TSTP Solution File: SWC339+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC339+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 May 21 05:13:18 EDT 2024
% Result : Theorem 1.19s 0.53s
% Output : Refutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 477
% Syntax : Number of formulae : 1392 ( 249 unt; 0 def)
% Number of atoms : 5617 ( 935 equ)
% Maximal formula atoms : 56 ( 4 avg)
% Number of connectives : 6892 (2667 ~;2696 |; 844 &)
% ( 387 <=>; 298 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 349 ( 347 usr; 311 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 2174 (1805 !; 369 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3851,plain,
$false,
inference(avatar_sat_refutation,[],[f650,f655,f660,f665,f670,f675,f684,f689,f694,f699,f704,f709,f714,f719,f724,f729,f734,f739,f744,f749,f753,f757,f761,f765,f769,f773,f777,f781,f785,f810,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,f1029,f1034,f1039,f1079,f1126,f1173,f1198,f1202,f1206,f1210,f1214,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1259,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1293,f1298,f1302,f1306,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1433,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1474,f1478,f1482,f1486,f1490,f1515,f1559,f1563,f1567,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1600,f1605,f1609,f1613,f1617,f1621,f1625,f1629,f1633,f1637,f1641,f1645,f1650,f1654,f1658,f1662,f1666,f1677,f1757,f1827,f1831,f1835,f1839,f1843,f1848,f1852,f1934,f1938,f1942,f1947,f1951,f1955,f1959,f2044,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2081,f2093,f2156,f2160,f2164,f2170,f2174,f2178,f2182,f2186,f2252,f2256,f2260,f2264,f2268,f2272,f2276,f2282,f2286,f2321,f2325,f2329,f2333,f2384,f2390,f2394,f2398,f2483,f2487,f2491,f2497,f2501,f2505,f2509,f2513,f2517,f2521,f2525,f2529,f2533,f2539,f2579,f2583,f2587,f2606,f2610,f2614,f2622,f2626,f2630,f2674,f2683,f2688,f2693,f2698,f2703,f2708,f2713,f2718,f2867,f2962,f2967,f2972,f2977,f2992,f2997,f3003,f3016,f3044,f3094,f3101,f3121,f3122,f3162,f3191,f3197,f3201,f3206,f3210,f3214,f3218,f3223,f3227,f3231,f3235,f3241,f3255,f3305,f3315,f3320,f3518,f3524,f3529,f3535,f3541,f3547,f3553,f3559,f3565,f3605,f3645,f3650,f3690,f3697,f3737,f3743,f3783,f3789,f3794,f3833,f3838,f3843,f3848,f3850]) ).
fof(f3850,plain,
( ~ spl71_2
| ~ spl71_1
| ~ spl71_3
| ~ spl71_4
| spl71_6
| ~ spl71_9
| ~ spl71_242 ),
inference(avatar_split_clause,[],[f2599,f2585,f686,f672,f662,f657,f647,f652]) ).
fof(f652,plain,
( spl71_2
<=> ssList(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).
fof(f647,plain,
( spl71_1
<=> ssList(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).
fof(f657,plain,
( spl71_3
<=> ssList(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_3])]) ).
fof(f662,plain,
( spl71_4
<=> ssList(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_4])]) ).
fof(f672,plain,
( spl71_6
<=> segmentP(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_6])]) ).
fof(f686,plain,
( spl71_9
<=> sK21 = app(app(sK22,sK20),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_9])]) ).
fof(f2585,plain,
( spl71_242
<=> ! [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,[spl71_242])]) ).
fof(f2599,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK23)
| ~ ssList(sK22)
| ~ ssList(sK20)
| ~ ssList(sK21)
| ~ spl71_9
| ~ spl71_242 ),
inference(superposition,[],[f2586,f688]) ).
fof(f688,plain,
( sK21 = app(app(sK22,sK20),sK23)
| ~ spl71_9 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f2586,plain,
( ! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) )
| ~ spl71_242 ),
inference(avatar_component_clause,[],[f2585]) ).
fof(f3848,plain,
( spl71_310
| ~ spl71_4
| ~ spl71_194 ),
inference(avatar_split_clause,[],[f2106,f2059,f662,f3846]) ).
fof(f3846,plain,
( spl71_310
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_310])]) ).
fof(f2059,plain,
( spl71_194
<=> ! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_194])]) ).
fof(f2106,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) )
| ~ spl71_4
| ~ spl71_194 ),
inference(resolution,[],[f2060,f664]) ).
fof(f664,plain,
( ssList(sK23)
| ~ spl71_4 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f2060,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) )
| ~ spl71_194 ),
inference(avatar_component_clause,[],[f2059]) ).
fof(f3843,plain,
( spl71_309
| ~ spl71_3
| ~ spl71_194 ),
inference(avatar_split_clause,[],[f2105,f2059,f657,f3841]) ).
fof(f3841,plain,
( spl71_309
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK22) = app(cons(X0,nil),sK22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_309])]) ).
fof(f2105,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK22) = app(cons(X0,nil),sK22) )
| ~ spl71_3
| ~ spl71_194 ),
inference(resolution,[],[f2060,f659]) ).
fof(f659,plain,
( ssList(sK22)
| ~ spl71_3 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f3838,plain,
( spl71_308
| ~ spl71_2
| ~ spl71_194 ),
inference(avatar_split_clause,[],[f2104,f2059,f652,f3836]) ).
fof(f3836,plain,
( spl71_308
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK21) = app(cons(X0,nil),sK21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_308])]) ).
fof(f2104,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK21) = app(cons(X0,nil),sK21) )
| ~ spl71_2
| ~ spl71_194 ),
inference(resolution,[],[f2060,f654]) ).
fof(f654,plain,
( ssList(sK21)
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f3833,plain,
( spl71_307
| ~ spl71_1
| ~ spl71_194 ),
inference(avatar_split_clause,[],[f2103,f2059,f647,f3831]) ).
fof(f3831,plain,
( spl71_307
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_307])]) ).
fof(f2103,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) )
| ~ spl71_1
| ~ spl71_194 ),
inference(resolution,[],[f2060,f649]) ).
fof(f649,plain,
( ssList(sK20)
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f3794,plain,
( spl71_306
| ~ spl71_13
| ~ spl71_271 ),
inference(avatar_split_clause,[],[f3261,f3091,f706,f3791]) ).
fof(f3791,plain,
( spl71_306
<=> cyclefreeP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_306])]) ).
fof(f706,plain,
( spl71_13
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_13])]) ).
fof(f3091,plain,
( spl71_271
<=> nil = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_271])]) ).
fof(f3261,plain,
( cyclefreeP(sK23)
| ~ spl71_13
| ~ spl71_271 ),
inference(superposition,[],[f708,f3093]) ).
fof(f3093,plain,
( nil = sK23
| ~ spl71_271 ),
inference(avatar_component_clause,[],[f3091]) ).
fof(f708,plain,
( cyclefreeP(nil)
| ~ spl71_13 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f3789,plain,
( spl71_305
| ~ spl71_276
| ~ spl71_304 ),
inference(avatar_split_clause,[],[f3784,f3780,f3194,f3786]) ).
fof(f3786,plain,
( spl71_305
<=> sK22 = cons(sK26(sK22),sK27(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_305])]) ).
fof(f3194,plain,
( spl71_276
<=> tl(sK22) = sK27(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_276])]) ).
fof(f3780,plain,
( spl71_304
<=> sK22 = cons(sK26(sK22),tl(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_304])]) ).
fof(f3784,plain,
( sK22 = cons(sK26(sK22),sK27(sK22))
| ~ spl71_276
| ~ spl71_304 ),
inference(forward_demodulation,[],[f3782,f3195]) ).
fof(f3195,plain,
( tl(sK22) = sK27(sK22)
| ~ spl71_276 ),
inference(avatar_component_clause,[],[f3194]) ).
fof(f3782,plain,
( sK22 = cons(sK26(sK22),tl(sK22))
| ~ spl71_304 ),
inference(avatar_component_clause,[],[f3780]) ).
fof(f3783,plain,
( spl71_269
| spl71_304
| ~ spl71_3
| ~ spl71_187
| ~ spl71_268 ),
inference(avatar_split_clause,[],[f3256,f3037,f1949,f657,f3780,f3041]) ).
fof(f3041,plain,
( spl71_269
<=> nil = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_269])]) ).
fof(f1949,plain,
( spl71_187
<=> ! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_187])]) ).
fof(f3037,plain,
( spl71_268
<=> hd(sK22) = sK26(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_268])]) ).
fof(f3256,plain,
( sK22 = cons(sK26(sK22),tl(sK22))
| nil = sK22
| ~ spl71_3
| ~ spl71_187
| ~ spl71_268 ),
inference(forward_demodulation,[],[f2007,f3039]) ).
fof(f3039,plain,
( hd(sK22) = sK26(sK22)
| ~ spl71_268 ),
inference(avatar_component_clause,[],[f3037]) ).
fof(f2007,plain,
( nil = sK22
| sK22 = cons(hd(sK22),tl(sK22))
| ~ spl71_3
| ~ spl71_187 ),
inference(resolution,[],[f1950,f659]) ).
fof(f1950,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl71_187 ),
inference(avatar_component_clause,[],[f1949]) ).
fof(f3743,plain,
( spl71_303
| ~ spl71_286
| ~ spl71_302 ),
inference(avatar_split_clause,[],[f3738,f3734,f3238,f3740]) ).
fof(f3740,plain,
( spl71_303
<=> sK20 = cons(sK26(sK20),sK27(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_303])]) ).
fof(f3238,plain,
( spl71_286
<=> tl(sK20) = sK27(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_286])]) ).
fof(f3734,plain,
( spl71_302
<=> sK20 = cons(sK26(sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_302])]) ).
fof(f3738,plain,
( sK20 = cons(sK26(sK20),sK27(sK20))
| ~ spl71_286
| ~ spl71_302 ),
inference(forward_demodulation,[],[f3736,f3240]) ).
fof(f3240,plain,
( tl(sK20) = sK27(sK20)
| ~ spl71_286 ),
inference(avatar_component_clause,[],[f3238]) ).
fof(f3736,plain,
( sK20 = cons(sK26(sK20),tl(sK20))
| ~ spl71_302 ),
inference(avatar_component_clause,[],[f3734]) ).
fof(f3737,plain,
( spl71_8
| spl71_302
| ~ spl71_1
| ~ spl71_187
| ~ spl71_259 ),
inference(avatar_split_clause,[],[f3248,f2864,f1949,f647,f3734,f681]) ).
fof(f681,plain,
( spl71_8
<=> nil = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_8])]) ).
fof(f2864,plain,
( spl71_259
<=> hd(sK20) = sK26(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_259])]) ).
fof(f3248,plain,
( sK20 = cons(sK26(sK20),tl(sK20))
| nil = sK20
| ~ spl71_1
| ~ spl71_187
| ~ spl71_259 ),
inference(forward_demodulation,[],[f2005,f2866]) ).
fof(f2866,plain,
( hd(sK20) = sK26(sK20)
| ~ spl71_259 ),
inference(avatar_component_clause,[],[f2864]) ).
fof(f2005,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20))
| ~ spl71_1
| ~ spl71_187 ),
inference(resolution,[],[f1950,f649]) ).
fof(f3697,plain,
( spl71_301
| ~ spl71_266
| ~ spl71_273
| ~ spl71_300 ),
inference(avatar_split_clause,[],[f3692,f3687,f3118,f3000,f3694]) ).
fof(f3694,plain,
( spl71_301
<=> sK21 = cons(sK26(sK21),sK27(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_301])]) ).
fof(f3000,plain,
( spl71_266
<=> hd(sK21) = sK26(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_266])]) ).
fof(f3118,plain,
( spl71_273
<=> tl(sK21) = sK27(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_273])]) ).
fof(f3687,plain,
( spl71_300
<=> sK21 = cons(hd(sK21),tl(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_300])]) ).
fof(f3692,plain,
( sK21 = cons(sK26(sK21),sK27(sK21))
| ~ spl71_266
| ~ spl71_273
| ~ spl71_300 ),
inference(forward_demodulation,[],[f3691,f3002]) ).
fof(f3002,plain,
( hd(sK21) = sK26(sK21)
| ~ spl71_266 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f3691,plain,
( sK21 = cons(hd(sK21),sK27(sK21))
| ~ spl71_273
| ~ spl71_300 ),
inference(forward_demodulation,[],[f3689,f3120]) ).
fof(f3120,plain,
( tl(sK21) = sK27(sK21)
| ~ spl71_273 ),
inference(avatar_component_clause,[],[f3118]) ).
fof(f3689,plain,
( sK21 = cons(hd(sK21),tl(sK21))
| ~ spl71_300 ),
inference(avatar_component_clause,[],[f3687]) ).
fof(f3690,plain,
( spl71_300
| spl71_264
| ~ spl71_2
| ~ spl71_187 ),
inference(avatar_split_clause,[],[f2006,f1949,f652,f2989,f3687]) ).
fof(f2989,plain,
( spl71_264
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_264])]) ).
fof(f2006,plain,
( nil = sK21
| sK21 = cons(hd(sK21),tl(sK21))
| ~ spl71_2
| ~ spl71_187 ),
inference(resolution,[],[f1950,f654]) ).
fof(f3650,plain,
( spl71_299
| spl71_269
| ~ spl71_3
| ~ spl71_185 ),
inference(avatar_split_clause,[],[f1971,f1940,f657,f3041,f3647]) ).
fof(f3647,plain,
( spl71_299
<=> sK22 = cons(sK25(sK22),sK24(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_299])]) ).
fof(f1940,plain,
( spl71_185
<=> ! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_185])]) ).
fof(f1971,plain,
( nil = sK22
| sK22 = cons(sK25(sK22),sK24(sK22))
| ~ spl71_3
| ~ spl71_185 ),
inference(resolution,[],[f1941,f659]) ).
fof(f1941,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK25(X0),sK24(X0)) = X0 )
| ~ spl71_185 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f3645,plain,
( spl71_298
| ~ spl71_12
| ~ spl71_271 ),
inference(avatar_split_clause,[],[f3260,f3091,f701,f3642]) ).
fof(f3642,plain,
( spl71_298
<=> duplicatefreeP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_298])]) ).
fof(f701,plain,
( spl71_12
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_12])]) ).
fof(f3260,plain,
( duplicatefreeP(sK23)
| ~ spl71_12
| ~ spl71_271 ),
inference(superposition,[],[f703,f3093]) ).
fof(f703,plain,
( duplicatefreeP(nil)
| ~ spl71_12 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f3605,plain,
( spl71_297
| spl71_264
| ~ spl71_2
| ~ spl71_185 ),
inference(avatar_split_clause,[],[f1970,f1940,f652,f2989,f3602]) ).
fof(f3602,plain,
( spl71_297
<=> sK21 = cons(sK25(sK21),sK24(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_297])]) ).
fof(f1970,plain,
( nil = sK21
| sK21 = cons(sK25(sK21),sK24(sK21))
| ~ spl71_2
| ~ spl71_185 ),
inference(resolution,[],[f1941,f654]) ).
fof(f3565,plain,
( spl71_296
| spl71_8
| ~ spl71_1
| ~ spl71_185 ),
inference(avatar_split_clause,[],[f1969,f1940,f647,f681,f3562]) ).
fof(f3562,plain,
( spl71_296
<=> sK20 = cons(sK25(sK20),sK24(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_296])]) ).
fof(f1969,plain,
( nil = sK20
| sK20 = cons(sK25(sK20),sK24(sK20))
| ~ spl71_1
| ~ spl71_185 ),
inference(resolution,[],[f1941,f649]) ).
fof(f3559,plain,
( spl71_295
| ~ spl71_18
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f821,f783,f731,f3556]) ).
fof(f3556,plain,
( spl71_295
<=> sP17(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_295])]) ).
fof(f731,plain,
( spl71_18
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_18])]) ).
fof(f783,plain,
( spl71_30
<=> ! [X0] :
( sP17(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_30])]) ).
fof(f821,plain,
( sP17(nil)
| ~ spl71_18
| ~ spl71_30 ),
inference(resolution,[],[f784,f733]) ).
fof(f733,plain,
( ssList(nil)
| ~ spl71_18 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f784,plain,
( ! [X0] :
( ~ ssList(X0)
| sP17(X0) )
| ~ spl71_30 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f3553,plain,
( spl71_294
| ~ spl71_18
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f816,f779,f731,f3550]) ).
fof(f3550,plain,
( spl71_294
<=> sP15(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_294])]) ).
fof(f779,plain,
( spl71_29
<=> ! [X0] :
( sP15(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_29])]) ).
fof(f816,plain,
( sP15(nil)
| ~ spl71_18
| ~ spl71_29 ),
inference(resolution,[],[f780,f733]) ).
fof(f780,plain,
( ! [X0] :
( ~ ssList(X0)
| sP15(X0) )
| ~ spl71_29 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f3547,plain,
( spl71_293
| ~ spl71_18
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f811,f775,f731,f3544]) ).
fof(f3544,plain,
( spl71_293
<=> sP13(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_293])]) ).
fof(f775,plain,
( spl71_28
<=> ! [X0] :
( sP13(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_28])]) ).
fof(f811,plain,
( sP13(nil)
| ~ spl71_18
| ~ spl71_28 ),
inference(resolution,[],[f776,f733]) ).
fof(f776,plain,
( ! [X0] :
( ~ ssList(X0)
| sP13(X0) )
| ~ spl71_28 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f3541,plain,
( spl71_292
| ~ spl71_18
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f801,f771,f731,f3538]) ).
fof(f3538,plain,
( spl71_292
<=> sP11(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_292])]) ).
fof(f771,plain,
( spl71_27
<=> ! [X0] :
( sP11(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_27])]) ).
fof(f801,plain,
( sP11(nil)
| ~ spl71_18
| ~ spl71_27 ),
inference(resolution,[],[f772,f733]) ).
fof(f772,plain,
( ! [X0] :
( ~ ssList(X0)
| sP11(X0) )
| ~ spl71_27 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f3535,plain,
( spl71_291
| ~ spl71_18
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f796,f767,f731,f3532]) ).
fof(f3532,plain,
( spl71_291
<=> sP9(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_291])]) ).
fof(f767,plain,
( spl71_26
<=> ! [X0] :
( sP9(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_26])]) ).
fof(f796,plain,
( sP9(nil)
| ~ spl71_18
| ~ spl71_26 ),
inference(resolution,[],[f768,f733]) ).
fof(f768,plain,
( ! [X0] :
( ~ ssList(X0)
| sP9(X0) )
| ~ spl71_26 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f3529,plain,
( spl71_290
| ~ spl71_18
| ~ spl71_25 ),
inference(avatar_split_clause,[],[f791,f763,f731,f3526]) ).
fof(f3526,plain,
( spl71_290
<=> sP7(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_290])]) ).
fof(f763,plain,
( spl71_25
<=> ! [X0] :
( sP7(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_25])]) ).
fof(f791,plain,
( sP7(nil)
| ~ spl71_18
| ~ spl71_25 ),
inference(resolution,[],[f764,f733]) ).
fof(f764,plain,
( ! [X0] :
( ~ ssList(X0)
| sP7(X0) )
| ~ spl71_25 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f3524,plain,
( spl71_289
| ~ spl71_11
| ~ spl71_271 ),
inference(avatar_split_clause,[],[f3259,f3091,f696,f3521]) ).
fof(f3521,plain,
( spl71_289
<=> equalelemsP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_289])]) ).
fof(f696,plain,
( spl71_11
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_11])]) ).
fof(f3259,plain,
( equalelemsP(sK23)
| ~ spl71_11
| ~ spl71_271 ),
inference(superposition,[],[f698,f3093]) ).
fof(f698,plain,
( equalelemsP(nil)
| ~ spl71_11 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f3518,plain,
( spl71_288
| ~ spl71_18
| ~ spl71_24 ),
inference(avatar_split_clause,[],[f786,f759,f731,f3515]) ).
fof(f3515,plain,
( spl71_288
<=> sP5(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_288])]) ).
fof(f759,plain,
( spl71_24
<=> ! [X0] :
( sP5(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_24])]) ).
fof(f786,plain,
( sP5(nil)
| ~ spl71_18
| ~ spl71_24 ),
inference(resolution,[],[f760,f733]) ).
fof(f760,plain,
( ! [X0] :
( ~ ssList(X0)
| sP5(X0) )
| ~ spl71_24 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f3320,plain,
( ~ spl71_287
| spl71_10
| ~ spl71_271 ),
inference(avatar_split_clause,[],[f3258,f3091,f691,f3317]) ).
fof(f3317,plain,
( spl71_287
<=> singletonP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_287])]) ).
fof(f691,plain,
( spl71_10
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_10])]) ).
fof(f3258,plain,
( ~ singletonP(sK23)
| spl71_10
| ~ spl71_271 ),
inference(superposition,[],[f693,f3093]) ).
fof(f693,plain,
( ~ singletonP(nil)
| spl71_10 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f3315,plain,
( spl71_276
| spl71_269
| ~ spl71_3
| ~ spl71_167 ),
inference(avatar_split_clause,[],[f1729,f1639,f657,f3041,f3194]) ).
fof(f1639,plain,
( spl71_167
<=> ! [X0] :
( tl(X0) = sK27(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_167])]) ).
fof(f1729,plain,
( nil = sK22
| tl(sK22) = sK27(sK22)
| ~ spl71_3
| ~ spl71_167 ),
inference(resolution,[],[f1640,f659]) ).
fof(f1640,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK27(X0) )
| ~ spl71_167 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f3305,plain,
( spl71_286
| spl71_8
| ~ spl71_1
| ~ spl71_167 ),
inference(avatar_split_clause,[],[f1727,f1639,f647,f681,f3238]) ).
fof(f1727,plain,
( nil = sK20
| tl(sK20) = sK27(sK20)
| ~ spl71_1
| ~ spl71_167 ),
inference(resolution,[],[f1640,f649]) ).
fof(f3255,plain,
( spl71_269
| ~ spl71_271
| ~ spl71_272 ),
inference(avatar_split_clause,[],[f3252,f3098,f3091,f3041]) ).
fof(f3098,plain,
( spl71_272
<=> sK22 = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_272])]) ).
fof(f3252,plain,
( nil = sK22
| ~ spl71_271
| ~ spl71_272 ),
inference(forward_demodulation,[],[f3093,f3100]) ).
fof(f3100,plain,
( sK22 = sK23
| ~ spl71_272 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f3241,plain,
( spl71_286
| spl71_274
| ~ spl71_1
| ~ spl71_167
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f3126,f3041,f1639,f647,f3159,f3238]) ).
fof(f3159,plain,
( spl71_274
<=> sK20 = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_274])]) ).
fof(f3126,plain,
( sK20 = sK22
| tl(sK20) = sK27(sK20)
| ~ spl71_1
| ~ spl71_167
| ~ spl71_269 ),
inference(forward_demodulation,[],[f1727,f3043]) ).
fof(f3043,plain,
( nil = sK22
| ~ spl71_269 ),
inference(avatar_component_clause,[],[f3041]) ).
fof(f3235,plain,
( spl71_285
| ~ spl71_4
| ~ spl71_171 ),
inference(avatar_split_clause,[],[f1795,f1656,f662,f3233]) ).
fof(f3233,plain,
( spl71_285
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_285])]) ).
fof(f1656,plain,
( spl71_171
<=> ! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_171])]) ).
fof(f1795,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 )
| ~ spl71_4
| ~ spl71_171 ),
inference(resolution,[],[f1657,f664]) ).
fof(f1657,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 )
| ~ spl71_171 ),
inference(avatar_component_clause,[],[f1656]) ).
fof(f3231,plain,
( spl71_284
| ~ spl71_3
| ~ spl71_171 ),
inference(avatar_split_clause,[],[f1794,f1656,f657,f3229]) ).
fof(f3229,plain,
( spl71_284
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_284])]) ).
fof(f1794,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 )
| ~ spl71_3
| ~ spl71_171 ),
inference(resolution,[],[f1657,f659]) ).
fof(f3227,plain,
( spl71_283
| ~ spl71_2
| ~ spl71_171 ),
inference(avatar_split_clause,[],[f1793,f1656,f652,f3225]) ).
fof(f3225,plain,
( spl71_283
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_283])]) ).
fof(f1793,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 )
| ~ spl71_2
| ~ spl71_171 ),
inference(resolution,[],[f1657,f654]) ).
fof(f3223,plain,
( spl71_282
| ~ spl71_1
| ~ spl71_171 ),
inference(avatar_split_clause,[],[f1792,f1656,f647,f3221]) ).
fof(f3221,plain,
( spl71_282
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_282])]) ).
fof(f1792,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 )
| ~ spl71_1
| ~ spl71_171 ),
inference(resolution,[],[f1657,f649]) ).
fof(f3218,plain,
( spl71_281
| ~ spl71_4
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1765,f1652,f662,f3216]) ).
fof(f3216,plain,
( spl71_281
<=> ! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_281])]) ).
fof(f1652,plain,
( spl71_170
<=> ! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_170])]) ).
fof(f1765,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) )
| ~ spl71_4
| ~ spl71_170 ),
inference(resolution,[],[f1653,f664]) ).
fof(f1653,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 )
| ~ spl71_170 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f3214,plain,
( spl71_280
| ~ spl71_3
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1764,f1652,f657,f3212]) ).
fof(f3212,plain,
( spl71_280
<=> ! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_280])]) ).
fof(f1764,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) )
| ~ spl71_3
| ~ spl71_170 ),
inference(resolution,[],[f1653,f659]) ).
fof(f3210,plain,
( spl71_279
| ~ spl71_2
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1763,f1652,f652,f3208]) ).
fof(f3208,plain,
( spl71_279
<=> ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_279])]) ).
fof(f1763,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) )
| ~ spl71_2
| ~ spl71_170 ),
inference(resolution,[],[f1653,f654]) ).
fof(f3206,plain,
( ~ spl71_278
| spl71_10
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f3045,f3041,f691,f3203]) ).
fof(f3203,plain,
( spl71_278
<=> singletonP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_278])]) ).
fof(f3045,plain,
( ~ singletonP(sK22)
| spl71_10
| ~ spl71_269 ),
inference(superposition,[],[f693,f3043]) ).
fof(f3201,plain,
( spl71_277
| ~ spl71_1
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1762,f1652,f647,f3199]) ).
fof(f3199,plain,
( spl71_277
<=> ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_277])]) ).
fof(f1762,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) )
| ~ spl71_1
| ~ spl71_170 ),
inference(resolution,[],[f1653,f649]) ).
fof(f3197,plain,
( ~ spl71_276
| ~ spl71_272
| spl71_275 ),
inference(avatar_split_clause,[],[f3192,f3188,f3098,f3194]) ).
fof(f3188,plain,
( spl71_275
<=> tl(sK23) = sK27(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_275])]) ).
fof(f3192,plain,
( tl(sK22) != sK27(sK22)
| ~ spl71_272
| spl71_275 ),
inference(forward_demodulation,[],[f3189,f3100]) ).
fof(f3189,plain,
( tl(sK23) != sK27(sK23)
| spl71_275 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f3191,plain,
( spl71_275
| spl71_271
| ~ spl71_4
| ~ spl71_167 ),
inference(avatar_split_clause,[],[f1730,f1639,f662,f3091,f3188]) ).
fof(f1730,plain,
( nil = sK23
| tl(sK23) = sK27(sK23)
| ~ spl71_4
| ~ spl71_167 ),
inference(resolution,[],[f1640,f664]) ).
fof(f3162,plain,
( ~ spl71_274
| spl71_8
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f3125,f3041,f681,f3159]) ).
fof(f3125,plain,
( sK20 != sK22
| spl71_8
| ~ spl71_269 ),
inference(forward_demodulation,[],[f683,f3043]) ).
fof(f683,plain,
( nil != sK20
| spl71_8 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f3122,plain,
( ~ spl71_2
| ~ spl71_40
| spl71_265 ),
inference(avatar_split_clause,[],[f2998,f2994,f860,f652]) ).
fof(f860,plain,
( spl71_40
<=> ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_40])]) ).
fof(f2994,plain,
( spl71_265
<=> segmentP(sK21,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_265])]) ).
fof(f2998,plain,
( ~ ssList(sK21)
| ~ spl71_40
| spl71_265 ),
inference(resolution,[],[f2996,f861]) ).
fof(f861,plain,
( ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) )
| ~ spl71_40 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f2996,plain,
( ~ segmentP(sK21,sK21)
| spl71_265 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f3121,plain,
( spl71_273
| spl71_264
| ~ spl71_2
| ~ spl71_167 ),
inference(avatar_split_clause,[],[f1728,f1639,f652,f2989,f3118]) ).
fof(f1728,plain,
( nil = sK21
| tl(sK21) = sK27(sK21)
| ~ spl71_2
| ~ spl71_167 ),
inference(resolution,[],[f1640,f654]) ).
fof(f3101,plain,
( spl71_272
| ~ spl71_269
| ~ spl71_271 ),
inference(avatar_split_clause,[],[f3095,f3091,f3041,f3098]) ).
fof(f3095,plain,
( sK22 = sK23
| ~ spl71_269
| ~ spl71_271 ),
inference(forward_demodulation,[],[f3093,f3043]) ).
fof(f3094,plain,
( spl71_270
| spl71_271
| ~ spl71_4
| ~ spl71_166 ),
inference(avatar_split_clause,[],[f1700,f1635,f662,f3091,f3087]) ).
fof(f3087,plain,
( spl71_270
<=> hd(sK23) = sK26(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_270])]) ).
fof(f1635,plain,
( spl71_166
<=> ! [X0] :
( hd(X0) = sK26(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_166])]) ).
fof(f1700,plain,
( nil = sK23
| hd(sK23) = sK26(sK23)
| ~ spl71_4
| ~ spl71_166 ),
inference(resolution,[],[f1636,f664]) ).
fof(f1636,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK26(X0) )
| ~ spl71_166 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f3044,plain,
( spl71_268
| spl71_269
| ~ spl71_3
| ~ spl71_166 ),
inference(avatar_split_clause,[],[f1699,f1635,f657,f3041,f3037]) ).
fof(f1699,plain,
( nil = sK22
| hd(sK22) = sK26(sK22)
| ~ spl71_3
| ~ spl71_166 ),
inference(resolution,[],[f1636,f659]) ).
fof(f3016,plain,
( spl71_267
| ~ spl71_7
| ~ spl71_9 ),
inference(avatar_split_clause,[],[f2871,f686,f677,f3013]) ).
fof(f3013,plain,
( spl71_267
<=> sK21 = app(app(sK22,sK21),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_267])]) ).
fof(f677,plain,
( spl71_7
<=> sK20 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_7])]) ).
fof(f2871,plain,
( sK21 = app(app(sK22,sK21),sK23)
| ~ spl71_7
| ~ spl71_9 ),
inference(superposition,[],[f688,f679]) ).
fof(f679,plain,
( sK20 = sK21
| ~ spl71_7 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f3003,plain,
( spl71_266
| ~ spl71_7
| ~ spl71_259 ),
inference(avatar_split_clause,[],[f2986,f2864,f677,f3000]) ).
fof(f2986,plain,
( hd(sK21) = sK26(sK21)
| ~ spl71_7
| ~ spl71_259 ),
inference(forward_demodulation,[],[f2866,f679]) ).
fof(f2997,plain,
( ~ spl71_265
| spl71_6
| ~ spl71_7 ),
inference(avatar_split_clause,[],[f2870,f677,f672,f2994]) ).
fof(f2870,plain,
( ~ segmentP(sK21,sK21)
| spl71_6
| ~ spl71_7 ),
inference(superposition,[],[f674,f679]) ).
fof(f674,plain,
( ~ segmentP(sK21,sK20)
| spl71_6 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f2992,plain,
( ~ spl71_264
| ~ spl71_7
| spl71_8 ),
inference(avatar_split_clause,[],[f2987,f681,f677,f2989]) ).
fof(f2987,plain,
( nil != sK21
| ~ spl71_7
| spl71_8 ),
inference(forward_demodulation,[],[f683,f679]) ).
fof(f2977,plain,
( spl71_263
| ~ spl71_7
| ~ spl71_8
| ~ spl71_12 ),
inference(avatar_split_clause,[],[f2920,f701,f681,f677,f2974]) ).
fof(f2974,plain,
( spl71_263
<=> duplicatefreeP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_263])]) ).
fof(f2920,plain,
( duplicatefreeP(sK21)
| ~ spl71_7
| ~ spl71_8
| ~ spl71_12 ),
inference(forward_demodulation,[],[f2884,f679]) ).
fof(f2884,plain,
( duplicatefreeP(sK20)
| ~ spl71_8
| ~ spl71_12 ),
inference(superposition,[],[f703,f682]) ).
fof(f682,plain,
( nil = sK20
| ~ spl71_8 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f2972,plain,
( spl71_262
| ~ spl71_7
| ~ spl71_8
| ~ spl71_11 ),
inference(avatar_split_clause,[],[f2919,f696,f681,f677,f2969]) ).
fof(f2969,plain,
( spl71_262
<=> equalelemsP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_262])]) ).
fof(f2919,plain,
( equalelemsP(sK21)
| ~ spl71_7
| ~ spl71_8
| ~ spl71_11 ),
inference(forward_demodulation,[],[f2883,f679]) ).
fof(f2883,plain,
( equalelemsP(sK20)
| ~ spl71_8
| ~ spl71_11 ),
inference(superposition,[],[f698,f682]) ).
fof(f2967,plain,
( ~ spl71_261
| ~ spl71_7
| ~ spl71_8
| spl71_10 ),
inference(avatar_split_clause,[],[f2918,f691,f681,f677,f2964]) ).
fof(f2964,plain,
( spl71_261
<=> singletonP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_261])]) ).
fof(f2918,plain,
( ~ singletonP(sK21)
| ~ spl71_7
| ~ spl71_8
| spl71_10 ),
inference(forward_demodulation,[],[f2882,f679]) ).
fof(f2882,plain,
( ~ singletonP(sK20)
| ~ spl71_8
| spl71_10 ),
inference(superposition,[],[f693,f682]) ).
fof(f2962,plain,
( spl71_260
| ~ spl71_5
| ~ spl71_7 ),
inference(avatar_split_clause,[],[f2869,f677,f667,f2959]) ).
fof(f2959,plain,
( spl71_260
<=> totalorderedP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_260])]) ).
fof(f667,plain,
( spl71_5
<=> totalorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_5])]) ).
fof(f2869,plain,
( totalorderedP(sK21)
| ~ spl71_5
| ~ spl71_7 ),
inference(superposition,[],[f669,f679]) ).
fof(f669,plain,
( totalorderedP(sK20)
| ~ spl71_5 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f2867,plain,
( spl71_259
| spl71_8
| ~ spl71_1
| ~ spl71_166 ),
inference(avatar_split_clause,[],[f1697,f1635,f647,f681,f2864]) ).
fof(f1697,plain,
( nil = sK20
| hd(sK20) = sK26(sK20)
| ~ spl71_1
| ~ spl71_166 ),
inference(resolution,[],[f1636,f649]) ).
fof(f2718,plain,
( spl71_258
| ~ spl71_4
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1406,f1325,f662,f2715]) ).
fof(f2715,plain,
( spl71_258
<=> sK23 = app(nil,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_258])]) ).
fof(f1325,plain,
( spl71_118
<=> ! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_118])]) ).
fof(f1406,plain,
( sK23 = app(nil,sK23)
| ~ spl71_4
| ~ spl71_118 ),
inference(resolution,[],[f1326,f664]) ).
fof(f1326,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl71_118 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f2713,plain,
( spl71_257
| ~ spl71_3
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1405,f1325,f657,f2710]) ).
fof(f2710,plain,
( spl71_257
<=> sK22 = app(nil,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_257])]) ).
fof(f1405,plain,
( sK22 = app(nil,sK22)
| ~ spl71_3
| ~ spl71_118 ),
inference(resolution,[],[f1326,f659]) ).
fof(f2708,plain,
( spl71_256
| ~ spl71_2
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1404,f1325,f652,f2705]) ).
fof(f2705,plain,
( spl71_256
<=> sK21 = app(nil,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_256])]) ).
fof(f1404,plain,
( sK21 = app(nil,sK21)
| ~ spl71_2
| ~ spl71_118 ),
inference(resolution,[],[f1326,f654]) ).
fof(f2703,plain,
( spl71_255
| ~ spl71_1
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1403,f1325,f647,f2700]) ).
fof(f2700,plain,
( spl71_255
<=> sK20 = app(nil,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_255])]) ).
fof(f1403,plain,
( sK20 = app(nil,sK20)
| ~ spl71_1
| ~ spl71_118 ),
inference(resolution,[],[f1326,f649]) ).
fof(f2698,plain,
( spl71_254
| ~ spl71_4
| ~ spl71_117 ),
inference(avatar_split_clause,[],[f1381,f1321,f662,f2695]) ).
fof(f2695,plain,
( spl71_254
<=> sK23 = app(sK23,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_254])]) ).
fof(f1321,plain,
( spl71_117
<=> ! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_117])]) ).
fof(f1381,plain,
( sK23 = app(sK23,nil)
| ~ spl71_4
| ~ spl71_117 ),
inference(resolution,[],[f1322,f664]) ).
fof(f1322,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl71_117 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f2693,plain,
( spl71_253
| ~ spl71_3
| ~ spl71_117 ),
inference(avatar_split_clause,[],[f1380,f1321,f657,f2690]) ).
fof(f2690,plain,
( spl71_253
<=> sK22 = app(sK22,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_253])]) ).
fof(f1380,plain,
( sK22 = app(sK22,nil)
| ~ spl71_3
| ~ spl71_117 ),
inference(resolution,[],[f1322,f659]) ).
fof(f2688,plain,
( spl71_252
| ~ spl71_2
| ~ spl71_117 ),
inference(avatar_split_clause,[],[f1379,f1321,f652,f2685]) ).
fof(f2685,plain,
( spl71_252
<=> sK21 = app(sK21,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_252])]) ).
fof(f1379,plain,
( sK21 = app(sK21,nil)
| ~ spl71_2
| ~ spl71_117 ),
inference(resolution,[],[f1322,f654]) ).
fof(f2683,plain,
( spl71_250
| ~ spl71_251
| ~ spl71_31
| ~ spl71_96 ),
inference(avatar_split_clause,[],[f1427,f1233,f807,f2680,f2676]) ).
fof(f2676,plain,
( spl71_250
<=> equalelemsP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_250])]) ).
fof(f2680,plain,
( spl71_251
<=> sP4(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_251])]) ).
fof(f807,plain,
( spl71_31
<=> sP5(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_31])]) ).
fof(f1233,plain,
( spl71_96
<=> ! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_96])]) ).
fof(f1427,plain,
( ~ sP4(sK20)
| equalelemsP(sK20)
| ~ spl71_31
| ~ spl71_96 ),
inference(resolution,[],[f809,f1234]) ).
fof(f1234,plain,
( ! [X0] :
( ~ sP5(X0)
| ~ sP4(X0)
| equalelemsP(X0) )
| ~ spl71_96 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f809,plain,
( sP5(sK20)
| ~ spl71_31 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f2674,plain,
( spl71_249
| ~ spl71_1
| ~ spl71_117 ),
inference(avatar_split_clause,[],[f1378,f1321,f647,f2671]) ).
fof(f2671,plain,
( spl71_249
<=> sK20 = app(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_249])]) ).
fof(f1378,plain,
( sK20 = app(sK20,nil)
| ~ spl71_1
| ~ spl71_117 ),
inference(resolution,[],[f1322,f649]) ).
fof(f2630,plain,
spl71_248,
inference(avatar_split_clause,[],[f625,f2628]) ).
fof(f2628,plain,
( spl71_248
<=> ! [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,[spl71_248])]) ).
fof(f625,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,[],[f523]) ).
fof(f523,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,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ( sP12(X0)
| ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssList(sK50(X0))
& ssItem(sK49(X0))
& ssItem(sK48(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,[sK48,sK49,sK50,sK51,sK52])],[f325,f330,f329,f328,f327,f326]) ).
fof(f326,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,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,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,[],[f324]) ).
fof(f324,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(f2626,plain,
spl71_247,
inference(avatar_split_clause,[],[f624,f2624]) ).
fof(f2624,plain,
( spl71_247
<=> ! [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,[spl71_247])]) ).
fof(f624,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,[],[f511]) ).
fof(f511,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,[],[f322]) ).
fof(f322,plain,
! [X0] :
( ( sP10(X0)
| ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssList(sK45(X0))
& ssItem(sK44(X0))
& ssItem(sK43(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,[sK43,sK44,sK45,sK46,sK47])],[f316,f321,f320,f319,f318,f317]) ).
fof(f317,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,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,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,[],[f315]) ).
fof(f315,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(f2622,plain,
spl71_246,
inference(avatar_split_clause,[],[f623,f2620]) ).
fof(f2620,plain,
( spl71_246
<=> ! [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,[spl71_246])]) ).
fof(f623,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,[],[f499]) ).
fof(f499,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,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ( sP8(X0)
| ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssList(sK40(X0))
& ssItem(sK39(X0))
& ssItem(sK38(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,[sK38,sK39,sK40,sK41,sK42])],[f307,f312,f311,f310,f309,f308]) ).
fof(f308,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,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,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,[],[f306]) ).
fof(f306,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(f2614,plain,
spl71_245,
inference(avatar_split_clause,[],[f627,f2612]) ).
fof(f2612,plain,
( spl71_245
<=> ! [X10,X9,X7,X6,X8] :
( leq(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,[spl71_245])]) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( leq(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,[],[f546]) ).
fof(f546,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)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( sP16(X0)
| ( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssList(sK60(X0))
& ssItem(sK59(X0))
& ssItem(sK58(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) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62])],[f343,f348,f347,f346,f345,f344]) ).
fof(f344,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(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(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,[sP16])]) ).
fof(f2610,plain,
spl71_244,
inference(avatar_split_clause,[],[f626,f2608]) ).
fof(f2608,plain,
( spl71_244
<=> ! [X10,X9,X7,X6,X8] :
( lt(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,[spl71_244])]) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( lt(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,[],[f535]) ).
fof(f535,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)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0] :
( ( sP14(X0)
| ( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssList(sK55(X0))
& ssItem(sK54(X0))
& ssItem(sK53(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) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f334,f339,f338,f337,f336,f335]) ).
fof(f335,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(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(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,[sP14])]) ).
fof(f2606,plain,
spl71_243,
inference(avatar_split_clause,[],[f574,f2604]) ).
fof(f2604,plain,
( spl71_243
<=> ! [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,[spl71_243])]) ).
fof(f574,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(f2587,plain,
spl71_242,
inference(avatar_split_clause,[],[f635,f2585]) ).
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,[],[f589]) ).
fof(f589,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,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f368,f370,f369]) ).
fof(f369,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f368,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,[],[f367]) ).
fof(f367,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,[],[f202]) ).
fof(f202,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(f2583,plain,
spl71_241,
inference(avatar_split_clause,[],[f631,f2581]) ).
fof(f2581,plain,
( spl71_241
<=> ! [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,[spl71_241])]) ).
fof(f631,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,[],[f570]) ).
fof(f570,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,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1))
& ssList(sK63(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f354,f356,f355]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0,X1] :
( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,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,[],[f353]) ).
fof(f353,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(f2579,plain,
spl71_240,
inference(avatar_split_clause,[],[f620,f2577]) ).
fof(f2577,plain,
( spl71_240
<=> ! [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,[spl71_240])]) ).
fof(f620,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,[],[f478]) ).
fof(f478,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,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ( sP4(X0)
| ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0))
& ssList(sK31(X0))
& ssItem(sK30(X0))
& ssItem(sK29(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,[sK29,sK30,sK31,sK32])],[f290,f294,f293,f292,f291]) ).
fof(f291,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] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
=> ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,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,[],[f289]) ).
fof(f289,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(f2539,plain,
spl71_239,
inference(avatar_split_clause,[],[f640,f2537]) ).
fof(f2537,plain,
( spl71_239
<=> ! [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,[spl71_239])]) ).
fof(f640,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,[],[f622]) ).
fof(f622,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,[],[f621]) ).
fof(f621,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,[],[f488]) ).
fof(f488,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,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ( sP6(X0)
| ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssList(sK35(X0))
& ssItem(sK34(X0))
& ssItem(sK33(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,[sK33,sK34,sK35,sK36,sK37])],[f298,f303,f302,f301,f300,f299]) ).
fof(f299,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] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
=> ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,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,[],[f297]) ).
fof(f297,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(f2533,plain,
spl71_238,
inference(avatar_split_clause,[],[f604,f2531]) ).
fof(f2531,plain,
( spl71_238
<=> ! [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,[spl71_238])]) ).
fof(f604,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(f2529,plain,
spl71_237,
inference(avatar_split_clause,[],[f595,f2527]) ).
fof(f2527,plain,
( spl71_237
<=> ! [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,[spl71_237])]) ).
fof(f595,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(f2525,plain,
spl71_236,
inference(avatar_split_clause,[],[f594,f2523]) ).
fof(f2523,plain,
( spl71_236
<=> ! [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,[spl71_236])]) ).
fof(f594,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(f2521,plain,
spl71_235,
inference(avatar_split_clause,[],[f588,f2519]) ).
fof(f2519,plain,
( spl71_235
<=> ! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_235])]) ).
fof(f588,plain,
! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f2517,plain,
spl71_234,
inference(avatar_split_clause,[],[f569,f2515]) ).
fof(f2515,plain,
( spl71_234
<=> ! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_234])]) ).
fof(f569,plain,
! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f2513,plain,
spl71_233,
inference(avatar_split_clause,[],[f552,f2511]) ).
fof(f2511,plain,
( spl71_233
<=> ! [X0] :
( sP16(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_233])]) ).
fof(f552,plain,
! [X0] :
( sP16(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ),
inference(cnf_transformation,[],[f349]) ).
fof(f2509,plain,
spl71_232,
inference(avatar_split_clause,[],[f541,f2507]) ).
fof(f2507,plain,
( spl71_232
<=> ! [X0] :
( sP14(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_232])]) ).
fof(f541,plain,
! [X0] :
( sP14(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ),
inference(cnf_transformation,[],[f340]) ).
fof(f2505,plain,
spl71_231,
inference(avatar_split_clause,[],[f529,f2503]) ).
fof(f2503,plain,
( spl71_231
<=> ! [X0] :
( sP12(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_231])]) ).
fof(f529,plain,
! [X0] :
( sP12(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ),
inference(cnf_transformation,[],[f331]) ).
fof(f2501,plain,
spl71_230,
inference(avatar_split_clause,[],[f517,f2499]) ).
fof(f2499,plain,
( spl71_230
<=> ! [X0] :
( sP10(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_230])]) ).
fof(f517,plain,
! [X0] :
( sP10(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ),
inference(cnf_transformation,[],[f322]) ).
fof(f2497,plain,
spl71_229,
inference(avatar_split_clause,[],[f505,f2495]) ).
fof(f2495,plain,
( spl71_229
<=> ! [X0] :
( sP8(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_229])]) ).
fof(f505,plain,
! [X0] :
( sP8(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ),
inference(cnf_transformation,[],[f313]) ).
fof(f2491,plain,
spl71_228,
inference(avatar_split_clause,[],[f494,f2489]) ).
fof(f2489,plain,
( spl71_228
<=> ! [X0] :
( sP6(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_228])]) ).
fof(f494,plain,
! [X0] :
( sP6(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ),
inference(cnf_transformation,[],[f304]) ).
fof(f2487,plain,
spl71_227,
inference(avatar_split_clause,[],[f434,f2485]) ).
fof(f2485,plain,
( spl71_227
<=> ! [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,[spl71_227])]) ).
fof(f434,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,[],[f266]) ).
fof(f266,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,[],[f265]) ).
fof(f265,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(f2483,plain,
spl71_226,
inference(avatar_split_clause,[],[f433,f2481]) ).
fof(f2481,plain,
( spl71_226
<=> ! [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,[spl71_226])]) ).
fof(f433,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,[],[f266]) ).
fof(f2398,plain,
spl71_225,
inference(avatar_split_clause,[],[f596,f2396]) ).
fof(f2396,plain,
( spl71_225
<=> ! [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,[spl71_225])]) ).
fof(f596,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(f2394,plain,
spl71_224,
inference(avatar_split_clause,[],[f593,f2392]) ).
fof(f2392,plain,
( spl71_224
<=> ! [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,[spl71_224])]) ).
fof(f593,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(f2390,plain,
spl71_223,
inference(avatar_split_clause,[],[f452,f2388]) ).
fof(f2388,plain,
( spl71_223
<=> ! [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,[spl71_223])]) ).
fof(f452,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,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,[],[f275]) ).
fof(f275,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(f2384,plain,
spl71_222,
inference(avatar_split_clause,[],[f430,f2382]) ).
fof(f2382,plain,
( spl71_222
<=> ! [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,[spl71_222])]) ).
fof(f430,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,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,[],[f263]) ).
fof(f263,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(f2333,plain,
spl71_221,
inference(avatar_split_clause,[],[f641,f2331]) ).
fof(f2331,plain,
( spl71_221
<=> ! [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,[spl71_221])]) ).
fof(f641,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f614]) ).
fof(f614,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,[],[f435]) ).
fof(f435,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,[],[f266]) ).
fof(f2329,plain,
spl71_220,
inference(avatar_split_clause,[],[f600,f2327]) ).
fof(f2327,plain,
( spl71_220
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_220])]) ).
fof(f600,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(f2325,plain,
spl71_219,
inference(avatar_split_clause,[],[f599,f2323]) ).
fof(f2323,plain,
( spl71_219
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_219])]) ).
fof(f599,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(f2321,plain,
spl71_218,
inference(avatar_split_clause,[],[f573,f2319]) ).
fof(f2319,plain,
( spl71_218
<=> ! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_218])]) ).
fof(f573,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(f2286,plain,
spl71_217,
inference(avatar_split_clause,[],[f603,f2284]) ).
fof(f2284,plain,
( spl71_217
<=> ! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_217])]) ).
fof(f603,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,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(f2282,plain,
spl71_216,
inference(avatar_split_clause,[],[f602,f2280]) ).
fof(f2280,plain,
( spl71_216
<=> ! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_216])]) ).
fof(f602,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,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(f2276,plain,
spl71_215,
inference(avatar_split_clause,[],[f601,f2274]) ).
fof(f2274,plain,
( spl71_215
<=> ! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_215])]) ).
fof(f601,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,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(f2272,plain,
spl71_214,
inference(avatar_split_clause,[],[f483,f2270]) ).
fof(f2270,plain,
( spl71_214
<=> ! [X0] :
( sP4(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_214])]) ).
fof(f483,plain,
! [X0] :
( sP4(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ),
inference(cnf_transformation,[],[f295]) ).
fof(f2268,plain,
spl71_213,
inference(avatar_split_clause,[],[f429,f2266]) ).
fof(f2266,plain,
( spl71_213
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_213])]) ).
fof(f429,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(f2264,plain,
spl71_212,
inference(avatar_split_clause,[],[f428,f2262]) ).
fof(f2262,plain,
( spl71_212
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_212])]) ).
fof(f428,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(f2260,plain,
spl71_211,
inference(avatar_split_clause,[],[f427,f2258]) ).
fof(f2258,plain,
( spl71_211
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_211])]) ).
fof(f427,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(f2256,plain,
spl71_210,
inference(avatar_split_clause,[],[f426,f2254]) ).
fof(f2254,plain,
( spl71_210
<=> ! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_210])]) ).
fof(f426,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(f2252,plain,
spl71_209,
inference(avatar_split_clause,[],[f425,f2250]) ).
fof(f2250,plain,
( spl71_209
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_209])]) ).
fof(f425,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(f2186,plain,
spl71_208,
inference(avatar_split_clause,[],[f598,f2184]) ).
fof(f2184,plain,
( spl71_208
<=> ! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_208])]) ).
fof(f598,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(f2182,plain,
spl71_207,
inference(avatar_split_clause,[],[f597,f2180]) ).
fof(f2180,plain,
( spl71_207
<=> ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_207])]) ).
fof(f597,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(f2178,plain,
spl71_206,
inference(avatar_split_clause,[],[f584,f2176]) ).
fof(f2176,plain,
( spl71_206
<=> ! [X0,X1] :
( app(X1,sK66(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_206])]) ).
fof(f584,plain,
! [X0,X1] :
( app(X1,sK66(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f364,f365]) ).
fof(f365,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f364,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,[],[f363]) ).
fof(f363,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,[],[f201]) ).
fof(f201,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(f2174,plain,
spl71_205,
inference(avatar_split_clause,[],[f581,f2172]) ).
fof(f2172,plain,
( spl71_205
<=> ! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_205])]) ).
fof(f581,plain,
! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f360,f361]) ).
fof(f361,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f360,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,[],[f359]) ).
fof(f359,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(f2170,plain,
spl71_204,
inference(avatar_split_clause,[],[f572,f2168]) ).
fof(f2168,plain,
( spl71_204
<=> ! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_204])]) ).
fof(f572,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(f2164,plain,
spl71_203,
inference(avatar_split_clause,[],[f454,f2162]) ).
fof(f2162,plain,
( spl71_203
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_203])]) ).
fof(f454,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f2160,plain,
spl71_202,
inference(avatar_split_clause,[],[f453,f2158]) ).
fof(f2158,plain,
( spl71_202
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_202])]) ).
fof(f453,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f2156,plain,
spl71_201,
inference(avatar_split_clause,[],[f432,f2154]) ).
fof(f2154,plain,
( spl71_201
<=> ! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_201])]) ).
fof(f432,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f2093,plain,
( spl71_200
| ~ spl71_4
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f825,f783,f662,f2090]) ).
fof(f2090,plain,
( spl71_200
<=> sP17(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_200])]) ).
fof(f825,plain,
( sP17(sK23)
| ~ spl71_4
| ~ spl71_30 ),
inference(resolution,[],[f784,f664]) ).
fof(f2081,plain,
spl71_199,
inference(avatar_split_clause,[],[f634,f2079]) ).
fof(f2079,plain,
( spl71_199
<=> ! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_199])]) ).
fof(f634,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f585]) ).
fof(f585,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f2077,plain,
spl71_198,
inference(avatar_split_clause,[],[f633,f2075]) ).
fof(f2075,plain,
( spl71_198
<=> ! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_198])]) ).
fof(f633,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f582]) ).
fof(f582,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f2073,plain,
spl71_197,
inference(avatar_split_clause,[],[f577,f2071]) ).
fof(f2071,plain,
( spl71_197
<=> ! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_197])]) ).
fof(f577,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,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(f2069,plain,
spl71_196,
inference(avatar_split_clause,[],[f576,f2067]) ).
fof(f2067,plain,
( spl71_196
<=> ! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_196])]) ).
fof(f576,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,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(f2065,plain,
spl71_195,
inference(avatar_split_clause,[],[f575,f2063]) ).
fof(f2063,plain,
( spl71_195
<=> ! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_195])]) ).
fof(f575,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(f2061,plain,
spl71_194,
inference(avatar_split_clause,[],[f566,f2059]) ).
fof(f566,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(f2057,plain,
spl71_193,
inference(avatar_split_clause,[],[f415,f2055]) ).
fof(f2055,plain,
( spl71_193
<=> ! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_193])]) ).
fof(f415,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(f2053,plain,
spl71_192,
inference(avatar_split_clause,[],[f414,f2051]) ).
fof(f2051,plain,
( spl71_192
<=> ! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_192])]) ).
fof(f414,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(f2049,plain,
( spl71_191
| ~ spl71_3
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f824,f783,f657,f2046]) ).
fof(f2046,plain,
( spl71_191
<=> sP17(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_191])]) ).
fof(f824,plain,
( sP17(sK22)
| ~ spl71_3
| ~ spl71_30 ),
inference(resolution,[],[f784,f659]) ).
fof(f2044,plain,
spl71_190,
inference(avatar_split_clause,[],[f412,f2042]) ).
fof(f2042,plain,
( spl71_190
<=> ! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_190])]) ).
fof(f412,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(f1959,plain,
spl71_189,
inference(avatar_split_clause,[],[f591,f1957]) ).
fof(f1957,plain,
( spl71_189
<=> ! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_189])]) ).
fof(f591,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,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,[],[f372]) ).
fof(f372,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(f1955,plain,
spl71_188,
inference(avatar_split_clause,[],[f590,f1953]) ).
fof(f1953,plain,
( spl71_188
<=> ! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_188])]) ).
fof(f590,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f1951,plain,
spl71_187,
inference(avatar_split_clause,[],[f468,f1949]) ).
fof(f468,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(f1947,plain,
( spl71_186
| ~ spl71_2
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f823,f783,f652,f1944]) ).
fof(f1944,plain,
( spl71_186
<=> sP17(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_186])]) ).
fof(f823,plain,
( sP17(sK21)
| ~ spl71_2
| ~ spl71_30 ),
inference(resolution,[],[f784,f654]) ).
fof(f1942,plain,
spl71_185,
inference(avatar_split_clause,[],[f465,f1940]) ).
fof(f465,plain,
! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0] :
( ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0))
& ssList(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f150,f278,f277]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
& ssList(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f278,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
=> ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(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(f1938,plain,
spl71_184,
inference(avatar_split_clause,[],[f450,f1936]) ).
fof(f1936,plain,
( spl71_184
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_184])]) ).
fof(f450,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1934,plain,
spl71_183,
inference(avatar_split_clause,[],[f442,f1932]) ).
fof(f1932,plain,
( spl71_183
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_183])]) ).
fof(f442,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f269]) ).
fof(f269,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1852,plain,
spl71_182,
inference(avatar_split_clause,[],[f587,f1850]) ).
fof(f1850,plain,
( spl71_182
<=> ! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_182])]) ).
fof(f587,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f1848,plain,
( spl71_181
| ~ spl71_1
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f822,f783,f647,f1845]) ).
fof(f1845,plain,
( spl71_181
<=> sP17(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_181])]) ).
fof(f822,plain,
( sP17(sK20)
| ~ spl71_1
| ~ spl71_30 ),
inference(resolution,[],[f784,f649]) ).
fof(f1843,plain,
spl71_180,
inference(avatar_split_clause,[],[f586,f1841]) ).
fof(f1841,plain,
( spl71_180
<=> ! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_180])]) ).
fof(f586,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f1839,plain,
spl71_179,
inference(avatar_split_clause,[],[f583,f1837]) ).
fof(f1837,plain,
( spl71_179
<=> ! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_179])]) ).
fof(f583,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f1835,plain,
spl71_178,
inference(avatar_split_clause,[],[f580,f1833]) ).
fof(f1833,plain,
( spl71_178
<=> ! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_178])]) ).
fof(f580,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f1831,plain,
spl71_177,
inference(avatar_split_clause,[],[f568,f1829]) ).
fof(f1829,plain,
( spl71_177
<=> ! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_177])]) ).
fof(f568,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1827,plain,
spl71_176,
inference(avatar_split_clause,[],[f567,f1825]) ).
fof(f1825,plain,
( spl71_176
<=> ! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_176])]) ).
fof(f567,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1757,plain,
( spl71_175
| ~ spl71_4
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f820,f779,f662,f1754]) ).
fof(f1754,plain,
( spl71_175
<=> sP15(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_175])]) ).
fof(f820,plain,
( sP15(sK23)
| ~ spl71_4
| ~ spl71_29 ),
inference(resolution,[],[f780,f664]) ).
fof(f1677,plain,
( spl71_174
| ~ spl71_3
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f819,f779,f657,f1674]) ).
fof(f1674,plain,
( spl71_174
<=> sP15(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_174])]) ).
fof(f819,plain,
( sP15(sK22)
| ~ spl71_3
| ~ spl71_29 ),
inference(resolution,[],[f780,f659]) ).
fof(f1666,plain,
spl71_173,
inference(avatar_split_clause,[],[f619,f1664]) ).
fof(f1664,plain,
( spl71_173
<=> ! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_173])]) ).
fof(f619,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f475]) ).
fof(f475,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f285,f286]) ).
fof(f286,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f285,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f284]) ).
fof(f284,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(f1662,plain,
spl71_172,
inference(avatar_split_clause,[],[f579,f1660]) ).
fof(f1660,plain,
( spl71_172
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_172])]) ).
fof(f579,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,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(f1658,plain,
spl71_171,
inference(avatar_split_clause,[],[f565,f1656]) ).
fof(f565,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(f1654,plain,
spl71_170,
inference(avatar_split_clause,[],[f564,f1652]) ).
fof(f564,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(f1650,plain,
( spl71_169
| ~ spl71_2
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f818,f779,f652,f1647]) ).
fof(f1647,plain,
( spl71_169
<=> sP15(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_169])]) ).
fof(f818,plain,
( sP15(sK21)
| ~ spl71_2
| ~ spl71_29 ),
inference(resolution,[],[f780,f654]) ).
fof(f1645,plain,
spl71_168,
inference(avatar_split_clause,[],[f474,f1643]) ).
fof(f1643,plain,
( spl71_168
<=> ! [X0] :
( cons(sK28(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_168])]) ).
fof(f474,plain,
! [X0] :
( cons(sK28(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f1641,plain,
spl71_167,
inference(avatar_split_clause,[],[f472,f1639]) ).
fof(f472,plain,
! [X0] :
( tl(X0) = sK27(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f160,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK27(X0)
& ssList(sK27(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(f1637,plain,
spl71_166,
inference(avatar_split_clause,[],[f470,f1635]) ).
fof(f470,plain,
! [X0] :
( hd(X0) = sK26(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f158,f280]) ).
fof(f280,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK26(X0)
& ssItem(sK26(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(f1633,plain,
spl71_165,
inference(avatar_split_clause,[],[f448,f1631]) ).
fof(f1631,plain,
( spl71_165
<=> ! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_165])]) ).
fof(f448,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1629,plain,
spl71_164,
inference(avatar_split_clause,[],[f445,f1627]) ).
fof(f1627,plain,
( spl71_164
<=> ! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_164])]) ).
fof(f445,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1625,plain,
spl71_163,
inference(avatar_split_clause,[],[f444,f1623]) ).
fof(f1623,plain,
( spl71_163
<=> ! [X0,X1] :
( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_163])]) ).
fof(f444,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f1621,plain,
spl71_162,
inference(avatar_split_clause,[],[f440,f1619]) ).
fof(f1619,plain,
( spl71_162
<=> ! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_162])]) ).
fof(f440,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1617,plain,
spl71_161,
inference(avatar_split_clause,[],[f437,f1615]) ).
fof(f1615,plain,
( spl71_161
<=> ! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_161])]) ).
fof(f437,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1613,plain,
spl71_160,
inference(avatar_split_clause,[],[f436,f1611]) ).
fof(f1611,plain,
( spl71_160
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_160])]) ).
fof(f436,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f1609,plain,
spl71_159,
inference(avatar_split_clause,[],[f423,f1607]) ).
fof(f1607,plain,
( spl71_159
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_159])]) ).
fof(f423,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,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,[],[f261]) ).
fof(f261,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(f1605,plain,
( spl71_158
| ~ spl71_1
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f817,f779,f647,f1602]) ).
fof(f1602,plain,
( spl71_158
<=> sP15(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_158])]) ).
fof(f817,plain,
( sP15(sK20)
| ~ spl71_1
| ~ spl71_29 ),
inference(resolution,[],[f780,f649]) ).
fof(f1600,plain,
spl71_157,
inference(avatar_split_clause,[],[f421,f1598]) ).
fof(f1598,plain,
( spl71_157
<=> ! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_157])]) ).
fof(f421,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,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(f1596,plain,
spl71_156,
inference(avatar_split_clause,[],[f420,f1594]) ).
fof(f1594,plain,
( spl71_156
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_156])]) ).
fof(f420,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f1592,plain,
spl71_155,
inference(avatar_split_clause,[],[f419,f1590]) ).
fof(f1590,plain,
( spl71_155
<=> ! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_155])]) ).
fof(f419,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,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(f1588,plain,
spl71_154,
inference(avatar_split_clause,[],[f418,f1586]) ).
fof(f1586,plain,
( spl71_154
<=> ! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_154])]) ).
fof(f418,plain,
! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f1584,plain,
spl71_153,
inference(avatar_split_clause,[],[f417,f1582]) ).
fof(f1582,plain,
( spl71_153
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_153])]) ).
fof(f417,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,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(f1580,plain,
spl71_152,
inference(avatar_split_clause,[],[f413,f1578]) ).
fof(f1578,plain,
( spl71_152
<=> ! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_152])]) ).
fof(f413,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(f1576,plain,
spl71_151,
inference(avatar_split_clause,[],[f411,f1574]) ).
fof(f1574,plain,
( spl71_151
<=> ! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_151])]) ).
fof(f411,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(f1572,plain,
( spl71_150
| ~ spl71_4
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f815,f775,f662,f1569]) ).
fof(f1569,plain,
( spl71_150
<=> sP13(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_150])]) ).
fof(f815,plain,
( sP13(sK23)
| ~ spl71_4
| ~ spl71_28 ),
inference(resolution,[],[f776,f664]) ).
fof(f1567,plain,
spl71_149,
inference(avatar_split_clause,[],[f642,f1565]) ).
fof(f1565,plain,
( spl71_149
<=> ! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_149])]) ).
fof(f642,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f613]) ).
fof(f613,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f431]) ).
fof(f431,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f1563,plain,
spl71_148,
inference(avatar_split_clause,[],[f563,f1561]) ).
fof(f1561,plain,
( spl71_148
<=> ! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_148])]) ).
fof(f563,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(f1559,plain,
spl71_147,
inference(avatar_split_clause,[],[f562,f1557]) ).
fof(f1557,plain,
( spl71_147
<=> ! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_147])]) ).
fof(f562,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(f1515,plain,
( spl71_146
| ~ spl71_3
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f814,f775,f657,f1512]) ).
fof(f1512,plain,
( spl71_146
<=> sP13(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_146])]) ).
fof(f814,plain,
( sP13(sK22)
| ~ spl71_3
| ~ spl71_28 ),
inference(resolution,[],[f776,f659]) ).
fof(f1490,plain,
spl71_145,
inference(avatar_split_clause,[],[f571,f1488]) ).
fof(f1488,plain,
( spl71_145
<=> ! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_145])]) ).
fof(f571,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(f1486,plain,
spl71_144,
inference(avatar_split_clause,[],[f561,f1484]) ).
fof(f1484,plain,
( spl71_144
<=> ! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_144])]) ).
fof(f561,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(f1482,plain,
spl71_143,
inference(avatar_split_clause,[],[f559,f1480]) ).
fof(f1480,plain,
( spl71_143
<=> ! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_143])]) ).
fof(f559,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,[],[f178]) ).
fof(f178,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(f1478,plain,
spl71_142,
inference(avatar_split_clause,[],[f557,f1476]) ).
fof(f1476,plain,
( spl71_142
<=> ! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_142])]) ).
fof(f557,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,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(f1474,plain,
( spl71_141
| ~ spl71_2
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f813,f775,f652,f1471]) ).
fof(f1471,plain,
( spl71_141
<=> sP13(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_141])]) ).
fof(f813,plain,
( sP13(sK21)
| ~ spl71_2
| ~ spl71_28 ),
inference(resolution,[],[f776,f654]) ).
fof(f1469,plain,
spl71_140,
inference(avatar_split_clause,[],[f555,f1467]) ).
fof(f1467,plain,
( spl71_140
<=> ! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_140])]) ).
fof(f555,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,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(f1465,plain,
spl71_139,
inference(avatar_split_clause,[],[f471,f1463]) ).
fof(f1463,plain,
( spl71_139
<=> ! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_139])]) ).
fof(f471,plain,
! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f1461,plain,
spl71_138,
inference(avatar_split_clause,[],[f469,f1459]) ).
fof(f1459,plain,
( spl71_138
<=> ! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_138])]) ).
fof(f469,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f1457,plain,
spl71_137,
inference(avatar_split_clause,[],[f467,f1455]) ).
fof(f1455,plain,
( spl71_137
<=> ! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_137])]) ).
fof(f467,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(f1453,plain,
spl71_136,
inference(avatar_split_clause,[],[f466,f1451]) ).
fof(f1451,plain,
( spl71_136
<=> ! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_136])]) ).
fof(f466,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(f1449,plain,
spl71_135,
inference(avatar_split_clause,[],[f464,f1447]) ).
fof(f1447,plain,
( spl71_135
<=> ! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_135])]) ).
fof(f464,plain,
! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f1445,plain,
spl71_134,
inference(avatar_split_clause,[],[f463,f1443]) ).
fof(f1443,plain,
( spl71_134
<=> ! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_134])]) ).
fof(f463,plain,
! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f1441,plain,
spl71_133,
inference(avatar_split_clause,[],[f447,f1439]) ).
fof(f1439,plain,
( spl71_133
<=> ! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_133])]) ).
fof(f447,plain,
! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1437,plain,
spl71_132,
inference(avatar_split_clause,[],[f439,f1435]) ).
fof(f1435,plain,
( spl71_132
<=> ! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_132])]) ).
fof(f439,plain,
! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1433,plain,
( spl71_131
| ~ spl71_1
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f812,f775,f647,f1430]) ).
fof(f1430,plain,
( spl71_131
<=> sP13(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_131])]) ).
fof(f812,plain,
( sP13(sK20)
| ~ spl71_1
| ~ spl71_28 ),
inference(resolution,[],[f776,f649]) ).
fof(f1376,plain,
spl71_130,
inference(avatar_split_clause,[],[f553,f1374]) ).
fof(f1374,plain,
( spl71_130
<=> ! [X0] :
( sP16(X0)
| ~ leq(sK58(X0),sK59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_130])]) ).
fof(f553,plain,
! [X0] :
( sP16(X0)
| ~ leq(sK58(X0),sK59(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1372,plain,
spl71_129,
inference(avatar_split_clause,[],[f542,f1370]) ).
fof(f1370,plain,
( spl71_129
<=> ! [X0] :
( sP14(X0)
| ~ lt(sK53(X0),sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_129])]) ).
fof(f542,plain,
! [X0] :
( sP14(X0)
| ~ lt(sK53(X0),sK54(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1368,plain,
spl71_128,
inference(avatar_split_clause,[],[f531,f1366]) ).
fof(f1366,plain,
( spl71_128
<=> ! [X0] :
( sP12(X0)
| leq(sK49(X0),sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_128])]) ).
fof(f531,plain,
! [X0] :
( sP12(X0)
| leq(sK49(X0),sK48(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f1364,plain,
spl71_127,
inference(avatar_split_clause,[],[f530,f1362]) ).
fof(f1362,plain,
( spl71_127
<=> ! [X0] :
( sP12(X0)
| leq(sK48(X0),sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_127])]) ).
fof(f530,plain,
! [X0] :
( sP12(X0)
| leq(sK48(X0),sK49(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f1360,plain,
spl71_126,
inference(avatar_split_clause,[],[f519,f1358]) ).
fof(f1358,plain,
( spl71_126
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK44(X0),sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_126])]) ).
fof(f519,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK44(X0),sK43(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f1356,plain,
spl71_125,
inference(avatar_split_clause,[],[f518,f1354]) ).
fof(f1354,plain,
( spl71_125
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK43(X0),sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_125])]) ).
fof(f518,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK43(X0),sK44(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f1352,plain,
( spl71_124
| ~ spl71_4
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f805,f771,f662,f1349]) ).
fof(f1349,plain,
( spl71_124
<=> sP11(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_124])]) ).
fof(f805,plain,
( sP11(sK23)
| ~ spl71_4
| ~ spl71_27 ),
inference(resolution,[],[f772,f664]) ).
fof(f1347,plain,
spl71_123,
inference(avatar_split_clause,[],[f507,f1345]) ).
fof(f1345,plain,
( spl71_123
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK39(X0),sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_123])]) ).
fof(f507,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK39(X0),sK38(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f1343,plain,
spl71_122,
inference(avatar_split_clause,[],[f506,f1341]) ).
fof(f1341,plain,
( spl71_122
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK38(X0),sK39(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_122])]) ).
fof(f506,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK38(X0),sK39(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f1339,plain,
spl71_121,
inference(avatar_split_clause,[],[f495,f1337]) ).
fof(f1337,plain,
( spl71_121
<=> ! [X0] :
( sP6(X0)
| sK33(X0) = sK34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_121])]) ).
fof(f495,plain,
! [X0] :
( sP6(X0)
| sK33(X0) = sK34(X0) ),
inference(cnf_transformation,[],[f304]) ).
fof(f1335,plain,
spl71_120,
inference(avatar_split_clause,[],[f484,f1333]) ).
fof(f1333,plain,
( spl71_120
<=> ! [X0] :
( sP4(X0)
| sK29(X0) != sK30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_120])]) ).
fof(f484,plain,
! [X0] :
( sP4(X0)
| sK29(X0) != sK30(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f1331,plain,
spl71_119,
inference(avatar_split_clause,[],[f473,f1329]) ).
fof(f1329,plain,
( spl71_119
<=> ! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_119])]) ).
fof(f473,plain,
! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f1327,plain,
spl71_118,
inference(avatar_split_clause,[],[f462,f1325]) ).
fof(f462,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(f1323,plain,
spl71_117,
inference(avatar_split_clause,[],[f461,f1321]) ).
fof(f461,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(f1319,plain,
spl71_116,
inference(avatar_split_clause,[],[f451,f1317]) ).
fof(f1317,plain,
( spl71_116
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_116])]) ).
fof(f451,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] :
( ( 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(f1315,plain,
spl71_115,
inference(avatar_split_clause,[],[f443,f1313]) ).
fof(f1313,plain,
( spl71_115
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_115])]) ).
fof(f443,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] :
( ( 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(f1311,plain,
( spl71_114
| ~ spl71_3
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f804,f771,f657,f1308]) ).
fof(f1308,plain,
( spl71_114
<=> sP11(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_114])]) ).
fof(f804,plain,
( sP11(sK22)
| ~ spl71_3
| ~ spl71_27 ),
inference(resolution,[],[f772,f659]) ).
fof(f1306,plain,
spl71_113,
inference(avatar_split_clause,[],[f388,f1304]) ).
fof(f1304,plain,
( spl71_113
<=> ! [X9,X7,X6,X8] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9)
| ~ ssItem(X8)
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7)
| ~ ssItem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_113])]) ).
fof(f388,plain,
! [X8,X6,X9,X7] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9)
| ~ ssItem(X8)
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != sK20
| nil = sK21 )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23)
& ssList(sK22)
& 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])],[f100,f256,f255,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(X1,sK18) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(X1,sK18) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != sK20
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != sK20
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) )
& ( nil != sK20
| nil = sK21 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& 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)
=> ( ( totalorderedP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X2
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X10,X12)
& app(cons(X12,nil),X13) = X2
& ssList(X13) )
& ssItem(X12) )
& app(X11,cons(X10,nil)) = X4
& ssList(X11) )
& ssItem(X10) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( totalorderedP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( totalorderedP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f1302,plain,
spl71_112,
inference(avatar_split_clause,[],[f387,f1300]) ).
fof(f1300,plain,
( spl71_112
<=> ! [X10,X11,X13,X12] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13)
| ~ ssItem(X12)
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11)
| ~ ssItem(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_112])]) ).
fof(f387,plain,
! [X10,X11,X12,X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13)
| ~ ssItem(X12)
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11)
| ~ ssItem(X10) ),
inference(cnf_transformation,[],[f257]) ).
fof(f1298,plain,
( spl71_111
| ~ spl71_2
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f803,f771,f652,f1295]) ).
fof(f1295,plain,
( spl71_111
<=> sP11(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_111])]) ).
fof(f803,plain,
( sP11(sK21)
| ~ spl71_2
| ~ spl71_27 ),
inference(resolution,[],[f772,f654]) ).
fof(f1293,plain,
( spl71_110
| ~ spl71_1
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f802,f771,f647,f1290]) ).
fof(f1290,plain,
( spl71_110
<=> sP11(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_110])]) ).
fof(f802,plain,
( sP11(sK20)
| ~ spl71_1
| ~ spl71_27 ),
inference(resolution,[],[f772,f649]) ).
fof(f1288,plain,
spl71_109,
inference(avatar_split_clause,[],[f545,f1286]) ).
fof(f1286,plain,
( spl71_109
<=> ! [X0] :
( totalorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_109])]) ).
fof(f545,plain,
! [X0] :
( totalorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ totalorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f1284,plain,
spl71_108,
inference(avatar_split_clause,[],[f544,f1282]) ).
fof(f1282,plain,
( spl71_108
<=> ! [X0] :
( sP16(X0)
| ~ totalorderedP(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_108])]) ).
fof(f544,plain,
! [X0] :
( sP16(X0)
| ~ totalorderedP(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1280,plain,
spl71_107,
inference(avatar_split_clause,[],[f534,f1278]) ).
fof(f1278,plain,
( spl71_107
<=> ! [X0] :
( strictorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_107])]) ).
fof(f534,plain,
! [X0] :
( strictorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ strictorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f1276,plain,
spl71_106,
inference(avatar_split_clause,[],[f533,f1274]) ).
fof(f1274,plain,
( spl71_106
<=> ! [X0] :
( sP14(X0)
| ~ strictorderedP(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_106])]) ).
fof(f533,plain,
! [X0] :
( sP14(X0)
| ~ strictorderedP(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f1272,plain,
spl71_105,
inference(avatar_split_clause,[],[f522,f1270]) ).
fof(f1270,plain,
( spl71_105
<=> ! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_105])]) ).
fof(f522,plain,
! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,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(f1268,plain,
spl71_104,
inference(avatar_split_clause,[],[f521,f1266]) ).
fof(f1266,plain,
( spl71_104
<=> ! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_104])]) ).
fof(f521,plain,
! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f1264,plain,
( spl71_103
| ~ spl71_4
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f800,f767,f662,f1261]) ).
fof(f1261,plain,
( spl71_103
<=> sP9(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_103])]) ).
fof(f800,plain,
( sP9(sK23)
| ~ spl71_4
| ~ spl71_26 ),
inference(resolution,[],[f768,f664]) ).
fof(f1259,plain,
spl71_102,
inference(avatar_split_clause,[],[f510,f1257]) ).
fof(f1257,plain,
( spl71_102
<=> ! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_102])]) ).
fof(f510,plain,
! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,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(f1255,plain,
spl71_101,
inference(avatar_split_clause,[],[f509,f1253]) ).
fof(f1253,plain,
( spl71_101
<=> ! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_101])]) ).
fof(f509,plain,
! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f1251,plain,
spl71_100,
inference(avatar_split_clause,[],[f498,f1249]) ).
fof(f1249,plain,
( spl71_100
<=> ! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_100])]) ).
fof(f498,plain,
! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,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(f1247,plain,
spl71_99,
inference(avatar_split_clause,[],[f497,f1245]) ).
fof(f1245,plain,
( spl71_99
<=> ! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_99])]) ).
fof(f497,plain,
! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f1243,plain,
spl71_98,
inference(avatar_split_clause,[],[f487,f1241]) ).
fof(f1241,plain,
( spl71_98
<=> ! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_98])]) ).
fof(f487,plain,
! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,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(f1239,plain,
spl71_97,
inference(avatar_split_clause,[],[f486,f1237]) ).
fof(f1237,plain,
( spl71_97
<=> ! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_97])]) ).
fof(f486,plain,
! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f1235,plain,
spl71_96,
inference(avatar_split_clause,[],[f477,f1233]) ).
fof(f477,plain,
! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,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(f1231,plain,
spl71_95,
inference(avatar_split_clause,[],[f476,f1229]) ).
fof(f1229,plain,
( spl71_95
<=> ! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_95])]) ).
fof(f476,plain,
! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f1227,plain,
spl71_94,
inference(avatar_split_clause,[],[f410,f1225]) ).
fof(f1225,plain,
( spl71_94
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_94])]) ).
fof(f410,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(f1223,plain,
spl71_93,
inference(avatar_split_clause,[],[f409,f1221]) ).
fof(f1221,plain,
( spl71_93
<=> ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_93])]) ).
fof(f409,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(f1219,plain,
( spl71_92
| ~ spl71_3
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f799,f767,f657,f1216]) ).
fof(f1216,plain,
( spl71_92
<=> sP9(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_92])]) ).
fof(f799,plain,
( sP9(sK22)
| ~ spl71_3
| ~ spl71_26 ),
inference(resolution,[],[f768,f659]) ).
fof(f1214,plain,
spl71_91,
inference(avatar_split_clause,[],[f408,f1212]) ).
fof(f1212,plain,
( spl71_91
<=> ! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_91])]) ).
fof(f408,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,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(f1210,plain,
spl71_90,
inference(avatar_split_clause,[],[f407,f1208]) ).
fof(f1208,plain,
( spl71_90
<=> ! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_90])]) ).
fof(f407,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,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(f1206,plain,
spl71_89,
inference(avatar_split_clause,[],[f406,f1204]) ).
fof(f1204,plain,
( spl71_89
<=> ! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_89])]) ).
fof(f406,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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(f1202,plain,
spl71_88,
inference(avatar_split_clause,[],[f405,f1200]) ).
fof(f1200,plain,
( spl71_88
<=> ! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_88])]) ).
fof(f405,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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(f1198,plain,
spl71_87,
inference(avatar_split_clause,[],[f404,f1196]) ).
fof(f1196,plain,
( spl71_87
<=> ! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_87])]) ).
fof(f404,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,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(f1173,plain,
( spl71_86
| ~ spl71_2
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f798,f767,f652,f1170]) ).
fof(f1170,plain,
( spl71_86
<=> sP9(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_86])]) ).
fof(f798,plain,
( sP9(sK21)
| ~ spl71_2
| ~ spl71_26 ),
inference(resolution,[],[f768,f654]) ).
fof(f1126,plain,
( spl71_85
| ~ spl71_1
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f797,f767,f647,f1123]) ).
fof(f1123,plain,
( spl71_85
<=> sP9(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_85])]) ).
fof(f797,plain,
( sP9(sK20)
| ~ spl71_1
| ~ spl71_26 ),
inference(resolution,[],[f768,f649]) ).
fof(f1079,plain,
( spl71_84
| ~ spl71_4
| ~ spl71_25 ),
inference(avatar_split_clause,[],[f795,f763,f662,f1076]) ).
fof(f1076,plain,
( spl71_84
<=> sP7(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_84])]) ).
fof(f795,plain,
( sP7(sK23)
| ~ spl71_4
| ~ spl71_25 ),
inference(resolution,[],[f764,f664]) ).
fof(f1039,plain,
( spl71_83
| ~ spl71_3
| ~ spl71_25 ),
inference(avatar_split_clause,[],[f794,f763,f657,f1036]) ).
fof(f1036,plain,
( spl71_83
<=> sP7(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_83])]) ).
fof(f794,plain,
( sP7(sK22)
| ~ spl71_3
| ~ spl71_25 ),
inference(resolution,[],[f764,f659]) ).
fof(f1034,plain,
( spl71_82
| ~ spl71_2
| ~ spl71_25 ),
inference(avatar_split_clause,[],[f793,f763,f652,f1031]) ).
fof(f1031,plain,
( spl71_82
<=> sP7(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_82])]) ).
fof(f793,plain,
( sP7(sK21)
| ~ spl71_2
| ~ spl71_25 ),
inference(resolution,[],[f764,f654]) ).
fof(f1029,plain,
spl71_81,
inference(avatar_split_clause,[],[f644,f1027]) ).
fof(f1027,plain,
( spl71_81
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_81])]) ).
fof(f644,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f611]) ).
fof(f611,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f416]) ).
fof(f416,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f1025,plain,
spl71_80,
inference(avatar_split_clause,[],[f639,f1023]) ).
fof(f1023,plain,
( spl71_80
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_80])]) ).
fof(f639,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f632]) ).
fof(f632,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f578]) ).
fof(f578,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f1021,plain,
spl71_79,
inference(avatar_split_clause,[],[f551,f1019]) ).
fof(f1019,plain,
( spl71_79
<=> ! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_79])]) ).
fof(f551,plain,
! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1017,plain,
spl71_78,
inference(avatar_split_clause,[],[f550,f1015]) ).
fof(f1015,plain,
( spl71_78
<=> ! [X0] :
( sP16(X0)
| ssList(sK61(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_78])]) ).
fof(f550,plain,
! [X0] :
( sP16(X0)
| ssList(sK61(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1013,plain,
spl71_77,
inference(avatar_split_clause,[],[f549,f1011]) ).
fof(f1011,plain,
( spl71_77
<=> ! [X0] :
( sP16(X0)
| ssList(sK60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_77])]) ).
fof(f549,plain,
! [X0] :
( sP16(X0)
| ssList(sK60(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1009,plain,
spl71_76,
inference(avatar_split_clause,[],[f548,f1007]) ).
fof(f1007,plain,
( spl71_76
<=> ! [X0] :
( sP16(X0)
| ssItem(sK59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_76])]) ).
fof(f548,plain,
! [X0] :
( sP16(X0)
| ssItem(sK59(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1005,plain,
spl71_75,
inference(avatar_split_clause,[],[f547,f1003]) ).
fof(f1003,plain,
( spl71_75
<=> ! [X0] :
( sP16(X0)
| ssItem(sK58(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_75])]) ).
fof(f547,plain,
! [X0] :
( sP16(X0)
| ssItem(sK58(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1001,plain,
spl71_74,
inference(avatar_split_clause,[],[f540,f999]) ).
fof(f999,plain,
( spl71_74
<=> ! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_74])]) ).
fof(f540,plain,
! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f997,plain,
spl71_73,
inference(avatar_split_clause,[],[f539,f995]) ).
fof(f995,plain,
( spl71_73
<=> ! [X0] :
( sP14(X0)
| ssList(sK56(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_73])]) ).
fof(f539,plain,
! [X0] :
( sP14(X0)
| ssList(sK56(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f993,plain,
( spl71_72
| ~ spl71_1
| ~ spl71_25 ),
inference(avatar_split_clause,[],[f792,f763,f647,f990]) ).
fof(f990,plain,
( spl71_72
<=> sP7(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_72])]) ).
fof(f792,plain,
( sP7(sK20)
| ~ spl71_1
| ~ spl71_25 ),
inference(resolution,[],[f764,f649]) ).
fof(f988,plain,
spl71_71,
inference(avatar_split_clause,[],[f538,f986]) ).
fof(f986,plain,
( spl71_71
<=> ! [X0] :
( sP14(X0)
| ssList(sK55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_71])]) ).
fof(f538,plain,
! [X0] :
( sP14(X0)
| ssList(sK55(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f984,plain,
spl71_70,
inference(avatar_split_clause,[],[f537,f982]) ).
fof(f982,plain,
( spl71_70
<=> ! [X0] :
( sP14(X0)
| ssItem(sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_70])]) ).
fof(f537,plain,
! [X0] :
( sP14(X0)
| ssItem(sK54(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f980,plain,
spl71_69,
inference(avatar_split_clause,[],[f536,f978]) ).
fof(f978,plain,
( spl71_69
<=> ! [X0] :
( sP14(X0)
| ssItem(sK53(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_69])]) ).
fof(f536,plain,
! [X0] :
( sP14(X0)
| ssItem(sK53(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f976,plain,
spl71_68,
inference(avatar_split_clause,[],[f528,f974]) ).
fof(f974,plain,
( spl71_68
<=> ! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_68])]) ).
fof(f528,plain,
! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f972,plain,
spl71_67,
inference(avatar_split_clause,[],[f527,f970]) ).
fof(f970,plain,
( spl71_67
<=> ! [X0] :
( sP12(X0)
| ssList(sK51(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_67])]) ).
fof(f527,plain,
! [X0] :
( sP12(X0)
| ssList(sK51(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f968,plain,
spl71_66,
inference(avatar_split_clause,[],[f526,f966]) ).
fof(f966,plain,
( spl71_66
<=> ! [X0] :
( sP12(X0)
| ssList(sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_66])]) ).
fof(f526,plain,
! [X0] :
( sP12(X0)
| ssList(sK50(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f964,plain,
spl71_65,
inference(avatar_split_clause,[],[f525,f962]) ).
fof(f962,plain,
( spl71_65
<=> ! [X0] :
( sP12(X0)
| ssItem(sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_65])]) ).
fof(f525,plain,
! [X0] :
( sP12(X0)
| ssItem(sK49(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f960,plain,
spl71_64,
inference(avatar_split_clause,[],[f524,f958]) ).
fof(f958,plain,
( spl71_64
<=> ! [X0] :
( sP12(X0)
| ssItem(sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_64])]) ).
fof(f524,plain,
! [X0] :
( sP12(X0)
| ssItem(sK48(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f956,plain,
spl71_63,
inference(avatar_split_clause,[],[f516,f954]) ).
fof(f954,plain,
( spl71_63
<=> ! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_63])]) ).
fof(f516,plain,
! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f952,plain,
spl71_62,
inference(avatar_split_clause,[],[f515,f950]) ).
fof(f950,plain,
( spl71_62
<=> ! [X0] :
( sP10(X0)
| ssList(sK46(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_62])]) ).
fof(f515,plain,
! [X0] :
( sP10(X0)
| ssList(sK46(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f948,plain,
( spl71_61
| ~ spl71_4
| ~ spl71_24 ),
inference(avatar_split_clause,[],[f790,f759,f662,f945]) ).
fof(f945,plain,
( spl71_61
<=> sP5(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_61])]) ).
fof(f790,plain,
( sP5(sK23)
| ~ spl71_4
| ~ spl71_24 ),
inference(resolution,[],[f760,f664]) ).
fof(f943,plain,
spl71_60,
inference(avatar_split_clause,[],[f514,f941]) ).
fof(f941,plain,
( spl71_60
<=> ! [X0] :
( sP10(X0)
| ssList(sK45(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_60])]) ).
fof(f514,plain,
! [X0] :
( sP10(X0)
| ssList(sK45(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f939,plain,
spl71_59,
inference(avatar_split_clause,[],[f513,f937]) ).
fof(f937,plain,
( spl71_59
<=> ! [X0] :
( sP10(X0)
| ssItem(sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_59])]) ).
fof(f513,plain,
! [X0] :
( sP10(X0)
| ssItem(sK44(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f935,plain,
spl71_58,
inference(avatar_split_clause,[],[f512,f933]) ).
fof(f933,plain,
( spl71_58
<=> ! [X0] :
( sP10(X0)
| ssItem(sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_58])]) ).
fof(f512,plain,
! [X0] :
( sP10(X0)
| ssItem(sK43(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f931,plain,
spl71_57,
inference(avatar_split_clause,[],[f504,f929]) ).
fof(f929,plain,
( spl71_57
<=> ! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_57])]) ).
fof(f504,plain,
! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f927,plain,
spl71_56,
inference(avatar_split_clause,[],[f503,f925]) ).
fof(f925,plain,
( spl71_56
<=> ! [X0] :
( sP8(X0)
| ssList(sK41(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_56])]) ).
fof(f503,plain,
! [X0] :
( sP8(X0)
| ssList(sK41(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f923,plain,
spl71_55,
inference(avatar_split_clause,[],[f502,f921]) ).
fof(f921,plain,
( spl71_55
<=> ! [X0] :
( sP8(X0)
| ssList(sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_55])]) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| ssList(sK40(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f919,plain,
spl71_54,
inference(avatar_split_clause,[],[f501,f917]) ).
fof(f917,plain,
( spl71_54
<=> ! [X0] :
( sP8(X0)
| ssItem(sK39(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_54])]) ).
fof(f501,plain,
! [X0] :
( sP8(X0)
| ssItem(sK39(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f915,plain,
spl71_53,
inference(avatar_split_clause,[],[f500,f913]) ).
fof(f913,plain,
( spl71_53
<=> ! [X0] :
( sP8(X0)
| ssItem(sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_53])]) ).
fof(f500,plain,
! [X0] :
( sP8(X0)
| ssItem(sK38(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f911,plain,
spl71_52,
inference(avatar_split_clause,[],[f493,f909]) ).
fof(f909,plain,
( spl71_52
<=> ! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_52])]) ).
fof(f493,plain,
! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f907,plain,
spl71_51,
inference(avatar_split_clause,[],[f492,f905]) ).
fof(f905,plain,
( spl71_51
<=> ! [X0] :
( sP6(X0)
| ssList(sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_51])]) ).
fof(f492,plain,
! [X0] :
( sP6(X0)
| ssList(sK36(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f903,plain,
( spl71_50
| ~ spl71_3
| ~ spl71_24 ),
inference(avatar_split_clause,[],[f789,f759,f657,f900]) ).
fof(f900,plain,
( spl71_50
<=> sP5(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_50])]) ).
fof(f789,plain,
( sP5(sK22)
| ~ spl71_3
| ~ spl71_24 ),
inference(resolution,[],[f760,f659]) ).
fof(f898,plain,
spl71_49,
inference(avatar_split_clause,[],[f491,f896]) ).
fof(f896,plain,
( spl71_49
<=> ! [X0] :
( sP6(X0)
| ssList(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_49])]) ).
fof(f491,plain,
! [X0] :
( sP6(X0)
| ssList(sK35(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f894,plain,
spl71_48,
inference(avatar_split_clause,[],[f490,f892]) ).
fof(f892,plain,
( spl71_48
<=> ! [X0] :
( sP6(X0)
| ssItem(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_48])]) ).
fof(f490,plain,
! [X0] :
( sP6(X0)
| ssItem(sK34(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f890,plain,
spl71_47,
inference(avatar_split_clause,[],[f489,f888]) ).
fof(f888,plain,
( spl71_47
<=> ! [X0] :
( sP6(X0)
| ssItem(sK33(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_47])]) ).
fof(f489,plain,
! [X0] :
( sP6(X0)
| ssItem(sK33(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f886,plain,
spl71_46,
inference(avatar_split_clause,[],[f482,f884]) ).
fof(f884,plain,
( spl71_46
<=> ! [X0] :
( sP4(X0)
| ssList(sK32(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_46])]) ).
fof(f482,plain,
! [X0] :
( sP4(X0)
| ssList(sK32(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f882,plain,
spl71_45,
inference(avatar_split_clause,[],[f481,f880]) ).
fof(f880,plain,
( spl71_45
<=> ! [X0] :
( sP4(X0)
| ssList(sK31(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_45])]) ).
fof(f481,plain,
! [X0] :
( sP4(X0)
| ssList(sK31(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f878,plain,
spl71_44,
inference(avatar_split_clause,[],[f480,f876]) ).
fof(f876,plain,
( spl71_44
<=> ! [X0] :
( sP4(X0)
| ssItem(sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_44])]) ).
fof(f480,plain,
! [X0] :
( sP4(X0)
| ssItem(sK30(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f874,plain,
spl71_43,
inference(avatar_split_clause,[],[f479,f872]) ).
fof(f872,plain,
( spl71_43
<=> ! [X0] :
( sP4(X0)
| ssItem(sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_43])]) ).
fof(f479,plain,
! [X0] :
( sP4(X0)
| ssItem(sK29(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f870,plain,
spl71_42,
inference(avatar_split_clause,[],[f460,f868]) ).
fof(f868,plain,
( spl71_42
<=> ! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_42])]) ).
fof(f460,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(f866,plain,
spl71_41,
inference(avatar_split_clause,[],[f459,f864]) ).
fof(f864,plain,
( spl71_41
<=> ! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_41])]) ).
fof(f459,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,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(f862,plain,
spl71_40,
inference(avatar_split_clause,[],[f458,f860]) ).
fof(f458,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,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,
( spl71_39
| ~ spl71_2
| ~ spl71_24 ),
inference(avatar_split_clause,[],[f788,f759,f652,f855]) ).
fof(f855,plain,
( spl71_39
<=> sP5(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_39])]) ).
fof(f788,plain,
( sP5(sK21)
| ~ spl71_2
| ~ spl71_24 ),
inference(resolution,[],[f760,f654]) ).
fof(f853,plain,
spl71_38,
inference(avatar_split_clause,[],[f457,f851]) ).
fof(f851,plain,
( spl71_38
<=> ! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_38])]) ).
fof(f457,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,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,
spl71_37,
inference(avatar_split_clause,[],[f456,f847]) ).
fof(f847,plain,
( spl71_37
<=> ! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_37])]) ).
fof(f456,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,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,
spl71_36,
inference(avatar_split_clause,[],[f455,f843]) ).
fof(f843,plain,
( spl71_36
<=> ! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_36])]) ).
fof(f455,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,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,
spl71_35,
inference(avatar_split_clause,[],[f403,f839]) ).
fof(f839,plain,
( spl71_35
<=> ! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_35])]) ).
fof(f403,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(f837,plain,
spl71_34,
inference(avatar_split_clause,[],[f402,f835]) ).
fof(f835,plain,
( spl71_34
<=> ! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_34])]) ).
fof(f402,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(f833,plain,
spl71_33,
inference(avatar_split_clause,[],[f401,f831]) ).
fof(f831,plain,
( spl71_33
<=> ! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_33])]) ).
fof(f401,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(f829,plain,
spl71_32,
inference(avatar_split_clause,[],[f400,f827]) ).
fof(f827,plain,
( spl71_32
<=> ! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_32])]) ).
fof(f400,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(f810,plain,
( spl71_31
| ~ spl71_1
| ~ spl71_24 ),
inference(avatar_split_clause,[],[f787,f759,f647,f807]) ).
fof(f787,plain,
( sP5(sK20)
| ~ spl71_1
| ~ spl71_24 ),
inference(resolution,[],[f760,f649]) ).
fof(f785,plain,
spl71_30,
inference(avatar_split_clause,[],[f554,f783]) ).
fof(f554,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] :
( ( 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,[],[f174]) ).
fof(f174,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(f781,plain,
spl71_29,
inference(avatar_split_clause,[],[f543,f779]) ).
fof(f543,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] :
( ( 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,[],[f172]) ).
fof(f172,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,
spl71_28,
inference(avatar_split_clause,[],[f532,f775]) ).
fof(f532,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(f773,plain,
spl71_27,
inference(avatar_split_clause,[],[f520,f771]) ).
fof(f520,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(f769,plain,
spl71_26,
inference(avatar_split_clause,[],[f508,f767]) ).
fof(f508,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(f765,plain,
spl71_25,
inference(avatar_split_clause,[],[f496,f763]) ).
fof(f496,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(f761,plain,
spl71_24,
inference(avatar_split_clause,[],[f485,f759]) ).
fof(f485,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(f757,plain,
spl71_23,
inference(avatar_split_clause,[],[f617,f755]) ).
fof(f755,plain,
( spl71_23
<=> ! [X1] : sP2(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_23])]) ).
fof(f617,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f449]) ).
fof(f449,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f753,plain,
spl71_22,
inference(avatar_split_clause,[],[f615,f751]) ).
fof(f751,plain,
( spl71_22
<=> ! [X1] : sP0(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_22])]) ).
fof(f615,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f441]) ).
fof(f441,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f749,plain,
~ spl71_21,
inference(avatar_split_clause,[],[f607,f746]) ).
fof(f746,plain,
( spl71_21
<=> sK69 = sK70 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_21])]) ).
fof(f607,plain,
sK69 != sK70,
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
( sK69 != sK70
& ssItem(sK70)
& ssItem(sK69) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f375,f374]) ).
fof(f374,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK69 != X1
& ssItem(X1) )
& ssItem(sK69) ) ),
introduced(choice_axiom,[]) ).
fof(f375,plain,
( ? [X1] :
( sK69 != X1
& ssItem(X1) )
=> ( sK69 != sK70
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f744,plain,
spl71_20,
inference(avatar_split_clause,[],[f606,f741]) ).
fof(f741,plain,
( spl71_20
<=> ssItem(sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_20])]) ).
fof(f606,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f376]) ).
fof(f739,plain,
spl71_19,
inference(avatar_split_clause,[],[f605,f736]) ).
fof(f736,plain,
( spl71_19
<=> ssItem(sK69) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_19])]) ).
fof(f605,plain,
ssItem(sK69),
inference(cnf_transformation,[],[f376]) ).
fof(f734,plain,
spl71_18,
inference(avatar_split_clause,[],[f399,f731]) ).
fof(f399,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f729,plain,
spl71_17,
inference(avatar_split_clause,[],[f398,f726]) ).
fof(f726,plain,
( spl71_17
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_17])]) ).
fof(f398,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f724,plain,
spl71_16,
inference(avatar_split_clause,[],[f397,f721]) ).
fof(f721,plain,
( spl71_16
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_16])]) ).
fof(f397,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f719,plain,
spl71_15,
inference(avatar_split_clause,[],[f396,f716]) ).
fof(f716,plain,
( spl71_15
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_15])]) ).
fof(f396,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f714,plain,
spl71_14,
inference(avatar_split_clause,[],[f395,f711]) ).
fof(f711,plain,
( spl71_14
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_14])]) ).
fof(f395,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f709,plain,
spl71_13,
inference(avatar_split_clause,[],[f394,f706]) ).
fof(f394,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f704,plain,
spl71_12,
inference(avatar_split_clause,[],[f393,f701]) ).
fof(f393,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f699,plain,
spl71_11,
inference(avatar_split_clause,[],[f392,f696]) ).
fof(f392,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f694,plain,
~ spl71_10,
inference(avatar_split_clause,[],[f391,f691]) ).
fof(f391,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f689,plain,
spl71_9,
inference(avatar_split_clause,[],[f385,f686]) ).
fof(f385,plain,
sK21 = app(app(sK22,sK20),sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f684,plain,
( spl71_7
| ~ spl71_8 ),
inference(avatar_split_clause,[],[f645,f681,f677]) ).
fof(f645,plain,
( nil != sK20
| sK20 = sK21 ),
inference(inner_rewriting,[],[f389]) ).
fof(f389,plain,
( nil != sK20
| nil = sK21 ),
inference(cnf_transformation,[],[f257]) ).
fof(f675,plain,
( ~ spl71_6
| ~ spl71_5 ),
inference(avatar_split_clause,[],[f608,f667,f672]) ).
fof(f608,plain,
( ~ totalorderedP(sK20)
| ~ segmentP(sK21,sK20) ),
inference(definition_unfolding,[],[f390,f382,f381,f382]) ).
fof(f381,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f257]) ).
fof(f382,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f257]) ).
fof(f390,plain,
( ~ totalorderedP(sK18)
| ~ segmentP(sK19,sK18) ),
inference(cnf_transformation,[],[f257]) ).
fof(f670,plain,
spl71_5,
inference(avatar_split_clause,[],[f386,f667]) ).
fof(f386,plain,
totalorderedP(sK20),
inference(cnf_transformation,[],[f257]) ).
fof(f665,plain,
spl71_4,
inference(avatar_split_clause,[],[f384,f662]) ).
fof(f384,plain,
ssList(sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f660,plain,
spl71_3,
inference(avatar_split_clause,[],[f383,f657]) ).
fof(f383,plain,
ssList(sK22),
inference(cnf_transformation,[],[f257]) ).
fof(f655,plain,
spl71_2,
inference(avatar_split_clause,[],[f380,f652]) ).
fof(f380,plain,
ssList(sK21),
inference(cnf_transformation,[],[f257]) ).
fof(f650,plain,
spl71_1,
inference(avatar_split_clause,[],[f379,f647]) ).
fof(f379,plain,
ssList(sK20),
inference(cnf_transformation,[],[f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC339+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 03:04:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (22980)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (22983)WARNING: value z3 for option sas not known
% 0.21/0.40 % (22984)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (22981)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (22982)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (22985)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40 % (22986)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (22983)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40 % (22987)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 TRYING [2]
% 0.21/0.44 TRYING [3]
% 0.21/0.44 TRYING [3]
% 0.21/0.49 TRYING [4]
% 0.21/0.50 TRYING [1]
% 0.21/0.50 TRYING [2]
% 0.21/0.50 TRYING [4]
% 0.21/0.51 % (22985)First to succeed.
% 0.21/0.51 TRYING [3]
% 1.19/0.53 % (22985)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22980"
% 1.19/0.53 % (22985)Refutation found. Thanks to Tanya!
% 1.19/0.53 % SZS status Theorem for theBenchmark
% 1.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.19/0.54 % (22985)------------------------------
% 1.19/0.54 % (22985)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.19/0.54 % (22985)Termination reason: Refutation
% 1.19/0.54
% 1.19/0.54 % (22985)Memory used [KB]: 3149
% 1.19/0.54 % (22985)Time elapsed: 0.130 s
% 1.19/0.54 % (22985)Instructions burned: 189 (million)
% 1.19/0.54 % (22980)Success in time 0.155 s
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