt0(xa,sz00)
| ~ spl32_2
| ~ spl32_29 ),
inference(resolution,[],[f455,f325]) ).
fof(f1457,plain,
( ~ spl32_41
| spl32_141
| ~ spl32_10
| ~ spl32_28 ),
inference(avatar_split_clause,[],[f503,f450,f360,f1454,f514]) ).
fof(f1454,plain,
( spl32_141
<=> aElement0(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_141])]) ).
fof(f503,plain,
( aElement0(sK11)
| ~ aSet0(xI)
| ~ spl32_10
| ~ spl32_28 ),
inference(resolution,[],[f451,f362]) ).
fof(f1451,plain,
( ~ spl32_139
| spl32_140
| spl32_9
| ~ spl32_10
| ~ spl32_8
| ~ spl32_10
| ~ spl32_55
| ~ spl32_111 ),
inference(avatar_split_clause,[],[f1288,f1053,f639,f360,f351,f360,f355,f1448,f1444]) ).
fof(f1288,plain,
( ~ aElementOf0(sK11,xI)
| sz00 = sK11
| sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| ~ spl32_8
| ~ spl32_10
| ~ spl32_55
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1287,f1164]) ).
fof(f1164,plain,
( sK10 = sK11
| ~ spl32_10
| ~ spl32_55 ),
inference(resolution,[],[f640,f362]) ).
fof(f1287,plain,
( sz00 = sK11
| sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_10
| ~ spl32_55
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1286,f1164]) ).
fof(f1286,plain,
( sz00 = sK9(sK11)
| ~ aElementOf0(sK9(sK11),xI)
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_10
| ~ spl32_55
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1285,f1164]) ).
fof(f1285,plain,
( ~ aElementOf0(sK9(sK11),xI)
| sz00 = sK9(sK10)
| sz00 = sK10
| ~ aElementOf0(sK10,xI)
| ~ spl32_8
| ~ spl32_10
| ~ spl32_55
| ~ spl32_111 ),
inference(forward_demodulation,[],[f1066,f1164]) ).
fof(f1441,plain,
( spl32_57
| ~ spl32_10
| ~ spl32_55 ),
inference(avatar_split_clause,[],[f1164,f639,f360,f648]) ).
fof(f1440,plain,
( spl32_138
| ~ spl32_30
| ~ spl32_103 ),
inference(avatar_split_clause,[],[f1010,f981,f458,f1437]) ).
fof(f1437,plain,
( spl32_138
<=> sz00 = sdtasdt0(sz00,sK9(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_138])]) ).
fof(f981,plain,
( spl32_103
<=> aElement0(sK9(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_103])]) ).
fof(f1010,plain,
( sz00 = sdtasdt0(sz00,sK9(sK11))
| ~ spl32_30
| ~ spl32_103 ),
inference(resolution,[],[f983,f459]) ).
fof(f983,plain,
( aElement0(sK9(sK11))
| ~ spl32_103 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f1411,plain,
( spl32_9
| ~ spl32_10
| ~ spl32_53 ),
inference(avatar_split_clause,[],[f636,f629,f360,f355]) ).
fof(f629,plain,
( spl32_53
<=> ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_53])]) ).
fof(f636,plain,
( sz00 = sK11
| ~ spl32_10
| ~ spl32_53 ),
inference(resolution,[],[f630,f362]) ).
fof(f630,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0 )
| ~ spl32_53 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f1409,plain,
( ~ spl32_1
| spl32_137
| ~ spl32_6
| ~ spl32_45 ),
inference(avatar_split_clause,[],[f597,f556,f343,f1407,f318]) ).
fof(f1407,plain,
( spl32_137
<=> ! [X0] :
( sP2(xI,sK9(X0))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_137])]) ).
fof(f597,plain,
( ! [X0] :
( sP2(xI,sK9(X0))
| ~ aIdeal0(xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_6
| ~ spl32_45 ),
inference(resolution,[],[f557,f344]) ).
fof(f1404,plain,
( spl32_136
| ~ spl32_6
| ~ spl32_10
| ~ spl32_55 ),
inference(avatar_split_clause,[],[f1180,f639,f360,f343,f1402]) ).
fof(f1402,plain,
( spl32_136
<=> ! [X0] :
( sK9(X0) = sK11
| sz00 = X0
| ~ aElementOf0(X0,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_136])]) ).
fof(f1180,plain,
( ! [X0] :
( sK9(X0) = sK11
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_6
| ~ spl32_10
| ~ spl32_55 ),
inference(forward_demodulation,[],[f1165,f1164]) ).
fof(f1165,plain,
( ! [X0] :
( sK9(X0) = sK10
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_6
| ~ spl32_55 ),
inference(resolution,[],[f640,f344]) ).
fof(f1387,plain,
spl32_135,
inference(avatar_split_clause,[],[f266,f1385]) ).
fof(f1385,plain,
( spl32_135
<=> ! [X4,X0,X5,X2,X1] :
( sP5(X0,X1,X2)
| sdtpldt0(X4,X5) != sK21(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK21(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_135])]) ).
fof(f266,plain,
! [X2,X0,X1,X4,X5] :
( sP5(X0,X1,X2)
| sdtpldt0(X4,X5) != sK21(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != sK21(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK21(X0,X1,X2),X2) )
& ( ( sK21(X0,X1,X2) = sdtpldt0(sK22(X0,X1,X2),sK23(X0,X1,X2))
& aElementOf0(sK23(X0,X1,X2),X0)
& aElementOf0(sK22(X0,X1,X2),X1) )
| aElementOf0(sK21(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ( sdtpldt0(sK24(X0,X1,X8),sK25(X0,X1,X8)) = X8
& aElementOf0(sK25(X0,X1,X8),X0)
& aElementOf0(sK24(X0,X1,X8),X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25])],[f161,f164,f163,f162]) ).
fof(f162,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) != sK21(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK21(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK21(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(sK21(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK21(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
=> ( sK21(X0,X1,X2) = sdtpldt0(sK22(X0,X1,X2),sK23(X0,X1,X2))
& aElementOf0(sK23(X0,X1,X2),X0)
& aElementOf0(sK22(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
=> ( sdtpldt0(sK24(X0,X1,X8),sK25(X0,X1,X8)) = X8
& aElementOf0(sK25(X0,X1,X8),X0)
& aElementOf0(sK24(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ( sP5(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) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f160]) ).
fof(f160,plain,
! [X1,X0,X2] :
( ( sP5(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) ) )
| ~ sP5(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X1,X0,X2] :
( sP5(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,[sP5])]) ).
fof(f1383,plain,
spl32_134,
inference(avatar_split_clause,[],[f265,f1381]) ).
fof(f1381,plain,
( spl32_134
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| sK21(X0,X1,X2) = sdtpldt0(sK22(X0,X1,X2),sK23(X0,X1,X2))
| aElementOf0(sK21(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_134])]) ).
fof(f265,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| sK21(X0,X1,X2) = sdtpldt0(sK22(X0,X1,X2),sK23(X0,X1,X2))
| aElementOf0(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f1378,plain,
( spl32_133
| ~ spl32_29
| ~ spl32_103 ),
inference(avatar_split_clause,[],[f1009,f981,f454,f1375]) ).
fof(f1375,plain,
( spl32_133
<=> sz00 = sdtasdt0(sK9(sK11),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_133])]) ).
fof(f1009,plain,
( sz00 = sdtasdt0(sK9(sK11),sz00)
| ~ spl32_29
| ~ spl32_103 ),
inference(resolution,[],[f983,f455]) ).
fof(f1373,plain,
spl32_132,
inference(avatar_split_clause,[],[f257,f1371]) ).
fof(f1371,plain,
( spl32_132
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ aElementOf0(sK20(X0,X1,X2),X0)
| ~ aElementOf0(sK20(X0,X1,X2),X1)
| ~ aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_132])]) ).
fof(f257,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ aElementOf0(sK20(X0,X1,X2),X0)
| ~ aElementOf0(sK20(X0,X1,X2),X1)
| ~ aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ aElementOf0(sK20(X0,X1,X2),X0)
| ~ aElementOf0(sK20(X0,X1,X2),X1)
| ~ aElementOf0(sK20(X0,X1,X2),X2) )
& ( ( aElementOf0(sK20(X0,X1,X2),X0)
& aElementOf0(sK20(X0,X1,X2),X1) )
| aElementOf0(sK20(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) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f157,f158]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK20(X0,X1,X2),X0)
| ~ aElementOf0(sK20(X0,X1,X2),X1)
| ~ aElementOf0(sK20(X0,X1,X2),X2) )
& ( ( aElementOf0(sK20(X0,X1,X2),X0)
& aElementOf0(sK20(X0,X1,X2),X1) )
| aElementOf0(sK20(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ( sP3(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) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f156]) ).
fof(f156,plain,
! [X1,X0,X2] :
( ( sP3(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) )
| ~ sP3(X1,X0,X2) ) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X1,X0,X2] :
( ( sP3(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) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1324,plain,
spl32_131,
inference(avatar_split_clause,[],[f305,f1322]) ).
fof(f1322,plain,
( spl32_131
<=> ! [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,[spl32_131])]) ).
fof(f305,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,[],[f108]) ).
fof(f108,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,[],[f107]) ).
fof(f107,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(f1320,plain,
spl32_130,
inference(avatar_split_clause,[],[f304,f1318]) ).
fof(f1318,plain,
( spl32_130
<=> ! [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,[spl32_130])]) ).
fof(f304,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,[],[f108]) ).
fof(f1292,plain,
( ~ spl32_10
| ~ spl32_10
| spl32_54
| ~ spl32_55 ),
inference(avatar_split_clause,[],[f1290,f639,f632,f360,f360]) ).
fof(f1290,plain,
( ~ aElementOf0(sK11,xI)
| ~ spl32_10
| spl32_54
| ~ spl32_55 ),
inference(forward_demodulation,[],[f633,f1164]) ).
fof(f633,plain,
( ~ aElementOf0(sK10,xI)
| spl32_54 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f1284,plain,
( spl32_129
| ~ spl32_10
| ~ spl32_55
| ~ spl32_56
| ~ spl32_128 ),
inference(avatar_split_clause,[],[f1280,f1274,f642,f639,f360,f1282]) ).
fof(f1282,plain,
( spl32_129
<=> ! [X0,X1] :
( sK11 = X1
| sK11 = sK29(X0,X1)
| iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_129])]) ).
fof(f1274,plain,
( spl32_128
<=> ! [X0,X1] :
( iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = sK29(X0,X1)
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_128])]) ).
fof(f1280,plain,
( ! [X0,X1] :
( sK11 = X1
| sK11 = sK29(X0,X1)
| iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl32_10
| ~ spl32_55
| ~ spl32_56
| ~ spl32_128 ),
inference(forward_demodulation,[],[f1279,f1164]) ).
fof(f1279,plain,
( ! [X0,X1] :
( sK10 = X1
| sK11 = sK29(X0,X1)
| iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl32_10
| ~ spl32_55
| ~ spl32_56
| ~ spl32_128 ),
inference(forward_demodulation,[],[f1278,f643]) ).
fof(f643,plain,
( sz00 = sK10
| ~ spl32_56 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f1278,plain,
( ! [X0,X1] :
( sK11 = sK29(X0,X1)
| iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl32_10
| ~ spl32_55
| ~ spl32_56
| ~ spl32_128 ),
inference(forward_demodulation,[],[f1277,f1164]) ).
fof(f1277,plain,
( ! [X0,X1] :
( sK10 = sK29(X0,X1)
| iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl32_56
| ~ spl32_128 ),
inference(forward_demodulation,[],[f1275,f643]) ).
fof(f1275,plain,
( ! [X0,X1] :
( iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = sK29(X0,X1)
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl32_128 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f1276,plain,
spl32_128,
inference(avatar_split_clause,[],[f280,f1274]) ).
fof(f280,plain,
! [X0,X1] :
( iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = sK29(X0,X1)
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ( ( iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = sK29(X0,X1) )
& sdtpldt0(sdtasdt0(sK28(X0,X1),X1),sK29(X0,X1)) = X0
& aElement0(sK29(X0,X1))
& aElement0(sK28(X0,X1)) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f84,f174]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
=> ( ( iLess0(sbrdtbr0(sK29(X0,X1)),sbrdtbr0(X1))
| sz00 = sK29(X0,X1) )
& sdtpldt0(sdtasdt0(sK28(X0,X1),X1),sK29(X0,X1)) = X0
& aElement0(sK29(X0,X1))
& aElement0(sK28(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( ( sz00 != X1
& aElement0(X1)
& aElement0(X0) )
=> ? [X2,X3] :
( ( sz00 != X3
=> iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).
fof(f1272,plain,
spl32_127,
inference(avatar_split_clause,[],[f233,f1270]) ).
fof(f1270,plain,
( spl32_127
<=> ! [X0,X1,X3] :
( sP0(X0,X1)
| sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3)
| ~ aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_127])]) ).
fof(f233,plain,
! [X3,X0,X1] :
( sP0(X0,X1)
| sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3)
| ~ aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK12(X0,X1),X1) )
& ( ( sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
& aElement0(sK13(X0,X1)) )
| aElementOf0(sK12(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(X0,sK14(X0,X5)) = X5
& aElement0(sK14(X0,X5)) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f135,f138,f137,f136]) ).
fof(f136,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK12(X0,X1),X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = sK12(X0,X1)
& aElement0(X4) )
| aElementOf0(sK12(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0,X1] :
( ? [X4] :
( sdtasdt0(X0,X4) = sK12(X0,X1)
& aElement0(X4) )
=> ( sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
& aElement0(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X0,X5] :
( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(X0,sK14(X0,X5)) = X5
& aElement0(sK14(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1268,plain,
spl32_126,
inference(avatar_split_clause,[],[f232,f1266]) ).
fof(f1266,plain,
( spl32_126
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_126])]) ).
fof(f232,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f1156,plain,
( spl32_56
| spl32_125
| ~ spl32_54
| ~ spl32_92 ),
inference(avatar_split_clause,[],[f943,f902,f632,f1153,f642]) ).
fof(f902,plain,
( spl32_92
<=> ! [X0] :
( aElement0(sK9(X0))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_92])]) ).
fof(f943,plain,
( aElement0(sK9(sK10))
| sz00 = sK10
| ~ spl32_54
| ~ spl32_92 ),
inference(resolution,[],[f903,f634]) ).
fof(f903,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| aElement0(sK9(X0))
| sz00 = X0 )
| ~ spl32_92 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1151,plain,
spl32_124,
inference(avatar_split_clause,[],[f279,f1149]) ).
fof(f1149,plain,
( spl32_124
<=> ! [X0,X1] :
( sdtpldt0(sdtasdt0(sK28(X0,X1),X1),sK29(X0,X1)) = X0
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_124])]) ).
fof(f279,plain,
! [X0,X1] :
( sdtpldt0(sdtasdt0(sK28(X0,X1),X1),sK29(X0,X1)) = X0
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f1147,plain,
spl32_123,
inference(avatar_split_clause,[],[f261,f1145]) ).
fof(f1145,plain,
( spl32_123
<=> ! [X0,X8,X2,X1] :
( sdtpldt0(sK24(X0,X1,X8),sK25(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_123])]) ).
fof(f261,plain,
! [X2,X0,X1,X8] :
( sdtpldt0(sK24(X0,X1,X8),sK25(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f1143,plain,
spl32_122,
inference(avatar_split_clause,[],[f256,f1141]) ).
fof(f1141,plain,
( spl32_122
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK20(X0,X1,X2),X0)
| aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_122])]) ).
fof(f256,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK20(X0,X1,X2),X0)
| aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f1139,plain,
spl32_121,
inference(avatar_split_clause,[],[f255,f1137]) ).
fof(f1137,plain,
( spl32_121
<=> ! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK20(X0,X1,X2),X1)
| aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_121])]) ).
fof(f255,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| aElementOf0(sK20(X0,X1,X2),X1)
| aElementOf0(sK20(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f1094,plain,
spl32_120,
inference(avatar_split_clause,[],[f303,f1092]) ).
fof(f1092,plain,
( spl32_120
<=> ! [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,[spl32_120])]) ).
fof(f303,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,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(f1090,plain,
spl32_119,
inference(avatar_split_clause,[],[f302,f1088]) ).
fof(f1088,plain,
( spl32_119
<=> ! [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,[spl32_119])]) ).
fof(f302,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f103]) ).
fof(f103,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(f1086,plain,
spl32_118,
inference(avatar_split_clause,[],[f248,f1084]) ).
fof(f1084,plain,
( spl32_118
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK18(X0,X1),X0)
| ~ aElementOf0(sK19(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_118])]) ).
fof(f248,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK18(X0,X1),X0)
| ~ aElementOf0(sK19(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( X0 = X1
| ( ~ aElementOf0(sK18(X0,X1),X0)
& aElementOf0(sK18(X0,X1),X1) )
| ( ~ aElementOf0(sK19(X0,X1),X1)
& aElementOf0(sK19(X0,X1),X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f72,f152,f151]) ).
fof(f151,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK18(X0,X1),X0)
& aElementOf0(sK18(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sK19(X0,X1),X1)
& aElementOf0(sK19(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f72,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,[],[f71]) ).
fof(f71,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,[],[f52]) ).
fof(f52,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(f1082,plain,
spl32_117,
inference(avatar_split_clause,[],[f247,f1080]) ).
fof(f1080,plain,
( spl32_117
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK18(X0,X1),X0)
| aElementOf0(sK19(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_117])]) ).
fof(f247,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK18(X0,X1),X0)
| aElementOf0(sK19(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f1078,plain,
spl32_116,
inference(avatar_split_clause,[],[f246,f1076]) ).
fof(f1076,plain,
( spl32_116
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK18(X0,X1),X1)
| ~ aElementOf0(sK19(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_116])]) ).
fof(f246,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK18(X0,X1),X1)
| ~ aElementOf0(sK19(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f1074,plain,
spl32_115,
inference(avatar_split_clause,[],[f245,f1072]) ).
fof(f1072,plain,
( spl32_115
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK18(X0,X1),X1)
| aElementOf0(sK19(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_115])]) ).
fof(f245,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK18(X0,X1),X1)
| aElementOf0(sK19(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f1070,plain,
spl32_114,
inference(avatar_split_clause,[],[f240,f1068]) ).
fof(f1068,plain,
( spl32_114
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
| ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_114])]) ).
fof(f240,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
| ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
& aElement0(sK15(X0,X1)) )
| ( ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0)
& aElementOf0(sK16(X0,X1),X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f142,f144,f143]) ).
fof(f143,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
& aElement0(sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0)
& aElementOf0(sK16(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0,X1] :
( ( sP2(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) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( ( sP2(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) ) )
| ~ sP2(X0,X1) ) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( ( sP2(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) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( sP2(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,[sP2])]) ).
fof(f1065,plain,
( spl32_113
| ~ spl32_10
| ~ spl32_53 ),
inference(avatar_split_clause,[],[f1056,f629,f360,f1063]) ).
fof(f1056,plain,
( ! [X0] :
( sK11 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_10
| ~ spl32_53 ),
inference(forward_demodulation,[],[f630,f636]) ).
fof(f1061,plain,
( spl32_112
| ~ spl32_17
| ~ spl32_103 ),
inference(avatar_split_clause,[],[f1008,f981,f395,f1058]) ).
fof(f1058,plain,
( spl32_112
<=> sP1(sK9(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_112])]) ).
fof(f1008,plain,
( sP1(sK9(sK11))
| ~ spl32_17
| ~ spl32_103 ),
inference(resolution,[],[f983,f396]) ).
fof(f1055,plain,
( spl32_53
| spl32_111 ),
inference(avatar_split_clause,[],[f203,f1053,f629]) ).
fof(f203,plain,
! [X2,X0] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK10))
| sz00 = X2
| ~ aElementOf0(X2,xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK10))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
& sz00 != sK10
& aElementOf0(sK10,xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f59,f126]) ).
fof(f126,plain,
( ? [X1] :
( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
& sz00 != X1
& aElementOf0(X1,xI) )
=> ( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK10))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
& sz00 != sK10
& aElementOf0(sK10,xI) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
& sz00 != X1
& aElementOf0(X1,xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
& sz00 != X1
& aElementOf0(X1,xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ( sz00 != X0
& aElementOf0(X0,xI) )
=> ? [X1] :
( ! [X2] :
( ( sz00 != X2
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& sz00 != X1
& aElementOf0(X1,xI) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f1028,plain,
spl32_110,
inference(avatar_split_clause,[],[f301,f1026]) ).
fof(f1026,plain,
( spl32_110
<=> ! [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,[spl32_110])]) ).
fof(f301,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,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,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,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(f1024,plain,
spl32_109,
inference(avatar_split_clause,[],[f300,f1022]) ).
fof(f1022,plain,
( spl32_109
<=> ! [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,[spl32_109])]) ).
fof(f300,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f1007,plain,
spl32_108,
inference(avatar_split_clause,[],[f298,f1005]) ).
fof(f1005,plain,
( spl32_108
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ doDivides0(sK31(X0,X1,X2),X0)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_108])]) ).
fof(f298,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ doDivides0(sK31(X0,X1,X2),X0)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ~ doDivides0(sK31(X0,X1,X2),X0)
& aDivisorOf0(sK31(X0,X1,X2),X1)
& aDivisorOf0(sK31(X0,X1,X2),X2) )
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) )
& ( ( ! [X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2) )
& aDivisorOf0(X0,X1)
& aDivisorOf0(X0,X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f184,f185]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ doDivides0(X3,X0)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2) )
=> ( ~ doDivides0(sK31(X0,X1,X2),X0)
& aDivisorOf0(sK31(X0,X1,X2),X1)
& aDivisorOf0(sK31(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ? [X3] :
( ~ doDivides0(X3,X0)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2) )
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) )
& ( ( ! [X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2) )
& aDivisorOf0(X0,X1)
& aDivisorOf0(X0,X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f183]) ).
fof(f183,plain,
! [X2,X1,X0] :
( ( sP7(X2,X1,X0)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ sP7(X2,X1,X0) ) ),
inference(flattening,[],[f182]) ).
fof(f182,plain,
! [X2,X1,X0] :
( ( sP7(X2,X1,X0)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ sP7(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X2,X1,X0] :
( sP7(X2,X1,X0)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f1003,plain,
spl32_107,
inference(avatar_split_clause,[],[f297,f1001]) ).
fof(f1001,plain,
( spl32_107
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| aDivisorOf0(sK31(X0,X1,X2),X1)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_107])]) ).
fof(f297,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| aDivisorOf0(sK31(X0,X1,X2),X1)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f999,plain,
spl32_106,
inference(avatar_split_clause,[],[f296,f997]) ).
fof(f997,plain,
( spl32_106
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| aDivisorOf0(sK31(X0,X1,X2),X2)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_106])]) ).
fof(f296,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| aDivisorOf0(sK31(X0,X1,X2),X2)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f995,plain,
spl32_105,
inference(avatar_split_clause,[],[f264,f993]) ).
fof(f993,plain,
( spl32_105
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| aElementOf0(sK23(X0,X1,X2),X0)
| aElementOf0(sK21(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_105])]) ).
fof(f264,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| aElementOf0(sK23(X0,X1,X2),X0)
| aElementOf0(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f991,plain,
spl32_104,
inference(avatar_split_clause,[],[f263,f989]) ).
fof(f989,plain,
( spl32_104
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| aElementOf0(sK22(X0,X1,X2),X1)
| aElementOf0(sK21(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_104])]) ).
fof(f263,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| aElementOf0(sK22(X0,X1,X2),X1)
| aElementOf0(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f984,plain,
( spl32_9
| spl32_103
| ~ spl32_10
| ~ spl32_92 ),
inference(avatar_split_clause,[],[f941,f902,f360,f981,f355]) ).
fof(f941,plain,
( aElement0(sK9(sK11))
| sz00 = sK11
| ~ spl32_10
| ~ spl32_92 ),
inference(resolution,[],[f903,f362]) ).
fof(f977,plain,
spl32_102,
inference(avatar_split_clause,[],[f309,f975]) ).
fof(f975,plain,
( spl32_102
<=> ! [X10,X0,X9,X2,X1] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_102])]) ).
fof(f309,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ),
inference(equality_resolution,[],[f262]) ).
fof(f262,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f973,plain,
spl32_101,
inference(avatar_split_clause,[],[f285,f971]) ).
fof(f971,plain,
( spl32_101
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_101])]) ).
fof(f285,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,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(f969,plain,
spl32_100,
inference(avatar_split_clause,[],[f274,f967]) ).
fof(f967,plain,
( spl32_100
<=> ! [X0,X3,X2,X1] :
( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X3,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_100])]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X3,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X2,X1)
& aElement0(sK26(X0,X1,X2,X3)) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f169,f170]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
=> ( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X2,X1)
& aElement0(sK26(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f169,plain,
! [X0,X1] :
( ! [X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f168]) ).
fof(f168,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP6(X1,X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP6(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f965,plain,
spl32_99,
inference(avatar_split_clause,[],[f273,f963]) ).
fof(f963,plain,
( spl32_99
<=> ! [X0,X3,X2,X1] :
( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X2,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_99])]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK26(X0,X1,X2,X3),X2,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f961,plain,
spl32_98,
inference(avatar_split_clause,[],[f269,f959]) ).
fof(f959,plain,
( spl32_98
<=> ! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_98])]) ).
fof(f269,plain,
! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP5(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP5(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP5(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f76,f117]) ).
fof(f76,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,[],[f75]) ).
fof(f75,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(f957,plain,
spl32_97,
inference(avatar_split_clause,[],[f239,f955]) ).
fof(f955,plain,
( spl32_97
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
| aElementOf0(sK16(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_97])]) ).
fof(f239,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK15(X0,X1),X1),X0)
| aElementOf0(sK16(X0,X1),X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f937,plain,
spl32_96,
inference(avatar_split_clause,[],[f289,f935]) ).
fof(f935,plain,
( spl32_96
<=> ! [X0,X1] :
( sdtasdt0(X0,sK30(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_96])]) ).
fof(f289,plain,
! [X0,X1] :
( sdtasdt0(X0,sK30(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ( sdtasdt0(X0,sK30(X0,X1)) = X1
& aElement0(sK30(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f178,f179]) ).
fof(f179,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
=> ( sdtasdt0(X0,sK30(X0,X1)) = X1
& aElement0(sK30(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f933,plain,
spl32_95,
inference(avatar_split_clause,[],[f276,f931]) ).
fof(f931,plain,
( spl32_95
<=> ! [X0,X1] :
( sP6(X1,X0)
| ~ aElementOf0(sK27(X0,X1),sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_95])]) ).
fof(f276,plain,
! [X0,X1] :
( sP6(X1,X0)
| ~ aElementOf0(sK27(X0,X1),sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f173,plain,
! [X0,X1] :
( sP6(X1,X0)
| ( ~ aElementOf0(sK27(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK27(X0,X1)) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f120,f172]) ).
fof(f172,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
=> ( ~ aElementOf0(sK27(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK27(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0,X1] :
( sP6(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(definition_folding,[],[f82,f119]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(X2,sdtpldt1(X0,X1)) )
=> ! [X3,X4] :
( ( aElement0(X4)
& aElement0(X3) )
=> ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) ) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(X2,sdtpldt1(X0,X1)) )
=> ! [X2,X3] :
( ( aElement0(X3)
& aElement0(X2) )
=> ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X1)
& sdteqdtlpzmzozddtrp0(X4,X2,X0)
& aElement0(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).
fof(f929,plain,
spl32_94,
inference(avatar_split_clause,[],[f238,f927]) ).
fof(f927,plain,
( spl32_94
<=> ! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK15(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_94])]) ).
fof(f238,plain,
! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK15(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK16(X0,X1)),X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f925,plain,
spl32_93,
inference(avatar_split_clause,[],[f231,f923]) ).
fof(f923,plain,
( spl32_93
<=> ! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK13(X0,X1))
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_93])]) ).
fof(f231,plain,
! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK13(X0,X1))
| aElementOf0(sK12(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f904,plain,
( ~ spl32_41
| spl32_92
| ~ spl32_6
| ~ spl32_28 ),
inference(avatar_split_clause,[],[f502,f450,f343,f902,f514]) ).
fof(f502,plain,
( ! [X0] :
( aElement0(sK9(X0))
| ~ aSet0(xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) )
| ~ spl32_6
| ~ spl32_28 ),
inference(resolution,[],[f451,f344]) ).
fof(f898,plain,
spl32_91,
inference(avatar_split_clause,[],[f312,f896]) ).
fof(f896,plain,
( spl32_91
<=> ! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_91])]) ).
fof(f312,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f290]) ).
fof(f290,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f894,plain,
spl32_90,
inference(avatar_split_clause,[],[f295,f892]) ).
fof(f892,plain,
( spl32_90
<=> ! [X2,X4,X0,X1] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_90])]) ).
fof(f295,plain,
! [X2,X0,X1,X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f890,plain,
spl32_89,
inference(avatar_split_clause,[],[f272,f888]) ).
fof(f888,plain,
( spl32_89
<=> ! [X0,X3,X2,X1] :
( aElement0(sK26(X0,X1,X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_89])]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( aElement0(sK26(X0,X1,X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f886,plain,
spl32_88,
inference(avatar_split_clause,[],[f260,f884]) ).
fof(f884,plain,
( spl32_88
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK25(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_88])]) ).
fof(f260,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK25(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f882,plain,
spl32_87,
inference(avatar_split_clause,[],[f259,f880]) ).
fof(f880,plain,
( spl32_87
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK24(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_87])]) ).
fof(f259,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK24(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f878,plain,
spl32_86,
inference(avatar_split_clause,[],[f254,f876]) ).
fof(f876,plain,
( spl32_86
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_86])]) ).
fof(f254,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f874,plain,
spl32_85,
inference(avatar_split_clause,[],[f229,f872]) ).
fof(f872,plain,
( spl32_85
<=> ! [X5,X0,X1] :
( sdtasdt0(X0,sK14(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_85])]) ).
fof(f229,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK14(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f866,plain,
spl32_84,
inference(avatar_split_clause,[],[f250,f864]) ).
fof(f864,plain,
( spl32_84
<=> ! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_84])]) ).
fof(f250,plain,
! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2) )
& ( sP3(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP3(X1,X0,X2) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f862,plain,
spl32_83,
inference(avatar_split_clause,[],[f237,f860]) ).
fof(f860,plain,
( spl32_83
<=> ! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK15(X0,X1))
| aElementOf0(sK16(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_83])]) ).
fof(f237,plain,
! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK15(X0,X1))
| aElementOf0(sK16(X0,X1),X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f786,plain,
spl32_82,
inference(avatar_split_clause,[],[f292,f784]) ).
fof(f784,plain,
( spl32_82
<=> ! [X2,X0,X1] :
( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_82])]) ).
fof(f292,plain,
! [X2,X0,X1] :
( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0) )
& ( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> sP7(X2,X1,X0) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f782,plain,
spl32_81,
inference(avatar_split_clause,[],[f291,f780]) ).
fof(f291,plain,
! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f778,plain,
spl32_80,
inference(avatar_split_clause,[],[f288,f776]) ).
fof(f776,plain,
( spl32_80
<=> ! [X0,X1] :
( aElement0(sK30(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_80])]) ).
fof(f288,plain,
! [X0,X1] :
( aElement0(sK30(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f774,plain,
spl32_79,
inference(avatar_split_clause,[],[f287,f772]) ).
fof(f772,plain,
( spl32_79
<=> ! [X0,X1] :
( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_79])]) ).
fof(f287,plain,
! [X0,X1] :
( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( ( ( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1) )
& ( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRel) ).
fof(f770,plain,
spl32_78,
inference(avatar_split_clause,[],[f286,f768]) ).
fof(f768,plain,
( spl32_78
<=> ! [X0,X1] :
( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_78])]) ).
fof(f286,plain,
! [X0,X1] :
( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f766,plain,
spl32_77,
inference(avatar_split_clause,[],[f284,f764]) ).
fof(f764,plain,
( spl32_77
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_77])]) ).
fof(f284,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,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(f762,plain,
( spl32_76
| ~ spl32_4
| ~ spl32_17 ),
inference(avatar_split_clause,[],[f403,f395,f333,f759]) ).
fof(f759,plain,
( spl32_76
<=> sP1(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_76])]) ).
fof(f403,plain,
( sP1(sz10)
| ~ spl32_4
| ~ spl32_17 ),
inference(resolution,[],[f396,f335]) ).
fof(f757,plain,
spl32_75,
inference(avatar_split_clause,[],[f283,f755]) ).
fof(f755,plain,
( spl32_75
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_75])]) ).
fof(f283,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,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(f753,plain,
spl32_74,
inference(avatar_split_clause,[],[f278,f751]) ).
fof(f751,plain,
( spl32_74
<=> ! [X0,X1] :
( aElement0(sK29(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_74])]) ).
fof(f278,plain,
! [X0,X1] :
( aElement0(sK29(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f749,plain,
spl32_73,
inference(avatar_split_clause,[],[f277,f747]) ).
fof(f747,plain,
( spl32_73
<=> ! [X0,X1] :
( aElement0(sK28(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_73])]) ).
fof(f277,plain,
! [X0,X1] :
( aElement0(sK28(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f745,plain,
spl32_72,
inference(avatar_split_clause,[],[f275,f743]) ).
fof(f743,plain,
( spl32_72
<=> ! [X0,X1] :
( sP6(X1,X0)
| aElement0(sK27(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_72])]) ).
fof(f275,plain,
! [X0,X1] :
( sP6(X1,X0)
| aElement0(sK27(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f741,plain,
spl32_71,
inference(avatar_split_clause,[],[f235,f739]) ).
fof(f739,plain,
( spl32_71
<=> ! [X5,X0,X1] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_71])]) ).
fof(f235,plain,
! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f729,plain,
spl32_70,
inference(avatar_split_clause,[],[f310,f727]) ).
fof(f727,plain,
( spl32_70
<=> ! [X0,X1] :
( sP5(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_70])]) ).
fof(f310,plain,
! [X0,X1] :
( sP5(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f268]) ).
fof(f268,plain,
! [X2,X0,X1] :
( sP5(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f725,plain,
spl32_69,
inference(avatar_split_clause,[],[f307,f723]) ).
fof(f723,plain,
( spl32_69
<=> ! [X6,X0,X1] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_69])]) ).
fof(f307,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| ~ sP0(X0,X1) ),
inference(equality_resolution,[],[f230]) ).
fof(f230,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f721,plain,
spl32_68,
inference(avatar_split_clause,[],[f253,f719]) ).
fof(f719,plain,
( spl32_68
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_68])]) ).
fof(f253,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f713,plain,
( spl32_67
| ~ spl32_10
| ~ spl32_53
| ~ spl32_60 ),
inference(avatar_split_clause,[],[f665,f661,f629,f360,f710]) ).
fof(f710,plain,
( spl32_67
<=> sP1(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_67])]) ).
fof(f661,plain,
( spl32_60
<=> sP1(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_60])]) ).
fof(f665,plain,
( sP1(sK11)
| ~ spl32_10
| ~ spl32_53
| ~ spl32_60 ),
inference(forward_demodulation,[],[f663,f636]) ).
fof(f663,plain,
( sP1(sz00)
| ~ spl32_60 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f708,plain,
spl32_66,
inference(avatar_split_clause,[],[f252,f706]) ).
fof(f706,plain,
( spl32_66
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_66])]) ).
fof(f252,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f704,plain,
spl32_65,
inference(avatar_split_clause,[],[f236,f702]) ).
fof(f702,plain,
( spl32_65
<=> ! [X4,X0,X1] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_65])]) ).
fof(f236,plain,
! [X0,X1,X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f700,plain,
spl32_64,
inference(avatar_split_clause,[],[f228,f698]) ).
fof(f698,plain,
( spl32_64
<=> ! [X5,X0,X1] :
( aElement0(sK14(X0,X5))
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_64])]) ).
fof(f228,plain,
! [X0,X1,X5] :
( aElement0(sK14(X0,X5))
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f696,plain,
spl32_63,
inference(avatar_split_clause,[],[f224,f694]) ).
fof(f694,plain,
( spl32_63
<=> ! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_63])]) ).
fof(f224,plain,
! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(f673,plain,
spl32_62,
inference(avatar_split_clause,[],[f308,f671]) ).
fof(f308,plain,
! [X0,X1] :
( sP3(X1,X0,sdtasasdt0(X0,X1))
| ~ sP4(X0,X1) ),
inference(equality_resolution,[],[f249]) ).
fof(f249,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f669,plain,
spl32_61,
inference(avatar_split_clause,[],[f226,f667]) ).
fof(f667,plain,
( spl32_61
<=> ! [X0,X1] :
( slsdtgt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_61])]) ).
fof(f226,plain,
! [X0,X1] :
( slsdtgt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| slsdtgt0(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f664,plain,
( spl32_60
| ~ spl32_5
| ~ spl32_17 ),
inference(avatar_split_clause,[],[f402,f395,f338,f661]) ).
fof(f402,plain,
( sP1(sz00)
| ~ spl32_5
| ~ spl32_17 ),
inference(resolution,[],[f396,f340]) ).
fof(f659,plain,
spl32_59,
inference(avatar_split_clause,[],[f221,f657]) ).
fof(f221,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,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(f655,plain,
spl32_58,
inference(avatar_split_clause,[],[f220,f653]) ).
fof(f220,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f651,plain,
( ~ spl32_57
| ~ spl32_10
| ~ spl32_53
| spl32_56 ),
inference(avatar_split_clause,[],[f646,f642,f629,f360,f648]) ).
fof(f646,plain,
( sK10 != sK11
| ~ spl32_10
| ~ spl32_53
| spl32_56 ),
inference(forward_demodulation,[],[f644,f636]) ).
fof(f644,plain,
( sz00 != sK10
| spl32_56 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f645,plain,
( spl32_55
| ~ spl32_56 ),
inference(avatar_split_clause,[],[f315,f642,f639]) ).
fof(f315,plain,
! [X0] :
( sz00 != sK10
| sK10 = X0
| ~ aElementOf0(X0,xI) ),
inference(inner_rewriting,[],[f202]) ).
fof(f202,plain,
! [X0] :
( sz00 != sK10
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f127]) ).
fof(f635,plain,
( spl32_53
| spl32_54 ),
inference(avatar_split_clause,[],[f201,f632,f629]) ).
fof(f201,plain,
! [X0] :
( aElementOf0(sK10,xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f127]) ).
fof(f586,plain,
spl32_52,
inference(avatar_split_clause,[],[f311,f584]) ).
fof(f584,plain,
( spl32_52
<=> ! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_52])]) ).
fof(f311,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f267]) ).
fof(f267,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f582,plain,
spl32_51,
inference(avatar_split_clause,[],[f282,f580]) ).
fof(f580,plain,
( spl32_51
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_51])]) ).
fof(f282,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,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(f578,plain,
spl32_50,
inference(avatar_split_clause,[],[f281,f576]) ).
fof(f576,plain,
( spl32_50
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_50])]) ).
fof(f281,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,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(f574,plain,
spl32_49,
inference(avatar_split_clause,[],[f271,f572]) ).
fof(f572,plain,
( spl32_49
<=> ! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_49])]) ).
fof(f271,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,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(f570,plain,
spl32_48,
inference(avatar_split_clause,[],[f270,f568]) ).
fof(f270,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,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(f566,plain,
spl32_47,
inference(avatar_split_clause,[],[f244,f564]) ).
fof(f564,plain,
( spl32_47
<=> ! [X0] :
( aIdeal0(X0)
| ~ sP2(X0,sK17(X0))
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_47])]) ).
fof(f244,plain,
! [X0] :
( aIdeal0(X0)
| ~ sP2(X0,sK17(X0))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ~ sP2(X0,sK17(X0))
& aElementOf0(sK17(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f148,f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
=> ( ~ sP2(X0,sK17(X0))
& aElementOf0(sK17(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(definition_folding,[],[f70,f112]) ).
fof(f70,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,[],[f51]) ).
fof(f51,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(f562,plain,
spl32_46,
inference(avatar_split_clause,[],[f243,f560]) ).
fof(f243,plain,
! [X0] :
( aIdeal0(X0)
| aElementOf0(sK17(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f558,plain,
spl32_45,
inference(avatar_split_clause,[],[f242,f556]) ).
fof(f242,plain,
! [X2,X0] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f554,plain,
spl32_44,
inference(avatar_split_clause,[],[f223,f552]) ).
fof(f552,plain,
( spl32_44
<=> ! [X0,X1] :
( doDivides0(X1,X0)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_44])]) ).
fof(f223,plain,
! [X0,X1] :
( doDivides0(X1,X0)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f550,plain,
spl32_43,
inference(avatar_split_clause,[],[f219,f548]) ).
fof(f219,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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(f546,plain,
spl32_42,
inference(avatar_split_clause,[],[f218,f544]) ).
fof(f218,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f517,plain,
( spl32_41
| ~ spl32_1
| ~ spl32_18 ),
inference(avatar_split_clause,[],[f406,f399,f318,f514]) ).
fof(f406,plain,
( aSet0(xI)
| ~ spl32_1
| ~ spl32_18 ),
inference(resolution,[],[f400,f320]) ).
fof(f320,plain,
( aIdeal0(xI)
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f501,plain,
spl32_40,
inference(avatar_split_clause,[],[f299,f499]) ).
fof(f499,plain,
( spl32_40
<=> ! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_40])]) ).
fof(f299,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f100,f122,f121]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
=> doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefGCD) ).
fof(f497,plain,
spl32_39,
inference(avatar_split_clause,[],[f294,f495]) ).
fof(f495,plain,
( spl32_39
<=> ! [X2,X0,X1] :
( aDivisorOf0(X0,X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_39])]) ).
fof(f294,plain,
! [X2,X0,X1] :
( aDivisorOf0(X0,X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f493,plain,
spl32_38,
inference(avatar_split_clause,[],[f293,f491]) ).
fof(f491,plain,
( spl32_38
<=> ! [X2,X0,X1] :
( aDivisorOf0(X0,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_38])]) ).
fof(f293,plain,
! [X2,X0,X1] :
( aDivisorOf0(X0,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f489,plain,
spl32_37,
inference(avatar_split_clause,[],[f258,f487]) ).
fof(f487,plain,
( spl32_37
<=> ! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_37])]) ).
fof(f258,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f74,f115,f114]) ).
fof(f74,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,[],[f73]) ).
fof(f73,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(f485,plain,
spl32_36,
inference(avatar_split_clause,[],[f222,f483]) ).
fof(f483,plain,
( spl32_36
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_36])]) ).
fof(f222,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f481,plain,
spl32_35,
inference(avatar_split_clause,[],[f217,f479]) ).
fof(f217,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,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(f477,plain,
spl32_34,
inference(avatar_split_clause,[],[f216,f475]) ).
fof(f216,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f473,plain,
spl32_33,
inference(avatar_split_clause,[],[f215,f471]) ).
fof(f215,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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(f469,plain,
( spl32_32
| ~ spl32_3
| ~ spl32_17 ),
inference(avatar_split_clause,[],[f405,f395,f328,f466]) ).
fof(f466,plain,
( spl32_32
<=> sP1(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_32])]) ).
fof(f405,plain,
( sP1(xb)
| ~ spl32_3
| ~ spl32_17 ),
inference(resolution,[],[f396,f330]) ).
fof(f464,plain,
spl32_31,
inference(avatar_split_clause,[],[f214,f462]) ).
fof(f214,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f460,plain,
spl32_30,
inference(avatar_split_clause,[],[f213,f458]) ).
fof(f213,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,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(f456,plain,
spl32_29,
inference(avatar_split_clause,[],[f212,f454]) ).
fof(f212,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f452,plain,
spl32_28,
inference(avatar_split_clause,[],[f209,f450]) ).
fof(f209,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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(f448,plain,
spl32_27,
inference(avatar_split_clause,[],[f193,f445]) ).
fof(f445,plain,
( spl32_27
<=> xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_27])]) ).
fof(f193,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f442,plain,
spl32_26,
inference(avatar_split_clause,[],[f306,f440]) ).
fof(f306,plain,
! [X0] :
( sP0(X0,slsdtgt0(X0))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( sP0(X0,X1)
| slsdtgt0(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f438,plain,
spl32_25,
inference(avatar_split_clause,[],[f251,f436]) ).
fof(f251,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f434,plain,
( spl32_24
| ~ spl32_2
| ~ spl32_17 ),
inference(avatar_split_clause,[],[f404,f395,f323,f431]) ).
fof(f431,plain,
( spl32_24
<=> sP1(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_24])]) ).
fof(f404,plain,
( sP1(xa)
| ~ spl32_2
| ~ spl32_17 ),
inference(resolution,[],[f396,f325]) ).
fof(f429,plain,
( ~ spl32_22
| ~ spl32_23 ),
inference(avatar_split_clause,[],[f314,f426,f422]) ).
fof(f422,plain,
( spl32_22
<=> xa = xb ),
introduced(avatar_definition,[new_symbols(naming,[spl32_22])]) ).
fof(f426,plain,
( spl32_23
<=> sz00 = xa ),
introduced(avatar_definition,[new_symbols(naming,[spl32_23])]) ).
fof(f314,plain,
( sz00 != xa
| xa != xb ),
inference(inner_rewriting,[],[f313]) ).
fof(f313,plain,
( sz00 != xb
| xa != xb ),
inference(inner_rewriting,[],[f200]) ).
fof(f200,plain,
( sz00 != xb
| sz00 != xa ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
( sz00 != xb
| sz00 != xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f418,plain,
spl32_21,
inference(avatar_split_clause,[],[f227,f416]) ).
fof(f227,plain,
! [X0,X1] :
( aSet0(X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f414,plain,
spl32_20,
inference(avatar_split_clause,[],[f211,f412]) ).
fof(f211,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,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(f410,plain,
spl32_19,
inference(avatar_split_clause,[],[f210,f408]) ).
fof(f210,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( aElement0(X0)
=> aIdeal0(slsdtgt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).
fof(f401,plain,
spl32_18,
inference(avatar_split_clause,[],[f241,f399]) ).
fof(f241,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f397,plain,
spl32_17,
inference(avatar_split_clause,[],[f234,f395]) ).
fof(f234,plain,
! [X0] :
( sP1(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( sP1(X0)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f69,f110,f109]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f393,plain,
spl32_16,
inference(avatar_split_clause,[],[f199,f390]) ).
fof(f390,plain,
( spl32_16
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_16])]) ).
fof(f199,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f388,plain,
spl32_15,
inference(avatar_split_clause,[],[f198,f385]) ).
fof(f198,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f43]) ).
fof(f383,plain,
spl32_14,
inference(avatar_split_clause,[],[f197,f380]) ).
fof(f380,plain,
( spl32_14
<=> aElementOf0(xa,slsdtgt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_14])]) ).
fof(f197,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f43]) ).
fof(f378,plain,
spl32_13,
inference(avatar_split_clause,[],[f196,f375]) ).
fof(f196,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f43]) ).
fof(f373,plain,
spl32_12,
inference(avatar_split_clause,[],[f191,f370]) ).
fof(f191,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
fof(f368,plain,
~ spl32_11,
inference(avatar_split_clause,[],[f208,f365]) ).
fof(f365,plain,
( spl32_11
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl32_11])]) ).
fof(f208,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f363,plain,
spl32_10,
inference(avatar_split_clause,[],[f316,f360]) ).
fof(f316,plain,
aElementOf0(sK11,xI),
inference(forward_demodulation,[],[f204,f193]) ).
fof(f204,plain,
aElementOf0(sK11,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( sz00 != sK11
& aElementOf0(sK11,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f44,f128]) ).
fof(f128,plain,
( ? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
=> ( sz00 != sK11
& aElementOf0(sK11,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f358,plain,
~ spl32_9,
inference(avatar_split_clause,[],[f205,f355]) ).
fof(f205,plain,
sz00 != sK11,
inference(cnf_transformation,[],[f129]) ).
fof(f353,plain,
spl32_8,
inference(avatar_split_clause,[],[f190,f351]) ).
fof(f190,plain,
! [X0] :
( iLess0(sbrdtbr0(sK9(X0)),sbrdtbr0(X0))
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK9(X0)),sbrdtbr0(X0))
& sz00 != sK9(X0)
& aElementOf0(sK9(X0),xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f57,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI) )
=> ( iLess0(sbrdtbr0(sK9(X0)),sbrdtbr0(X0))
& sz00 != sK9(X0)
& aElementOf0(sK9(X0),xI) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI) )
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& aElementOf0(X0,xI) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& aElementOf0(X0,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f349,plain,
spl32_7,
inference(avatar_split_clause,[],[f189,f347]) ).
fof(f189,plain,
! [X0] :
( sz00 != sK9(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f125]) ).
fof(f345,plain,
spl32_6,
inference(avatar_split_clause,[],[f188,f343]) ).
fof(f188,plain,
! [X0] :
( aElementOf0(sK9(X0),xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f125]) ).
fof(f341,plain,
spl32_5,
inference(avatar_split_clause,[],[f207,f338]) ).
fof(f207,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f336,plain,
spl32_4,
inference(avatar_split_clause,[],[f206,f333]) ).
fof(f206,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f331,plain,
spl32_3,
inference(avatar_split_clause,[],[f195,f328]) ).
fof(f195,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f326,plain,
spl32_2,
inference(avatar_split_clause,[],[f194,f323]) ).
fof(f194,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f321,plain,
spl32_1,
inference(avatar_split_clause,[],[f192,f318]) ).
fof(f192,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG112+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:16:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (4156)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (4160)WARNING: value z3 for option sas not known
% 0.15/0.38 % (4158)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (4159)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (4161)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (4164)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)
% 0.15/0.38 % (4162)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)
% 0.15/0.38 % (4160)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)
% 0.15/0.38 % (4163)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [3]
% 0.22/0.44 % (4162)First to succeed.
% 0.22/0.45 TRYING [4]
% 0.22/0.45 % (4162)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4156"
% 0.22/0.45 % (4162)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.46 % (4162)------------------------------
% 0.22/0.46 % (4162)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.46 % (4162)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (4162)Memory used [KB]: 1958
% 0.22/0.46 % (4162)Time elapsed: 0.068 s
% 0.22/0.46 % (4162)Instructions burned: 101 (million)
% 0.22/0.46 % (4156)Success in time 0.09 s
%------------------------------------------------------------------------------