TSTP Solution File: SWC189+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC189+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:09:17 EDT 2024
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 468
% Syntax : Number of formulae : 1345 ( 252 unt; 0 def)
% Number of atoms : 5326 ( 890 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 6403 (2422 ~;2483 |; 816 &)
% ( 376 <=>; 306 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 338 ( 336 usr; 300 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 11 con; 0-2 aty)
% Number of variables : 2106 (1717 !; 389 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3772,plain,
$false,
inference(avatar_sat_refutation,[],[f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f744,f748,f753,f757,f761,f765,f769,f773,f777,f781,f811,f825,f829,f833,f837,f841,f845,f849,f853,f858,f862,f866,f870,f874,f878,f882,f886,f890,f894,f898,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1030,f1035,f1082,f1129,f1176,f1194,f1200,f1204,f1208,f1212,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1295,f1300,f1304,f1308,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1358,f1362,f1366,f1370,f1425,f1429,f1433,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1483,f1487,f1525,f1556,f1560,f1564,f1570,f1574,f1578,f1582,f1586,f1590,f1594,f1598,f1602,f1606,f1611,f1615,f1619,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1656,f1660,f1676,f1811,f1821,f1825,f1829,f1833,f1837,f1841,f1872,f1928,f1932,f1936,f1940,f1944,f1948,f1953,f2038,f2042,f2046,f2050,f2055,f2059,f2063,f2067,f2071,f2075,f2132,f2150,f2154,f2158,f2162,f2166,f2170,f2176,f2180,f2246,f2250,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2313,f2317,f2323,f2327,f2378,f2382,f2386,f2390,f2477,f2481,f2485,f2489,f2493,f2497,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2531,f2573,f2577,f2581,f2598,f2602,f2608,f2616,f2620,f2624,f2668,f2673,f2678,f2683,f2692,f2697,f2702,f2707,f2712,f2865,f2879,f2893,f2908,f2918,f2962,f2976,f2981,f3030,f3036,f3106,f3108,f3142,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3384,f3390,f3396,f3401,f3407,f3413,f3419,f3425,f3431,f3478,f3556,f3561,f3575,f3616,f3661,f3667,f3687,f3728,f3734,f3771]) ).
fof(f3771,plain,
( ~ spl73_3
| ~ spl73_4
| ~ spl73_5
| ~ spl73_6
| spl73_7
| ~ spl73_22
| ~ spl73_86 ),
inference(avatar_split_clause,[],[f1196,f1192,f750,f677,f672,f667,f662,f657]) ).
fof(f657,plain,
( spl73_3
<=> ssItem(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_3])]) ).
fof(f662,plain,
( spl73_4
<=> ssItem(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_4])]) ).
fof(f667,plain,
( spl73_5
<=> ssList(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_5])]) ).
fof(f672,plain,
( spl73_6
<=> ssList(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_6])]) ).
fof(f677,plain,
( spl73_7
<=> sK22 = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_7])]) ).
fof(f750,plain,
( spl73_22
<=> sK20 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_22])]) ).
fof(f1192,plain,
( spl73_86
<=> ! [X10,X11,X9,X8] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11)
| ~ ssList(X10)
| ~ ssItem(X9)
| ~ ssItem(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_86])]) ).
fof(f1196,plain,
( sK22 = sK23
| ~ ssList(sK25)
| ~ ssList(sK24)
| ~ ssItem(sK23)
| ~ ssItem(sK22)
| ~ spl73_22
| ~ spl73_86 ),
inference(trivial_inequality_removal,[],[f1195]) ).
fof(f1195,plain,
( sK20 != sK20
| sK22 = sK23
| ~ ssList(sK25)
| ~ ssList(sK24)
| ~ ssItem(sK23)
| ~ ssItem(sK22)
| ~ spl73_22
| ~ spl73_86 ),
inference(superposition,[],[f1193,f752]) ).
fof(f752,plain,
( sK20 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25)
| ~ spl73_22 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f1193,plain,
( ! [X10,X11,X8,X9] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11)
| ~ ssList(X10)
| ~ ssItem(X9)
| ~ ssItem(X8) )
| ~ spl73_86 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f3734,plain,
( spl73_299
| ~ spl73_269
| ~ spl73_298 ),
inference(avatar_split_clause,[],[f3729,f3725,f3027,f3731]) ).
fof(f3731,plain,
( spl73_299
<=> sK25 = cons(sK28(sK25),sK29(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_299])]) ).
fof(f3027,plain,
( spl73_269
<=> tl(sK25) = sK29(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_269])]) ).
fof(f3725,plain,
( spl73_298
<=> sK25 = cons(sK28(sK25),tl(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_298])]) ).
fof(f3729,plain,
( sK25 = cons(sK28(sK25),sK29(sK25))
| ~ spl73_269
| ~ spl73_298 ),
inference(forward_demodulation,[],[f3727,f3029]) ).
fof(f3029,plain,
( tl(sK25) = sK29(sK25)
| ~ spl73_269 ),
inference(avatar_component_clause,[],[f3027]) ).
fof(f3727,plain,
( sK25 = cons(sK28(sK25),tl(sK25))
| ~ spl73_298 ),
inference(avatar_component_clause,[],[f3725]) ).
fof(f3728,plain,
( spl73_291
| spl73_298
| ~ spl73_6
| ~ spl73_184
| ~ spl73_260
| ~ spl73_263 ),
inference(avatar_split_clause,[],[f3546,f2901,f2876,f1938,f672,f3725,f3558]) ).
fof(f3558,plain,
( spl73_291
<=> sK21 = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_291])]) ).
fof(f1938,plain,
( spl73_184
<=> ! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_184])]) ).
fof(f2876,plain,
( spl73_260
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_260])]) ).
fof(f2901,plain,
( spl73_263
<=> hd(sK25) = sK28(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_263])]) ).
fof(f3546,plain,
( sK25 = cons(sK28(sK25),tl(sK25))
| sK21 = sK25
| ~ spl73_6
| ~ spl73_184
| ~ spl73_260
| ~ spl73_263 ),
inference(forward_demodulation,[],[f3545,f2903]) ).
fof(f2903,plain,
( hd(sK25) = sK28(sK25)
| ~ spl73_263 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f3545,plain,
( sK21 = sK25
| sK25 = cons(hd(sK25),tl(sK25))
| ~ spl73_6
| ~ spl73_184
| ~ spl73_260 ),
inference(forward_demodulation,[],[f2002,f2878]) ).
fof(f2878,plain,
( nil = sK21
| ~ spl73_260 ),
inference(avatar_component_clause,[],[f2876]) ).
fof(f2002,plain,
( nil = sK25
| sK25 = cons(hd(sK25),tl(sK25))
| ~ spl73_6
| ~ spl73_184 ),
inference(resolution,[],[f1939,f674]) ).
fof(f674,plain,
( ssList(sK25)
| ~ spl73_6 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f1939,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl73_184 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f3687,plain,
( spl73_297
| spl73_291
| ~ spl73_6
| ~ spl73_183
| ~ spl73_260 ),
inference(avatar_split_clause,[],[f3544,f2876,f1934,f672,f3558,f3684]) ).
fof(f3684,plain,
( spl73_297
<=> sK25 = cons(sK27(sK25),sK26(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_297])]) ).
fof(f1934,plain,
( spl73_183
<=> ! [X0] :
( cons(sK27(X0),sK26(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_183])]) ).
fof(f3544,plain,
( sK21 = sK25
| sK25 = cons(sK27(sK25),sK26(sK25))
| ~ spl73_6
| ~ spl73_183
| ~ spl73_260 ),
inference(forward_demodulation,[],[f1966,f2878]) ).
fof(f1966,plain,
( nil = sK25
| sK25 = cons(sK27(sK25),sK26(sK25))
| ~ spl73_6
| ~ spl73_183 ),
inference(resolution,[],[f1935,f674]) ).
fof(f1935,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK27(X0),sK26(X0)) = X0 )
| ~ spl73_183 ),
inference(avatar_component_clause,[],[f1934]) ).
fof(f3667,plain,
( ~ spl73_296
| spl73_8
| ~ spl73_260 ),
inference(avatar_split_clause,[],[f3433,f2876,f682,f3664]) ).
fof(f3664,plain,
( spl73_296
<=> singletonP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_296])]) ).
fof(f682,plain,
( spl73_8
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_8])]) ).
fof(f3433,plain,
( ~ singletonP(sK21)
| spl73_8
| ~ spl73_260 ),
inference(superposition,[],[f684,f2878]) ).
fof(f684,plain,
( ~ singletonP(nil)
| spl73_8 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f3661,plain,
( spl73_294
| spl73_295
| ~ spl73_5
| ~ spl73_183
| ~ spl73_260 ),
inference(avatar_split_clause,[],[f3527,f2876,f1934,f667,f3658,f3654]) ).
fof(f3654,plain,
( spl73_294
<=> sK24 = cons(sK27(sK24),sK26(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_294])]) ).
fof(f3658,plain,
( spl73_295
<=> sK21 = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_295])]) ).
fof(f3527,plain,
( sK21 = sK24
| sK24 = cons(sK27(sK24),sK26(sK24))
| ~ spl73_5
| ~ spl73_183
| ~ spl73_260 ),
inference(forward_demodulation,[],[f1965,f2878]) ).
fof(f1965,plain,
( nil = sK24
| sK24 = cons(sK27(sK24),sK26(sK24))
| ~ spl73_5
| ~ spl73_183 ),
inference(resolution,[],[f1935,f669]) ).
fof(f669,plain,
( ssList(sK24)
| ~ spl73_5 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f3616,plain,
( spl73_293
| spl73_290
| ~ spl73_1
| ~ spl73_183
| ~ spl73_260 ),
inference(avatar_split_clause,[],[f3522,f2876,f1934,f647,f3553,f3613]) ).
fof(f3613,plain,
( spl73_293
<=> sK20 = cons(sK27(sK20),sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_293])]) ).
fof(f3553,plain,
( spl73_290
<=> sK20 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_290])]) ).
fof(f647,plain,
( spl73_1
<=> ssList(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_1])]) ).
fof(f3522,plain,
( sK20 = sK21
| sK20 = cons(sK27(sK20),sK26(sK20))
| ~ spl73_1
| ~ spl73_183
| ~ spl73_260 ),
inference(forward_demodulation,[],[f1963,f2878]) ).
fof(f1963,plain,
( nil = sK20
| sK20 = cons(sK27(sK20),sK26(sK20))
| ~ spl73_1
| ~ spl73_183 ),
inference(resolution,[],[f1935,f649]) ).
fof(f649,plain,
( ssList(sK20)
| ~ spl73_1 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f3575,plain,
( spl73_290
| spl73_292
| ~ spl73_1
| ~ spl73_184
| ~ spl73_257
| ~ spl73_260
| ~ spl73_265 ),
inference(avatar_split_clause,[],[f3521,f2915,f2876,f2858,f1938,f647,f3572,f3553]) ).
fof(f3572,plain,
( spl73_292
<=> sK20 = cons(sK28(sK20),sK29(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_292])]) ).
fof(f2858,plain,
( spl73_257
<=> hd(sK20) = sK28(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_257])]) ).
fof(f2915,plain,
( spl73_265
<=> tl(sK20) = sK29(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_265])]) ).
fof(f3521,plain,
( sK20 = cons(sK28(sK20),sK29(sK20))
| sK20 = sK21
| ~ spl73_1
| ~ spl73_184
| ~ spl73_257
| ~ spl73_260
| ~ spl73_265 ),
inference(forward_demodulation,[],[f3520,f2860]) ).
fof(f2860,plain,
( hd(sK20) = sK28(sK20)
| ~ spl73_257 ),
inference(avatar_component_clause,[],[f2858]) ).
fof(f3520,plain,
( sK20 = cons(hd(sK20),sK29(sK20))
| sK20 = sK21
| ~ spl73_1
| ~ spl73_184
| ~ spl73_260
| ~ spl73_265 ),
inference(forward_demodulation,[],[f3519,f2917]) ).
fof(f2917,plain,
( tl(sK20) = sK29(sK20)
| ~ spl73_265 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f3519,plain,
( sK20 = sK21
| sK20 = cons(hd(sK20),tl(sK20))
| ~ spl73_1
| ~ spl73_184
| ~ spl73_260 ),
inference(forward_demodulation,[],[f1999,f2878]) ).
fof(f1999,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20))
| ~ spl73_1
| ~ spl73_184 ),
inference(resolution,[],[f1939,f649]) ).
fof(f3561,plain,
( ~ spl73_291
| ~ spl73_260
| spl73_264 ),
inference(avatar_split_clause,[],[f3551,f2905,f2876,f3558]) ).
fof(f2905,plain,
( spl73_264
<=> nil = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_264])]) ).
fof(f3551,plain,
( sK21 != sK25
| ~ spl73_260
| spl73_264 ),
inference(forward_demodulation,[],[f2906,f2878]) ).
fof(f2906,plain,
( nil != sK25
| spl73_264 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f3556,plain,
( ~ spl73_290
| spl73_258
| ~ spl73_260 ),
inference(avatar_split_clause,[],[f3514,f2876,f2862,f3553]) ).
fof(f2862,plain,
( spl73_258
<=> nil = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_258])]) ).
fof(f3514,plain,
( sK20 != sK21
| spl73_258
| ~ spl73_260 ),
inference(forward_demodulation,[],[f2863,f2878]) ).
fof(f2863,plain,
( nil != sK20
| spl73_258 ),
inference(avatar_component_clause,[],[f2862]) ).
fof(f3478,plain,
( spl73_270
| spl73_289
| ~ spl73_5
| ~ spl73_184
| ~ spl73_261
| ~ spl73_264
| ~ spl73_267 ),
inference(avatar_split_clause,[],[f3120,f2973,f2905,f2886,f1938,f667,f3475,f3033]) ).
fof(f3033,plain,
( spl73_270
<=> sK24 = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_270])]) ).
fof(f3475,plain,
( spl73_289
<=> sK24 = cons(sK28(sK24),sK29(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_289])]) ).
fof(f2886,plain,
( spl73_261
<=> hd(sK24) = sK28(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_261])]) ).
fof(f2973,plain,
( spl73_267
<=> tl(sK24) = sK29(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_267])]) ).
fof(f3120,plain,
( sK24 = cons(sK28(sK24),sK29(sK24))
| sK24 = sK25
| ~ spl73_5
| ~ spl73_184
| ~ spl73_261
| ~ spl73_264
| ~ spl73_267 ),
inference(forward_demodulation,[],[f3119,f2888]) ).
fof(f2888,plain,
( hd(sK24) = sK28(sK24)
| ~ spl73_261 ),
inference(avatar_component_clause,[],[f2886]) ).
fof(f3119,plain,
( sK24 = cons(hd(sK24),sK29(sK24))
| sK24 = sK25
| ~ spl73_5
| ~ spl73_184
| ~ spl73_264
| ~ spl73_267 ),
inference(forward_demodulation,[],[f3118,f2975]) ).
fof(f2975,plain,
( tl(sK24) = sK29(sK24)
| ~ spl73_267 ),
inference(avatar_component_clause,[],[f2973]) ).
fof(f3118,plain,
( sK24 = sK25
| sK24 = cons(hd(sK24),tl(sK24))
| ~ spl73_5
| ~ spl73_184
| ~ spl73_264 ),
inference(forward_demodulation,[],[f2001,f2907]) ).
fof(f2907,plain,
( nil = sK25
| ~ spl73_264 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f2001,plain,
( nil = sK24
| sK24 = cons(hd(sK24),tl(sK24))
| ~ spl73_5
| ~ spl73_184 ),
inference(resolution,[],[f1939,f669]) ).
fof(f3431,plain,
( spl73_288
| spl73_260
| ~ spl73_2
| ~ spl73_183 ),
inference(avatar_split_clause,[],[f1964,f1934,f652,f2876,f3428]) ).
fof(f3428,plain,
( spl73_288
<=> sK21 = cons(sK27(sK21),sK26(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_288])]) ).
fof(f652,plain,
( spl73_2
<=> ssList(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_2])]) ).
fof(f1964,plain,
( nil = sK21
| sK21 = cons(sK27(sK21),sK26(sK21))
| ~ spl73_2
| ~ spl73_183 ),
inference(resolution,[],[f1935,f654]) ).
fof(f654,plain,
( ssList(sK21)
| ~ spl73_2 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f3425,plain,
( spl73_287
| ~ spl73_16
| ~ spl73_29 ),
inference(avatar_split_clause,[],[f817,f779,f722,f3422]) ).
fof(f3422,plain,
( spl73_287
<=> sP17(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_287])]) ).
fof(f722,plain,
( spl73_16
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_16])]) ).
fof(f779,plain,
( spl73_29
<=> ! [X0] :
( sP17(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_29])]) ).
fof(f817,plain,
( sP17(nil)
| ~ spl73_16
| ~ spl73_29 ),
inference(resolution,[],[f780,f724]) ).
fof(f724,plain,
( ssList(nil)
| ~ spl73_16 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f780,plain,
( ! [X0] :
( ~ ssList(X0)
| sP17(X0) )
| ~ spl73_29 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f3419,plain,
( spl73_286
| ~ spl73_16
| ~ spl73_28 ),
inference(avatar_split_clause,[],[f812,f775,f722,f3416]) ).
fof(f3416,plain,
( spl73_286
<=> sP15(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_286])]) ).
fof(f775,plain,
( spl73_28
<=> ! [X0] :
( sP15(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_28])]) ).
fof(f812,plain,
( sP15(nil)
| ~ spl73_16
| ~ spl73_28 ),
inference(resolution,[],[f776,f724]) ).
fof(f776,plain,
( ! [X0] :
( ~ ssList(X0)
| sP15(X0) )
| ~ spl73_28 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f3413,plain,
( spl73_285
| ~ spl73_16
| ~ spl73_27 ),
inference(avatar_split_clause,[],[f802,f771,f722,f3410]) ).
fof(f3410,plain,
( spl73_285
<=> sP13(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_285])]) ).
fof(f771,plain,
( spl73_27
<=> ! [X0] :
( sP13(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_27])]) ).
fof(f802,plain,
( sP13(nil)
| ~ spl73_16
| ~ spl73_27 ),
inference(resolution,[],[f772,f724]) ).
fof(f772,plain,
( ! [X0] :
( ~ ssList(X0)
| sP13(X0) )
| ~ spl73_27 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f3407,plain,
( spl73_284
| ~ spl73_16
| ~ spl73_26 ),
inference(avatar_split_clause,[],[f797,f767,f722,f3404]) ).
fof(f3404,plain,
( spl73_284
<=> sP11(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_284])]) ).
fof(f767,plain,
( spl73_26
<=> ! [X0] :
( sP11(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_26])]) ).
fof(f797,plain,
( sP11(nil)
| ~ spl73_16
| ~ spl73_26 ),
inference(resolution,[],[f768,f724]) ).
fof(f768,plain,
( ! [X0] :
( ~ ssList(X0)
| sP11(X0) )
| ~ spl73_26 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f3401,plain,
( spl73_283
| ~ spl73_16
| ~ spl73_25 ),
inference(avatar_split_clause,[],[f792,f763,f722,f3398]) ).
fof(f3398,plain,
( spl73_283
<=> sP9(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_283])]) ).
fof(f763,plain,
( spl73_25
<=> ! [X0] :
( sP9(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_25])]) ).
fof(f792,plain,
( sP9(nil)
| ~ spl73_16
| ~ spl73_25 ),
inference(resolution,[],[f764,f724]) ).
fof(f764,plain,
( ! [X0] :
( ~ ssList(X0)
| sP9(X0) )
| ~ spl73_25 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f3396,plain,
( ~ spl73_282
| spl73_8
| ~ spl73_264 ),
inference(avatar_split_clause,[],[f3047,f2905,f682,f3393]) ).
fof(f3393,plain,
( spl73_282
<=> singletonP(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_282])]) ).
fof(f3047,plain,
( ~ singletonP(sK25)
| spl73_8
| ~ spl73_264 ),
inference(superposition,[],[f684,f2907]) ).
fof(f3390,plain,
( spl73_281
| ~ spl73_16
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f787,f759,f722,f3387]) ).
fof(f3387,plain,
( spl73_281
<=> sP7(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_281])]) ).
fof(f759,plain,
( spl73_24
<=> ! [X0] :
( sP7(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_24])]) ).
fof(f787,plain,
( sP7(nil)
| ~ spl73_16
| ~ spl73_24 ),
inference(resolution,[],[f760,f724]) ).
fof(f760,plain,
( ! [X0] :
( ~ ssList(X0)
| sP7(X0) )
| ~ spl73_24 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f3384,plain,
( spl73_280
| ~ spl73_16
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f782,f755,f722,f3381]) ).
fof(f3381,plain,
( spl73_280
<=> sP5(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_280])]) ).
fof(f755,plain,
( spl73_23
<=> ! [X0] :
( sP5(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_23])]) ).
fof(f782,plain,
( sP5(nil)
| ~ spl73_16
| ~ spl73_23 ),
inference(resolution,[],[f756,f724]) ).
fof(f756,plain,
( ! [X0] :
( ~ ssList(X0)
| sP5(X0) )
| ~ spl73_23 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f3179,plain,
( spl73_279
| ~ spl73_6
| ~ spl73_168 ),
inference(avatar_split_clause,[],[f1784,f1645,f672,f3177]) ).
fof(f3177,plain,
( spl73_279
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK25)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_279])]) ).
fof(f1645,plain,
( spl73_168
<=> ! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_168])]) ).
fof(f1784,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK25)) = X0 )
| ~ spl73_6
| ~ spl73_168 ),
inference(resolution,[],[f1646,f674]) ).
fof(f1646,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 )
| ~ spl73_168 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f3175,plain,
( spl73_278
| ~ spl73_5
| ~ spl73_168 ),
inference(avatar_split_clause,[],[f1783,f1645,f667,f3173]) ).
fof(f3173,plain,
( spl73_278
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK24)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_278])]) ).
fof(f1783,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK24)) = X0 )
| ~ spl73_5
| ~ spl73_168 ),
inference(resolution,[],[f1646,f669]) ).
fof(f3171,plain,
( spl73_277
| ~ spl73_2
| ~ spl73_168 ),
inference(avatar_split_clause,[],[f1782,f1645,f652,f3169]) ).
fof(f3169,plain,
( spl73_277
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_277])]) ).
fof(f1782,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 )
| ~ spl73_2
| ~ spl73_168 ),
inference(resolution,[],[f1646,f654]) ).
fof(f3167,plain,
( spl73_276
| ~ spl73_1
| ~ spl73_168 ),
inference(avatar_split_clause,[],[f1781,f1645,f647,f3165]) ).
fof(f3165,plain,
( spl73_276
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_276])]) ).
fof(f1781,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 )
| ~ spl73_1
| ~ spl73_168 ),
inference(resolution,[],[f1646,f649]) ).
fof(f3163,plain,
( spl73_275
| ~ spl73_6
| ~ spl73_167 ),
inference(avatar_split_clause,[],[f1754,f1641,f672,f3161]) ).
fof(f3161,plain,
( spl73_275
<=> ! [X0] :
( ~ ssItem(X0)
| sK25 = tl(cons(X0,sK25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_275])]) ).
fof(f1641,plain,
( spl73_167
<=> ! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_167])]) ).
fof(f1754,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK25 = tl(cons(X0,sK25)) )
| ~ spl73_6
| ~ spl73_167 ),
inference(resolution,[],[f1642,f674]) ).
fof(f1642,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 )
| ~ spl73_167 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f3159,plain,
( spl73_274
| ~ spl73_5
| ~ spl73_167 ),
inference(avatar_split_clause,[],[f1753,f1641,f667,f3157]) ).
fof(f3157,plain,
( spl73_274
<=> ! [X0] :
( ~ ssItem(X0)
| sK24 = tl(cons(X0,sK24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_274])]) ).
fof(f1753,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK24 = tl(cons(X0,sK24)) )
| ~ spl73_5
| ~ spl73_167 ),
inference(resolution,[],[f1642,f669]) ).
fof(f3155,plain,
( spl73_273
| ~ spl73_2
| ~ spl73_167 ),
inference(avatar_split_clause,[],[f1752,f1641,f652,f3153]) ).
fof(f3153,plain,
( spl73_273
<=> ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_273])]) ).
fof(f1752,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) )
| ~ spl73_2
| ~ spl73_167 ),
inference(resolution,[],[f1642,f654]) ).
fof(f3142,plain,
( ~ spl73_272
| spl73_258
| ~ spl73_264 ),
inference(avatar_split_clause,[],[f3137,f2905,f2862,f3139]) ).
fof(f3139,plain,
( spl73_272
<=> sK20 = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_272])]) ).
fof(f3137,plain,
( sK20 != sK25
| spl73_258
| ~ spl73_264 ),
inference(forward_demodulation,[],[f2863,f2907]) ).
fof(f3108,plain,
( spl73_251
| ~ spl73_9
| ~ spl73_258 ),
inference(avatar_split_clause,[],[f2920,f2862,f687,f2685]) ).
fof(f2685,plain,
( spl73_251
<=> equalelemsP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_251])]) ).
fof(f687,plain,
( spl73_9
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_9])]) ).
fof(f2920,plain,
( equalelemsP(sK20)
| ~ spl73_9
| ~ spl73_258 ),
inference(superposition,[],[f689,f2864]) ).
fof(f2864,plain,
( nil = sK20
| ~ spl73_258 ),
inference(avatar_component_clause,[],[f2862]) ).
fof(f689,plain,
( equalelemsP(nil)
| ~ spl73_9 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f3106,plain,
( spl73_271
| ~ spl73_1
| ~ spl73_167 ),
inference(avatar_split_clause,[],[f1751,f1641,f647,f3104]) ).
fof(f3104,plain,
( spl73_271
<=> ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_271])]) ).
fof(f1751,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) )
| ~ spl73_1
| ~ spl73_167 ),
inference(resolution,[],[f1642,f649]) ).
fof(f3036,plain,
( spl73_270
| ~ spl73_262
| ~ spl73_264 ),
inference(avatar_split_clause,[],[f3031,f2905,f2890,f3033]) ).
fof(f2890,plain,
( spl73_262
<=> nil = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_262])]) ).
fof(f3031,plain,
( sK24 = sK25
| ~ spl73_262
| ~ spl73_264 ),
inference(forward_demodulation,[],[f2907,f2892]) ).
fof(f2892,plain,
( nil = sK24
| ~ spl73_262 ),
inference(avatar_component_clause,[],[f2890]) ).
fof(f3030,plain,
( spl73_269
| spl73_264
| ~ spl73_6
| ~ spl73_165 ),
inference(avatar_split_clause,[],[f1724,f1633,f672,f2905,f3027]) ).
fof(f1633,plain,
( spl73_165
<=> ! [X0] :
( tl(X0) = sK29(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_165])]) ).
fof(f1724,plain,
( nil = sK25
| tl(sK25) = sK29(sK25)
| ~ spl73_6
| ~ spl73_165 ),
inference(resolution,[],[f1634,f674]) ).
fof(f1634,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK29(X0) )
| ~ spl73_165 ),
inference(avatar_component_clause,[],[f1633]) ).
fof(f2981,plain,
( ~ spl73_268
| spl73_8
| ~ spl73_258 ),
inference(avatar_split_clause,[],[f2919,f2862,f682,f2978]) ).
fof(f2978,plain,
( spl73_268
<=> singletonP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_268])]) ).
fof(f2919,plain,
( ~ singletonP(sK20)
| spl73_8
| ~ spl73_258 ),
inference(superposition,[],[f684,f2864]) ).
fof(f2976,plain,
( spl73_267
| spl73_262
| ~ spl73_5
| ~ spl73_165 ),
inference(avatar_split_clause,[],[f1723,f1633,f667,f2890,f2973]) ).
fof(f1723,plain,
( nil = sK24
| tl(sK24) = sK29(sK24)
| ~ spl73_5
| ~ spl73_165 ),
inference(resolution,[],[f1634,f669]) ).
fof(f2962,plain,
( spl73_266
| spl73_260
| ~ spl73_2
| ~ spl73_165 ),
inference(avatar_split_clause,[],[f1722,f1633,f652,f2876,f2959]) ).
fof(f2959,plain,
( spl73_266
<=> tl(sK21) = sK29(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_266])]) ).
fof(f1722,plain,
( nil = sK21
| tl(sK21) = sK29(sK21)
| ~ spl73_2
| ~ spl73_165 ),
inference(resolution,[],[f1634,f654]) ).
fof(f2918,plain,
( spl73_265
| spl73_258
| ~ spl73_1
| ~ spl73_165 ),
inference(avatar_split_clause,[],[f1721,f1633,f647,f2862,f2915]) ).
fof(f1721,plain,
( nil = sK20
| tl(sK20) = sK29(sK20)
| ~ spl73_1
| ~ spl73_165 ),
inference(resolution,[],[f1634,f649]) ).
fof(f2908,plain,
( spl73_263
| spl73_264
| ~ spl73_6
| ~ spl73_164 ),
inference(avatar_split_clause,[],[f1694,f1629,f672,f2905,f2901]) ).
fof(f1629,plain,
( spl73_164
<=> ! [X0] :
( hd(X0) = sK28(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_164])]) ).
fof(f1694,plain,
( nil = sK25
| hd(sK25) = sK28(sK25)
| ~ spl73_6
| ~ spl73_164 ),
inference(resolution,[],[f1630,f674]) ).
fof(f1630,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK28(X0) )
| ~ spl73_164 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f2893,plain,
( spl73_261
| spl73_262
| ~ spl73_5
| ~ spl73_164 ),
inference(avatar_split_clause,[],[f1693,f1629,f667,f2890,f2886]) ).
fof(f1693,plain,
( nil = sK24
| hd(sK24) = sK28(sK24)
| ~ spl73_5
| ~ spl73_164 ),
inference(resolution,[],[f1630,f669]) ).
fof(f2879,plain,
( spl73_259
| spl73_260
| ~ spl73_2
| ~ spl73_164 ),
inference(avatar_split_clause,[],[f1692,f1629,f652,f2876,f2872]) ).
fof(f2872,plain,
( spl73_259
<=> hd(sK21) = sK28(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_259])]) ).
fof(f1692,plain,
( nil = sK21
| hd(sK21) = sK28(sK21)
| ~ spl73_2
| ~ spl73_164 ),
inference(resolution,[],[f1630,f654]) ).
fof(f2865,plain,
( spl73_257
| spl73_258
| ~ spl73_1
| ~ spl73_164 ),
inference(avatar_split_clause,[],[f1691,f1629,f647,f2862,f2858]) ).
fof(f1691,plain,
( nil = sK20
| hd(sK20) = sK28(sK20)
| ~ spl73_1
| ~ spl73_164 ),
inference(resolution,[],[f1630,f649]) ).
fof(f2712,plain,
( spl73_256
| ~ spl73_6
| ~ spl73_116 ),
inference(avatar_split_clause,[],[f1400,f1319,f672,f2709]) ).
fof(f2709,plain,
( spl73_256
<=> sK25 = app(nil,sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_256])]) ).
fof(f1319,plain,
( spl73_116
<=> ! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_116])]) ).
fof(f1400,plain,
( sK25 = app(nil,sK25)
| ~ spl73_6
| ~ spl73_116 ),
inference(resolution,[],[f1320,f674]) ).
fof(f1320,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl73_116 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f2707,plain,
( spl73_255
| ~ spl73_5
| ~ spl73_116 ),
inference(avatar_split_clause,[],[f1399,f1319,f667,f2704]) ).
fof(f2704,plain,
( spl73_255
<=> sK24 = app(nil,sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_255])]) ).
fof(f1399,plain,
( sK24 = app(nil,sK24)
| ~ spl73_5
| ~ spl73_116 ),
inference(resolution,[],[f1320,f669]) ).
fof(f2702,plain,
( spl73_254
| ~ spl73_2
| ~ spl73_116 ),
inference(avatar_split_clause,[],[f1398,f1319,f652,f2699]) ).
fof(f2699,plain,
( spl73_254
<=> sK21 = app(nil,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_254])]) ).
fof(f1398,plain,
( sK21 = app(nil,sK21)
| ~ spl73_2
| ~ spl73_116 ),
inference(resolution,[],[f1320,f654]) ).
fof(f2697,plain,
( spl73_253
| ~ spl73_1
| ~ spl73_116 ),
inference(avatar_split_clause,[],[f1397,f1319,f647,f2694]) ).
fof(f2694,plain,
( spl73_253
<=> sK20 = app(nil,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_253])]) ).
fof(f1397,plain,
( sK20 = app(nil,sK20)
| ~ spl73_1
| ~ spl73_116 ),
inference(resolution,[],[f1320,f649]) ).
fof(f2692,plain,
( spl73_251
| ~ spl73_252
| ~ spl73_30
| ~ spl73_96 ),
inference(avatar_split_clause,[],[f1565,f1235,f808,f2689,f2685]) ).
fof(f2689,plain,
( spl73_252
<=> sP4(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_252])]) ).
fof(f808,plain,
( spl73_30
<=> sP5(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_30])]) ).
fof(f1235,plain,
( spl73_96
<=> ! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_96])]) ).
fof(f1565,plain,
( ~ sP4(sK20)
| equalelemsP(sK20)
| ~ spl73_30
| ~ spl73_96 ),
inference(resolution,[],[f810,f1236]) ).
fof(f1236,plain,
( ! [X0] :
( ~ sP5(X0)
| ~ sP4(X0)
| equalelemsP(X0) )
| ~ spl73_96 ),
inference(avatar_component_clause,[],[f1235]) ).
fof(f810,plain,
( sP5(sK20)
| ~ spl73_30 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f2683,plain,
( spl73_250
| ~ spl73_6
| ~ spl73_115 ),
inference(avatar_split_clause,[],[f1375,f1315,f672,f2680]) ).
fof(f2680,plain,
( spl73_250
<=> sK25 = app(sK25,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_250])]) ).
fof(f1315,plain,
( spl73_115
<=> ! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_115])]) ).
fof(f1375,plain,
( sK25 = app(sK25,nil)
| ~ spl73_6
| ~ spl73_115 ),
inference(resolution,[],[f1316,f674]) ).
fof(f1316,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl73_115 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f2678,plain,
( spl73_249
| ~ spl73_5
| ~ spl73_115 ),
inference(avatar_split_clause,[],[f1374,f1315,f667,f2675]) ).
fof(f2675,plain,
( spl73_249
<=> sK24 = app(sK24,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_249])]) ).
fof(f1374,plain,
( sK24 = app(sK24,nil)
| ~ spl73_5
| ~ spl73_115 ),
inference(resolution,[],[f1316,f669]) ).
fof(f2673,plain,
( spl73_248
| ~ spl73_2
| ~ spl73_115 ),
inference(avatar_split_clause,[],[f1373,f1315,f652,f2670]) ).
fof(f2670,plain,
( spl73_248
<=> sK21 = app(sK21,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_248])]) ).
fof(f1373,plain,
( sK21 = app(sK21,nil)
| ~ spl73_2
| ~ spl73_115 ),
inference(resolution,[],[f1316,f654]) ).
fof(f2668,plain,
( spl73_247
| ~ spl73_1
| ~ spl73_115 ),
inference(avatar_split_clause,[],[f1372,f1315,f647,f2665]) ).
fof(f2665,plain,
( spl73_247
<=> sK20 = app(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_247])]) ).
fof(f1372,plain,
( sK20 = app(sK20,nil)
| ~ spl73_1
| ~ spl73_115 ),
inference(resolution,[],[f1316,f649]) ).
fof(f2624,plain,
spl73_246,
inference(avatar_split_clause,[],[f626,f2622]) ).
fof(f2622,plain,
( spl73_246
<=> ! [X10,X9,X7,X6,X8] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_246])]) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f524]) ).
fof(f524,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( sP12(X0)
| ( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
& ssList(sK54(X0))
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssItem(sK51(X0))
& ssItem(sK50(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52,sK53,sK54])],[f327,f332,f331,f330,f329,f328]) ).
fof(f328,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK50(X0))
& leq(sK50(X0),X2)
& app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK50(X0))
& leq(sK50(X0),X2)
& app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ? [X5] :
( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK51(X0),sK50(X0))
& leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
& ssList(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( sP12(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2620,plain,
spl73_245,
inference(avatar_split_clause,[],[f625,f2618]) ).
fof(f2618,plain,
( spl73_245
<=> ! [X10,X9,X7,X6,X8] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_245])]) ).
fof(f625,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f512]) ).
fof(f512,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ( sP10(X0)
| ( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
& ssList(sK49(X0))
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssItem(sK46(X0))
& ssItem(sK45(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47,sK48,sK49])],[f318,f323,f322,f321,f320,f319]) ).
fof(f319,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK45(X0))
& ~ lt(sK45(X0),X2)
& app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK45(X0))
& ~ lt(sK45(X0),X2)
& app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f322,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK46(X0),sK45(X0))
& ~ lt(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
& ssList(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f317]) ).
fof(f317,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( sP10(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f2616,plain,
spl73_244,
inference(avatar_split_clause,[],[f624,f2614]) ).
fof(f2614,plain,
( spl73_244
<=> ! [X10,X9,X7,X6,X8] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_244])]) ).
fof(f624,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f500]) ).
fof(f500,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0] :
( ( sP8(X0)
| ( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
& ssList(sK44(X0))
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssItem(sK41(X0))
& ssItem(sK40(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43,sK44])],[f309,f314,f313,f312,f311,f310]) ).
fof(f310,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK40(X0))
& ~ leq(sK40(X0),X2)
& app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK40(X0))
& ~ leq(sK40(X0),X2)
& app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK41(X0),sK40(X0))
& ~ leq(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
& ssList(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f308]) ).
fof(f308,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( sP8(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2608,plain,
spl73_243,
inference(avatar_split_clause,[],[f628,f2606]) ).
fof(f2606,plain,
( spl73_243
<=> ! [X10,X9,X7,X6,X8] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_243])]) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( sP16(X0)
| ( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0
& ssList(sK64(X0))
& ssList(sK63(X0))
& ssList(sK62(X0))
& ssItem(sK61(X0))
& ssItem(sK60(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61,sK62,sK63,sK64])],[f345,f350,f349,f348,f347,f346]) ).
fof(f346,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),X2)
& app(app(X3,cons(sK60(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),X2)
& app(app(X3,cons(sK60(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(X3,cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(X3,cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),X5)) = X0
& ssList(X5) )
& ssList(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK60(X0),sK61(X0))
& app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0
& ssList(sK64(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f344]) ).
fof(f344,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f2602,plain,
spl73_242,
inference(avatar_split_clause,[],[f627,f2600]) ).
fof(f2600,plain,
( spl73_242
<=> ! [X10,X9,X7,X6,X8] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_242])]) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f536]) ).
fof(f536,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( sP14(X0)
| ( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
& ssList(sK59(X0))
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssItem(sK56(X0))
& ssItem(sK55(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58,sK59])],[f336,f341,f340,f339,f338,f337]) ).
fof(f337,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),X2)
& app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),X2)
& app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f340,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
& ssList(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f335]) ).
fof(f335,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f2598,plain,
spl73_241,
inference(avatar_split_clause,[],[f575,f2596]) ).
fof(f2596,plain,
( spl73_241
<=> ! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_241])]) ).
fof(f575,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
fof(f2581,plain,
spl73_240,
inference(avatar_split_clause,[],[f635,f2579]) ).
fof(f2579,plain,
( spl73_240
<=> ! [X2,X1,X3] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_240])]) ).
fof(f635,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f587]) ).
fof(f587,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
& ssList(sK69(X0,X1))
& ssList(sK68(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69])],[f366,f368,f367]) ).
fof(f367,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK68(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f368,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK68(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f2577,plain,
spl73_239,
inference(avatar_split_clause,[],[f632,f2575]) ).
fof(f2575,plain,
( spl73_239
<=> ! [X2,X1,X3] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_239])]) ).
fof(f632,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f571]) ).
fof(f571,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
& ssList(sK66(X0,X1))
& ssList(sK65(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66])],[f356,f358,f357]) ).
fof(f357,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK65(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f358,plain,
! [X0,X1] :
( ? [X5] :
( app(sK65(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2573,plain,
spl73_238,
inference(avatar_split_clause,[],[f621,f2571]) ).
fof(f2571,plain,
( spl73_238
<=> ! [X5,X7,X6,X8] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_238])]) ).
fof(f621,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ( sP4(X0)
| ( sK31(X0) != sK32(X0)
& app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0
& ssList(sK34(X0))
& ssList(sK33(X0))
& ssItem(sK32(X0))
& ssItem(sK31(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34])],[f292,f296,f295,f294,f293]) ).
fof(f293,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK31(X0) != X2
& app(X3,cons(sK31(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK31(X0) != X2
& app(X3,cons(sK31(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK31(X0) != sK32(X0)
& app(X3,cons(sK31(X0),cons(sK32(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK31(X0) != sK32(X0)
& app(X3,cons(sK31(X0),cons(sK32(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK31(X0) != sK32(X0)
& app(sK33(X0),cons(sK31(X0),cons(sK32(X0),X4))) = X0
& ssList(X4) )
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0] :
( ? [X4] :
( sK31(X0) != sK32(X0)
& app(sK33(X0),cons(sK31(X0),cons(sK32(X0),X4))) = X0
& ssList(X4) )
=> ( sK31(X0) != sK32(X0)
& app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0
& ssList(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( sP4(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f2531,plain,
spl73_237,
inference(avatar_split_clause,[],[f641,f2529]) ).
fof(f2529,plain,
( spl73_237
<=> ! [X10,X7,X9,X8] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_237])]) ).
fof(f641,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f623]) ).
fof(f623,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f622]) ).
fof(f622,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP6(X0) ),
inference(equality_resolution,[],[f489]) ).
fof(f489,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ( sP6(X0)
| ( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
& ssList(sK39(X0))
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssItem(sK36(X0))
& ssItem(sK35(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f300,f305,f304,f303,f302,f301]) ).
fof(f301,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK35(X0) = X2
& app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK35(X0) = X2
& app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f304,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ? [X5] :
( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
& ssList(X5) )
=> ( sK35(X0) = sK36(X0)
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
& ssList(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sP6(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2527,plain,
spl73_236,
inference(avatar_split_clause,[],[f605,f2525]) ).
fof(f2525,plain,
( spl73_236
<=> ! [X0,X3,X2,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_236])]) ).
fof(f605,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f2523,plain,
spl73_235,
inference(avatar_split_clause,[],[f596,f2521]) ).
fof(f2521,plain,
( spl73_235
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_235])]) ).
fof(f596,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
fof(f2519,plain,
spl73_234,
inference(avatar_split_clause,[],[f595,f2517]) ).
fof(f2517,plain,
( spl73_234
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_234])]) ).
fof(f595,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f2515,plain,
spl73_233,
inference(avatar_split_clause,[],[f586,f2513]) ).
fof(f2513,plain,
( spl73_233
<=> ! [X0,X1] :
( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_233])]) ).
fof(f586,plain,
! [X0,X1] :
( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f2511,plain,
spl73_232,
inference(avatar_split_clause,[],[f570,f2509]) ).
fof(f2509,plain,
( spl73_232
<=> ! [X0,X1] :
( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_232])]) ).
fof(f570,plain,
! [X0,X1] :
( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f2507,plain,
spl73_231,
inference(avatar_split_clause,[],[f553,f2505]) ).
fof(f2505,plain,
( spl73_231
<=> ! [X0] :
( sP16(X0)
| app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_231])]) ).
fof(f553,plain,
! [X0] :
( sP16(X0)
| app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0 ),
inference(cnf_transformation,[],[f351]) ).
fof(f2503,plain,
spl73_230,
inference(avatar_split_clause,[],[f542,f2501]) ).
fof(f2501,plain,
( spl73_230
<=> ! [X0] :
( sP14(X0)
| app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_230])]) ).
fof(f542,plain,
! [X0] :
( sP14(X0)
| app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0 ),
inference(cnf_transformation,[],[f342]) ).
fof(f2497,plain,
spl73_229,
inference(avatar_split_clause,[],[f530,f2495]) ).
fof(f2495,plain,
( spl73_229
<=> ! [X0] :
( sP12(X0)
| app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_229])]) ).
fof(f530,plain,
! [X0] :
( sP12(X0)
| app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0 ),
inference(cnf_transformation,[],[f333]) ).
fof(f2493,plain,
spl73_228,
inference(avatar_split_clause,[],[f518,f2491]) ).
fof(f2491,plain,
( spl73_228
<=> ! [X0] :
( sP10(X0)
| app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_228])]) ).
fof(f518,plain,
! [X0] :
( sP10(X0)
| app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0 ),
inference(cnf_transformation,[],[f324]) ).
fof(f2489,plain,
spl73_227,
inference(avatar_split_clause,[],[f506,f2487]) ).
fof(f2487,plain,
( spl73_227
<=> ! [X0] :
( sP8(X0)
| app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_227])]) ).
fof(f506,plain,
! [X0] :
( sP8(X0)
| app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0 ),
inference(cnf_transformation,[],[f315]) ).
fof(f2485,plain,
spl73_226,
inference(avatar_split_clause,[],[f495,f2483]) ).
fof(f2483,plain,
( spl73_226
<=> ! [X0] :
( sP6(X0)
| app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_226])]) ).
fof(f495,plain,
! [X0] :
( sP6(X0)
| app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0 ),
inference(cnf_transformation,[],[f306]) ).
fof(f2481,plain,
spl73_225,
inference(avatar_split_clause,[],[f435,f2479]) ).
fof(f2479,plain,
( spl73_225
<=> ! [X0,X3,X2,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_225])]) ).
fof(f435,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f2477,plain,
spl73_224,
inference(avatar_split_clause,[],[f434,f2475]) ).
fof(f2475,plain,
( spl73_224
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_224])]) ).
fof(f434,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f2390,plain,
spl73_223,
inference(avatar_split_clause,[],[f597,f2388]) ).
fof(f2388,plain,
( spl73_223
<=> ! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_223])]) ).
fof(f597,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f2386,plain,
spl73_222,
inference(avatar_split_clause,[],[f594,f2384]) ).
fof(f2384,plain,
( spl73_222
<=> ! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_222])]) ).
fof(f594,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f2382,plain,
spl73_221,
inference(avatar_split_clause,[],[f453,f2380]) ).
fof(f2380,plain,
( spl73_221
<=> ! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_221])]) ).
fof(f453,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f2378,plain,
spl73_220,
inference(avatar_split_clause,[],[f431,f2376]) ).
fof(f2376,plain,
( spl73_220
<=> ! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_220])]) ).
fof(f431,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f2327,plain,
spl73_219,
inference(avatar_split_clause,[],[f642,f2325]) ).
fof(f2325,plain,
( spl73_219
<=> ! [X2,X1,X3] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_219])]) ).
fof(f642,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f615,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f2323,plain,
spl73_218,
inference(avatar_split_clause,[],[f601,f2321]) ).
fof(f2321,plain,
( spl73_218
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_218])]) ).
fof(f601,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
fof(f2317,plain,
spl73_217,
inference(avatar_split_clause,[],[f600,f2315]) ).
fof(f2315,plain,
( spl73_217
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_217])]) ).
fof(f600,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
fof(f2313,plain,
spl73_216,
inference(avatar_split_clause,[],[f574,f2311]) ).
fof(f2311,plain,
( spl73_216
<=> ! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_216])]) ).
fof(f574,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
fof(f2278,plain,
spl73_215,
inference(avatar_split_clause,[],[f604,f2276]) ).
fof(f2276,plain,
( spl73_215
<=> ! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_215])]) ).
fof(f604,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f2274,plain,
spl73_214,
inference(avatar_split_clause,[],[f603,f2272]) ).
fof(f2272,plain,
( spl73_214
<=> ! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_214])]) ).
fof(f603,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f2270,plain,
spl73_213,
inference(avatar_split_clause,[],[f602,f2268]) ).
fof(f2268,plain,
( spl73_213
<=> ! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_213])]) ).
fof(f602,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f2266,plain,
spl73_212,
inference(avatar_split_clause,[],[f484,f2264]) ).
fof(f2264,plain,
( spl73_212
<=> ! [X0] :
( sP4(X0)
| app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_212])]) ).
fof(f484,plain,
! [X0] :
( sP4(X0)
| app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0 ),
inference(cnf_transformation,[],[f297]) ).
fof(f2262,plain,
spl73_211,
inference(avatar_split_clause,[],[f430,f2260]) ).
fof(f2260,plain,
( spl73_211
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_211])]) ).
fof(f430,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f2258,plain,
spl73_210,
inference(avatar_split_clause,[],[f429,f2256]) ).
fof(f2256,plain,
( spl73_210
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_210])]) ).
fof(f429,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f2254,plain,
spl73_209,
inference(avatar_split_clause,[],[f428,f2252]) ).
fof(f2252,plain,
( spl73_209
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_209])]) ).
fof(f428,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f2250,plain,
spl73_208,
inference(avatar_split_clause,[],[f427,f2248]) ).
fof(f2248,plain,
( spl73_208
<=> ! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_208])]) ).
fof(f427,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f2246,plain,
spl73_207,
inference(avatar_split_clause,[],[f426,f2244]) ).
fof(f2244,plain,
( spl73_207
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_207])]) ).
fof(f426,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
fof(f2180,plain,
spl73_206,
inference(avatar_split_clause,[],[f599,f2178]) ).
fof(f2178,plain,
( spl73_206
<=> ! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_206])]) ).
fof(f599,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f2176,plain,
spl73_205,
inference(avatar_split_clause,[],[f598,f2174]) ).
fof(f2174,plain,
( spl73_205
<=> ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_205])]) ).
fof(f598,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f2170,plain,
spl73_204,
inference(avatar_split_clause,[],[f589,f2168]) ).
fof(f2168,plain,
( spl73_204
<=> ! [X0,X1] :
( app(X1,sK70(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_204])]) ).
fof(f589,plain,
! [X0,X1] :
( app(X1,sK70(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK70(X0,X1)) = X0
& ssList(sK70(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f371,f372]) ).
fof(f372,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK70(X0,X1)) = X0
& ssList(sK70(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f2166,plain,
spl73_203,
inference(avatar_split_clause,[],[f582,f2164]) ).
fof(f2164,plain,
( spl73_203
<=> ! [X0,X1] :
( app(sK67(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_203])]) ).
fof(f582,plain,
! [X0,X1] :
( app(sK67(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK67(X0,X1),X1) = X0
& ssList(sK67(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f362,f363]) ).
fof(f363,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK67(X0,X1),X1) = X0
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f2162,plain,
spl73_202,
inference(avatar_split_clause,[],[f573,f2160]) ).
fof(f2160,plain,
( spl73_202
<=> ! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_202])]) ).
fof(f573,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
fof(f2158,plain,
spl73_201,
inference(avatar_split_clause,[],[f455,f2156]) ).
fof(f2156,plain,
( spl73_201
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_201])]) ).
fof(f455,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f2154,plain,
spl73_200,
inference(avatar_split_clause,[],[f454,f2152]) ).
fof(f2152,plain,
( spl73_200
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_200])]) ).
fof(f454,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f2150,plain,
spl73_199,
inference(avatar_split_clause,[],[f433,f2148]) ).
fof(f2148,plain,
( spl73_199
<=> ! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_199])]) ).
fof(f433,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f2132,plain,
( spl73_198
| ~ spl73_6
| ~ spl73_29 ),
inference(avatar_split_clause,[],[f821,f779,f672,f2129]) ).
fof(f2129,plain,
( spl73_198
<=> sP17(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_198])]) ).
fof(f821,plain,
( sP17(sK25)
| ~ spl73_6
| ~ spl73_29 ),
inference(resolution,[],[f780,f674]) ).
fof(f2075,plain,
spl73_197,
inference(avatar_split_clause,[],[f636,f2073]) ).
fof(f2073,plain,
( spl73_197
<=> ! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_197])]) ).
fof(f636,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f590]) ).
fof(f590,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f2071,plain,
spl73_196,
inference(avatar_split_clause,[],[f634,f2069]) ).
fof(f2069,plain,
( spl73_196
<=> ! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_196])]) ).
fof(f634,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f583]) ).
fof(f583,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f2067,plain,
spl73_195,
inference(avatar_split_clause,[],[f578,f2065]) ).
fof(f2065,plain,
( spl73_195
<=> ! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_195])]) ).
fof(f578,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f2063,plain,
spl73_194,
inference(avatar_split_clause,[],[f577,f2061]) ).
fof(f2061,plain,
( spl73_194
<=> ! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_194])]) ).
fof(f577,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f2059,plain,
spl73_193,
inference(avatar_split_clause,[],[f576,f2057]) ).
fof(f2057,plain,
( spl73_193
<=> ! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_193])]) ).
fof(f576,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f2055,plain,
( spl73_192
| ~ spl73_5
| ~ spl73_29 ),
inference(avatar_split_clause,[],[f820,f779,f667,f2052]) ).
fof(f2052,plain,
( spl73_192
<=> sP17(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_192])]) ).
fof(f820,plain,
( sP17(sK24)
| ~ spl73_5
| ~ spl73_29 ),
inference(resolution,[],[f780,f669]) ).
fof(f2050,plain,
spl73_191,
inference(avatar_split_clause,[],[f567,f2048]) ).
fof(f2048,plain,
( spl73_191
<=> ! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_191])]) ).
fof(f567,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f2046,plain,
spl73_190,
inference(avatar_split_clause,[],[f416,f2044]) ).
fof(f2044,plain,
( spl73_190
<=> ! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_190])]) ).
fof(f416,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f2042,plain,
spl73_189,
inference(avatar_split_clause,[],[f415,f2040]) ).
fof(f2040,plain,
( spl73_189
<=> ! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_189])]) ).
fof(f415,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f2038,plain,
spl73_188,
inference(avatar_split_clause,[],[f413,f2036]) ).
fof(f2036,plain,
( spl73_188
<=> ! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_188])]) ).
fof(f413,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
fof(f1953,plain,
( spl73_187
| ~ spl73_2
| ~ spl73_29 ),
inference(avatar_split_clause,[],[f819,f779,f652,f1950]) ).
fof(f1950,plain,
( spl73_187
<=> sP17(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_187])]) ).
fof(f819,plain,
( sP17(sK21)
| ~ spl73_2
| ~ spl73_29 ),
inference(resolution,[],[f780,f654]) ).
fof(f1948,plain,
spl73_186,
inference(avatar_split_clause,[],[f592,f1946]) ).
fof(f1946,plain,
( spl73_186
<=> ! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_186])]) ).
fof(f592,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f1944,plain,
spl73_185,
inference(avatar_split_clause,[],[f591,f1942]) ).
fof(f1942,plain,
( spl73_185
<=> ! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_185])]) ).
fof(f591,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f1940,plain,
spl73_184,
inference(avatar_split_clause,[],[f469,f1938]) ).
fof(f469,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f1936,plain,
spl73_183,
inference(avatar_split_clause,[],[f466,f1934]) ).
fof(f466,plain,
! [X0] :
( cons(sK27(X0),sK26(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ( cons(sK27(X0),sK26(X0)) = X0
& ssItem(sK27(X0))
& ssList(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f150,f280,f279]) ).
fof(f279,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK26(X0)) = X0
& ssItem(X2) )
& ssList(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f280,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK26(X0)) = X0
& ssItem(X2) )
=> ( cons(sK27(X0),sK26(X0)) = X0
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f1932,plain,
spl73_182,
inference(avatar_split_clause,[],[f451,f1930]) ).
fof(f1930,plain,
( spl73_182
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_182])]) ).
fof(f451,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f275]) ).
fof(f275,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f274]) ).
fof(f274,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1928,plain,
spl73_181,
inference(avatar_split_clause,[],[f443,f1926]) ).
fof(f1926,plain,
( spl73_181
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_181])]) ).
fof(f443,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f271]) ).
fof(f271,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1872,plain,
( spl73_180
| ~ spl73_1
| ~ spl73_29 ),
inference(avatar_split_clause,[],[f818,f779,f647,f1869]) ).
fof(f1869,plain,
( spl73_180
<=> sP17(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_180])]) ).
fof(f818,plain,
( sP17(sK20)
| ~ spl73_1
| ~ spl73_29 ),
inference(resolution,[],[f780,f649]) ).
fof(f1841,plain,
spl73_179,
inference(avatar_split_clause,[],[f588,f1839]) ).
fof(f1839,plain,
( spl73_179
<=> ! [X0,X1] :
( ssList(sK70(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_179])]) ).
fof(f588,plain,
! [X0,X1] :
( ssList(sK70(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f1837,plain,
spl73_178,
inference(avatar_split_clause,[],[f585,f1835]) ).
fof(f1835,plain,
( spl73_178
<=> ! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_178])]) ).
fof(f585,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f1833,plain,
spl73_177,
inference(avatar_split_clause,[],[f584,f1831]) ).
fof(f1831,plain,
( spl73_177
<=> ! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_177])]) ).
fof(f584,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f1829,plain,
spl73_176,
inference(avatar_split_clause,[],[f581,f1827]) ).
fof(f1827,plain,
( spl73_176
<=> ! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_176])]) ).
fof(f581,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f1825,plain,
spl73_175,
inference(avatar_split_clause,[],[f569,f1823]) ).
fof(f1823,plain,
( spl73_175
<=> ! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_175])]) ).
fof(f569,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f1821,plain,
spl73_174,
inference(avatar_split_clause,[],[f568,f1819]) ).
fof(f1819,plain,
( spl73_174
<=> ! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_174])]) ).
fof(f568,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f1811,plain,
( spl73_173
| ~ spl73_6
| ~ spl73_28 ),
inference(avatar_split_clause,[],[f816,f775,f672,f1808]) ).
fof(f1808,plain,
( spl73_173
<=> sP15(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_173])]) ).
fof(f816,plain,
( sP15(sK25)
| ~ spl73_6
| ~ spl73_28 ),
inference(resolution,[],[f776,f674]) ).
fof(f1676,plain,
( spl73_172
| ~ spl73_5
| ~ spl73_28 ),
inference(avatar_split_clause,[],[f815,f775,f667,f1673]) ).
fof(f1673,plain,
( spl73_172
<=> sP15(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_172])]) ).
fof(f815,plain,
( sP15(sK24)
| ~ spl73_5
| ~ spl73_28 ),
inference(resolution,[],[f776,f669]) ).
fof(f1660,plain,
spl73_171,
inference(avatar_split_clause,[],[f620,f1658]) ).
fof(f1658,plain,
( spl73_171
<=> ! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_171])]) ).
fof(f620,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f476]) ).
fof(f476,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK30(X0),nil) = X0
& ssItem(sK30(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f287,f288]) ).
fof(f288,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK30(X0),nil) = X0
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f287,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f1656,plain,
( spl73_170
| ~ spl73_2
| ~ spl73_28 ),
inference(avatar_split_clause,[],[f814,f775,f652,f1653]) ).
fof(f1653,plain,
( spl73_170
<=> sP15(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_170])]) ).
fof(f814,plain,
( sP15(sK21)
| ~ spl73_2
| ~ spl73_28 ),
inference(resolution,[],[f776,f654]) ).
fof(f1651,plain,
spl73_169,
inference(avatar_split_clause,[],[f580,f1649]) ).
fof(f1649,plain,
( spl73_169
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_169])]) ).
fof(f580,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f1647,plain,
spl73_168,
inference(avatar_split_clause,[],[f566,f1645]) ).
fof(f566,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f1643,plain,
spl73_167,
inference(avatar_split_clause,[],[f565,f1641]) ).
fof(f565,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f1639,plain,
spl73_166,
inference(avatar_split_clause,[],[f475,f1637]) ).
fof(f1637,plain,
( spl73_166
<=> ! [X0] :
( cons(sK30(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_166])]) ).
fof(f475,plain,
! [X0] :
( cons(sK30(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f1635,plain,
spl73_165,
inference(avatar_split_clause,[],[f473,f1633]) ).
fof(f473,plain,
! [X0] :
( tl(X0) = sK29(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ( tl(X0) = sK29(X0)
& ssList(sK29(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f160,f284]) ).
fof(f284,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK29(X0)
& ssList(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f1631,plain,
spl73_164,
inference(avatar_split_clause,[],[f471,f1629]) ).
fof(f471,plain,
! [X0] :
( hd(X0) = sK28(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ( hd(X0) = sK28(X0)
& ssItem(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f158,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK28(X0)
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f1627,plain,
spl73_163,
inference(avatar_split_clause,[],[f449,f1625]) ).
fof(f1625,plain,
( spl73_163
<=> ! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_163])]) ).
fof(f449,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f1623,plain,
spl73_162,
inference(avatar_split_clause,[],[f446,f1621]) ).
fof(f1621,plain,
( spl73_162
<=> ! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_162])]) ).
fof(f446,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1619,plain,
spl73_161,
inference(avatar_split_clause,[],[f445,f1617]) ).
fof(f1617,plain,
( spl73_161
<=> ! [X0,X1] :
( sP2(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_161])]) ).
fof(f445,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f1615,plain,
spl73_160,
inference(avatar_split_clause,[],[f441,f1613]) ).
fof(f1613,plain,
( spl73_160
<=> ! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_160])]) ).
fof(f441,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f1611,plain,
( spl73_159
| ~ spl73_1
| ~ spl73_28 ),
inference(avatar_split_clause,[],[f813,f775,f647,f1608]) ).
fof(f1608,plain,
( spl73_159
<=> sP15(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_159])]) ).
fof(f813,plain,
( sP15(sK20)
| ~ spl73_1
| ~ spl73_28 ),
inference(resolution,[],[f776,f649]) ).
fof(f1606,plain,
spl73_158,
inference(avatar_split_clause,[],[f438,f1604]) ).
fof(f1604,plain,
( spl73_158
<=> ! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_158])]) ).
fof(f438,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1602,plain,
spl73_157,
inference(avatar_split_clause,[],[f437,f1600]) ).
fof(f1600,plain,
( spl73_157
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_157])]) ).
fof(f437,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f1598,plain,
spl73_156,
inference(avatar_split_clause,[],[f424,f1596]) ).
fof(f1596,plain,
( spl73_156
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_156])]) ).
fof(f424,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f1594,plain,
spl73_155,
inference(avatar_split_clause,[],[f422,f1592]) ).
fof(f1592,plain,
( spl73_155
<=> ! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_155])]) ).
fof(f422,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f1590,plain,
spl73_154,
inference(avatar_split_clause,[],[f421,f1588]) ).
fof(f1588,plain,
( spl73_154
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_154])]) ).
fof(f421,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f1586,plain,
spl73_153,
inference(avatar_split_clause,[],[f420,f1584]) ).
fof(f1584,plain,
( spl73_153
<=> ! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_153])]) ).
fof(f420,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f1582,plain,
spl73_152,
inference(avatar_split_clause,[],[f419,f1580]) ).
fof(f1580,plain,
( spl73_152
<=> ! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_152])]) ).
fof(f419,plain,
! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f1578,plain,
spl73_151,
inference(avatar_split_clause,[],[f418,f1576]) ).
fof(f1576,plain,
( spl73_151
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_151])]) ).
fof(f418,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f1574,plain,
spl73_150,
inference(avatar_split_clause,[],[f414,f1572]) ).
fof(f1572,plain,
( spl73_150
<=> ! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_150])]) ).
fof(f414,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f1570,plain,
spl73_149,
inference(avatar_split_clause,[],[f412,f1568]) ).
fof(f1568,plain,
( spl73_149
<=> ! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_149])]) ).
fof(f412,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f1564,plain,
spl73_148,
inference(avatar_split_clause,[],[f643,f1562]) ).
fof(f1562,plain,
( spl73_148
<=> ! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_148])]) ).
fof(f643,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f614]) ).
fof(f614,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1560,plain,
spl73_147,
inference(avatar_split_clause,[],[f564,f1558]) ).
fof(f1558,plain,
( spl73_147
<=> ! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_147])]) ).
fof(f564,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f1556,plain,
spl73_146,
inference(avatar_split_clause,[],[f563,f1554]) ).
fof(f1554,plain,
( spl73_146
<=> ! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_146])]) ).
fof(f563,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f1525,plain,
( spl73_145
| ~ spl73_6
| ~ spl73_27 ),
inference(avatar_split_clause,[],[f806,f771,f672,f1522]) ).
fof(f1522,plain,
( spl73_145
<=> sP13(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_145])]) ).
fof(f806,plain,
( sP13(sK25)
| ~ spl73_6
| ~ spl73_27 ),
inference(resolution,[],[f772,f674]) ).
fof(f1487,plain,
spl73_144,
inference(avatar_split_clause,[],[f572,f1485]) ).
fof(f1485,plain,
( spl73_144
<=> ! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_144])]) ).
fof(f572,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f1483,plain,
( spl73_143
| ~ spl73_5
| ~ spl73_27 ),
inference(avatar_split_clause,[],[f805,f771,f667,f1480]) ).
fof(f1480,plain,
( spl73_143
<=> sP13(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_143])]) ).
fof(f805,plain,
( sP13(sK24)
| ~ spl73_5
| ~ spl73_27 ),
inference(resolution,[],[f772,f669]) ).
fof(f1478,plain,
spl73_142,
inference(avatar_split_clause,[],[f562,f1476]) ).
fof(f1476,plain,
( spl73_142
<=> ! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_142])]) ).
fof(f562,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f1474,plain,
spl73_141,
inference(avatar_split_clause,[],[f560,f1472]) ).
fof(f1472,plain,
( spl73_141
<=> ! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_141])]) ).
fof(f560,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f1470,plain,
spl73_140,
inference(avatar_split_clause,[],[f558,f1468]) ).
fof(f1468,plain,
( spl73_140
<=> ! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_140])]) ).
fof(f558,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f1466,plain,
spl73_139,
inference(avatar_split_clause,[],[f556,f1464]) ).
fof(f1464,plain,
( spl73_139
<=> ! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_139])]) ).
fof(f556,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f1462,plain,
spl73_138,
inference(avatar_split_clause,[],[f472,f1460]) ).
fof(f1460,plain,
( spl73_138
<=> ! [X0] :
( ssList(sK29(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_138])]) ).
fof(f472,plain,
! [X0] :
( ssList(sK29(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f1458,plain,
spl73_137,
inference(avatar_split_clause,[],[f470,f1456]) ).
fof(f1456,plain,
( spl73_137
<=> ! [X0] :
( ssItem(sK28(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_137])]) ).
fof(f470,plain,
! [X0] :
( ssItem(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f1454,plain,
spl73_136,
inference(avatar_split_clause,[],[f468,f1452]) ).
fof(f1452,plain,
( spl73_136
<=> ! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_136])]) ).
fof(f468,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f1450,plain,
spl73_135,
inference(avatar_split_clause,[],[f467,f1448]) ).
fof(f1448,plain,
( spl73_135
<=> ! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_135])]) ).
fof(f467,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f1446,plain,
spl73_134,
inference(avatar_split_clause,[],[f465,f1444]) ).
fof(f1444,plain,
( spl73_134
<=> ! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_134])]) ).
fof(f465,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f1442,plain,
spl73_133,
inference(avatar_split_clause,[],[f464,f1440]) ).
fof(f1440,plain,
( spl73_133
<=> ! [X0] :
( ssList(sK26(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_133])]) ).
fof(f464,plain,
! [X0] :
( ssList(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f1438,plain,
( spl73_132
| ~ spl73_2
| ~ spl73_27 ),
inference(avatar_split_clause,[],[f804,f771,f652,f1435]) ).
fof(f1435,plain,
( spl73_132
<=> sP13(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_132])]) ).
fof(f804,plain,
( sP13(sK21)
| ~ spl73_2
| ~ spl73_27 ),
inference(resolution,[],[f772,f654]) ).
fof(f1433,plain,
spl73_131,
inference(avatar_split_clause,[],[f448,f1431]) ).
fof(f1431,plain,
( spl73_131
<=> ! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_131])]) ).
fof(f448,plain,
! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f1429,plain,
spl73_130,
inference(avatar_split_clause,[],[f440,f1427]) ).
fof(f1427,plain,
( spl73_130
<=> ! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_130])]) ).
fof(f440,plain,
! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f1425,plain,
( spl73_129
| ~ spl73_1
| ~ spl73_27 ),
inference(avatar_split_clause,[],[f803,f771,f647,f1422]) ).
fof(f1422,plain,
( spl73_129
<=> sP13(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_129])]) ).
fof(f803,plain,
( sP13(sK20)
| ~ spl73_1
| ~ spl73_27 ),
inference(resolution,[],[f772,f649]) ).
fof(f1370,plain,
spl73_128,
inference(avatar_split_clause,[],[f554,f1368]) ).
fof(f1368,plain,
( spl73_128
<=> ! [X0] :
( sP16(X0)
| ~ lt(sK60(X0),sK61(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_128])]) ).
fof(f554,plain,
! [X0] :
( sP16(X0)
| ~ lt(sK60(X0),sK61(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1366,plain,
spl73_127,
inference(avatar_split_clause,[],[f543,f1364]) ).
fof(f1364,plain,
( spl73_127
<=> ! [X0] :
( sP14(X0)
| ~ leq(sK55(X0),sK56(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_127])]) ).
fof(f543,plain,
! [X0] :
( sP14(X0)
| ~ leq(sK55(X0),sK56(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f1362,plain,
spl73_126,
inference(avatar_split_clause,[],[f532,f1360]) ).
fof(f1360,plain,
( spl73_126
<=> ! [X0] :
( sP12(X0)
| leq(sK51(X0),sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_126])]) ).
fof(f532,plain,
! [X0] :
( sP12(X0)
| leq(sK51(X0),sK50(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f1358,plain,
( spl73_125
| ~ spl73_6
| ~ spl73_26 ),
inference(avatar_split_clause,[],[f801,f767,f672,f1355]) ).
fof(f1355,plain,
( spl73_125
<=> sP11(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_125])]) ).
fof(f801,plain,
( sP11(sK25)
| ~ spl73_6
| ~ spl73_26 ),
inference(resolution,[],[f768,f674]) ).
fof(f1353,plain,
spl73_124,
inference(avatar_split_clause,[],[f531,f1351]) ).
fof(f1351,plain,
( spl73_124
<=> ! [X0] :
( sP12(X0)
| leq(sK50(X0),sK51(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_124])]) ).
fof(f531,plain,
! [X0] :
( sP12(X0)
| leq(sK50(X0),sK51(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f1349,plain,
spl73_123,
inference(avatar_split_clause,[],[f520,f1347]) ).
fof(f1347,plain,
( spl73_123
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK46(X0),sK45(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_123])]) ).
fof(f520,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK46(X0),sK45(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f1345,plain,
spl73_122,
inference(avatar_split_clause,[],[f519,f1343]) ).
fof(f1343,plain,
( spl73_122
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK45(X0),sK46(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_122])]) ).
fof(f519,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK45(X0),sK46(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f1341,plain,
spl73_121,
inference(avatar_split_clause,[],[f508,f1339]) ).
fof(f1339,plain,
( spl73_121
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK41(X0),sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_121])]) ).
fof(f508,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK41(X0),sK40(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f1337,plain,
spl73_120,
inference(avatar_split_clause,[],[f507,f1335]) ).
fof(f1335,plain,
( spl73_120
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK40(X0),sK41(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_120])]) ).
fof(f507,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK40(X0),sK41(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f1333,plain,
spl73_119,
inference(avatar_split_clause,[],[f496,f1331]) ).
fof(f1331,plain,
( spl73_119
<=> ! [X0] :
( sP6(X0)
| sK35(X0) = sK36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_119])]) ).
fof(f496,plain,
! [X0] :
( sP6(X0)
| sK35(X0) = sK36(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f1329,plain,
spl73_118,
inference(avatar_split_clause,[],[f485,f1327]) ).
fof(f1327,plain,
( spl73_118
<=> ! [X0] :
( sP4(X0)
| sK31(X0) != sK32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_118])]) ).
fof(f485,plain,
! [X0] :
( sP4(X0)
| sK31(X0) != sK32(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f1325,plain,
spl73_117,
inference(avatar_split_clause,[],[f474,f1323]) ).
fof(f1323,plain,
( spl73_117
<=> ! [X0] :
( ssItem(sK30(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_117])]) ).
fof(f474,plain,
! [X0] :
( ssItem(sK30(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f1321,plain,
spl73_116,
inference(avatar_split_clause,[],[f463,f1319]) ).
fof(f463,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f1317,plain,
spl73_115,
inference(avatar_split_clause,[],[f462,f1315]) ).
fof(f462,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f1313,plain,
( spl73_114
| ~ spl73_5
| ~ spl73_26 ),
inference(avatar_split_clause,[],[f800,f767,f667,f1310]) ).
fof(f1310,plain,
( spl73_114
<=> sP11(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_114])]) ).
fof(f800,plain,
( sP11(sK24)
| ~ spl73_5
| ~ spl73_26 ),
inference(resolution,[],[f768,f669]) ).
fof(f1308,plain,
spl73_113,
inference(avatar_split_clause,[],[f452,f1306]) ).
fof(f1306,plain,
( spl73_113
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_113])]) ).
fof(f452,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f228,f227]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f1304,plain,
spl73_112,
inference(avatar_split_clause,[],[f444,f1302]) ).
fof(f1302,plain,
( spl73_112
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_112])]) ).
fof(f444,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f225,f224]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f1300,plain,
( spl73_111
| ~ spl73_2
| ~ spl73_26 ),
inference(avatar_split_clause,[],[f799,f767,f652,f1297]) ).
fof(f1297,plain,
( spl73_111
<=> sP11(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_111])]) ).
fof(f799,plain,
( sP11(sK21)
| ~ spl73_2
| ~ spl73_26 ),
inference(resolution,[],[f768,f654]) ).
fof(f1295,plain,
( spl73_110
| ~ spl73_1
| ~ spl73_26 ),
inference(avatar_split_clause,[],[f798,f767,f647,f1292]) ).
fof(f1292,plain,
( spl73_110
<=> sP11(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_110])]) ).
fof(f798,plain,
( sP11(sK20)
| ~ spl73_1
| ~ spl73_26 ),
inference(resolution,[],[f768,f649]) ).
fof(f1290,plain,
spl73_109,
inference(avatar_split_clause,[],[f546,f1288]) ).
fof(f1288,plain,
( spl73_109
<=> ! [X0] :
( strictorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_109])]) ).
fof(f546,plain,
! [X0] :
( strictorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ strictorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f1286,plain,
spl73_108,
inference(avatar_split_clause,[],[f545,f1284]) ).
fof(f1284,plain,
( spl73_108
<=> ! [X0] :
( sP16(X0)
| ~ strictorderedP(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_108])]) ).
fof(f545,plain,
! [X0] :
( sP16(X0)
| ~ strictorderedP(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f1282,plain,
spl73_107,
inference(avatar_split_clause,[],[f535,f1280]) ).
fof(f1280,plain,
( spl73_107
<=> ! [X0] :
( totalorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_107])]) ).
fof(f535,plain,
! [X0] :
( totalorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ totalorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f1278,plain,
spl73_106,
inference(avatar_split_clause,[],[f534,f1276]) ).
fof(f1276,plain,
( spl73_106
<=> ! [X0] :
( sP14(X0)
| ~ totalorderedP(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_106])]) ).
fof(f534,plain,
! [X0] :
( sP14(X0)
| ~ totalorderedP(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f1274,plain,
spl73_105,
inference(avatar_split_clause,[],[f523,f1272]) ).
fof(f1272,plain,
( spl73_105
<=> ! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_105])]) ).
fof(f523,plain,
! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f1270,plain,
spl73_104,
inference(avatar_split_clause,[],[f522,f1268]) ).
fof(f1268,plain,
( spl73_104
<=> ! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_104])]) ).
fof(f522,plain,
! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f325]) ).
fof(f1266,plain,
spl73_103,
inference(avatar_split_clause,[],[f511,f1264]) ).
fof(f1264,plain,
( spl73_103
<=> ! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_103])]) ).
fof(f511,plain,
! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ strictorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f1262,plain,
( spl73_102
| ~ spl73_6
| ~ spl73_25 ),
inference(avatar_split_clause,[],[f796,f763,f672,f1259]) ).
fof(f1259,plain,
( spl73_102
<=> sP9(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_102])]) ).
fof(f796,plain,
( sP9(sK25)
| ~ spl73_6
| ~ spl73_25 ),
inference(resolution,[],[f764,f674]) ).
fof(f1257,plain,
spl73_101,
inference(avatar_split_clause,[],[f510,f1255]) ).
fof(f1255,plain,
( spl73_101
<=> ! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_101])]) ).
fof(f510,plain,
! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f1253,plain,
spl73_100,
inference(avatar_split_clause,[],[f499,f1251]) ).
fof(f1251,plain,
( spl73_100
<=> ! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_100])]) ).
fof(f499,plain,
! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ totalorderP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f1249,plain,
spl73_99,
inference(avatar_split_clause,[],[f498,f1247]) ).
fof(f1247,plain,
( spl73_99
<=> ! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_99])]) ).
fof(f498,plain,
! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f1245,plain,
spl73_98,
inference(avatar_split_clause,[],[f488,f1243]) ).
fof(f1243,plain,
( spl73_98
<=> ! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_98])]) ).
fof(f488,plain,
! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f1241,plain,
spl73_97,
inference(avatar_split_clause,[],[f487,f1239]) ).
fof(f1239,plain,
( spl73_97
<=> ! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_97])]) ).
fof(f487,plain,
! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f1237,plain,
spl73_96,
inference(avatar_split_clause,[],[f478,f1235]) ).
fof(f478,plain,
! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ equalelemsP(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1233,plain,
spl73_95,
inference(avatar_split_clause,[],[f477,f1231]) ).
fof(f1231,plain,
( spl73_95
<=> ! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_95])]) ).
fof(f477,plain,
! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f1229,plain,
spl73_94,
inference(avatar_split_clause,[],[f411,f1227]) ).
fof(f1227,plain,
( spl73_94
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_94])]) ).
fof(f411,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f1225,plain,
spl73_93,
inference(avatar_split_clause,[],[f410,f1223]) ).
fof(f1223,plain,
( spl73_93
<=> ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_93])]) ).
fof(f410,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f1221,plain,
spl73_92,
inference(avatar_split_clause,[],[f409,f1219]) ).
fof(f1219,plain,
( spl73_92
<=> ! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_92])]) ).
fof(f409,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
fof(f1217,plain,
( spl73_91
| ~ spl73_5
| ~ spl73_25 ),
inference(avatar_split_clause,[],[f795,f763,f667,f1214]) ).
fof(f1214,plain,
( spl73_91
<=> sP9(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_91])]) ).
fof(f795,plain,
( sP9(sK24)
| ~ spl73_5
| ~ spl73_25 ),
inference(resolution,[],[f764,f669]) ).
fof(f1212,plain,
spl73_90,
inference(avatar_split_clause,[],[f408,f1210]) ).
fof(f1210,plain,
( spl73_90
<=> ! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_90])]) ).
fof(f408,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f1208,plain,
spl73_89,
inference(avatar_split_clause,[],[f407,f1206]) ).
fof(f1206,plain,
( spl73_89
<=> ! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_89])]) ).
fof(f407,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f1204,plain,
spl73_88,
inference(avatar_split_clause,[],[f406,f1202]) ).
fof(f1202,plain,
( spl73_88
<=> ! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_88])]) ).
fof(f406,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
fof(f1200,plain,
spl73_87,
inference(avatar_split_clause,[],[f405,f1198]) ).
fof(f1198,plain,
( spl73_87
<=> ! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_87])]) ).
fof(f405,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f1194,plain,
spl73_86,
inference(avatar_split_clause,[],[f385,f1192]) ).
fof(f385,plain,
! [X10,X11,X8,X9] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11)
| ~ ssList(X10)
| ~ ssItem(X9)
| ~ ssItem(X8) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
( sK22 != sK23
& sK18 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25)
& ssList(sK25)
& ssList(sK24)
& ssItem(sK23)
& ssItem(sK22)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25])],[f100,f258,f257,f256,f255,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != sK20
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK18
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( sK22 != X5
& sK18 = app(app(app(X6,cons(sK22,nil)),cons(X5,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
( ? [X5] :
( ? [X6] :
( ? [X7] :
( sK22 != X5
& sK18 = app(app(app(X6,cons(sK22,nil)),cons(X5,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( ? [X7] :
( sK22 != sK23
& sK18 = app(app(app(X6,cons(sK22,nil)),cons(sK23,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
( ? [X6] :
( ? [X7] :
( sK22 != sK23
& sK18 = app(app(app(X6,cons(sK22,nil)),cons(sK23,nil)),X7)
& ssList(X7) )
& ssList(X6) )
=> ( ? [X7] :
( sK22 != sK23
& sK18 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),X7)
& ssList(X7) )
& ssList(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
( ? [X7] :
( sK22 != sK23
& sK18 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),X7)
& ssList(X7) )
=> ( sK22 != sK23
& sK18 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25)
& ssList(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X2
| X8 = X9
| ~ ssList(X11) )
| ~ ssList(X10) )
| ~ ssItem(X9) )
| ~ ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) = X2
& X8 != X9
& ssList(X11) )
& ssList(X10) )
& ssItem(X9) )
& ssItem(X8) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( X8 = X9
| app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X0 ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X2
& X4 != X5
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( X8 = X9
| app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X0 ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X2
& X4 != X5
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f1176,plain,
( spl73_85
| ~ spl73_2
| ~ spl73_25 ),
inference(avatar_split_clause,[],[f794,f763,f652,f1173]) ).
fof(f1173,plain,
( spl73_85
<=> sP9(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_85])]) ).
fof(f794,plain,
( sP9(sK21)
| ~ spl73_2
| ~ spl73_25 ),
inference(resolution,[],[f764,f654]) ).
fof(f1129,plain,
( spl73_84
| ~ spl73_1
| ~ spl73_25 ),
inference(avatar_split_clause,[],[f793,f763,f647,f1126]) ).
fof(f1126,plain,
( spl73_84
<=> sP9(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_84])]) ).
fof(f793,plain,
( sP9(sK20)
| ~ spl73_1
| ~ spl73_25 ),
inference(resolution,[],[f764,f649]) ).
fof(f1082,plain,
( spl73_83
| ~ spl73_6
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f791,f759,f672,f1079]) ).
fof(f1079,plain,
( spl73_83
<=> sP7(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_83])]) ).
fof(f791,plain,
( sP7(sK25)
| ~ spl73_6
| ~ spl73_24 ),
inference(resolution,[],[f760,f674]) ).
fof(f1035,plain,
( spl73_82
| ~ spl73_5
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f790,f759,f667,f1032]) ).
fof(f1032,plain,
( spl73_82
<=> sP7(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_82])]) ).
fof(f790,plain,
( sP7(sK24)
| ~ spl73_5
| ~ spl73_24 ),
inference(resolution,[],[f760,f669]) ).
fof(f1030,plain,
( spl73_81
| ~ spl73_2
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f789,f759,f652,f1027]) ).
fof(f1027,plain,
( spl73_81
<=> sP7(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_81])]) ).
fof(f789,plain,
( sP7(sK21)
| ~ spl73_2
| ~ spl73_24 ),
inference(resolution,[],[f760,f654]) ).
fof(f1025,plain,
spl73_80,
inference(avatar_split_clause,[],[f645,f1023]) ).
fof(f1023,plain,
( spl73_80
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_80])]) ).
fof(f645,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f612]) ).
fof(f612,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f1021,plain,
spl73_79,
inference(avatar_split_clause,[],[f640,f1019]) ).
fof(f1019,plain,
( spl73_79
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_79])]) ).
fof(f640,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f633]) ).
fof(f633,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f579]) ).
fof(f579,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f1017,plain,
spl73_78,
inference(avatar_split_clause,[],[f552,f1015]) ).
fof(f1015,plain,
( spl73_78
<=> ! [X0] :
( sP16(X0)
| ssList(sK64(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_78])]) ).
fof(f552,plain,
! [X0] :
( sP16(X0)
| ssList(sK64(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1013,plain,
spl73_77,
inference(avatar_split_clause,[],[f551,f1011]) ).
fof(f1011,plain,
( spl73_77
<=> ! [X0] :
( sP16(X0)
| ssList(sK63(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_77])]) ).
fof(f551,plain,
! [X0] :
( sP16(X0)
| ssList(sK63(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1009,plain,
spl73_76,
inference(avatar_split_clause,[],[f550,f1007]) ).
fof(f1007,plain,
( spl73_76
<=> ! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_76])]) ).
fof(f550,plain,
! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1005,plain,
spl73_75,
inference(avatar_split_clause,[],[f549,f1003]) ).
fof(f1003,plain,
( spl73_75
<=> ! [X0] :
( sP16(X0)
| ssItem(sK61(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_75])]) ).
fof(f549,plain,
! [X0] :
( sP16(X0)
| ssItem(sK61(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1001,plain,
spl73_74,
inference(avatar_split_clause,[],[f548,f999]) ).
fof(f999,plain,
( spl73_74
<=> ! [X0] :
( sP16(X0)
| ssItem(sK60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_74])]) ).
fof(f548,plain,
! [X0] :
( sP16(X0)
| ssItem(sK60(X0)) ),
inference(cnf_transformation,[],[f351]) ).
fof(f997,plain,
spl73_73,
inference(avatar_split_clause,[],[f541,f995]) ).
fof(f995,plain,
( spl73_73
<=> ! [X0] :
( sP14(X0)
| ssList(sK59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_73])]) ).
fof(f541,plain,
! [X0] :
( sP14(X0)
| ssList(sK59(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f993,plain,
( spl73_72
| ~ spl73_1
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f788,f759,f647,f990]) ).
fof(f990,plain,
( spl73_72
<=> sP7(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_72])]) ).
fof(f788,plain,
( sP7(sK20)
| ~ spl73_1
| ~ spl73_24 ),
inference(resolution,[],[f760,f649]) ).
fof(f988,plain,
spl73_71,
inference(avatar_split_clause,[],[f540,f986]) ).
fof(f986,plain,
( spl73_71
<=> ! [X0] :
( sP14(X0)
| ssList(sK58(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_71])]) ).
fof(f540,plain,
! [X0] :
( sP14(X0)
| ssList(sK58(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f984,plain,
spl73_70,
inference(avatar_split_clause,[],[f539,f982]) ).
fof(f982,plain,
( spl73_70
<=> ! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_70])]) ).
fof(f539,plain,
! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f980,plain,
spl73_69,
inference(avatar_split_clause,[],[f538,f978]) ).
fof(f978,plain,
( spl73_69
<=> ! [X0] :
( sP14(X0)
| ssItem(sK56(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_69])]) ).
fof(f538,plain,
! [X0] :
( sP14(X0)
| ssItem(sK56(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f976,plain,
spl73_68,
inference(avatar_split_clause,[],[f537,f974]) ).
fof(f974,plain,
( spl73_68
<=> ! [X0] :
( sP14(X0)
| ssItem(sK55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_68])]) ).
fof(f537,plain,
! [X0] :
( sP14(X0)
| ssItem(sK55(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f972,plain,
spl73_67,
inference(avatar_split_clause,[],[f529,f970]) ).
fof(f970,plain,
( spl73_67
<=> ! [X0] :
( sP12(X0)
| ssList(sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_67])]) ).
fof(f529,plain,
! [X0] :
( sP12(X0)
| ssList(sK54(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f968,plain,
spl73_66,
inference(avatar_split_clause,[],[f528,f966]) ).
fof(f966,plain,
( spl73_66
<=> ! [X0] :
( sP12(X0)
| ssList(sK53(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_66])]) ).
fof(f528,plain,
! [X0] :
( sP12(X0)
| ssList(sK53(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f964,plain,
spl73_65,
inference(avatar_split_clause,[],[f527,f962]) ).
fof(f962,plain,
( spl73_65
<=> ! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_65])]) ).
fof(f527,plain,
! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f960,plain,
spl73_64,
inference(avatar_split_clause,[],[f526,f958]) ).
fof(f958,plain,
( spl73_64
<=> ! [X0] :
( sP12(X0)
| ssItem(sK51(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_64])]) ).
fof(f526,plain,
! [X0] :
( sP12(X0)
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f956,plain,
spl73_63,
inference(avatar_split_clause,[],[f525,f954]) ).
fof(f954,plain,
( spl73_63
<=> ! [X0] :
( sP12(X0)
| ssItem(sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_63])]) ).
fof(f525,plain,
! [X0] :
( sP12(X0)
| ssItem(sK50(X0)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f952,plain,
spl73_62,
inference(avatar_split_clause,[],[f517,f950]) ).
fof(f950,plain,
( spl73_62
<=> ! [X0] :
( sP10(X0)
| ssList(sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_62])]) ).
fof(f517,plain,
! [X0] :
( sP10(X0)
| ssList(sK49(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f948,plain,
( spl73_61
| ~ spl73_6
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f786,f755,f672,f945]) ).
fof(f945,plain,
( spl73_61
<=> sP5(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_61])]) ).
fof(f786,plain,
( sP5(sK25)
| ~ spl73_6
| ~ spl73_23 ),
inference(resolution,[],[f756,f674]) ).
fof(f943,plain,
spl73_60,
inference(avatar_split_clause,[],[f516,f941]) ).
fof(f941,plain,
( spl73_60
<=> ! [X0] :
( sP10(X0)
| ssList(sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_60])]) ).
fof(f516,plain,
! [X0] :
( sP10(X0)
| ssList(sK48(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f939,plain,
spl73_59,
inference(avatar_split_clause,[],[f515,f937]) ).
fof(f937,plain,
( spl73_59
<=> ! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_59])]) ).
fof(f515,plain,
! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f935,plain,
spl73_58,
inference(avatar_split_clause,[],[f514,f933]) ).
fof(f933,plain,
( spl73_58
<=> ! [X0] :
( sP10(X0)
| ssItem(sK46(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_58])]) ).
fof(f514,plain,
! [X0] :
( sP10(X0)
| ssItem(sK46(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f931,plain,
spl73_57,
inference(avatar_split_clause,[],[f513,f929]) ).
fof(f929,plain,
( spl73_57
<=> ! [X0] :
( sP10(X0)
| ssItem(sK45(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_57])]) ).
fof(f513,plain,
! [X0] :
( sP10(X0)
| ssItem(sK45(X0)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f927,plain,
spl73_56,
inference(avatar_split_clause,[],[f505,f925]) ).
fof(f925,plain,
( spl73_56
<=> ! [X0] :
( sP8(X0)
| ssList(sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_56])]) ).
fof(f505,plain,
! [X0] :
( sP8(X0)
| ssList(sK44(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f923,plain,
spl73_55,
inference(avatar_split_clause,[],[f504,f921]) ).
fof(f921,plain,
( spl73_55
<=> ! [X0] :
( sP8(X0)
| ssList(sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_55])]) ).
fof(f504,plain,
! [X0] :
( sP8(X0)
| ssList(sK43(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f919,plain,
spl73_54,
inference(avatar_split_clause,[],[f503,f917]) ).
fof(f917,plain,
( spl73_54
<=> ! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_54])]) ).
fof(f503,plain,
! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f915,plain,
spl73_53,
inference(avatar_split_clause,[],[f502,f913]) ).
fof(f913,plain,
( spl73_53
<=> ! [X0] :
( sP8(X0)
| ssItem(sK41(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_53])]) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| ssItem(sK41(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f911,plain,
spl73_52,
inference(avatar_split_clause,[],[f501,f909]) ).
fof(f909,plain,
( spl73_52
<=> ! [X0] :
( sP8(X0)
| ssItem(sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_52])]) ).
fof(f501,plain,
! [X0] :
( sP8(X0)
| ssItem(sK40(X0)) ),
inference(cnf_transformation,[],[f315]) ).
fof(f907,plain,
spl73_51,
inference(avatar_split_clause,[],[f494,f905]) ).
fof(f905,plain,
( spl73_51
<=> ! [X0] :
( sP6(X0)
| ssList(sK39(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_51])]) ).
fof(f494,plain,
! [X0] :
( sP6(X0)
| ssList(sK39(X0)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f903,plain,
( spl73_50
| ~ spl73_5
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f785,f755,f667,f900]) ).
fof(f900,plain,
( spl73_50
<=> sP5(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_50])]) ).
fof(f785,plain,
( sP5(sK24)
| ~ spl73_5
| ~ spl73_23 ),
inference(resolution,[],[f756,f669]) ).
fof(f898,plain,
spl73_49,
inference(avatar_split_clause,[],[f493,f896]) ).
fof(f896,plain,
( spl73_49
<=> ! [X0] :
( sP6(X0)
| ssList(sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_49])]) ).
fof(f493,plain,
! [X0] :
( sP6(X0)
| ssList(sK38(X0)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f894,plain,
spl73_48,
inference(avatar_split_clause,[],[f492,f892]) ).
fof(f892,plain,
( spl73_48
<=> ! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_48])]) ).
fof(f492,plain,
! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f890,plain,
spl73_47,
inference(avatar_split_clause,[],[f491,f888]) ).
fof(f888,plain,
( spl73_47
<=> ! [X0] :
( sP6(X0)
| ssItem(sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_47])]) ).
fof(f491,plain,
! [X0] :
( sP6(X0)
| ssItem(sK36(X0)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f886,plain,
spl73_46,
inference(avatar_split_clause,[],[f490,f884]) ).
fof(f884,plain,
( spl73_46
<=> ! [X0] :
( sP6(X0)
| ssItem(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_46])]) ).
fof(f490,plain,
! [X0] :
( sP6(X0)
| ssItem(sK35(X0)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f882,plain,
spl73_45,
inference(avatar_split_clause,[],[f483,f880]) ).
fof(f880,plain,
( spl73_45
<=> ! [X0] :
( sP4(X0)
| ssList(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_45])]) ).
fof(f483,plain,
! [X0] :
( sP4(X0)
| ssList(sK34(X0)) ),
inference(cnf_transformation,[],[f297]) ).
fof(f878,plain,
spl73_44,
inference(avatar_split_clause,[],[f482,f876]) ).
fof(f876,plain,
( spl73_44
<=> ! [X0] :
( sP4(X0)
| ssList(sK33(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_44])]) ).
fof(f482,plain,
! [X0] :
( sP4(X0)
| ssList(sK33(X0)) ),
inference(cnf_transformation,[],[f297]) ).
fof(f874,plain,
spl73_43,
inference(avatar_split_clause,[],[f481,f872]) ).
fof(f872,plain,
( spl73_43
<=> ! [X0] :
( sP4(X0)
| ssItem(sK32(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_43])]) ).
fof(f481,plain,
! [X0] :
( sP4(X0)
| ssItem(sK32(X0)) ),
inference(cnf_transformation,[],[f297]) ).
fof(f870,plain,
spl73_42,
inference(avatar_split_clause,[],[f480,f868]) ).
fof(f868,plain,
( spl73_42
<=> ! [X0] :
( sP4(X0)
| ssItem(sK31(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_42])]) ).
fof(f480,plain,
! [X0] :
( sP4(X0)
| ssItem(sK31(X0)) ),
inference(cnf_transformation,[],[f297]) ).
fof(f866,plain,
spl73_41,
inference(avatar_split_clause,[],[f461,f864]) ).
fof(f864,plain,
( spl73_41
<=> ! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_41])]) ).
fof(f461,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f862,plain,
spl73_40,
inference(avatar_split_clause,[],[f460,f860]) ).
fof(f860,plain,
( spl73_40
<=> ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_40])]) ).
fof(f460,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f858,plain,
( spl73_39
| ~ spl73_2
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f784,f755,f652,f855]) ).
fof(f855,plain,
( spl73_39
<=> sP5(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_39])]) ).
fof(f784,plain,
( sP5(sK21)
| ~ spl73_2
| ~ spl73_23 ),
inference(resolution,[],[f756,f654]) ).
fof(f853,plain,
spl73_38,
inference(avatar_split_clause,[],[f459,f851]) ).
fof(f851,plain,
( spl73_38
<=> ! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_38])]) ).
fof(f459,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f849,plain,
spl73_37,
inference(avatar_split_clause,[],[f458,f847]) ).
fof(f847,plain,
( spl73_37
<=> ! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_37])]) ).
fof(f458,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f845,plain,
spl73_36,
inference(avatar_split_clause,[],[f457,f843]) ).
fof(f843,plain,
( spl73_36
<=> ! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_36])]) ).
fof(f457,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f841,plain,
spl73_35,
inference(avatar_split_clause,[],[f456,f839]) ).
fof(f839,plain,
( spl73_35
<=> ! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_35])]) ).
fof(f456,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f837,plain,
spl73_34,
inference(avatar_split_clause,[],[f404,f835]) ).
fof(f835,plain,
( spl73_34
<=> ! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_34])]) ).
fof(f404,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f833,plain,
spl73_33,
inference(avatar_split_clause,[],[f403,f831]) ).
fof(f831,plain,
( spl73_33
<=> ! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_33])]) ).
fof(f403,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
fof(f829,plain,
spl73_32,
inference(avatar_split_clause,[],[f402,f827]) ).
fof(f827,plain,
( spl73_32
<=> ! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_32])]) ).
fof(f402,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f825,plain,
spl73_31,
inference(avatar_split_clause,[],[f401,f823]) ).
fof(f823,plain,
( spl73_31
<=> ! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_31])]) ).
fof(f401,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f811,plain,
( spl73_30
| ~ spl73_1
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f783,f755,f647,f808]) ).
fof(f783,plain,
( sP5(sK20)
| ~ spl73_1
| ~ spl73_23 ),
inference(resolution,[],[f756,f649]) ).
fof(f781,plain,
spl73_29,
inference(avatar_split_clause,[],[f555,f779]) ).
fof(f555,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f249,f248]) ).
fof(f175,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
fof(f777,plain,
spl73_28,
inference(avatar_split_clause,[],[f544,f775]) ).
fof(f544,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f246,f245]) ).
fof(f173,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
fof(f773,plain,
spl73_27,
inference(avatar_split_clause,[],[f533,f771]) ).
fof(f533,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f243,f242]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f769,plain,
spl73_26,
inference(avatar_split_clause,[],[f521,f767]) ).
fof(f521,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f240,f239]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f765,plain,
spl73_25,
inference(avatar_split_clause,[],[f509,f763]) ).
fof(f509,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f237,f236]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f761,plain,
spl73_24,
inference(avatar_split_clause,[],[f497,f759]) ).
fof(f497,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f234,f233]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f757,plain,
spl73_23,
inference(avatar_split_clause,[],[f486,f755]) ).
fof(f486,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f231,f230]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f753,plain,
spl73_22,
inference(avatar_split_clause,[],[f609,f750]) ).
fof(f609,plain,
sK20 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25),
inference(definition_unfolding,[],[f390,f384]) ).
fof(f384,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f259]) ).
fof(f390,plain,
sK18 = app(app(app(sK24,cons(sK22,nil)),cons(sK23,nil)),sK25),
inference(cnf_transformation,[],[f259]) ).
fof(f748,plain,
spl73_21,
inference(avatar_split_clause,[],[f618,f746]) ).
fof(f746,plain,
( spl73_21
<=> ! [X1] : sP2(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_21])]) ).
fof(f618,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f450]) ).
fof(f450,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f276]) ).
fof(f744,plain,
spl73_20,
inference(avatar_split_clause,[],[f616,f742]) ).
fof(f742,plain,
( spl73_20
<=> ! [X1] : sP0(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_20])]) ).
fof(f616,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f272]) ).
fof(f740,plain,
~ spl73_19,
inference(avatar_split_clause,[],[f608,f737]) ).
fof(f737,plain,
( spl73_19
<=> sK71 = sK72 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_19])]) ).
fof(f608,plain,
sK71 != sK72,
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
( sK71 != sK72
& ssItem(sK72)
& ssItem(sK71) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f2,f377,f376]) ).
fof(f376,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK71 != X1
& ssItem(X1) )
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f377,plain,
( ? [X1] :
( sK71 != X1
& ssItem(X1) )
=> ( sK71 != sK72
& ssItem(sK72) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f735,plain,
spl73_18,
inference(avatar_split_clause,[],[f607,f732]) ).
fof(f732,plain,
( spl73_18
<=> ssItem(sK72) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_18])]) ).
fof(f607,plain,
ssItem(sK72),
inference(cnf_transformation,[],[f378]) ).
fof(f730,plain,
spl73_17,
inference(avatar_split_clause,[],[f606,f727]) ).
fof(f727,plain,
( spl73_17
<=> ssItem(sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_17])]) ).
fof(f606,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f378]) ).
fof(f725,plain,
spl73_16,
inference(avatar_split_clause,[],[f400,f722]) ).
fof(f400,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f720,plain,
spl73_15,
inference(avatar_split_clause,[],[f399,f717]) ).
fof(f717,plain,
( spl73_15
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_15])]) ).
fof(f399,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f715,plain,
spl73_14,
inference(avatar_split_clause,[],[f398,f712]) ).
fof(f712,plain,
( spl73_14
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_14])]) ).
fof(f398,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f710,plain,
spl73_13,
inference(avatar_split_clause,[],[f397,f707]) ).
fof(f707,plain,
( spl73_13
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_13])]) ).
fof(f397,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f705,plain,
spl73_12,
inference(avatar_split_clause,[],[f396,f702]) ).
fof(f702,plain,
( spl73_12
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_12])]) ).
fof(f396,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f700,plain,
spl73_11,
inference(avatar_split_clause,[],[f395,f697]) ).
fof(f697,plain,
( spl73_11
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_11])]) ).
fof(f395,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f695,plain,
spl73_10,
inference(avatar_split_clause,[],[f394,f692]) ).
fof(f692,plain,
( spl73_10
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_10])]) ).
fof(f394,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f690,plain,
spl73_9,
inference(avatar_split_clause,[],[f393,f687]) ).
fof(f393,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f685,plain,
~ spl73_8,
inference(avatar_split_clause,[],[f392,f682]) ).
fof(f392,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f680,plain,
~ spl73_7,
inference(avatar_split_clause,[],[f391,f677]) ).
fof(f391,plain,
sK22 != sK23,
inference(cnf_transformation,[],[f259]) ).
fof(f675,plain,
spl73_6,
inference(avatar_split_clause,[],[f389,f672]) ).
fof(f389,plain,
ssList(sK25),
inference(cnf_transformation,[],[f259]) ).
fof(f670,plain,
spl73_5,
inference(avatar_split_clause,[],[f388,f667]) ).
fof(f388,plain,
ssList(sK24),
inference(cnf_transformation,[],[f259]) ).
fof(f665,plain,
spl73_4,
inference(avatar_split_clause,[],[f387,f662]) ).
fof(f387,plain,
ssItem(sK23),
inference(cnf_transformation,[],[f259]) ).
fof(f660,plain,
spl73_3,
inference(avatar_split_clause,[],[f386,f657]) ).
fof(f386,plain,
ssItem(sK22),
inference(cnf_transformation,[],[f259]) ).
fof(f655,plain,
spl73_2,
inference(avatar_split_clause,[],[f382,f652]) ).
fof(f382,plain,
ssList(sK21),
inference(cnf_transformation,[],[f259]) ).
fof(f650,plain,
spl73_1,
inference(avatar_split_clause,[],[f381,f647]) ).
fof(f381,plain,
ssList(sK20),
inference(cnf_transformation,[],[f259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC189+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 04:11:26 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (28800)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (28804)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (28803)WARNING: value z3 for option sas not known
% 0.14/0.37 % (28802)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (28805)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (28801)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (28806)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (28803)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (28807)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [3]
% 0.14/0.42 TRYING [4]
% 0.20/0.44 TRYING [4]
% 0.20/0.46 % (28805)First to succeed.
% 0.20/0.46 TRYING [1]
% 0.20/0.46 TRYING [2]
% 0.20/0.47 TRYING [3]
% 0.20/0.48 % (28805)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (28805)------------------------------
% 0.20/0.49 % (28805)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.49 % (28805)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (28805)Memory used [KB]: 3074
% 0.20/0.49 % (28805)Time elapsed: 0.106 s
% 0.20/0.49 % (28805)Instructions burned: 189 (million)
% 0.20/0.49 % (28805)------------------------------
% 0.20/0.49 % (28805)------------------------------
% 0.20/0.49 % (28800)Success in time 0.135 s
%------------------------------------------------------------------------------