TSTP Solution File: SWW648_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW648_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n025.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 : Sat Sep 2 14:12:39 EDT 2023
% Result : Theorem 3.13s 0.86s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 618
% Syntax : Number of formulae : 1949 ( 214 unt; 54 typ; 0 def)
% Number of atoms : 5455 (1230 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 6451 (2891 ~;2894 |; 118 &)
% ( 492 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 2251 ( 472 atm; 797 fun; 349 num; 633 var)
% Number of types : 10 ( 8 usr; 1 ari)
% Number of type conns : 61 ( 28 >; 33 *; 0 +; 0 <<)
% Number of predicates : 490 ( 486 usr; 485 prp; 0-3 aty)
% Number of functors : 52 ( 44 usr; 23 con; 0-5 aty)
% Number of variables : 3608 (;3526 !; 82 ?;3608 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(type_def_9,type,
a: $tType ).
tff(type_def_10,type,
list_lpa1cm_a1rp: $tType ).
tff(type_def_11,type,
lpa1cm_a1rp: $tType ).
tff(type_def_12,type,
list_a1: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
list: ty > ty ).
tff(func_def_13,type,
nil: ty > uni ).
tff(func_def_14,type,
cons: ( ty * uni * uni ) > uni ).
tff(func_def_15,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_16,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(func_def_17,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(func_def_18,type,
length: ( ty * uni ) > $int ).
tff(func_def_21,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff(func_def_22,type,
reverse: ( ty * uni ) > uni ).
tff(func_def_23,type,
tuple2: ( ty * ty ) > ty ).
tff(func_def_24,type,
tuple21: ( ty * ty * uni * uni ) > uni ).
tff(func_def_25,type,
tuple2_proj_1: ( ty * ty * uni ) > uni ).
tff(func_def_26,type,
tuple2_proj_2: ( ty * ty * uni ) > uni ).
tff(func_def_27,type,
combine: ( ty * ty * uni * uni ) > uni ).
tff(func_def_28,type,
a1: ty ).
tff(func_def_29,type,
t2tb: a > uni ).
tff(func_def_30,type,
tb2t: uni > a ).
tff(func_def_31,type,
t2tb1: list_lpa1cm_a1rp > uni ).
tff(func_def_32,type,
tb2t1: uni > list_lpa1cm_a1rp ).
tff(func_def_33,type,
t2tb2: lpa1cm_a1rp > uni ).
tff(func_def_34,type,
tb2t2: uni > lpa1cm_a1rp ).
tff(func_def_35,type,
t2tb3: list_a1 > uni ).
tff(func_def_36,type,
tb2t3: uni > list_a1 ).
tff(func_def_38,type,
sK0: list_a1 ).
tff(func_def_39,type,
sK1: list_a1 ).
tff(func_def_40,type,
sK2: a ).
tff(func_def_41,type,
sK3: list_a1 ).
tff(func_def_42,type,
sK4: list_lpa1cm_a1rp ).
tff(func_def_43,type,
sK5: list_a1 ).
tff(func_def_44,type,
sK6: a ).
tff(func_def_45,type,
sK7: list_a1 ).
tff(func_def_46,type,
sK8: list_a1 ).
tff(func_def_47,type,
sK9: ( ty * uni * uni ) > uni ).
tff(func_def_48,type,
sK10: ( ty * uni * uni ) > uni ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(pred_def_3,type,
mem: ( ty * uni * uni ) > $o ).
tff(f14255,plain,
$false,
inference(avatar_sat_refutation,[],[f242,f247,f252,f257,f262,f267,f272,f276,f281,f285,f290,f294,f298,f302,f306,f310,f314,f318,f322,f326,f330,f334,f338,f342,f346,f350,f354,f360,f369,f373,f377,f381,f386,f390,f394,f398,f402,f411,f415,f419,f423,f427,f431,f435,f439,f443,f448,f452,f456,f460,f474,f478,f482,f486,f490,f494,f505,f517,f521,f525,f529,f533,f537,f561,f565,f569,f573,f578,f582,f586,f590,f646,f651,f655,f659,f663,f667,f671,f724,f728,f746,f750,f755,f759,f763,f818,f822,f826,f830,f875,f879,f883,f911,f915,f919,f930,f934,f951,f964,f968,f991,f1001,f1025,f1031,f1035,f1070,f1086,f1106,f1124,f1129,f1133,f1158,f1162,f1168,f1184,f1188,f1192,f1228,f1232,f1236,f1241,f1246,f1251,f1255,f1259,f1263,f1267,f1271,f1351,f1357,f1361,f1365,f1369,f1373,f1378,f1382,f1386,f1390,f1394,f1494,f1498,f1503,f1507,f1511,f1516,f1520,f1524,f1528,f1532,f1536,f1540,f1544,f1549,f1553,f1557,f1561,f1869,f1873,f1883,f1887,f1891,f1895,f1899,f1903,f1975,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2244,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2541,f2545,f2549,f2553,f2763,f2886,f2890,f2894,f2898,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2948,f3128,f3167,f3171,f3175,f3179,f3183,f3187,f3193,f3197,f3201,f3205,f3209,f3213,f3374,f3469,f3473,f3478,f3482,f3486,f3490,f3494,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3526,f3530,f3534,f3622,f4007,f4079,f4083,f4087,f4091,f4095,f4099,f4161,f4460,f4464,f4468,f4472,f4476,f4665,f4669,f4673,f4677,f4774,f4778,f4782,f4786,f4790,f4794,f4876,f4954,f4958,f4962,f4966,f4970,f4984,f5035,f5039,f5043,f5187,f5191,f5271,f5275,f5279,f5283,f5287,f5291,f5295,f5299,f5303,f5683,f5687,f5831,f5835,f5908,f5912,f5916,f5920,f6031,f6055,f6087,f6091,f6157,f6186,f6288,f6354,f6358,f6362,f6442,f6446,f6450,f6454,f6458,f6462,f6466,f6470,f6569,f6590,f6594,f6598,f6602,f6606,f6610,f6623,f6648,f6652,f6656,f6660,f6665,f6670,f6686,f6696,f6736,f6756,f6760,f6764,f6768,f6772,f6776,f6780,f6784,f6797,f6854,f6867,f6874,f7303,f7402,f7433,f7480,f7487,f7563,f7585,f7634,f7640,f7646,f7670,f7678,f7748,f7750,f7754,f7758,f7762,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f8129,f8627,f8631,f8635,f8639,f8643,f8647,f8648,f8678,f8682,f8922,f8973,f8977,f8981,f8985,f8989,f8993,f9012,f9063,f9068,f9072,f9145,f9149,f9177,f9182,f9187,f9191,f9195,f9317,f9480,f9486,f9498,f9500,f9512,f9648,f10440,f10533,f10538,f10766,f10770,f10848,f10860,f10869,f10901,f10905,f10909,f10913,f10961,f10962,f11005,f11026,f11030,f11034,f11099,f11103,f11107,f11111,f11115,f11119,f11153,f11157,f11161,f11519,f11731,f11735,f11739,f11743,f11905,f11909,f11921,f11933,f11938,f11960,f12111,f12115,f12154,f12158,f12162,f12166,f12170,f12175,f12223,f12227,f12231,f12235,f12239,f12243,f12247,f12293,f12783,f12787,f12791,f12795,f12799,f12803,f12807,f12811,f12815,f12819,f12823,f13737,f13756,f13760,f13764,f13768,f13772,f13776,f13826,f13853,f13857,f13861,f13865,f13869,f13873,f13877,f13881,f13886,f13890,f13894,f14254]) ).
tff(f14254,plain,
( ~ spl11_22
| spl11_482 ),
inference(avatar_contradiction_clause,[],[f14253]) ).
tff(f14253,plain,
( $false
| ~ spl11_22
| spl11_482 ),
inference(trivial_inequality_removal,[],[f14252]) ).
tff(f14252,plain,
( ( sK1 != sK1 )
| ~ spl11_22
| spl11_482 ),
inference(superposition,[],[f13885,f333]) ).
tff(f333,plain,
( ! [X0: list_a1] : ( tb2t3(t2tb3(X0)) = X0 )
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f332]) ).
tff(f332,plain,
( spl11_22
<=> ! [X0: list_a1] : ( tb2t3(t2tb3(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).
tff(f13885,plain,
( ( sK1 != tb2t3(t2tb3(sK1)) )
| spl11_482 ),
inference(avatar_component_clause,[],[f13883]) ).
tff(f13883,plain,
( spl11_482
<=> ( sK1 = tb2t3(t2tb3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_482])]) ).
tff(f13894,plain,
( spl11_484
| ~ spl11_119
| ~ spl11_161 ),
inference(avatar_split_clause,[],[f1940,f1881,f1186,f13892]) ).
tff(f13892,plain,
( spl11_484
<=> ! [X4: $int,X3: $int] :
( $less($sum(1,X3),X4)
| ~ $less($sum(X3,1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_484])]) ).
tff(f1186,plain,
( spl11_119
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_119])]) ).
tff(f1881,plain,
( spl11_161
<=> ! [X20: $int,X21: $int,X19: $int] :
( $less(X21,$sum(X19,$sum(X20,1)))
| $less($sum(X19,X20),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_161])]) ).
tff(f1940,plain,
( ! [X3: $int,X4: $int] :
( $less($sum(1,X3),X4)
| ~ $less($sum(X3,1),X4) )
| ~ spl11_119
| ~ spl11_161 ),
inference(resolution,[],[f1882,f1187]) ).
tff(f1187,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl11_119 ),
inference(avatar_component_clause,[],[f1186]) ).
tff(f1882,plain,
( ! [X21: $int,X19: $int,X20: $int] :
( $less(X21,$sum(X19,$sum(X20,1)))
| $less($sum(X19,X20),X21) )
| ~ spl11_161 ),
inference(avatar_component_clause,[],[f1881]) ).
tff(f13890,plain,
( spl11_483
| ~ spl11_118
| ~ spl11_160 ),
inference(avatar_split_clause,[],[f1916,f1871,f1182,f13888]) ).
tff(f13888,plain,
( spl11_483
<=> ! [X0: $int,X1: $int] :
( ~ $less($sum(1,X0),X1)
| $less($sum(X0,1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_483])]) ).
tff(f1182,plain,
( spl11_118
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_118])]) ).
tff(f1871,plain,
( spl11_160
<=> ! [X18: $int,X16: $int,X17: $int] :
( ~ $less(X18,$sum(X16,$sum(X17,1)))
| ~ $less($sum(X16,X17),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_160])]) ).
tff(f1916,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(1,X0),X1)
| $less($sum(X0,1),X1) )
| ~ spl11_118
| ~ spl11_160 ),
inference(resolution,[],[f1872,f1183]) ).
tff(f1183,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl11_118 ),
inference(avatar_component_clause,[],[f1182]) ).
tff(f1872,plain,
( ! [X18: $int,X16: $int,X17: $int] :
( ~ $less(X18,$sum(X16,$sum(X17,1)))
| ~ $less($sum(X16,X17),X18) )
| ~ spl11_160 ),
inference(avatar_component_clause,[],[f1871]) ).
tff(f13886,plain,
( ~ spl11_482
| ~ spl11_38
| ~ spl11_43
| ~ spl11_47
| ~ spl11_60
| ~ spl11_79
| ~ spl11_100
| ~ spl11_255
| ~ spl11_472 ),
inference(avatar_split_clause,[],[f13849,f13774,f4004,f966,f722,f523,f445,f429,f408,f13883]) ).
tff(f408,plain,
( spl11_38
<=> ( t2tb3(sK5) = cons(a1,t2tb(sK6),t2tb3(sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_38])]) ).
tff(f429,plain,
( spl11_43
<=> ! [X0: ty,X1: uni] : ( reverse(X0,reverse(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_43])]) ).
tff(f445,plain,
( spl11_47
<=> ( t2tb3(sK1) = infix_plpl(a1,t2tb3(sK8),t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_47])]) ).
tff(f523,plain,
( spl11_60
<=> ! [X0: ty,X1: uni] : ( length(X0,X1) = length(X0,reverse(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_60])]) ).
tff(f722,plain,
( spl11_79
<=> ! [X2: uni,X0: ty,X1: uni] : ( length(X0,cons(X0,X1,X2)) = $sum(1,length(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_79])]) ).
tff(f966,plain,
( spl11_100
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] : ( infix_plpl(X0,reverse(X0,cons(X0,X3,X1)),X2) = infix_plpl(X0,reverse(X0,X1),cons(X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_100])]) ).
tff(f4004,plain,
( spl11_255
<=> ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_255])]) ).
tff(f13774,plain,
( spl11_472
<=> ! [X0: uni] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),X0)) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8))))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_472])]) ).
tff(f13849,plain,
( ( sK1 != tb2t3(t2tb3(sK1)) )
| ~ spl11_38
| ~ spl11_43
| ~ spl11_47
| ~ spl11_60
| ~ spl11_79
| ~ spl11_100
| ~ spl11_255
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13848,f447]) ).
tff(f447,plain,
( ( t2tb3(sK1) = infix_plpl(a1,t2tb3(sK8),t2tb3(sK5)) )
| ~ spl11_47 ),
inference(avatar_component_clause,[],[f445]) ).
tff(f13848,plain,
( ( sK1 != tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_43
| ~ spl11_60
| ~ spl11_79
| ~ spl11_100
| ~ spl11_255
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13847,f430]) ).
tff(f430,plain,
( ! [X0: ty,X1: uni] : ( reverse(X0,reverse(X0,X1)) = X1 )
| ~ spl11_43 ),
inference(avatar_component_clause,[],[f429]) ).
tff(f13847,plain,
( ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,reverse(a1,t2tb3(sK8))),t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_60
| ~ spl11_79
| ~ spl11_100
| ~ spl11_255
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13846,f410]) ).
tff(f410,plain,
( ( t2tb3(sK5) = cons(a1,t2tb(sK6),t2tb3(sK7)) )
| ~ spl11_38 ),
inference(avatar_component_clause,[],[f408]) ).
tff(f13846,plain,
( ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,reverse(a1,t2tb3(sK8))),cons(a1,t2tb(sK6),t2tb3(sK7)))) )
| ~ spl11_60
| ~ spl11_79
| ~ spl11_100
| ~ spl11_255
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13845,f967]) ).
tff(f967,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,reverse(X0,cons(X0,X3,X1)),X2) = infix_plpl(X0,reverse(X0,X1),cons(X0,X3,X2)) )
| ~ spl11_100 ),
inference(avatar_component_clause,[],[f966]) ).
tff(f13845,plain,
( ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))),t2tb3(sK7))) )
| ~ spl11_60
| ~ spl11_79
| ~ spl11_255
| ~ spl11_472 ),
inference(trivial_inequality_removal,[],[f13844]) ).
tff(f13844,plain,
( ( length(a1,t2tb3(sK0)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))),t2tb3(sK7))) )
| ~ spl11_60
| ~ spl11_79
| ~ spl11_255
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13843,f4006]) ).
tff(f4006,plain,
( ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK8))) )
| ~ spl11_255 ),
inference(avatar_component_clause,[],[f4004]) ).
tff(f13843,plain,
( ( length(a1,t2tb3(sK0)) != $sum(1,length(a1,t2tb3(sK8))) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))),t2tb3(sK7))) )
| ~ spl11_60
| ~ spl11_79
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13842,f524]) ).
tff(f524,plain,
( ! [X0: ty,X1: uni] : ( length(X0,X1) = length(X0,reverse(X0,X1)) )
| ~ spl11_60 ),
inference(avatar_component_clause,[],[f523]) ).
tff(f13842,plain,
( ( length(a1,t2tb3(sK0)) != $sum(1,length(a1,reverse(a1,t2tb3(sK8)))) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))),t2tb3(sK7))) )
| ~ spl11_79
| ~ spl11_472 ),
inference(forward_demodulation,[],[f13841,f723]) ).
tff(f723,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( length(X0,cons(X0,X1,X2)) = $sum(1,length(X0,X2)) )
| ~ spl11_79 ),
inference(avatar_component_clause,[],[f722]) ).
tff(f13841,plain,
( ( length(a1,t2tb3(sK0)) != length(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8)))),t2tb3(sK7))) )
| ~ spl11_472 ),
inference(equality_resolution,[],[f13775]) ).
tff(f13775,plain,
( ! [X0: uni] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),X0)) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8))))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) )
| ~ spl11_472 ),
inference(avatar_component_clause,[],[f13774]) ).
tff(f13881,plain,
( spl11_481
| ~ spl11_114
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f1571,f1505,f1131,f13879]) ).
tff(f13879,plain,
( spl11_481
<=> ! [X4: $int,X3: $int] :
( $less(X3,$sum(X4,1))
| $less(X4,$sum(X3,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_481])]) ).
tff(f1131,plain,
( spl11_114
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_114])]) ).
tff(f1505,plain,
( spl11_145
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_145])]) ).
tff(f1571,plain,
( ! [X3: $int,X4: $int] :
( $less(X3,$sum(X4,1))
| $less(X4,$sum(X3,1)) )
| ~ spl11_114
| ~ spl11_145 ),
inference(resolution,[],[f1506,f1132]) ).
tff(f1132,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl11_114 ),
inference(avatar_component_clause,[],[f1131]) ).
tff(f1506,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl11_145 ),
inference(avatar_component_clause,[],[f1505]) ).
tff(f13877,plain,
( spl11_480
| ~ spl11_39
| ~ spl11_134 ),
inference(avatar_split_clause,[],[f1433,f1363,f413,f13875]) ).
tff(f13875,plain,
( spl11_480
<=> ! [X2: $int,X4: $int,X3: $int] :
( $less($sum(X3,X4),$sum(X3,X2))
| ~ $less(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_480])]) ).
tff(f413,plain,
( spl11_39
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_39])]) ).
tff(f1363,plain,
( spl11_134
<=> ! [X4: $int,X2: $int,X3: $int] :
( $less($sum(X3,X2),$sum(X4,X3))
| ~ $less(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_134])]) ).
tff(f1433,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( $less($sum(X3,X4),$sum(X3,X2))
| ~ $less(X4,X2) )
| ~ spl11_39
| ~ spl11_134 ),
inference(superposition,[],[f1364,f414]) ).
tff(f414,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl11_39 ),
inference(avatar_component_clause,[],[f413]) ).
tff(f1364,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( $less($sum(X3,X2),$sum(X4,X3))
| ~ $less(X2,X4) )
| ~ spl11_134 ),
inference(avatar_component_clause,[],[f1363]) ).
tff(f13873,plain,
( spl11_479
| ~ spl11_123
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1411,f1359,f1234,f13871]) ).
tff(f13871,plain,
( spl11_479
<=> ! [X8: $int,X7: $int] :
( $less(0,$uminus($sum(X7,X8)))
| ~ $less(X8,$uminus(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_479])]) ).
tff(f1234,plain,
( spl11_123
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_123])]) ).
tff(f1359,plain,
( spl11_133
<=> ! [X4: $int,X3: $int] : ( $sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_133])]) ).
tff(f1411,plain,
( ! [X8: $int,X7: $int] :
( $less(0,$uminus($sum(X7,X8)))
| ~ $less(X8,$uminus(X7)) )
| ~ spl11_123
| ~ spl11_133 ),
inference(superposition,[],[f1235,f1360]) ).
tff(f1360,plain,
( ! [X3: $int,X4: $int] : ( $sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3)) )
| ~ spl11_133 ),
inference(avatar_component_clause,[],[f1359]) ).
tff(f1235,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl11_123 ),
inference(avatar_component_clause,[],[f1234]) ).
tff(f13869,plain,
( spl11_478
| ~ spl11_125
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1410,f1359,f1249,f13867]) ).
tff(f13867,plain,
( spl11_478
<=> ! [X6: $int,X5: $int] :
( $less($uminus($sum(X5,X6)),0)
| ~ $less($uminus(X5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_478])]) ).
tff(f1249,plain,
( spl11_125
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_125])]) ).
tff(f1410,plain,
( ! [X6: $int,X5: $int] :
( $less($uminus($sum(X5,X6)),0)
| ~ $less($uminus(X5),X6) )
| ~ spl11_125
| ~ spl11_133 ),
inference(superposition,[],[f1250,f1360]) ).
tff(f1250,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl11_125 ),
inference(avatar_component_clause,[],[f1249]) ).
tff(f13865,plain,
( spl11_477
| ~ spl11_64
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1320,f1249,f559,f13863]) ).
tff(f13863,plain,
( spl11_477
<=> ! [X9: $int,X8: $int] :
( $less($uminus($sum(X9,X8)),0)
| ~ $less($uminus(X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_477])]) ).
tff(f559,plain,
( spl11_64
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_64])]) ).
tff(f1320,plain,
( ! [X8: $int,X9: $int] :
( $less($uminus($sum(X9,X8)),0)
| ~ $less($uminus(X8),X9) )
| ~ spl11_64
| ~ spl11_125 ),
inference(superposition,[],[f1250,f560]) ).
tff(f560,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl11_64 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f13861,plain,
( spl11_476
| ~ spl11_64
| ~ spl11_123 ),
inference(avatar_split_clause,[],[f1313,f1234,f559,f13859]) ).
tff(f13859,plain,
( spl11_476
<=> ! [X9: $int,X8: $int] :
( $less(0,$uminus($sum(X9,X8)))
| ~ $less(X9,$uminus(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_476])]) ).
tff(f1313,plain,
( ! [X8: $int,X9: $int] :
( $less(0,$uminus($sum(X9,X8)))
| ~ $less(X9,$uminus(X8)) )
| ~ spl11_64
| ~ spl11_123 ),
inference(superposition,[],[f1235,f560]) ).
tff(f13857,plain,
( spl11_475
| ~ spl11_80
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1074,f1068,f726,f13855]) ).
tff(f13855,plain,
( spl11_475
<=> ! [X12: uni,X11: uni,X9: ty,X10: ty] : ( match_list(list(X9),X10,nil(X10),X11,X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_475])]) ).
tff(f726,plain,
( spl11_80
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_80])]) ).
tff(f1068,plain,
( spl11_107
<=> ! [X0: ty,X1: uni] : sort(list(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_107])]) ).
tff(f1074,plain,
( ! [X10: ty,X11: uni,X9: ty,X12: uni] : ( match_list(list(X9),X10,nil(X10),X11,X12) = X11 )
| ~ spl11_80
| ~ spl11_107 ),
inference(resolution,[],[f1069,f727]) ).
tff(f727,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ~ sort(X1,X2)
| ( match_list(X1,X0,nil(X0),X2,X3) = X2 ) )
| ~ spl11_80 ),
inference(avatar_component_clause,[],[f726]) ).
tff(f1069,plain,
( ! [X0: ty,X1: uni] : sort(list(X0),X1)
| ~ spl11_107 ),
inference(avatar_component_clause,[],[f1068]) ).
tff(f13853,plain,
( spl11_474
| ~ spl11_76
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1073,f1068,f661,f13851]) ).
tff(f13851,plain,
( spl11_474
<=> ! [X6: ty,X7: uni,X8: uni] : ( cons_proj_1(list(X6),cons(list(X6),X7,X8)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_474])]) ).
tff(f661,plain,
( spl11_76
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_76])]) ).
tff(f1073,plain,
( ! [X8: uni,X6: ty,X7: uni] : ( cons_proj_1(list(X6),cons(list(X6),X7,X8)) = X7 )
| ~ spl11_76
| ~ spl11_107 ),
inference(resolution,[],[f1069,f662]) ).
tff(f662,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ sort(X0,X1)
| ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 ) )
| ~ spl11_76 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f13826,plain,
( spl11_473
| ~ spl11_427
| ~ spl11_438 ),
inference(avatar_split_clause,[],[f12147,f12109,f11159,f13824]) ).
tff(f13824,plain,
( spl11_473
<=> ! [X6: uni] : ~ $less($sum(4,length(a1,infix_plpl(a1,t2tb3(sK8),X6))),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_473])]) ).
tff(f11159,plain,
( spl11_427
<=> ! [X2: uni,X0: uni,X1: uni] : ( $sum(2,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) = length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,X2)),cons(a1,X1,t2tb3(sK8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_427])]) ).
tff(f12109,plain,
( spl11_438
<=> ! [X5: ty,X7: uni] : ~ $less($sum(2,length(X5,X7)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_438])]) ).
tff(f12147,plain,
( ! [X6: uni] : ~ $less($sum(4,length(a1,infix_plpl(a1,t2tb3(sK8),X6))),0)
| ~ spl11_427
| ~ spl11_438 ),
inference(evaluation,[],[f12123]) ).
tff(f12123,plain,
( ! [X6: uni] : ~ $less($sum(2,$sum(2,length(a1,infix_plpl(a1,t2tb3(sK8),X6)))),0)
| ~ spl11_427
| ~ spl11_438 ),
inference(superposition,[],[f12110,f11160]) ).
tff(f11160,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( $sum(2,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) = length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,X2)),cons(a1,X1,t2tb3(sK8)))) )
| ~ spl11_427 ),
inference(avatar_component_clause,[],[f11159]) ).
tff(f12110,plain,
( ! [X7: uni,X5: ty] : ~ $less($sum(2,length(X5,X7)),0)
| ~ spl11_438 ),
inference(avatar_component_clause,[],[f12109]) ).
tff(f13776,plain,
( spl11_472
| ~ spl11_33
| ~ spl11_432
| ~ spl11_465 ),
inference(avatar_split_clause,[],[f13738,f13735,f11903,f383,f13774]) ).
tff(f383,plain,
( spl11_33
<=> ( t2tb3(sK0) = cons(a1,t2tb(sK2),t2tb3(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).
tff(f11903,plain,
( spl11_432
<=> ! [X0: uni,X1: uni] : ( combine(a1,a1,cons(a1,X0,t2tb3(sK3)),cons(a1,X1,reverse(a1,t2tb3(sK8)))) = cons(tuple2(a1,a1),tuple21(a1,a1,X0,X1),t2tb1(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_432])]) ).
tff(f13735,plain,
( spl11_465
<=> ! [X0: uni] :
( ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),X0)) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_465])]) ).
tff(f13738,plain,
( ! [X0: uni] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),X0)) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,t2tb(sK6),reverse(a1,t2tb3(sK8))))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) )
| ~ spl11_33
| ~ spl11_432
| ~ spl11_465 ),
inference(forward_demodulation,[],[f13736,f11940]) ).
tff(f11940,plain,
( ! [X2: uni] : ( cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),X2),t2tb1(sK4)) = combine(a1,a1,t2tb3(sK0),cons(a1,X2,reverse(a1,t2tb3(sK8)))) )
| ~ spl11_33
| ~ spl11_432 ),
inference(superposition,[],[f11904,f385]) ).
tff(f385,plain,
( ( t2tb3(sK0) = cons(a1,t2tb(sK2),t2tb3(sK3)) )
| ~ spl11_33 ),
inference(avatar_component_clause,[],[f383]) ).
tff(f11904,plain,
( ! [X0: uni,X1: uni] : ( combine(a1,a1,cons(a1,X0,t2tb3(sK3)),cons(a1,X1,reverse(a1,t2tb3(sK8)))) = cons(tuple2(a1,a1),tuple21(a1,a1,X0,X1),t2tb1(sK4)) )
| ~ spl11_432 ),
inference(avatar_component_clause,[],[f11903]) ).
tff(f13736,plain,
( ! [X0: uni] :
( ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),X0)) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) )
| ~ spl11_465 ),
inference(avatar_component_clause,[],[f13735]) ).
tff(f13772,plain,
( spl11_471
| ~ spl11_38
| ~ spl11_312 ),
inference(avatar_split_clause,[],[f6176,f6155,f408,f13770]) ).
tff(f13770,plain,
( spl11_471
<=> ! [X44: ty,X47: uni,X46: uni,X45: uni] :
( mem(tuple2(X44,a1),X45,combine(a1,X44,cons(X44,X46,X47),t2tb3(sK5)))
| ~ mem(tuple2(X44,a1),X45,combine(a1,X44,X47,t2tb3(sK7)))
| ~ sort(tuple2(X44,a1),tuple21(X44,a1,X46,t2tb(sK6)))
| ~ sort(tuple2(X44,a1),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_471])]) ).
tff(f6155,plain,
( spl11_312
<=> ! [X26: ty,X31: uni,X29: uni,X27: uni,X25: ty,X28: uni,X30: uni] :
( mem(tuple2(X25,X26),X31,combine(X26,X25,cons(X25,X27,X29),cons(X26,X28,X30)))
| ~ mem(tuple2(X25,X26),X31,combine(X26,X25,X29,X30))
| ~ sort(tuple2(X25,X26),tuple21(X25,X26,X27,X28))
| ~ sort(tuple2(X25,X26),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_312])]) ).
tff(f6176,plain,
( ! [X46: uni,X47: uni,X44: ty,X45: uni] :
( mem(tuple2(X44,a1),X45,combine(a1,X44,cons(X44,X46,X47),t2tb3(sK5)))
| ~ mem(tuple2(X44,a1),X45,combine(a1,X44,X47,t2tb3(sK7)))
| ~ sort(tuple2(X44,a1),tuple21(X44,a1,X46,t2tb(sK6)))
| ~ sort(tuple2(X44,a1),X45) )
| ~ spl11_38
| ~ spl11_312 ),
inference(superposition,[],[f6156,f410]) ).
tff(f6156,plain,
( ! [X31: uni,X28: uni,X29: uni,X26: ty,X27: uni,X25: ty,X30: uni] :
( mem(tuple2(X25,X26),X31,combine(X26,X25,cons(X25,X27,X29),cons(X26,X28,X30)))
| ~ mem(tuple2(X25,X26),X31,combine(X26,X25,X29,X30))
| ~ sort(tuple2(X25,X26),tuple21(X25,X26,X27,X28))
| ~ sort(tuple2(X25,X26),X31) )
| ~ spl11_312 ),
inference(avatar_component_clause,[],[f6155]) ).
tff(f13768,plain,
( spl11_470
| ~ spl11_33
| ~ spl11_312 ),
inference(avatar_split_clause,[],[f6175,f6155,f383,f13766]) ).
tff(f13766,plain,
( spl11_470
<=> ! [X41: uni,X40: ty,X42: uni,X43: uni] :
( mem(tuple2(X40,a1),X41,combine(a1,X40,cons(X40,X42,X43),t2tb3(sK0)))
| ~ mem(tuple2(X40,a1),X41,combine(a1,X40,X43,t2tb3(sK3)))
| ~ sort(tuple2(X40,a1),tuple21(X40,a1,X42,t2tb(sK2)))
| ~ sort(tuple2(X40,a1),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_470])]) ).
tff(f6175,plain,
( ! [X40: ty,X41: uni,X42: uni,X43: uni] :
( mem(tuple2(X40,a1),X41,combine(a1,X40,cons(X40,X42,X43),t2tb3(sK0)))
| ~ mem(tuple2(X40,a1),X41,combine(a1,X40,X43,t2tb3(sK3)))
| ~ sort(tuple2(X40,a1),tuple21(X40,a1,X42,t2tb(sK2)))
| ~ sort(tuple2(X40,a1),X41) )
| ~ spl11_33
| ~ spl11_312 ),
inference(superposition,[],[f6156,f385]) ).
tff(f13764,plain,
( spl11_469
| ~ spl11_38
| ~ spl11_312 ),
inference(avatar_split_clause,[],[f6169,f6155,f408,f13762]) ).
tff(f13762,plain,
( spl11_469
<=> ! [X44: ty,X47: uni,X46: uni,X45: uni] :
( mem(tuple2(a1,X44),X45,combine(X44,a1,t2tb3(sK5),cons(X44,X46,X47)))
| ~ mem(tuple2(a1,X44),X45,combine(X44,a1,t2tb3(sK7),X47))
| ~ sort(tuple2(a1,X44),tuple21(a1,X44,t2tb(sK6),X46))
| ~ sort(tuple2(a1,X44),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_469])]) ).
tff(f6169,plain,
( ! [X46: uni,X47: uni,X44: ty,X45: uni] :
( mem(tuple2(a1,X44),X45,combine(X44,a1,t2tb3(sK5),cons(X44,X46,X47)))
| ~ mem(tuple2(a1,X44),X45,combine(X44,a1,t2tb3(sK7),X47))
| ~ sort(tuple2(a1,X44),tuple21(a1,X44,t2tb(sK6),X46))
| ~ sort(tuple2(a1,X44),X45) )
| ~ spl11_38
| ~ spl11_312 ),
inference(superposition,[],[f6156,f410]) ).
tff(f13760,plain,
( spl11_468
| ~ spl11_33
| ~ spl11_312 ),
inference(avatar_split_clause,[],[f6168,f6155,f383,f13758]) ).
tff(f13758,plain,
( spl11_468
<=> ! [X41: uni,X40: ty,X42: uni,X43: uni] :
( mem(tuple2(a1,X40),X41,combine(X40,a1,t2tb3(sK0),cons(X40,X42,X43)))
| ~ mem(tuple2(a1,X40),X41,combine(X40,a1,t2tb3(sK3),X43))
| ~ sort(tuple2(a1,X40),tuple21(a1,X40,t2tb(sK2),X42))
| ~ sort(tuple2(a1,X40),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_468])]) ).
tff(f6168,plain,
( ! [X40: ty,X41: uni,X42: uni,X43: uni] :
( mem(tuple2(a1,X40),X41,combine(X40,a1,t2tb3(sK0),cons(X40,X42,X43)))
| ~ mem(tuple2(a1,X40),X41,combine(X40,a1,t2tb3(sK3),X43))
| ~ sort(tuple2(a1,X40),tuple21(a1,X40,t2tb(sK2),X42))
| ~ sort(tuple2(a1,X40),X41) )
| ~ spl11_33
| ~ spl11_312 ),
inference(superposition,[],[f6156,f385]) ).
tff(f13756,plain,
( ~ spl11_466
| spl11_467
| ~ spl11_31
| ~ spl11_79
| ~ spl11_131
| ~ spl11_189
| ~ spl11_191 ),
inference(avatar_split_clause,[],[f2489,f2086,f2078,f1349,f722,f375,f13754,f13750]) ).
tff(f13750,plain,
( spl11_466
<=> ( 1 = length(a1,t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_466])]) ).
tff(f13754,plain,
( spl11_467
<=> ! [X0: uni] :
( ( sK1 != tb2t3(cons(a1,X0,t2tb3(sK7))) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_467])]) ).
tff(f375,plain,
( spl11_31
<=> ! [X0: ty] : ( 0 = length(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
tff(f1349,plain,
( spl11_131
<=> ! [X0: uni] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,X0))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,X0,t2tb3(sK7))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_131])]) ).
tff(f2078,plain,
( spl11_189
<=> ! [X4: uni,X5: uni,X3: ty] : ( infix_plpl(X3,cons(X3,X5,nil(X3)),X4) = cons(X3,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_189])]) ).
tff(f2086,plain,
( spl11_191
<=> ! [X0: ty,X1: uni] : ( cons(X0,X1,nil(X0)) = reverse(X0,cons(X0,X1,nil(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_191])]) ).
tff(f2489,plain,
( ! [X0: uni] :
( ( sK1 != tb2t3(cons(a1,X0,t2tb3(sK7))) )
| ( 1 != length(a1,t2tb3(sK0)) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) ) )
| ~ spl11_31
| ~ spl11_79
| ~ spl11_131
| ~ spl11_189
| ~ spl11_191 ),
inference(forward_demodulation,[],[f2488,f2079]) ).
tff(f2079,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( infix_plpl(X3,cons(X3,X5,nil(X3)),X4) = cons(X3,X5,X4) )
| ~ spl11_189 ),
inference(avatar_component_clause,[],[f2078]) ).
tff(f2488,plain,
( ! [X0: uni] :
( ( 1 != length(a1,t2tb3(sK0)) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) )
| ( sK1 != tb2t3(infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK7))) ) )
| ~ spl11_31
| ~ spl11_79
| ~ spl11_131
| ~ spl11_191 ),
inference(evaluation,[],[f2487]) ).
tff(f2487,plain,
( ! [X0: uni] :
( ( length(a1,t2tb3(sK0)) != $sum(1,0) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) )
| ( sK1 != tb2t3(infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK7))) ) )
| ~ spl11_31
| ~ spl11_79
| ~ spl11_131
| ~ spl11_191 ),
inference(forward_demodulation,[],[f2486,f376]) ).
tff(f376,plain,
( ! [X0: ty] : ( 0 = length(X0,nil(X0)) )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f375]) ).
tff(f2486,plain,
( ! [X0: uni] :
( ( length(a1,t2tb3(sK0)) != $sum(1,length(a1,nil(a1))) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) )
| ( sK1 != tb2t3(infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK7))) ) )
| ~ spl11_79
| ~ spl11_131
| ~ spl11_191 ),
inference(forward_demodulation,[],[f2480,f723]) ).
tff(f2480,plain,
( ! [X0: uni] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),cons(a1,X0,nil(a1)))) )
| ( length(a1,t2tb3(sK0)) != length(a1,cons(a1,X0,nil(a1))) )
| ( sK1 != tb2t3(infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK7))) ) )
| ~ spl11_131
| ~ spl11_191 ),
inference(superposition,[],[f1350,f2087]) ).
tff(f2087,plain,
( ! [X0: ty,X1: uni] : ( cons(X0,X1,nil(X0)) = reverse(X0,cons(X0,X1,nil(X0))) )
| ~ spl11_191 ),
inference(avatar_component_clause,[],[f2086]) ).
tff(f1350,plain,
( ! [X0: uni] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,X0))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,X0,t2tb3(sK7))) ) )
| ~ spl11_131 ),
inference(avatar_component_clause,[],[f1349]) ).
tff(f13737,plain,
( spl11_465
| ~ spl11_43
| ~ spl11_60
| ~ spl11_131 ),
inference(avatar_split_clause,[],[f1353,f1349,f523,f429,f13735]) ).
tff(f1353,plain,
( ! [X0: uni] :
( ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),X0)) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) )
| ~ spl11_43
| ~ spl11_60
| ~ spl11_131 ),
inference(forward_demodulation,[],[f1352,f524]) ).
tff(f1352,plain,
( ! [X0: uni] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),X0)) )
| ( length(a1,t2tb3(sK0)) != length(a1,reverse(a1,X0)) )
| ( sK1 != tb2t3(infix_plpl(a1,reverse(a1,X0),t2tb3(sK7))) ) )
| ~ spl11_43
| ~ spl11_131 ),
inference(superposition,[],[f1350,f430]) ).
tff(f12823,plain,
( spl11_464
| ~ spl11_29
| ~ spl11_193 ),
inference(avatar_split_clause,[],[f2592,f2494,f367,f12821]) ).
tff(f12821,plain,
( spl11_464
<=> ! [X11: $int,X10: $int] : ( $uminus(X11) = $sum($uminus($sum(X10,X11)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_464])]) ).
tff(f367,plain,
( spl11_29
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).
tff(f2494,plain,
( spl11_193
<=> ! [X9: $int,X8: $int,X10: $int] : ( $sum($uminus(X8),$sum($uminus(X9),X10)) = $sum($uminus($sum(X9,X8)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_193])]) ).
tff(f2592,plain,
( ! [X10: $int,X11: $int] : ( $uminus(X11) = $sum($uminus($sum(X10,X11)),X10) )
| ~ spl11_29
| ~ spl11_193 ),
inference(evaluation,[],[f2557]) ).
tff(f2557,plain,
( ! [X10: $int,X11: $int] : ( $sum($uminus($sum(X10,X11)),$uminus($uminus(X10))) = $sum($uminus(X11),0) )
| ~ spl11_29
| ~ spl11_193 ),
inference(superposition,[],[f2495,f368]) ).
tff(f368,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl11_29 ),
inference(avatar_component_clause,[],[f367]) ).
tff(f2495,plain,
( ! [X10: $int,X8: $int,X9: $int] : ( $sum($uminus(X8),$sum($uminus(X9),X10)) = $sum($uminus($sum(X9,X8)),X10) )
| ~ spl11_193 ),
inference(avatar_component_clause,[],[f2494]) ).
tff(f12819,plain,
( spl11_463
| ~ spl11_114
| ~ spl11_152 ),
inference(avatar_split_clause,[],[f1650,f1534,f1131,f12817]) ).
tff(f12817,plain,
( spl11_463
<=> ! [X38: $int,X37: $int] : $less($sum(X37,X38),$sum(X38,$sum(X37,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_463])]) ).
tff(f1534,plain,
( spl11_152
<=> ! [X4: $int,X2: $int,X3: $int] : ( $sum(X2,$sum(X3,X4)) = $sum($sum(X3,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_152])]) ).
tff(f1650,plain,
( ! [X38: $int,X37: $int] : $less($sum(X37,X38),$sum(X38,$sum(X37,1)))
| ~ spl11_114
| ~ spl11_152 ),
inference(superposition,[],[f1132,f1535]) ).
tff(f1535,plain,
( ! [X2: $int,X3: $int,X4: $int] : ( $sum(X2,$sum(X3,X4)) = $sum($sum(X3,X2),X4) )
| ~ spl11_152 ),
inference(avatar_component_clause,[],[f1534]) ).
tff(f12815,plain,
( spl11_462
| ~ spl11_29
| ~ spl11_135 ),
inference(avatar_split_clause,[],[f1455,f1367,f367,f12813]) ).
tff(f12813,plain,
( spl11_462
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_462])]) ).
tff(f1367,plain,
( spl11_135
<=> ! [X2: $int,X4: $int,X3: $int] :
( $less($sum(X4,X3),$sum(X3,X2))
| ~ $less(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_135])]) ).
tff(f1455,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) )
| ~ spl11_29
| ~ spl11_135 ),
inference(superposition,[],[f1368,f368]) ).
tff(f1368,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( $less($sum(X4,X3),$sum(X3,X2))
| ~ $less(X4,X2) )
| ~ spl11_135 ),
inference(avatar_component_clause,[],[f1367]) ).
tff(f12811,plain,
( spl11_461
| ~ spl11_29
| ~ spl11_134 ),
inference(avatar_split_clause,[],[f1423,f1363,f367,f12809]) ).
tff(f12809,plain,
( spl11_461
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_461])]) ).
tff(f1423,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) )
| ~ spl11_29
| ~ spl11_134 ),
inference(superposition,[],[f1364,f368]) ).
tff(f12807,plain,
( spl11_460
| ~ spl11_120
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1408,f1359,f1190,f12805]) ).
tff(f12805,plain,
( spl11_460
<=> ! [X2: $int,X3: $int] : ( $uminus(X3) = $sum(X2,$uminus($sum(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_460])]) ).
tff(f1190,plain,
( spl11_120
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_120])]) ).
tff(f1408,plain,
( ! [X2: $int,X3: $int] : ( $uminus(X3) = $sum(X2,$uminus($sum(X2,X3))) )
| ~ spl11_120
| ~ spl11_133 ),
inference(superposition,[],[f1191,f1360]) ).
tff(f1191,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl11_120 ),
inference(avatar_component_clause,[],[f1190]) ).
tff(f12803,plain,
( spl11_459
| ~ spl11_64
| ~ spl11_133 ),
inference(avatar_split_clause,[],[f1403,f1359,f559,f12801]) ).
tff(f12801,plain,
( spl11_459
<=> ! [X2: $int,X3: $int] : ( $uminus($sum(X3,X2)) = $uminus($sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_459])]) ).
tff(f1403,plain,
( ! [X2: $int,X3: $int] : ( $uminus($sum(X3,X2)) = $uminus($sum(X2,X3)) )
| ~ spl11_64
| ~ spl11_133 ),
inference(superposition,[],[f1360,f560]) ).
tff(f12799,plain,
( spl11_458
| ~ spl11_39
| ~ spl11_125 ),
inference(avatar_split_clause,[],[f1317,f1249,f413,f12797]) ).
tff(f12797,plain,
( spl11_458
<=> ! [X2: $int,X1: $int] :
( $less($sum($uminus(X2),X1),0)
| ~ $less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_458])]) ).
tff(f1317,plain,
( ! [X2: $int,X1: $int] :
( $less($sum($uminus(X2),X1),0)
| ~ $less(X1,X2) )
| ~ spl11_39
| ~ spl11_125 ),
inference(superposition,[],[f1250,f414]) ).
tff(f12795,plain,
( spl11_457
| ~ spl11_39
| ~ spl11_123 ),
inference(avatar_split_clause,[],[f1310,f1234,f413,f12793]) ).
tff(f12793,plain,
( spl11_457
<=> ! [X2: $int,X1: $int] :
( $less(0,$sum($uminus(X2),X1))
| ~ $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_457])]) ).
tff(f1310,plain,
( ! [X2: $int,X1: $int] :
( $less(0,$sum($uminus(X2),X1))
| ~ $less(X2,X1) )
| ~ spl11_39
| ~ spl11_123 ),
inference(superposition,[],[f1235,f414]) ).
tff(f12791,plain,
( spl11_456
| ~ spl11_64
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1210,f1190,f559,f12789]) ).
tff(f12789,plain,
( spl11_456
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_456])]) ).
tff(f1210,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) )
| ~ spl11_64
| ~ spl11_120 ),
inference(superposition,[],[f1191,f560]) ).
tff(f12787,plain,
( spl11_455
| ~ spl11_375
| ~ spl11_440 ),
inference(avatar_split_clause,[],[f12261,f12152,f7828,f12785]) ).
tff(f12785,plain,
( spl11_455
<=> ! [X66: uni,X65: ty,X68: uni] : ( match_list(list(X65),a1,t2tb3(sK5),X68,X66) = X66 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_455])]) ).
tff(f7828,plain,
( spl11_375
<=> ! [X35: uni,X34: uni,X36: uni,X33: bool,X32: ty] : ( match_bool(X32,X33,X34,X35) = match_list(X32,a1,t2tb3(sK5),X36,match_bool(X32,X33,X34,X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_375])]) ).
tff(f12152,plain,
( spl11_440
<=> ! [X2: uni,X0: ty,X1: uni] : ( match_bool(list(X0),true,X1,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_440])]) ).
tff(f12261,plain,
( ! [X65: ty,X68: uni,X66: uni] : ( match_list(list(X65),a1,t2tb3(sK5),X68,X66) = X66 )
| ~ spl11_375
| ~ spl11_440 ),
inference(superposition,[],[f7829,f12153]) ).
tff(f12153,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( match_bool(list(X0),true,X1,X2) = X1 )
| ~ spl11_440 ),
inference(avatar_component_clause,[],[f12152]) ).
tff(f7829,plain,
( ! [X36: uni,X34: uni,X35: uni,X32: ty,X33: bool] : ( match_bool(X32,X33,X34,X35) = match_list(X32,a1,t2tb3(sK5),X36,match_bool(X32,X33,X34,X35)) )
| ~ spl11_375 ),
inference(avatar_component_clause,[],[f7828]) ).
tff(f12783,plain,
( spl11_454
| ~ spl11_73
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1153,f1131,f649,f12781]) ).
tff(f12781,plain,
( spl11_454
<=> ! [X2: $int,X3: $int] : $less($sum(X2,X3),$sum(X2,$sum(X3,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_454])]) ).
tff(f649,plain,
( spl11_73
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_73])]) ).
tff(f1153,plain,
( ! [X2: $int,X3: $int] : $less($sum(X2,X3),$sum(X2,$sum(X3,1)))
| ~ spl11_73
| ~ spl11_114 ),
inference(superposition,[],[f1132,f650]) ).
tff(f650,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl11_73 ),
inference(avatar_component_clause,[],[f649]) ).
tff(f12293,plain,
( spl11_453
| ~ spl11_374
| ~ spl11_440 ),
inference(avatar_split_clause,[],[f12260,f12152,f7824,f12291]) ).
tff(f12291,plain,
( spl11_453
<=> ! [X61: ty,X64: uni,X62: uni] : ( match_list(list(X61),a1,t2tb3(sK0),X64,X62) = X62 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_453])]) ).
tff(f7824,plain,
( spl11_374
<=> ! [X31: uni,X29: uni,X27: ty,X28: bool,X30: uni] : ( match_bool(X27,X28,X29,X30) = match_list(X27,a1,t2tb3(sK0),X31,match_bool(X27,X28,X29,X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_374])]) ).
tff(f12260,plain,
( ! [X62: uni,X61: ty,X64: uni] : ( match_list(list(X61),a1,t2tb3(sK0),X64,X62) = X62 )
| ~ spl11_374
| ~ spl11_440 ),
inference(superposition,[],[f7825,f12153]) ).
tff(f7825,plain,
( ! [X31: uni,X28: bool,X29: uni,X27: ty,X30: uni] : ( match_bool(X27,X28,X29,X30) = match_list(X27,a1,t2tb3(sK0),X31,match_bool(X27,X28,X29,X30)) )
| ~ spl11_374 ),
inference(avatar_component_clause,[],[f7824]) ).
tff(f12247,plain,
( spl11_452
| ~ spl11_29
| ~ spl11_120
| ~ spl11_195 ),
inference(avatar_split_clause,[],[f2715,f2502,f1190,f367,f12245]) ).
tff(f12245,plain,
( spl11_452
<=> ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_452])]) ).
tff(f2502,plain,
( spl11_195
<=> ! [X9: $int,X7: $int,X6: $int,X8: $int] :
( $less($sum(X6,$sum(X7,X8)),$sum(X9,X8))
| ~ $less($sum(X6,X7),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_195])]) ).
tff(f2715,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) )
| ~ spl11_29
| ~ spl11_120
| ~ spl11_195 ),
inference(forward_demodulation,[],[f2690,f368]) ).
tff(f2690,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X0)),X2) )
| ~ spl11_120
| ~ spl11_195 ),
inference(superposition,[],[f2503,f1191]) ).
tff(f2503,plain,
( ! [X8: $int,X6: $int,X9: $int,X7: $int] :
( $less($sum(X6,$sum(X7,X8)),$sum(X9,X8))
| ~ $less($sum(X6,X7),X9) )
| ~ spl11_195 ),
inference(avatar_component_clause,[],[f2502]) ).
tff(f12243,plain,
( spl11_451
| ~ spl11_29
| ~ spl11_120
| ~ spl11_194 ),
inference(avatar_split_clause,[],[f2661,f2498,f1190,f367,f12241]) ).
tff(f12241,plain,
( spl11_451
<=> ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_451])]) ).
tff(f2498,plain,
( spl11_194
<=> ! [X3: $int,X4: $int,X5: $int,X2: $int] :
( $less($sum(X5,X4),$sum(X2,$sum(X3,X4)))
| ~ $less(X5,$sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_194])]) ).
tff(f2661,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) )
| ~ spl11_29
| ~ spl11_120
| ~ spl11_194 ),
inference(forward_demodulation,[],[f2652,f368]) ).
tff(f2652,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),X1)
| ~ $less(X2,$sum(X0,$uminus(X0))) )
| ~ spl11_120
| ~ spl11_194 ),
inference(superposition,[],[f2499,f1191]) ).
tff(f2499,plain,
( ! [X2: $int,X3: $int,X4: $int,X5: $int] :
( $less($sum(X5,X4),$sum(X2,$sum(X3,X4)))
| ~ $less(X5,$sum(X2,X3)) )
| ~ spl11_194 ),
inference(avatar_component_clause,[],[f2498]) ).
tff(f12239,plain,
( spl11_450
| ~ spl11_29
| ~ spl11_153 ),
inference(avatar_split_clause,[],[f1732,f1538,f367,f12237]) ).
tff(f12237,plain,
( spl11_450
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_450])]) ).
tff(f1538,plain,
( spl11_153
<=> ! [X6: $int,X5: $int,X7: $int] : ( $sum(X5,$sum(X6,X7)) = $sum(X7,$sum(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_153])]) ).
tff(f1732,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 )
| ~ spl11_29
| ~ spl11_153 ),
inference(evaluation,[],[f1665]) ).
tff(f1665,plain,
( ! [X0: $int,X1: $int] : ( $sum(X1,0) = $sum($uminus(X0),$sum(X1,X0)) )
| ~ spl11_29
| ~ spl11_153 ),
inference(superposition,[],[f1539,f368]) ).
tff(f1539,plain,
( ! [X6: $int,X7: $int,X5: $int] : ( $sum(X5,$sum(X6,X7)) = $sum(X7,$sum(X5,X6)) )
| ~ spl11_153 ),
inference(avatar_component_clause,[],[f1538]) ).
tff(f12235,plain,
( spl11_449
| ~ spl11_29
| ~ spl11_152 ),
inference(avatar_split_clause,[],[f1657,f1534,f367,f12233]) ).
tff(f12233,plain,
( spl11_449
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_449])]) ).
tff(f1657,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 )
| ~ spl11_29
| ~ spl11_152 ),
inference(evaluation,[],[f1625]) ).
tff(f1625,plain,
( ! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum($uminus(X0),$sum(X0,X1)) )
| ~ spl11_29
| ~ spl11_152 ),
inference(superposition,[],[f1535,f368]) ).
tff(f12231,plain,
( spl11_448
| ~ spl11_119
| ~ spl11_134 ),
inference(avatar_split_clause,[],[f1420,f1363,f1186,f12229]) ).
tff(f12229,plain,
( spl11_448
<=> ! [X2: $int,X3: $int] :
( ~ $less(X2,1)
| ~ $less(X3,$sum(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_448])]) ).
tff(f1420,plain,
( ! [X2: $int,X3: $int] :
( ~ $less(X2,1)
| ~ $less(X3,$sum(X3,X2)) )
| ~ spl11_119
| ~ spl11_134 ),
inference(resolution,[],[f1364,f1187]) ).
tff(f12227,plain,
( spl11_447
| ~ spl11_119
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1223,f1190,f1186,f12225]) ).
tff(f12225,plain,
( spl11_447
<=> ! [X13: $int,X14: $int] :
( ~ $less(X14,X13)
| ~ $less($sum(-1,X13),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_447])]) ).
tff(f1223,plain,
( ! [X14: $int,X13: $int] :
( ~ $less(X14,X13)
| ~ $less($sum(-1,X13),X14) )
| ~ spl11_119
| ~ spl11_120 ),
inference(evaluation,[],[f1219]) ).
tff(f1219,plain,
( ! [X14: $int,X13: $int] :
( ~ $less(X14,X13)
| ~ $less($sum($uminus(1),X13),X14) )
| ~ spl11_119
| ~ spl11_120 ),
inference(superposition,[],[f1187,f1191]) ).
tff(f12223,plain,
( spl11_446
| ~ spl11_118
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1222,f1190,f1182,f12221]) ).
tff(f12221,plain,
( spl11_446
<=> ! [X16: $int,X15: $int] :
( $less(X16,X15)
| $less($sum(-1,X15),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_446])]) ).
tff(f1222,plain,
( ! [X16: $int,X15: $int] :
( $less(X16,X15)
| $less($sum(-1,X15),X16) )
| ~ spl11_118
| ~ spl11_120 ),
inference(evaluation,[],[f1220]) ).
tff(f1220,plain,
( ! [X16: $int,X15: $int] :
( $less(X16,X15)
| $less($sum($uminus(1),X15),X16) )
| ~ spl11_118
| ~ spl11_120 ),
inference(superposition,[],[f1183,f1191]) ).
tff(f12175,plain,
( spl11_445
| ~ spl11_42
| ~ spl11_44
| ~ spl11_45
| ~ spl11_79
| ~ spl11_401 ),
inference(avatar_split_clause,[],[f10594,f9484,f722,f437,f433,f425,f12172]) ).
tff(f12172,plain,
( spl11_445
<=> ( length(a1,t2tb3(sK8)) = $sum(1,length(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_445])]) ).
tff(f425,plain,
( spl11_42
<=> ! [X0: ty] : ( nil(X0) = reverse(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_42])]) ).
tff(f433,plain,
( spl11_44
<=> ! [X0: ty,X1: uni] : ( infix_plpl(X0,X1,nil(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_44])]) ).
tff(f437,plain,
( spl11_45
<=> ! [X0: ty,X1: uni] : ( infix_plpl(X0,nil(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_45])]) ).
tff(f9484,plain,
( spl11_401
<=> ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),X3)) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_401])]) ).
tff(f10594,plain,
( ( length(a1,t2tb3(sK8)) = $sum(1,length(a1,t2tb3(sK8))) )
| ~ spl11_42
| ~ spl11_44
| ~ spl11_45
| ~ spl11_79
| ~ spl11_401 ),
inference(forward_demodulation,[],[f10593,f434]) ).
tff(f434,plain,
( ! [X0: ty,X1: uni] : ( infix_plpl(X0,X1,nil(X0)) = X1 )
| ~ spl11_44 ),
inference(avatar_component_clause,[],[f433]) ).
tff(f10593,plain,
( ( $sum(1,length(a1,t2tb3(sK8))) = length(a1,infix_plpl(a1,t2tb3(sK8),nil(a1))) )
| ~ spl11_42
| ~ spl11_45
| ~ spl11_79
| ~ spl11_401 ),
inference(forward_demodulation,[],[f10592,f723]) ).
tff(f10592,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),nil(a1))) = length(a1,cons(a1,X0,t2tb3(sK8))) )
| ~ spl11_42
| ~ spl11_45
| ~ spl11_401 ),
inference(forward_demodulation,[],[f10563,f438]) ).
tff(f438,plain,
( ! [X0: ty,X1: uni] : ( infix_plpl(X0,nil(X0),X1) = X1 )
| ~ spl11_45 ),
inference(avatar_component_clause,[],[f437]) ).
tff(f10563,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),nil(a1))) = length(a1,infix_plpl(a1,nil(a1),cons(a1,X0,t2tb3(sK8)))) )
| ~ spl11_42
| ~ spl11_401 ),
inference(superposition,[],[f9485,f426]) ).
tff(f426,plain,
( ! [X0: ty] : ( nil(X0) = reverse(X0,nil(X0)) )
| ~ spl11_42 ),
inference(avatar_component_clause,[],[f425]) ).
tff(f9485,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),X3)) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) )
| ~ spl11_401 ),
inference(avatar_component_clause,[],[f9484]) ).
tff(f12170,plain,
( spl11_444
| ~ spl11_39
| ~ spl11_120 ),
inference(avatar_split_clause,[],[f1212,f1190,f413,f12168]) ).
tff(f12168,plain,
( spl11_444
<=> ! [X4: $int,X3: $int] : ( $sum(X3,$sum(X4,$uminus(X3))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_444])]) ).
tff(f1212,plain,
( ! [X3: $int,X4: $int] : ( $sum(X3,$sum(X4,$uminus(X3))) = X4 )
| ~ spl11_39
| ~ spl11_120 ),
inference(superposition,[],[f1191,f414]) ).
tff(f12166,plain,
( spl11_443
| ~ spl11_65
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1205,f1186,f563,f12164]) ).
tff(f12164,plain,
( spl11_443
<=> ! [X7: $int,X8: $int] :
( ~ $less(X7,$sum(X8,X7))
| ~ $less(X8,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_443])]) ).
tff(f563,plain,
( spl11_65
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_65])]) ).
tff(f1205,plain,
( ! [X8: $int,X7: $int] :
( ~ $less(X7,$sum(X8,X7))
| ~ $less(X8,1) )
| ~ spl11_65
| ~ spl11_119 ),
inference(resolution,[],[f1187,f564]) ).
tff(f564,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl11_65 ),
inference(avatar_component_clause,[],[f563]) ).
tff(f12162,plain,
( spl11_442
| ~ spl11_58
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1150,f1131,f515,f12160]) ).
tff(f12160,plain,
( spl11_442
<=> ! [X2: $int,X1: $int] :
( ~ $less(X1,X2)
| $less(X1,$sum(X2,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_442])]) ).
tff(f515,plain,
( spl11_58
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_58])]) ).
tff(f1150,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(X1,X2)
| $less(X1,$sum(X2,1)) )
| ~ spl11_58
| ~ spl11_114 ),
inference(resolution,[],[f1132,f516]) ).
tff(f516,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl11_58 ),
inference(avatar_component_clause,[],[f515]) ).
tff(f12158,plain,
( spl11_441
| ~ spl11_69
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1072,f1068,f580,f12156]) ).
tff(f12156,plain,
( spl11_441
<=> ! [X4: uni,X5: uni,X3: ty] : ( match_bool(list(X3),false,X4,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_441])]) ).
tff(f580,plain,
( spl11_69
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).
tff(f1072,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( match_bool(list(X3),false,X4,X5) = X5 )
| ~ spl11_69
| ~ spl11_107 ),
inference(resolution,[],[f1069,f581]) ).
tff(f581,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ sort(X0,X2)
| ( match_bool(X0,false,X1,X2) = X2 ) )
| ~ spl11_69 ),
inference(avatar_component_clause,[],[f580]) ).
tff(f12154,plain,
( spl11_440
| ~ spl11_67
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f1071,f1068,f571,f12152]) ).
tff(f571,plain,
( spl11_67
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_67])]) ).
tff(f1071,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( match_bool(list(X0),true,X1,X2) = X1 )
| ~ spl11_67
| ~ spl11_107 ),
inference(resolution,[],[f1069,f572]) ).
tff(f572,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ sort(X0,X1)
| ( match_bool(X0,true,X1,X2) = X1 ) )
| ~ spl11_67 ),
inference(avatar_component_clause,[],[f571]) ).
tff(f12115,plain,
( spl11_439
| ~ spl11_119
| ~ spl11_123 ),
inference(avatar_split_clause,[],[f1307,f1234,f1186,f12113]) ).
tff(f12113,plain,
( spl11_439
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_439])]) ).
tff(f1307,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl11_119
| ~ spl11_123 ),
inference(resolution,[],[f1235,f1187]) ).
tff(f12111,plain,
( spl11_438
| ~ spl11_79
| ~ spl11_116 ),
inference(avatar_split_clause,[],[f1180,f1160,f722,f12109]) ).
tff(f1160,plain,
( spl11_116
<=> ! [X5: uni,X3: ty] : ~ $less($sum(1,length(X3,X5)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_116])]) ).
tff(f1180,plain,
( ! [X7: uni,X5: ty] : ~ $less($sum(2,length(X5,X7)),0)
| ~ spl11_79
| ~ spl11_116 ),
inference(evaluation,[],[f1179]) ).
tff(f1179,plain,
( ! [X7: uni,X5: ty] : ~ $less($sum(1,$sum(1,length(X5,X7))),0)
| ~ spl11_79
| ~ spl11_116 ),
inference(superposition,[],[f1161,f723]) ).
tff(f1161,plain,
( ! [X3: ty,X5: uni] : ~ $less($sum(1,length(X3,X5)),0)
| ~ spl11_116 ),
inference(avatar_component_clause,[],[f1160]) ).
tff(f11960,plain,
( spl11_437
| ~ spl11_38
| ~ spl11_308
| ~ spl11_435 ),
inference(avatar_split_clause,[],[f11934,f11931,f6029,f408,f11958]) ).
tff(f11958,plain,
( spl11_437
<=> ! [X36: uni,X37: uni,X35: ty] : ( combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK0))) = combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_437])]) ).
tff(f6029,plain,
( spl11_308
<=> ! [X5: ty,X9: uni,X10: uni,X6: ty,X8: uni,X7: uni] : ( combine(X5,X6,cons(X6,X9,nil(X6)),cons(X5,X10,cons(X5,X7,X8))) = cons(tuple2(X6,X5),tuple21(X6,X5,X9,X10),nil(tuple2(X6,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_308])]) ).
tff(f11931,plain,
( spl11_435
<=> ! [X36: uni,X37: uni,X35: ty] : ( cons(tuple2(X35,a1),tuple21(X35,a1,X36,X37),nil(tuple2(X35,a1))) = combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_435])]) ).
tff(f11934,plain,
( ! [X36: uni,X37: uni,X35: ty] : ( combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK0))) = combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_308
| ~ spl11_435 ),
inference(forward_demodulation,[],[f11932,f6040]) ).
tff(f6040,plain,
( ! [X40: uni,X38: ty,X39: uni] : ( cons(tuple2(X38,a1),tuple21(X38,a1,X39,X40),nil(tuple2(X38,a1))) = combine(a1,X38,cons(X38,X39,nil(X38)),cons(a1,X40,t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_308 ),
inference(superposition,[],[f6030,f410]) ).
tff(f6030,plain,
( ! [X10: uni,X8: uni,X6: ty,X9: uni,X7: uni,X5: ty] : ( combine(X5,X6,cons(X6,X9,nil(X6)),cons(X5,X10,cons(X5,X7,X8))) = cons(tuple2(X6,X5),tuple21(X6,X5,X9,X10),nil(tuple2(X6,X5))) )
| ~ spl11_308 ),
inference(avatar_component_clause,[],[f6029]) ).
tff(f11932,plain,
( ! [X36: uni,X37: uni,X35: ty] : ( cons(tuple2(X35,a1),tuple21(X35,a1,X36,X37),nil(tuple2(X35,a1))) = combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK0))) )
| ~ spl11_435 ),
inference(avatar_component_clause,[],[f11931]) ).
tff(f11938,plain,
( spl11_436
| ~ spl11_38
| ~ spl11_308 ),
inference(avatar_split_clause,[],[f6040,f6029,f408,f11936]) ).
tff(f11936,plain,
( spl11_436
<=> ! [X38: ty,X39: uni,X40: uni] : ( cons(tuple2(X38,a1),tuple21(X38,a1,X39,X40),nil(tuple2(X38,a1))) = combine(a1,X38,cons(X38,X39,nil(X38)),cons(a1,X40,t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_436])]) ).
tff(f11933,plain,
( spl11_435
| ~ spl11_33
| ~ spl11_308 ),
inference(avatar_split_clause,[],[f6039,f6029,f383,f11931]) ).
tff(f6039,plain,
( ! [X36: uni,X37: uni,X35: ty] : ( cons(tuple2(X35,a1),tuple21(X35,a1,X36,X37),nil(tuple2(X35,a1))) = combine(a1,X35,cons(X35,X36,nil(X35)),cons(a1,X37,t2tb3(sK0))) )
| ~ spl11_33
| ~ spl11_308 ),
inference(superposition,[],[f6030,f385]) ).
tff(f11921,plain,
( ~ spl11_222
| spl11_434
| ~ spl11_38
| ~ spl11_300 ),
inference(avatar_split_clause,[],[f5727,f5681,f408,f11919,f2941]) ).
tff(f2941,plain,
( spl11_222
<=> sort(a1,t2tb(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_222])]) ).
tff(f11919,plain,
( spl11_434
<=> ! [X25: uni,X26: uni] :
( ~ mem(a1,X25,infix_plpl(a1,t2tb3(sK5),X26))
| ~ sort(a1,X25)
| mem(a1,X25,infix_plpl(a1,t2tb3(sK7),X26))
| ( t2tb(sK6) = X25 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_434])]) ).
tff(f5681,plain,
( spl11_300
<=> ! [X5: ty,X9: uni,X7: uni,X6: uni,X8: uni] :
( ~ mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ( X6 = X9 )
| mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_300])]) ).
tff(f5727,plain,
( ! [X26: uni,X25: uni] :
( ~ mem(a1,X25,infix_plpl(a1,t2tb3(sK5),X26))
| ( t2tb(sK6) = X25 )
| mem(a1,X25,infix_plpl(a1,t2tb3(sK7),X26))
| ~ sort(a1,t2tb(sK6))
| ~ sort(a1,X25) )
| ~ spl11_38
| ~ spl11_300 ),
inference(superposition,[],[f5682,f410]) ).
tff(f5682,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] :
( ~ mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ( X6 = X9 )
| mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) )
| ~ spl11_300 ),
inference(avatar_component_clause,[],[f5681]) ).
tff(f11909,plain,
( ~ spl11_203
| spl11_433
| ~ spl11_33
| ~ spl11_300 ),
inference(avatar_split_clause,[],[f5726,f5681,f383,f11907,f2534]) ).
tff(f2534,plain,
( spl11_203
<=> sort(a1,t2tb(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_203])]) ).
tff(f11907,plain,
( spl11_433
<=> ! [X24: uni,X23: uni] :
( ~ mem(a1,X23,infix_plpl(a1,t2tb3(sK0),X24))
| ~ sort(a1,X23)
| mem(a1,X23,infix_plpl(a1,t2tb3(sK3),X24))
| ( t2tb(sK2) = X23 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_433])]) ).
tff(f5726,plain,
( ! [X24: uni,X23: uni] :
( ~ mem(a1,X23,infix_plpl(a1,t2tb3(sK0),X24))
| ( t2tb(sK2) = X23 )
| mem(a1,X23,infix_plpl(a1,t2tb3(sK3),X24))
| ~ sort(a1,t2tb(sK2))
| ~ sort(a1,X23) )
| ~ spl11_33
| ~ spl11_300 ),
inference(superposition,[],[f5682,f385]) ).
tff(f11905,plain,
( spl11_432
| ~ spl11_28
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1027,f999,f357,f11903]) ).
tff(f357,plain,
( spl11_28
<=> ( t2tb1(sK4) = combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).
tff(f999,plain,
( spl11_102
<=> ! [X5: uni,X3: uni,X4: uni,X0: ty,X6: uni,X1: ty] : ( combine(X1,X0,cons(X0,X5,X6),cons(X1,X3,X4)) = cons(tuple2(X0,X1),tuple21(X0,X1,X5,X3),combine(X1,X0,X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_102])]) ).
tff(f1027,plain,
( ! [X0: uni,X1: uni] : ( combine(a1,a1,cons(a1,X0,t2tb3(sK3)),cons(a1,X1,reverse(a1,t2tb3(sK8)))) = cons(tuple2(a1,a1),tuple21(a1,a1,X0,X1),t2tb1(sK4)) )
| ~ spl11_28
| ~ spl11_102 ),
inference(superposition,[],[f1000,f359]) ).
tff(f359,plain,
( ( t2tb1(sK4) = combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8))) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f357]) ).
tff(f1000,plain,
( ! [X3: uni,X0: ty,X1: ty,X6: uni,X4: uni,X5: uni] : ( combine(X1,X0,cons(X0,X5,X6),cons(X1,X3,X4)) = cons(tuple2(X0,X1),tuple21(X0,X1,X5,X3),combine(X1,X0,X6,X4)) )
| ~ spl11_102 ),
inference(avatar_component_clause,[],[f999]) ).
tff(f11743,plain,
( spl11_431
| ~ spl11_38
| ~ spl11_303 ),
inference(avatar_split_clause,[],[f5864,f5833,f408,f11741]) ).
tff(f11741,plain,
( spl11_431
<=> ! [X38: ty,X40: uni,X39: uni] : ( $sum(1,length(tuple2(X38,a1),combine(a1,X38,X39,t2tb3(sK7)))) = length(tuple2(X38,a1),combine(a1,X38,cons(X38,X40,X39),t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_431])]) ).
tff(f5833,plain,
( spl11_303
<=> ! [X17: uni,X13: ty,X14: uni,X12: ty,X16: uni,X15: uni] : ( $sum(1,length(tuple2(X12,X13),combine(X13,X12,X16,X17))) = length(tuple2(X12,X13),combine(X13,X12,cons(X12,X14,X16),cons(X13,X15,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_303])]) ).
tff(f5864,plain,
( ! [X40: uni,X38: ty,X39: uni] : ( $sum(1,length(tuple2(X38,a1),combine(a1,X38,X39,t2tb3(sK7)))) = length(tuple2(X38,a1),combine(a1,X38,cons(X38,X40,X39),t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_303 ),
inference(superposition,[],[f5834,f410]) ).
tff(f5834,plain,
( ! [X16: uni,X14: uni,X17: uni,X15: uni,X12: ty,X13: ty] : ( $sum(1,length(tuple2(X12,X13),combine(X13,X12,X16,X17))) = length(tuple2(X12,X13),combine(X13,X12,cons(X12,X14,X16),cons(X13,X15,X17))) )
| ~ spl11_303 ),
inference(avatar_component_clause,[],[f5833]) ).
tff(f11739,plain,
( spl11_430
| ~ spl11_33
| ~ spl11_303 ),
inference(avatar_split_clause,[],[f5863,f5833,f383,f11737]) ).
tff(f11737,plain,
( spl11_430
<=> ! [X36: uni,X37: uni,X35: ty] : ( $sum(1,length(tuple2(X35,a1),combine(a1,X35,X36,t2tb3(sK3)))) = length(tuple2(X35,a1),combine(a1,X35,cons(X35,X37,X36),t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_430])]) ).
tff(f5863,plain,
( ! [X36: uni,X37: uni,X35: ty] : ( $sum(1,length(tuple2(X35,a1),combine(a1,X35,X36,t2tb3(sK3)))) = length(tuple2(X35,a1),combine(a1,X35,cons(X35,X37,X36),t2tb3(sK0))) )
| ~ spl11_33
| ~ spl11_303 ),
inference(superposition,[],[f5834,f385]) ).
tff(f11735,plain,
( spl11_429
| ~ spl11_38
| ~ spl11_303 ),
inference(avatar_split_clause,[],[f5857,f5833,f408,f11733]) ).
tff(f11733,plain,
( spl11_429
<=> ! [X38: ty,X40: uni,X39: uni] : ( $sum(1,length(tuple2(a1,X38),combine(X38,a1,t2tb3(sK7),X39))) = length(tuple2(a1,X38),combine(X38,a1,t2tb3(sK5),cons(X38,X40,X39))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_429])]) ).
tff(f5857,plain,
( ! [X40: uni,X38: ty,X39: uni] : ( $sum(1,length(tuple2(a1,X38),combine(X38,a1,t2tb3(sK7),X39))) = length(tuple2(a1,X38),combine(X38,a1,t2tb3(sK5),cons(X38,X40,X39))) )
| ~ spl11_38
| ~ spl11_303 ),
inference(superposition,[],[f5834,f410]) ).
tff(f11731,plain,
( spl11_428
| ~ spl11_33
| ~ spl11_303 ),
inference(avatar_split_clause,[],[f5856,f5833,f383,f11729]) ).
tff(f11729,plain,
( spl11_428
<=> ! [X36: uni,X37: uni,X35: ty] : ( $sum(1,length(tuple2(a1,X35),combine(X35,a1,t2tb3(sK3),X36))) = length(tuple2(a1,X35),combine(X35,a1,t2tb3(sK0),cons(X35,X37,X36))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_428])]) ).
tff(f5856,plain,
( ! [X36: uni,X37: uni,X35: ty] : ( $sum(1,length(tuple2(a1,X35),combine(X35,a1,t2tb3(sK3),X36))) = length(tuple2(a1,X35),combine(X35,a1,t2tb3(sK0),cons(X35,X37,X36))) )
| ~ spl11_33
| ~ spl11_303 ),
inference(superposition,[],[f5834,f385]) ).
tff(f11519,plain,
( spl11_1
| ~ spl11_391
| ~ spl11_393 ),
inference(avatar_split_clause,[],[f11122,f9147,f9009,f239]) ).
tff(f239,plain,
( spl11_1
<=> $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
tff(f9009,plain,
( spl11_391
<=> ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_391])]) ).
tff(f9147,plain,
( spl11_393
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_393])]) ).
tff(f11122,plain,
( $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0)))
| ~ spl11_391
| ~ spl11_393 ),
inference(superposition,[],[f9148,f9011]) ).
tff(f9011,plain,
( ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK1))) )
| ~ spl11_391 ),
inference(avatar_component_clause,[],[f9009]) ).
tff(f9148,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl11_393 ),
inference(avatar_component_clause,[],[f9147]) ).
tff(f11161,plain,
( spl11_427
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106
| ~ spl11_216
| ~ spl11_217
| ~ spl11_260
| ~ spl11_261
| ~ spl11_297 ),
inference(avatar_split_clause,[],[f5622,f5293,f4097,f4093,f2921,f2917,f1033,f1029,f966,f820,f722,f649,f413,f11159]) ).
tff(f820,plain,
( spl11_87
<=> ! [X2: uni,X0: ty,X1: uni] : ( length(X0,infix_plpl(X0,X1,X2)) = $sum(length(X0,X1),length(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_87])]) ).
tff(f1029,plain,
( spl11_105
<=> ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK3),X0)) = length(a1,infix_plpl(a1,t2tb3(sK8),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_105])]) ).
tff(f1033,plain,
( spl11_106
<=> ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK3))) = length(a1,infix_plpl(a1,X0,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_106])]) ).
tff(f2917,plain,
( spl11_216
<=> ! [X4: uni,X5: uni,X3: ty] : ( length(X3,infix_plpl(X3,reverse(X3,X4),X5)) = length(X3,infix_plpl(X3,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_216])]) ).
tff(f2921,plain,
( spl11_217
<=> ! [X4: uni,X5: uni,X3: ty] : ( length(X3,infix_plpl(X3,X5,reverse(X3,X4))) = length(X3,infix_plpl(X3,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_217])]) ).
tff(f4093,plain,
( spl11_260
<=> ! [X9: uni,X7: uni,X6: ty,X8: uni] : ( length(X6,infix_plpl(X6,cons(X6,X7,X8),X9)) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_260])]) ).
tff(f4097,plain,
( spl11_261
<=> ! [X9: uni,X7: uni,X6: ty,X8: uni] : ( length(X6,infix_plpl(X6,X9,cons(X6,X7,X8))) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_261])]) ).
tff(f5293,plain,
( spl11_297
<=> ! [X17: ty,X20: uni,X18: uni,X21: uni,X19: uni] : ( infix_plpl(X17,cons(X17,X21,reverse(X17,cons(X17,X18,X19))),X20) = infix_plpl(X17,cons(X17,X21,reverse(X17,X19)),cons(X17,X18,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_297])]) ).
tff(f5622,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( $sum(2,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) = length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,X2)),cons(a1,X1,t2tb3(sK8)))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106
| ~ spl11_216
| ~ spl11_217
| ~ spl11_260
| ~ spl11_261
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5621,f5294]) ).
tff(f5294,plain,
( ! [X21: uni,X18: uni,X19: uni,X17: ty,X20: uni] : ( infix_plpl(X17,cons(X17,X21,reverse(X17,cons(X17,X18,X19))),X20) = infix_plpl(X17,cons(X17,X21,reverse(X17,X19)),cons(X17,X18,X20)) )
| ~ spl11_297 ),
inference(avatar_component_clause,[],[f5293]) ).
tff(f5621,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(2,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106
| ~ spl11_216
| ~ spl11_217
| ~ spl11_260
| ~ spl11_261
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5620,f1030]) ).
tff(f1030,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK3),X0)) = length(a1,infix_plpl(a1,t2tb3(sK8),X0)) )
| ~ spl11_105 ),
inference(avatar_component_clause,[],[f1029]) ).
tff(f5620,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(2,length(a1,infix_plpl(a1,t2tb3(sK3),X2))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106
| ~ spl11_216
| ~ spl11_217
| ~ spl11_260
| ~ spl11_261
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5619,f2922]) ).
tff(f2922,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,X5,reverse(X3,X4))) = length(X3,infix_plpl(X3,X5,X4)) )
| ~ spl11_217 ),
inference(avatar_component_clause,[],[f2921]) ).
tff(f5619,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(2,length(a1,infix_plpl(a1,t2tb3(sK3),reverse(a1,X2)))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106
| ~ spl11_216
| ~ spl11_260
| ~ spl11_261
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5618,f4426]) ).
tff(f4426,plain,
( ! [X10: ty,X14: uni,X12: uni] : ( $sum(2,length(X10,infix_plpl(X10,X12,X14))) = $sum(2,length(X10,infix_plpl(X10,X14,X12))) )
| ~ spl11_260
| ~ spl11_261 ),
inference(evaluation,[],[f4425]) ).
tff(f4425,plain,
( ! [X10: ty,X14: uni,X12: uni] : ( $sum(2,length(X10,infix_plpl(X10,X12,X14))) = $sum(1,$sum(1,length(X10,infix_plpl(X10,X14,X12)))) )
| ~ spl11_260
| ~ spl11_261 ),
inference(forward_demodulation,[],[f4424,f4098]) ).
tff(f4098,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,X9,cons(X6,X7,X8))) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) )
| ~ spl11_261 ),
inference(avatar_component_clause,[],[f4097]) ).
tff(f4424,plain,
( ! [X10: ty,X14: uni,X12: uni,X13: uni] : ( $sum(1,length(X10,infix_plpl(X10,X12,cons(X10,X13,X14)))) = $sum(2,length(X10,infix_plpl(X10,X12,X14))) )
| ~ spl11_260
| ~ spl11_261 ),
inference(evaluation,[],[f4423]) ).
tff(f4423,plain,
( ! [X10: ty,X14: uni,X12: uni,X13: uni] : ( $sum(1,length(X10,infix_plpl(X10,X12,cons(X10,X13,X14)))) = $sum(1,$sum(1,length(X10,infix_plpl(X10,X12,X14)))) )
| ~ spl11_260
| ~ spl11_261 ),
inference(forward_demodulation,[],[f4387,f4098]) ).
tff(f4387,plain,
( ! [X10: ty,X11: uni,X14: uni,X12: uni,X13: uni] : ( $sum(1,length(X10,infix_plpl(X10,X12,cons(X10,X13,X14)))) = $sum(1,length(X10,infix_plpl(X10,X14,cons(X10,X11,X12)))) )
| ~ spl11_260
| ~ spl11_261 ),
inference(superposition,[],[f4098,f4094]) ).
tff(f4094,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,cons(X6,X7,X8),X9)) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) )
| ~ spl11_260 ),
inference(avatar_component_clause,[],[f4093]) ).
tff(f5618,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(2,length(a1,infix_plpl(a1,reverse(a1,X2),t2tb3(sK3)))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106
| ~ spl11_216
| ~ spl11_297 ),
inference(evaluation,[],[f5617]) ).
tff(f5617,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(1,$sum(1,length(a1,infix_plpl(a1,reverse(a1,X2),t2tb3(sK3))))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106
| ~ spl11_216
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5616,f3075]) ).
tff(f3075,plain,
( ! [X3: ty,X6: uni,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,cons(X3,X4,X5),X6)) = $sum(1,length(X3,infix_plpl(X3,X6,X5))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_216 ),
inference(forward_demodulation,[],[f3074,f859]) ).
tff(f859,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,X9,cons(X6,X7,X8))) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(forward_demodulation,[],[f858,f821]) ).
tff(f821,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( length(X0,infix_plpl(X0,X1,X2)) = $sum(length(X0,X1),length(X0,X2)) )
| ~ spl11_87 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f858,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,X9,cons(X6,X7,X8))) = $sum(1,$sum(length(X6,X8),length(X6,X9))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(forward_demodulation,[],[f842,f678]) ).
tff(f678,plain,
( ! [X6: $int,X7: $int,X5: $int] : ( $sum(X5,$sum(X6,X7)) = $sum(X7,$sum(X5,X6)) )
| ~ spl11_39
| ~ spl11_73 ),
inference(superposition,[],[f650,f414]) ).
tff(f842,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,X9,cons(X6,X7,X8))) = $sum(length(X6,X9),$sum(1,length(X6,X8))) )
| ~ spl11_79
| ~ spl11_87 ),
inference(superposition,[],[f821,f723]) ).
tff(f3074,plain,
( ! [X3: ty,X6: uni,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,cons(X3,X4,X5),X6)) = length(X3,infix_plpl(X3,X5,cons(X3,X4,X6))) )
| ~ spl11_100
| ~ spl11_216 ),
inference(forward_demodulation,[],[f3057,f2918]) ).
tff(f2918,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,reverse(X3,X4),X5)) = length(X3,infix_plpl(X3,X4,X5)) )
| ~ spl11_216 ),
inference(avatar_component_clause,[],[f2917]) ).
tff(f3057,plain,
( ! [X3: ty,X6: uni,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,cons(X3,X4,X5),X6)) = length(X3,infix_plpl(X3,reverse(X3,X5),cons(X3,X4,X6))) )
| ~ spl11_100
| ~ spl11_216 ),
inference(superposition,[],[f2918,f967]) ).
tff(f5616,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = $sum(1,length(a1,infix_plpl(a1,cons(a1,X1,t2tb3(sK3)),reverse(a1,X2)))) )
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106
| ~ spl11_216
| ~ spl11_297 ),
inference(forward_demodulation,[],[f5584,f3075]) ).
tff(f5584,plain,
( ! [X2: uni,X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,cons(a1,X1,X2))),t2tb3(sK8))) = length(a1,infix_plpl(a1,cons(a1,X0,reverse(a1,X2)),cons(a1,X1,t2tb3(sK3)))) )
| ~ spl11_106
| ~ spl11_297 ),
inference(superposition,[],[f1034,f5294]) ).
tff(f1034,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK3))) = length(a1,infix_plpl(a1,X0,t2tb3(sK8))) )
| ~ spl11_106 ),
inference(avatar_component_clause,[],[f1033]) ).
tff(f11157,plain,
( spl11_426
| ~ spl11_38
| ~ spl11_297 ),
inference(avatar_split_clause,[],[f5578,f5293,f408,f11155]) ).
tff(f11155,plain,
( spl11_426
<=> ! [X25: uni,X26: uni] : ( infix_plpl(a1,cons(a1,X25,reverse(a1,t2tb3(sK7))),cons(a1,t2tb(sK6),X26)) = infix_plpl(a1,cons(a1,X25,reverse(a1,t2tb3(sK5))),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_426])]) ).
tff(f5578,plain,
( ! [X26: uni,X25: uni] : ( infix_plpl(a1,cons(a1,X25,reverse(a1,t2tb3(sK7))),cons(a1,t2tb(sK6),X26)) = infix_plpl(a1,cons(a1,X25,reverse(a1,t2tb3(sK5))),X26) )
| ~ spl11_38
| ~ spl11_297 ),
inference(superposition,[],[f5294,f410]) ).
tff(f11153,plain,
( spl11_425
| ~ spl11_33
| ~ spl11_297 ),
inference(avatar_split_clause,[],[f5577,f5293,f383,f11151]) ).
tff(f11151,plain,
( spl11_425
<=> ! [X24: uni,X23: uni] : ( infix_plpl(a1,cons(a1,X23,reverse(a1,t2tb3(sK3))),cons(a1,t2tb(sK2),X24)) = infix_plpl(a1,cons(a1,X23,reverse(a1,t2tb3(sK0))),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_425])]) ).
tff(f5577,plain,
( ! [X24: uni,X23: uni] : ( infix_plpl(a1,cons(a1,X23,reverse(a1,t2tb3(sK3))),cons(a1,t2tb(sK2),X24)) = infix_plpl(a1,cons(a1,X23,reverse(a1,t2tb3(sK0))),X24) )
| ~ spl11_33
| ~ spl11_297 ),
inference(superposition,[],[f5294,f385]) ).
tff(f11119,plain,
( spl11_424
| ~ spl11_38
| ~ spl11_296 ),
inference(avatar_split_clause,[],[f5494,f5289,f408,f11117]) ).
tff(f11117,plain,
( spl11_424
<=> ! [X25: uni,X26: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK7)),infix_plpl(a1,cons(a1,t2tb(sK6),X25),X26)) = infix_plpl(a1,reverse(a1,t2tb3(sK5)),infix_plpl(a1,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_424])]) ).
tff(f5289,plain,
( spl11_296
<=> ! [X13: uni,X14: uni,X12: ty,X16: uni,X15: uni] : ( infix_plpl(X12,reverse(X12,cons(X12,X13,X14)),infix_plpl(X12,X15,X16)) = infix_plpl(X12,reverse(X12,X14),infix_plpl(X12,cons(X12,X13,X15),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_296])]) ).
tff(f5494,plain,
( ! [X26: uni,X25: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK7)),infix_plpl(a1,cons(a1,t2tb(sK6),X25),X26)) = infix_plpl(a1,reverse(a1,t2tb3(sK5)),infix_plpl(a1,X25,X26)) )
| ~ spl11_38
| ~ spl11_296 ),
inference(superposition,[],[f5290,f410]) ).
tff(f5290,plain,
( ! [X16: uni,X14: uni,X15: uni,X12: ty,X13: uni] : ( infix_plpl(X12,reverse(X12,cons(X12,X13,X14)),infix_plpl(X12,X15,X16)) = infix_plpl(X12,reverse(X12,X14),infix_plpl(X12,cons(X12,X13,X15),X16)) )
| ~ spl11_296 ),
inference(avatar_component_clause,[],[f5289]) ).
tff(f11115,plain,
( spl11_423
| ~ spl11_33
| ~ spl11_296 ),
inference(avatar_split_clause,[],[f5493,f5289,f383,f11113]) ).
tff(f11113,plain,
( spl11_423
<=> ! [X24: uni,X23: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK3)),infix_plpl(a1,cons(a1,t2tb(sK2),X23),X24)) = infix_plpl(a1,reverse(a1,t2tb3(sK0)),infix_plpl(a1,X23,X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_423])]) ).
tff(f5493,plain,
( ! [X24: uni,X23: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK3)),infix_plpl(a1,cons(a1,t2tb(sK2),X23),X24)) = infix_plpl(a1,reverse(a1,t2tb3(sK0)),infix_plpl(a1,X23,X24)) )
| ~ spl11_33
| ~ spl11_296 ),
inference(superposition,[],[f5290,f385]) ).
tff(f11111,plain,
( spl11_422
| ~ spl11_38
| ~ spl11_295 ),
inference(avatar_split_clause,[],[f5477,f5285,f408,f11109]) ).
tff(f11109,plain,
( spl11_422
<=> ! [X25: uni,X26: uni] :
( ~ mem(a1,X25,infix_plpl(a1,reverse(a1,X26),t2tb3(sK5)))
| mem(a1,X25,reverse(a1,cons(a1,t2tb(sK6),X26)))
| mem(a1,X25,t2tb3(sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_422])]) ).
tff(f5285,plain,
( spl11_295
<=> ! [X10: uni,X11: uni,X7: ty,X9: uni,X8: uni] :
( ~ mem(X7,X11,infix_plpl(X7,reverse(X7,X9),cons(X7,X8,X10)))
| mem(X7,X11,reverse(X7,cons(X7,X8,X9)))
| mem(X7,X11,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_295])]) ).
tff(f5477,plain,
( ! [X26: uni,X25: uni] :
( ~ mem(a1,X25,infix_plpl(a1,reverse(a1,X26),t2tb3(sK5)))
| mem(a1,X25,reverse(a1,cons(a1,t2tb(sK6),X26)))
| mem(a1,X25,t2tb3(sK7)) )
| ~ spl11_38
| ~ spl11_295 ),
inference(superposition,[],[f5286,f410]) ).
tff(f5286,plain,
( ! [X10: uni,X11: uni,X8: uni,X9: uni,X7: ty] :
( ~ mem(X7,X11,infix_plpl(X7,reverse(X7,X9),cons(X7,X8,X10)))
| mem(X7,X11,reverse(X7,cons(X7,X8,X9)))
| mem(X7,X11,X10) )
| ~ spl11_295 ),
inference(avatar_component_clause,[],[f5285]) ).
tff(f11107,plain,
( spl11_421
| ~ spl11_33
| ~ spl11_295 ),
inference(avatar_split_clause,[],[f5476,f5285,f383,f11105]) ).
tff(f11105,plain,
( spl11_421
<=> ! [X24: uni,X23: uni] :
( ~ mem(a1,X23,infix_plpl(a1,reverse(a1,X24),t2tb3(sK0)))
| mem(a1,X23,reverse(a1,cons(a1,t2tb(sK2),X24)))
| mem(a1,X23,t2tb3(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_421])]) ).
tff(f5476,plain,
( ! [X24: uni,X23: uni] :
( ~ mem(a1,X23,infix_plpl(a1,reverse(a1,X24),t2tb3(sK0)))
| mem(a1,X23,reverse(a1,cons(a1,t2tb(sK2),X24)))
| mem(a1,X23,t2tb3(sK3)) )
| ~ spl11_33
| ~ spl11_295 ),
inference(superposition,[],[f5286,f385]) ).
tff(f11103,plain,
( spl11_420
| ~ spl11_38
| ~ spl11_294 ),
inference(avatar_split_clause,[],[f5376,f5281,f408,f11101]) ).
tff(f11101,plain,
( spl11_420
<=> ! [X25: uni,X26: uni] : ( infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK7),X25)),cons(a1,t2tb(sK6),X26)) = infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK5),X25)),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_420])]) ).
tff(f5281,plain,
( spl11_294
<=> ! [X5: ty,X9: uni,X7: uni,X6: uni,X8: uni] : ( infix_plpl(X5,reverse(X5,infix_plpl(X5,X7,X8)),cons(X5,X6,X9)) = infix_plpl(X5,reverse(X5,infix_plpl(X5,cons(X5,X6,X7),X8)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_294])]) ).
tff(f5376,plain,
( ! [X26: uni,X25: uni] : ( infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK7),X25)),cons(a1,t2tb(sK6),X26)) = infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK5),X25)),X26) )
| ~ spl11_38
| ~ spl11_294 ),
inference(superposition,[],[f5282,f410]) ).
tff(f5282,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] : ( infix_plpl(X5,reverse(X5,infix_plpl(X5,X7,X8)),cons(X5,X6,X9)) = infix_plpl(X5,reverse(X5,infix_plpl(X5,cons(X5,X6,X7),X8)),X9) )
| ~ spl11_294 ),
inference(avatar_component_clause,[],[f5281]) ).
tff(f11099,plain,
( spl11_419
| ~ spl11_33
| ~ spl11_294 ),
inference(avatar_split_clause,[],[f5375,f5281,f383,f11097]) ).
tff(f11097,plain,
( spl11_419
<=> ! [X24: uni,X23: uni] : ( infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK3),X23)),cons(a1,t2tb(sK2),X24)) = infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK0),X23)),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_419])]) ).
tff(f5375,plain,
( ! [X24: uni,X23: uni] : ( infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK3),X23)),cons(a1,t2tb(sK2),X24)) = infix_plpl(a1,reverse(a1,infix_plpl(a1,t2tb3(sK0),X23)),X24) )
| ~ spl11_33
| ~ spl11_294 ),
inference(superposition,[],[f5282,f385]) ).
tff(f11034,plain,
( spl11_418
| ~ spl11_29
| ~ spl11_120
| ~ spl11_161 ),
inference(avatar_split_clause,[],[f1956,f1881,f1190,f367,f11032]) ).
tff(f11032,plain,
( spl11_418
<=> ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_418])]) ).
tff(f1956,plain,
( ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) )
| ~ spl11_29
| ~ spl11_120
| ~ spl11_161 ),
inference(forward_demodulation,[],[f1949,f368]) ).
tff(f1949,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less($sum(X0,$uminus(X0)),X1) )
| ~ spl11_120
| ~ spl11_161 ),
inference(superposition,[],[f1882,f1191]) ).
tff(f11030,plain,
( spl11_417
| ~ spl11_29
| ~ spl11_120
| ~ spl11_160 ),
inference(avatar_split_clause,[],[f1934,f1871,f1190,f367,f11028]) ).
tff(f11028,plain,
( spl11_417
<=> ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_417])]) ).
tff(f1934,plain,
( ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) )
| ~ spl11_29
| ~ spl11_120
| ~ spl11_160 ),
inference(forward_demodulation,[],[f1926,f368]) ).
tff(f1926,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,1)
| ~ $less($sum(X0,$uminus(X0)),X1) )
| ~ spl11_120
| ~ spl11_160 ),
inference(superposition,[],[f1872,f1191]) ).
tff(f11026,plain,
( spl11_416
| ~ spl11_29
| ~ spl11_119 ),
inference(avatar_split_clause,[],[f1209,f1186,f367,f11024]) ).
tff(f11024,plain,
( spl11_416
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_416])]) ).
tff(f1209,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) )
| ~ spl11_29
| ~ spl11_119 ),
inference(evaluation,[],[f1206]) ).
tff(f1206,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) )
| ~ spl11_29
| ~ spl11_119 ),
inference(superposition,[],[f1187,f368]) ).
tff(f11005,plain,
( spl11_403
| ~ spl11_109
| ~ spl11_159 ),
inference(avatar_split_clause,[],[f6814,f1867,f1083,f9510]) ).
tff(f9510,plain,
( spl11_403
<=> ! [X0: $int] :
( ( length(a1,t2tb3(sK1)) = X0 )
| $less(X0,length(a1,t2tb3(sK1)))
| $less(length(a1,t2tb3(sK0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_403])]) ).
tff(f1083,plain,
( spl11_109
<=> $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_109])]) ).
tff(f1867,plain,
( spl11_159
<=> ! [X2: $int,X1: $int,X3: $int] :
( $less(X2,X1)
| ( X1 = X2 )
| ~ $less(X3,X1)
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_159])]) ).
tff(f6814,plain,
( ! [X0: $int] :
( ( length(a1,t2tb3(sK1)) = X0 )
| $less(X0,length(a1,t2tb3(sK1)))
| $less(length(a1,t2tb3(sK0)),X0) )
| ~ spl11_109
| ~ spl11_159 ),
inference(resolution,[],[f1085,f1868]) ).
tff(f1868,plain,
( ! [X2: $int,X3: $int,X1: $int] :
( ~ $less(X3,X1)
| ( X1 = X2 )
| $less(X2,X1)
| $less(X3,X2) )
| ~ spl11_159 ),
inference(avatar_component_clause,[],[f1867]) ).
tff(f1085,plain,
( $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK1)))
| ~ spl11_109 ),
inference(avatar_component_clause,[],[f1083]) ).
tff(f10962,plain,
( spl11_112
| ~ spl11_255
| ~ spl11_393 ),
inference(avatar_split_clause,[],[f9159,f9147,f4004,f1121]) ).
tff(f1121,plain,
( spl11_112
<=> $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_112])]) ).
tff(f9159,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK0)))
| ~ spl11_255
| ~ spl11_393 ),
inference(superposition,[],[f9148,f4006]) ).
tff(f10961,plain,
( spl11_415
| ~ spl11_29
| ~ spl11_118 ),
inference(avatar_split_clause,[],[f1199,f1182,f367,f10959]) ).
tff(f10959,plain,
( spl11_415
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_415])]) ).
tff(f1199,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl11_29
| ~ spl11_118 ),
inference(evaluation,[],[f1196]) ).
tff(f1196,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl11_29
| ~ spl11_118 ),
inference(superposition,[],[f1183,f368]) ).
tff(f10913,plain,
( spl11_414
| ~ spl11_38
| ~ spl11_298 ),
inference(avatar_split_clause,[],[f5678,f5297,f408,f10911]) ).
tff(f10911,plain,
( spl11_414
<=> ! [X38: uni,X36: ty,X35: ty,X37: uni] : ( nil(tuple2(X35,tuple2(X36,a1))) = combine(tuple2(X36,a1),X35,nil(X35),combine(a1,X36,cons(X36,X37,X38),t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_414])]) ).
tff(f5297,plain,
( spl11_298
<=> ! [X18: ty,X19: ty,X20: uni,X21: uni,X23: uni,X22: uni,X24: ty] : ( nil(tuple2(X24,tuple2(X18,X19))) = combine(tuple2(X18,X19),X24,nil(X24),combine(X19,X18,cons(X18,X20,X22),cons(X19,X21,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_298])]) ).
tff(f5678,plain,
( ! [X38: uni,X36: ty,X37: uni,X35: ty] : ( nil(tuple2(X35,tuple2(X36,a1))) = combine(tuple2(X36,a1),X35,nil(X35),combine(a1,X36,cons(X36,X37,X38),t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_298 ),
inference(superposition,[],[f5298,f410]) ).
tff(f5298,plain,
( ! [X21: uni,X18: ty,X19: ty,X24: ty,X22: uni,X23: uni,X20: uni] : ( nil(tuple2(X24,tuple2(X18,X19))) = combine(tuple2(X18,X19),X24,nil(X24),combine(X19,X18,cons(X18,X20,X22),cons(X19,X21,X23))) )
| ~ spl11_298 ),
inference(avatar_component_clause,[],[f5297]) ).
tff(f10909,plain,
( spl11_413
| ~ spl11_33
| ~ spl11_298 ),
inference(avatar_split_clause,[],[f5677,f5297,f383,f10907]) ).
tff(f10907,plain,
( spl11_413
<=> ! [X31: ty,X34: uni,X33: uni,X32: ty] : ( nil(tuple2(X31,tuple2(X32,a1))) = combine(tuple2(X32,a1),X31,nil(X31),combine(a1,X32,cons(X32,X33,X34),t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_413])]) ).
tff(f5677,plain,
( ! [X31: ty,X34: uni,X32: ty,X33: uni] : ( nil(tuple2(X31,tuple2(X32,a1))) = combine(tuple2(X32,a1),X31,nil(X31),combine(a1,X32,cons(X32,X33,X34),t2tb3(sK0))) )
| ~ spl11_33
| ~ spl11_298 ),
inference(superposition,[],[f5298,f385]) ).
tff(f10905,plain,
( spl11_412
| ~ spl11_38
| ~ spl11_298 ),
inference(avatar_split_clause,[],[f5672,f5297,f408,f10903]) ).
tff(f10903,plain,
( spl11_412
<=> ! [X38: uni,X36: ty,X35: ty,X37: uni] : ( nil(tuple2(X35,tuple2(a1,X36))) = combine(tuple2(a1,X36),X35,nil(X35),combine(X36,a1,t2tb3(sK5),cons(X36,X37,X38))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_412])]) ).
tff(f5672,plain,
( ! [X38: uni,X36: ty,X37: uni,X35: ty] : ( nil(tuple2(X35,tuple2(a1,X36))) = combine(tuple2(a1,X36),X35,nil(X35),combine(X36,a1,t2tb3(sK5),cons(X36,X37,X38))) )
| ~ spl11_38
| ~ spl11_298 ),
inference(superposition,[],[f5298,f410]) ).
tff(f10901,plain,
( spl11_411
| ~ spl11_33
| ~ spl11_298 ),
inference(avatar_split_clause,[],[f5671,f5297,f383,f10899]) ).
tff(f10899,plain,
( spl11_411
<=> ! [X31: ty,X34: uni,X33: uni,X32: ty] : ( nil(tuple2(X31,tuple2(a1,X32))) = combine(tuple2(a1,X32),X31,nil(X31),combine(X32,a1,t2tb3(sK0),cons(X32,X33,X34))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_411])]) ).
tff(f5671,plain,
( ! [X31: ty,X34: uni,X32: ty,X33: uni] : ( nil(tuple2(X31,tuple2(a1,X32))) = combine(tuple2(a1,X32),X31,nil(X31),combine(X32,a1,t2tb3(sK0),cons(X32,X33,X34))) )
| ~ spl11_33
| ~ spl11_298 ),
inference(superposition,[],[f5298,f385]) ).
tff(f10869,plain,
( spl11_124
| ~ spl11_44
| ~ spl11_354 ),
inference(avatar_split_clause,[],[f8592,f7400,f433,f1238]) ).
tff(f1238,plain,
( spl11_124
<=> ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_124])]) ).
tff(f7400,plain,
( spl11_354
<=> ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_354])]) ).
tff(f8592,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) )
| ~ spl11_44
| ~ spl11_354 ),
inference(forward_demodulation,[],[f8565,f434]) ).
tff(f8565,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,infix_plpl(a1,t2tb3(sK8),nil(a1))) )
| ~ spl11_44
| ~ spl11_354 ),
inference(superposition,[],[f7401,f434]) ).
tff(f7401,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) )
| ~ spl11_354 ),
inference(avatar_component_clause,[],[f7400]) ).
tff(f10860,plain,
( ~ spl11_222
| spl11_410
| ~ spl11_38
| ~ spl11_287 ),
inference(avatar_split_clause,[],[f5117,f5037,f408,f10858,f2941]) ).
tff(f10858,plain,
( spl11_410
<=> ! [X25: uni,X26: uni] :
( mem(a1,X25,infix_plpl(a1,t2tb3(sK5),X26))
| ~ sort(a1,X25)
| ~ mem(a1,X25,infix_plpl(a1,t2tb3(sK7),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_410])]) ).
tff(f5037,plain,
( spl11_287
<=> ! [X5: ty,X9: uni,X7: uni,X6: uni,X8: uni] :
( mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ~ mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_287])]) ).
tff(f5117,plain,
( ! [X26: uni,X25: uni] :
( mem(a1,X25,infix_plpl(a1,t2tb3(sK5),X26))
| ~ mem(a1,X25,infix_plpl(a1,t2tb3(sK7),X26))
| ~ sort(a1,t2tb(sK6))
| ~ sort(a1,X25) )
| ~ spl11_38
| ~ spl11_287 ),
inference(superposition,[],[f5038,f410]) ).
tff(f5038,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] :
( mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ~ mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) )
| ~ spl11_287 ),
inference(avatar_component_clause,[],[f5037]) ).
tff(f10848,plain,
( ~ spl11_203
| spl11_409
| ~ spl11_33
| ~ spl11_287 ),
inference(avatar_split_clause,[],[f5116,f5037,f383,f10846,f2534]) ).
tff(f10846,plain,
( spl11_409
<=> ! [X24: uni,X23: uni] :
( mem(a1,X23,infix_plpl(a1,t2tb3(sK0),X24))
| ~ sort(a1,X23)
| ~ mem(a1,X23,infix_plpl(a1,t2tb3(sK3),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_409])]) ).
tff(f5116,plain,
( ! [X24: uni,X23: uni] :
( mem(a1,X23,infix_plpl(a1,t2tb3(sK0),X24))
| ~ mem(a1,X23,infix_plpl(a1,t2tb3(sK3),X24))
| ~ sort(a1,t2tb(sK2))
| ~ sort(a1,X23) )
| ~ spl11_33
| ~ spl11_287 ),
inference(superposition,[],[f5038,f385]) ).
tff(f10770,plain,
( spl11_408
| ~ spl11_106
| ~ spl11_199 ),
inference(avatar_split_clause,[],[f2757,f2518,f1033,f10768]) ).
tff(f10768,plain,
( spl11_408
<=> ! [X4: uni,X5: uni] :
( ( 0 != $sum(1,length(a1,infix_plpl(a1,X4,t2tb3(sK8)))) )
| ( nil(a1) = cons(a1,X5,infix_plpl(a1,X4,t2tb3(sK3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_408])]) ).
tff(f2518,plain,
( spl11_199
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( 0 != $sum(1,length(X0,X2)) )
| ( nil(X0) = cons(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_199])]) ).
tff(f2757,plain,
( ! [X4: uni,X5: uni] :
( ( 0 != $sum(1,length(a1,infix_plpl(a1,X4,t2tb3(sK8)))) )
| ( nil(a1) = cons(a1,X5,infix_plpl(a1,X4,t2tb3(sK3))) ) )
| ~ spl11_106
| ~ spl11_199 ),
inference(superposition,[],[f2519,f1034]) ).
tff(f2519,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ( 0 != $sum(1,length(X0,X2)) )
| ( nil(X0) = cons(X0,X1,X2) ) )
| ~ spl11_199 ),
inference(avatar_component_clause,[],[f2518]) ).
tff(f10766,plain,
( spl11_407
| ~ spl11_105
| ~ spl11_199 ),
inference(avatar_split_clause,[],[f2756,f2518,f1029,f10764]) ).
tff(f10764,plain,
( spl11_407
<=> ! [X2: uni,X3: uni] :
( ( 0 != $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) )
| ( nil(a1) = cons(a1,X3,infix_plpl(a1,t2tb3(sK3),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_407])]) ).
tff(f2756,plain,
( ! [X2: uni,X3: uni] :
( ( 0 != $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X2))) )
| ( nil(a1) = cons(a1,X3,infix_plpl(a1,t2tb3(sK3),X2)) ) )
| ~ spl11_105
| ~ spl11_199 ),
inference(superposition,[],[f2519,f1030]) ).
tff(f10538,plain,
( spl11_406
| ~ spl11_47
| ~ spl11_108
| ~ spl11_246 ),
inference(avatar_split_clause,[],[f3873,f3504,f1079,f445,f10536]) ).
tff(f10536,plain,
( spl11_406
<=> ! [X24: $int] :
( $less($sum(X24,length(a1,t2tb3(sK5))),length(a1,t2tb3(sK0)))
| ~ $less(X24,length(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_406])]) ).
tff(f1079,plain,
( spl11_108
<=> ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_108])]) ).
tff(f3504,plain,
( spl11_246
<=> ! [X5: uni,X4: ty,X7: $int,X6: uni] :
( $less($sum(X7,length(X4,X6)),length(X4,infix_plpl(X4,X5,X6)))
| ~ $less(X7,length(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_246])]) ).
tff(f3873,plain,
( ! [X24: $int] :
( $less($sum(X24,length(a1,t2tb3(sK5))),length(a1,t2tb3(sK0)))
| ~ $less(X24,length(a1,t2tb3(sK8))) )
| ~ spl11_47
| ~ spl11_108
| ~ spl11_246 ),
inference(forward_demodulation,[],[f3841,f1081]) ).
tff(f1081,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK1)) )
| ~ spl11_108 ),
inference(avatar_component_clause,[],[f1079]) ).
tff(f3841,plain,
( ! [X24: $int] :
( $less($sum(X24,length(a1,t2tb3(sK5))),length(a1,t2tb3(sK1)))
| ~ $less(X24,length(a1,t2tb3(sK8))) )
| ~ spl11_47
| ~ spl11_246 ),
inference(superposition,[],[f3505,f447]) ).
tff(f3505,plain,
( ! [X6: uni,X7: $int,X4: ty,X5: uni] :
( $less($sum(X7,length(X4,X6)),length(X4,infix_plpl(X4,X5,X6)))
| ~ $less(X7,length(X4,X5)) )
| ~ spl11_246 ),
inference(avatar_component_clause,[],[f3504]) ).
tff(f10533,plain,
( spl11_404
| ~ spl11_405
| ~ spl11_108
| ~ spl11_199 ),
inference(avatar_split_clause,[],[f2755,f2518,f1079,f10530,f10527]) ).
tff(f10527,plain,
( spl11_404
<=> ! [X1: uni] : ( nil(a1) = cons(a1,X1,t2tb3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_404])]) ).
tff(f10530,plain,
( spl11_405
<=> ( 0 = $sum(1,length(a1,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_405])]) ).
tff(f2755,plain,
( ! [X1: uni] :
( ( 0 != $sum(1,length(a1,t2tb3(sK0))) )
| ( nil(a1) = cons(a1,X1,t2tb3(sK1)) ) )
| ~ spl11_108
| ~ spl11_199 ),
inference(superposition,[],[f2519,f1081]) ).
tff(f10440,plain,
( spl11_339
| ~ spl11_87
| ~ spl11_108
| ~ spl11_354 ),
inference(avatar_split_clause,[],[f8427,f7400,f1079,f820,f6668]) ).
tff(f6668,plain,
( spl11_339
<=> ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_339])]) ).
tff(f8427,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) )
| ~ spl11_87
| ~ spl11_108
| ~ spl11_354 ),
inference(forward_demodulation,[],[f1094,f7401]) ).
tff(f1094,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK0),X1)) )
| ~ spl11_87
| ~ spl11_108 ),
inference(forward_demodulation,[],[f1090,f821]) ).
tff(f1090,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = $sum(length(a1,t2tb3(sK0)),length(a1,X1)) )
| ~ spl11_87
| ~ spl11_108 ),
inference(superposition,[],[f821,f1081]) ).
tff(f9648,plain,
( spl11_340
| ~ spl11_112
| ~ spl11_351 ),
inference(avatar_split_clause,[],[f7636,f6865,f1121,f6683]) ).
tff(f6683,plain,
( spl11_340
<=> $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_340])]) ).
tff(f6865,plain,
( spl11_351
<=> ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK8)))
| ~ $less(X2,length(a1,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_351])]) ).
tff(f7636,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_112
| ~ spl11_351 ),
inference(resolution,[],[f1122,f6866]) ).
tff(f6866,plain,
( ! [X2: $int] :
( ~ $less(X2,length(a1,t2tb3(sK0)))
| $less(X2,length(a1,t2tb3(sK8))) )
| ~ spl11_351 ),
inference(avatar_component_clause,[],[f6865]) ).
tff(f1122,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK0)))
| ~ spl11_112 ),
inference(avatar_component_clause,[],[f1121]) ).
tff(f9512,plain,
( spl11_403
| ~ spl11_109
| ~ spl11_159 ),
inference(avatar_split_clause,[],[f6814,f1867,f1083,f9510]) ).
tff(f9500,plain,
( spl11_401
| ~ spl11_124
| ~ spl11_202
| ~ spl11_402 ),
inference(avatar_split_clause,[],[f9499,f9496,f2530,f1238,f9484]) ).
tff(f2530,plain,
( spl11_202
<=> ! [X4: uni,X5: uni,X3: ty] : ( $sum(length(X3,X5),length(X3,X4)) = length(X3,infix_plpl(X3,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_202])]) ).
tff(f9496,plain,
( spl11_402
<=> ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) = length(a1,infix_plpl(a1,t2tb3(sK0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_402])]) ).
tff(f9499,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),X3)) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) )
| ~ spl11_124
| ~ spl11_202
| ~ spl11_402 ),
inference(forward_demodulation,[],[f9497,f8947]) ).
tff(f8947,plain,
( ! [X7: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),X7)) = length(a1,infix_plpl(a1,t2tb3(sK0),X7)) )
| ~ spl11_124
| ~ spl11_202 ),
inference(forward_demodulation,[],[f8939,f2531]) ).
tff(f2531,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( $sum(length(X3,X5),length(X3,X4)) = length(X3,infix_plpl(X3,X4,X5)) )
| ~ spl11_202 ),
inference(avatar_component_clause,[],[f2530]) ).
tff(f8939,plain,
( ! [X7: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X7)) = $sum(length(a1,X7),length(a1,t2tb3(sK8))) )
| ~ spl11_124
| ~ spl11_202 ),
inference(superposition,[],[f2531,f1240]) ).
tff(f1240,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) )
| ~ spl11_124 ),
inference(avatar_component_clause,[],[f1238]) ).
tff(f9497,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) = length(a1,infix_plpl(a1,t2tb3(sK0),X3)) )
| ~ spl11_402 ),
inference(avatar_component_clause,[],[f9496]) ).
tff(f9498,plain,
( spl11_402
| ~ spl11_371
| ~ spl11_400 ),
inference(avatar_split_clause,[],[f9481,f9478,f7812,f9496]) ).
tff(f7812,plain,
( spl11_371
<=> ! [X15: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X15)) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_371])]) ).
tff(f9478,plain,
( spl11_400
<=> ! [X2: uni,X3: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X3))) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_400])]) ).
tff(f9481,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) = length(a1,infix_plpl(a1,t2tb3(sK0),X3)) )
| ~ spl11_371
| ~ spl11_400 ),
inference(forward_demodulation,[],[f9479,f7813]) ).
tff(f7813,plain,
( ! [X15: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X15)) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X15))) )
| ~ spl11_371 ),
inference(avatar_component_clause,[],[f7812]) ).
tff(f9479,plain,
( ! [X2: uni,X3: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X3))) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) )
| ~ spl11_400 ),
inference(avatar_component_clause,[],[f9478]) ).
tff(f9486,plain,
( spl11_401
| ~ spl11_354
| ~ spl11_371
| ~ spl11_400 ),
inference(avatar_split_clause,[],[f9482,f9478,f7812,f7400,f9484]) ).
tff(f9482,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK8),X3)) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) )
| ~ spl11_354
| ~ spl11_371
| ~ spl11_400 ),
inference(forward_demodulation,[],[f9481,f7401]) ).
tff(f9480,plain,
( spl11_400
| ~ spl11_39
| ~ spl11_60
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1060,f1033,f1029,f966,f820,f722,f649,f523,f413,f9478]) ).
tff(f1060,plain,
( ! [X2: uni,X3: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X3))) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK8)))) )
| ~ spl11_39
| ~ spl11_60
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106 ),
inference(forward_demodulation,[],[f1059,f967]) ).
tff(f1059,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,cons(a1,X2,X3)),t2tb3(sK8))) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X3))) )
| ~ spl11_39
| ~ spl11_60
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_105
| ~ spl11_106 ),
inference(forward_demodulation,[],[f1058,f1030]) ).
tff(f1058,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,cons(a1,X2,X3)),t2tb3(sK8))) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK3),X3))) )
| ~ spl11_39
| ~ spl11_60
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106 ),
inference(forward_demodulation,[],[f1057,f859]) ).
tff(f1057,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,cons(a1,X2,X3)),t2tb3(sK8))) = length(a1,infix_plpl(a1,X3,cons(a1,X2,t2tb3(sK3)))) )
| ~ spl11_60
| ~ spl11_87
| ~ spl11_100
| ~ spl11_106 ),
inference(forward_demodulation,[],[f1048,f853]) ).
tff(f853,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,reverse(X3,X4),X5)) = length(X3,infix_plpl(X3,X4,X5)) )
| ~ spl11_60
| ~ spl11_87 ),
inference(forward_demodulation,[],[f837,f821]) ).
tff(f837,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,reverse(X3,X4),X5)) = $sum(length(X3,X4),length(X3,X5)) )
| ~ spl11_60
| ~ spl11_87 ),
inference(superposition,[],[f821,f524]) ).
tff(f1048,plain,
( ! [X2: uni,X3: uni] : ( length(a1,infix_plpl(a1,reverse(a1,cons(a1,X2,X3)),t2tb3(sK8))) = length(a1,infix_plpl(a1,reverse(a1,X3),cons(a1,X2,t2tb3(sK3)))) )
| ~ spl11_100
| ~ spl11_106 ),
inference(superposition,[],[f1034,f967]) ).
tff(f9317,plain,
( spl11_399
| ~ spl11_254
| ~ spl11_393 ),
inference(avatar_split_clause,[],[f9158,f9147,f3619,f9314]) ).
tff(f9314,plain,
( spl11_399
<=> $less(length(a1,t2tb3(sK7)),length(a1,t2tb3(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_399])]) ).
tff(f3619,plain,
( spl11_254
<=> ( $sum(1,length(a1,t2tb3(sK7))) = length(a1,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_254])]) ).
tff(f9158,plain,
( $less(length(a1,t2tb3(sK7)),length(a1,t2tb3(sK5)))
| ~ spl11_254
| ~ spl11_393 ),
inference(superposition,[],[f9148,f3621]) ).
tff(f3621,plain,
( ( $sum(1,length(a1,t2tb3(sK7))) = length(a1,t2tb3(sK5)) )
| ~ spl11_254 ),
inference(avatar_component_clause,[],[f3619]) ).
tff(f9195,plain,
( spl11_398
| ~ spl11_47
| ~ spl11_276 ),
inference(avatar_split_clause,[],[f4904,f4784,f445,f9193]) ).
tff(f9193,plain,
( spl11_398
<=> ! [X36: uni,X35: uni] :
( ~ mem(a1,X35,infix_plpl(a1,X36,t2tb3(sK1)))
| mem(a1,X35,infix_plpl(a1,X36,t2tb3(sK8)))
| mem(a1,X35,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_398])]) ).
tff(f4784,plain,
( spl11_276
<=> ! [X10: uni,X9: uni,X7: uni,X6: ty,X8: uni] :
( ~ mem(X6,X10,infix_plpl(X6,X7,infix_plpl(X6,X8,X9)))
| mem(X6,X10,infix_plpl(X6,X7,X8))
| mem(X6,X10,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_276])]) ).
tff(f4904,plain,
( ! [X36: uni,X35: uni] :
( ~ mem(a1,X35,infix_plpl(a1,X36,t2tb3(sK1)))
| mem(a1,X35,infix_plpl(a1,X36,t2tb3(sK8)))
| mem(a1,X35,t2tb3(sK5)) )
| ~ spl11_47
| ~ spl11_276 ),
inference(superposition,[],[f4785,f447]) ).
tff(f4785,plain,
( ! [X10: uni,X8: uni,X6: ty,X9: uni,X7: uni] :
( ~ mem(X6,X10,infix_plpl(X6,X7,infix_plpl(X6,X8,X9)))
| mem(X6,X10,infix_plpl(X6,X7,X8))
| mem(X6,X10,X9) )
| ~ spl11_276 ),
inference(avatar_component_clause,[],[f4784]) ).
tff(f9191,plain,
( spl11_397
| ~ spl11_91
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1056,f1033,f877,f9189]) ).
tff(f9189,plain,
( spl11_397
<=> ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,X0,infix_plpl(a1,X1,t2tb3(sK3)))) = length(a1,infix_plpl(a1,X0,infix_plpl(a1,X1,t2tb3(sK8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_397])]) ).
tff(f877,plain,
( spl11_91
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] : ( infix_plpl(X0,X1,infix_plpl(X0,X2,X3)) = infix_plpl(X0,infix_plpl(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_91])]) ).
tff(f1056,plain,
( ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,X0,infix_plpl(a1,X1,t2tb3(sK3)))) = length(a1,infix_plpl(a1,X0,infix_plpl(a1,X1,t2tb3(sK8)))) )
| ~ spl11_91
| ~ spl11_106 ),
inference(forward_demodulation,[],[f1047,f878]) ).
tff(f878,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,X1,infix_plpl(X0,X2,X3)) = infix_plpl(X0,infix_plpl(X0,X1,X2),X3) )
| ~ spl11_91 ),
inference(avatar_component_clause,[],[f877]) ).
tff(f1047,plain,
( ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,infix_plpl(a1,X0,X1),t2tb3(sK8))) = length(a1,infix_plpl(a1,X0,infix_plpl(a1,X1,t2tb3(sK3)))) )
| ~ spl11_91
| ~ spl11_106 ),
inference(superposition,[],[f1034,f878]) ).
tff(f9187,plain,
( spl11_396
| ~ spl11_87
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1042,f1029,f820,f9185]) ).
tff(f9185,plain,
( spl11_396
<=> ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,X1,infix_plpl(a1,t2tb3(sK3),X0))) = length(a1,infix_plpl(a1,X1,infix_plpl(a1,t2tb3(sK8),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_396])]) ).
tff(f1042,plain,
( ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,X1,infix_plpl(a1,t2tb3(sK3),X0))) = length(a1,infix_plpl(a1,X1,infix_plpl(a1,t2tb3(sK8),X0))) )
| ~ spl11_87
| ~ spl11_105 ),
inference(forward_demodulation,[],[f1037,f821]) ).
tff(f1037,plain,
( ! [X0: uni,X1: uni] : ( length(a1,infix_plpl(a1,X1,infix_plpl(a1,t2tb3(sK3),X0))) = $sum(length(a1,X1),length(a1,infix_plpl(a1,t2tb3(sK8),X0))) )
| ~ spl11_87
| ~ spl11_105 ),
inference(superposition,[],[f821,f1030]) ).
tff(f9182,plain,
( ~ spl11_222
| spl11_395
| ~ spl11_38
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f994,f989,f408,f9180,f2941]) ).
tff(f9180,plain,
( spl11_395
<=> ! [X1: uni] :
( ~ mem(a1,X1,t2tb3(sK5))
| ~ sort(a1,X1)
| mem(a1,X1,t2tb3(sK7))
| ( t2tb(sK6) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_395])]) ).
tff(f989,plain,
( spl11_101
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,X3)
| ( X1 = X2 )
| ~ mem(X0,X1,cons(X0,X2,X3))
| ~ sort(X0,X2)
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_101])]) ).
tff(f994,plain,
( ! [X1: uni] :
( ~ mem(a1,X1,t2tb3(sK5))
| ( t2tb(sK6) = X1 )
| mem(a1,X1,t2tb3(sK7))
| ~ sort(a1,t2tb(sK6))
| ~ sort(a1,X1) )
| ~ spl11_38
| ~ spl11_101 ),
inference(superposition,[],[f990,f410]) ).
tff(f990,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( ~ mem(X0,X1,cons(X0,X2,X3))
| ( X1 = X2 )
| mem(X0,X1,X3)
| ~ sort(X0,X2)
| ~ sort(X0,X1) )
| ~ spl11_101 ),
inference(avatar_component_clause,[],[f989]) ).
tff(f9177,plain,
( ~ spl11_203
| spl11_394
| ~ spl11_33
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f993,f989,f383,f9175,f2534]) ).
tff(f9175,plain,
( spl11_394
<=> ! [X0: uni] :
( ~ mem(a1,X0,t2tb3(sK0))
| ~ sort(a1,X0)
| mem(a1,X0,t2tb3(sK3))
| ( t2tb(sK2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_394])]) ).
tff(f993,plain,
( ! [X0: uni] :
( ~ mem(a1,X0,t2tb3(sK0))
| ( t2tb(sK2) = X0 )
| mem(a1,X0,t2tb3(sK3))
| ~ sort(a1,t2tb(sK2))
| ~ sort(a1,X0) )
| ~ spl11_33
| ~ spl11_101 ),
inference(superposition,[],[f990,f385]) ).
tff(f9149,plain,
( spl11_393
| ~ spl11_39
| ~ spl11_114 ),
inference(avatar_split_clause,[],[f1151,f1131,f413,f9147]) ).
tff(f1151,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl11_39
| ~ spl11_114 ),
inference(superposition,[],[f1132,f414]) ).
tff(f9145,plain,
( ~ spl11_392
| ~ spl11_124
| spl11_391 ),
inference(avatar_split_clause,[],[f9067,f9009,f1238,f9142]) ).
tff(f9142,plain,
( spl11_392
<=> ( length(a1,t2tb3(sK8)) = $sum(1,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_392])]) ).
tff(f9067,plain,
( ( length(a1,t2tb3(sK8)) != $sum(1,length(a1,t2tb3(sK1))) )
| ~ spl11_124
| spl11_391 ),
inference(forward_demodulation,[],[f9010,f1240]) ).
tff(f9010,plain,
( ( length(a1,t2tb3(sK0)) != $sum(1,length(a1,t2tb3(sK1))) )
| spl11_391 ),
inference(avatar_component_clause,[],[f9009]) ).
tff(f9072,plain,
( spl11_376
| ~ spl11_109
| ~ spl11_124
| ~ spl11_159 ),
inference(avatar_split_clause,[],[f9066,f1867,f1238,f1083,f8127]) ).
tff(f8127,plain,
( spl11_376
<=> ! [X0: $int] :
( ( length(a1,t2tb3(sK1)) = X0 )
| $less(X0,length(a1,t2tb3(sK1)))
| $less(length(a1,t2tb3(sK8)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_376])]) ).
tff(f9066,plain,
( ! [X0: $int] :
( $less(length(a1,t2tb3(sK8)),X0)
| ( length(a1,t2tb3(sK1)) = X0 )
| $less(X0,length(a1,t2tb3(sK1))) )
| ~ spl11_109
| ~ spl11_124
| ~ spl11_159 ),
inference(forward_demodulation,[],[f6814,f1240]) ).
tff(f9068,plain,
( spl11_111
| ~ spl11_109
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f9065,f1238,f1083,f1103]) ).
tff(f1103,plain,
( spl11_111
<=> $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_111])]) ).
tff(f9065,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1)))
| ~ spl11_109
| ~ spl11_124 ),
inference(forward_demodulation,[],[f1085,f1240]) ).
tff(f9063,plain,
( spl11_340
| ~ spl11_44
| ~ spl11_111
| ~ spl11_339 ),
inference(avatar_split_clause,[],[f9054,f6668,f1103,f433,f6683]) ).
tff(f9054,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_44
| ~ spl11_111
| ~ spl11_339 ),
inference(forward_demodulation,[],[f1105,f8457]) ).
tff(f8457,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,t2tb3(sK8)) )
| ~ spl11_44
| ~ spl11_339 ),
inference(forward_demodulation,[],[f8432,f434]) ).
tff(f8432,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,infix_plpl(a1,t2tb3(sK8),nil(a1))) )
| ~ spl11_44
| ~ spl11_339 ),
inference(superposition,[],[f6669,f434]) ).
tff(f6669,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) )
| ~ spl11_339 ),
inference(avatar_component_clause,[],[f6668]) ).
tff(f1105,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1)))
| ~ spl11_111 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f9012,plain,
( spl11_391
| ~ spl11_79
| ~ spl11_189
| ~ spl11_255
| ~ spl11_349 ),
inference(avatar_split_clause,[],[f7490,f6782,f4004,f2078,f722,f9009]) ).
tff(f6782,plain,
( spl11_349
<=> ! [X3: uni] : ( length(a1,infix_plpl(a1,X3,t2tb3(sK1))) = length(a1,infix_plpl(a1,X3,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_349])]) ).
tff(f7490,plain,
( ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK1))) )
| ~ spl11_79
| ~ spl11_189
| ~ spl11_255
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7358,f4006]) ).
tff(f7358,plain,
( ( $sum(1,length(a1,t2tb3(sK8))) = $sum(1,length(a1,t2tb3(sK1))) )
| ~ spl11_79
| ~ spl11_189
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7357,f723]) ).
tff(f7357,plain,
( ! [X0: uni] : ( $sum(1,length(a1,t2tb3(sK1))) = length(a1,cons(a1,X0,t2tb3(sK8))) )
| ~ spl11_79
| ~ spl11_189
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7356,f2079]) ).
tff(f7356,plain,
( ! [X0: uni] : ( $sum(1,length(a1,t2tb3(sK1))) = length(a1,infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK8))) )
| ~ spl11_79
| ~ spl11_189
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7324,f723]) ).
tff(f7324,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,cons(a1,X0,nil(a1)),t2tb3(sK8))) = length(a1,cons(a1,X0,t2tb3(sK1))) )
| ~ spl11_189
| ~ spl11_349 ),
inference(superposition,[],[f6783,f2079]) ).
tff(f6783,plain,
( ! [X3: uni] : ( length(a1,infix_plpl(a1,X3,t2tb3(sK1))) = length(a1,infix_plpl(a1,X3,t2tb3(sK8))) )
| ~ spl11_349 ),
inference(avatar_component_clause,[],[f6782]) ).
tff(f8993,plain,
( spl11_390
| ~ spl11_38
| ~ spl11_278 ),
inference(avatar_split_clause,[],[f4947,f4792,f408,f8991]) ).
tff(f8991,plain,
( spl11_390
<=> ! [X32: uni,X30: ty,X31: uni] : ( combine(a1,X30,X31,t2tb3(sK7)) = cons_proj_2(tuple2(X30,a1),combine(a1,X30,cons(X30,X32,X31),t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_390])]) ).
tff(f4792,plain,
( spl11_278
<=> ! [X6: ty,X10: uni,X11: uni,X9: uni,X8: uni,X7: ty] : ( combine(X7,X6,X10,X11) = cons_proj_2(tuple2(X6,X7),combine(X7,X6,cons(X6,X8,X10),cons(X7,X9,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_278])]) ).
tff(f4947,plain,
( ! [X31: uni,X32: uni,X30: ty] : ( combine(a1,X30,X31,t2tb3(sK7)) = cons_proj_2(tuple2(X30,a1),combine(a1,X30,cons(X30,X32,X31),t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_278 ),
inference(superposition,[],[f4793,f410]) ).
tff(f4793,plain,
( ! [X10: uni,X11: uni,X8: uni,X6: ty,X9: uni,X7: ty] : ( combine(X7,X6,X10,X11) = cons_proj_2(tuple2(X6,X7),combine(X7,X6,cons(X6,X8,X10),cons(X7,X9,X11))) )
| ~ spl11_278 ),
inference(avatar_component_clause,[],[f4792]) ).
tff(f8989,plain,
( spl11_389
| ~ spl11_33
| ~ spl11_278 ),
inference(avatar_split_clause,[],[f4946,f4792,f383,f8987]) ).
tff(f8987,plain,
( spl11_389
<=> ! [X29: uni,X27: ty,X28: uni] : ( combine(a1,X27,X28,t2tb3(sK3)) = cons_proj_2(tuple2(X27,a1),combine(a1,X27,cons(X27,X29,X28),t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_389])]) ).
tff(f4946,plain,
( ! [X28: uni,X29: uni,X27: ty] : ( combine(a1,X27,X28,t2tb3(sK3)) = cons_proj_2(tuple2(X27,a1),combine(a1,X27,cons(X27,X29,X28),t2tb3(sK0))) )
| ~ spl11_33
| ~ spl11_278 ),
inference(superposition,[],[f4793,f385]) ).
tff(f8985,plain,
( spl11_388
| ~ spl11_38
| ~ spl11_278 ),
inference(avatar_split_clause,[],[f4941,f4792,f408,f8983]) ).
tff(f8983,plain,
( spl11_388
<=> ! [X32: uni,X30: ty,X31: uni] : ( combine(X30,a1,t2tb3(sK7),X31) = cons_proj_2(tuple2(a1,X30),combine(X30,a1,t2tb3(sK5),cons(X30,X32,X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_388])]) ).
tff(f4941,plain,
( ! [X31: uni,X32: uni,X30: ty] : ( combine(X30,a1,t2tb3(sK7),X31) = cons_proj_2(tuple2(a1,X30),combine(X30,a1,t2tb3(sK5),cons(X30,X32,X31))) )
| ~ spl11_38
| ~ spl11_278 ),
inference(superposition,[],[f4793,f410]) ).
tff(f8981,plain,
( spl11_387
| ~ spl11_33
| ~ spl11_278 ),
inference(avatar_split_clause,[],[f4940,f4792,f383,f8979]) ).
tff(f8979,plain,
( spl11_387
<=> ! [X29: uni,X27: ty,X28: uni] : ( combine(X27,a1,t2tb3(sK3),X28) = cons_proj_2(tuple2(a1,X27),combine(X27,a1,t2tb3(sK0),cons(X27,X29,X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_387])]) ).
tff(f4940,plain,
( ! [X28: uni,X29: uni,X27: ty] : ( combine(X27,a1,t2tb3(sK3),X28) = cons_proj_2(tuple2(a1,X27),combine(X27,a1,t2tb3(sK0),cons(X27,X29,X28))) )
| ~ spl11_33
| ~ spl11_278 ),
inference(superposition,[],[f4793,f385]) ).
tff(f8977,plain,
( spl11_386
| ~ spl11_38
| ~ spl11_277 ),
inference(avatar_split_clause,[],[f4927,f4788,f408,f8975]) ).
tff(f8975,plain,
( spl11_386
<=> ! [X25: uni,X26: uni] :
( mem(a1,X25,infix_plpl(a1,reverse(a1,X26),t2tb3(sK5)))
| ~ mem(a1,X25,reverse(a1,cons(a1,t2tb(sK6),X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_386])]) ).
tff(f4788,plain,
( spl11_277
<=> ! [X31: uni,X29: uni,X27: ty,X28: uni,X30: uni] :
( mem(X27,X31,infix_plpl(X27,reverse(X27,X29),cons(X27,X28,X30)))
| ~ mem(X27,X31,reverse(X27,cons(X27,X28,X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_277])]) ).
tff(f4927,plain,
( ! [X26: uni,X25: uni] :
( mem(a1,X25,infix_plpl(a1,reverse(a1,X26),t2tb3(sK5)))
| ~ mem(a1,X25,reverse(a1,cons(a1,t2tb(sK6),X26))) )
| ~ spl11_38
| ~ spl11_277 ),
inference(superposition,[],[f4789,f410]) ).
tff(f4789,plain,
( ! [X31: uni,X28: uni,X29: uni,X27: ty,X30: uni] :
( mem(X27,X31,infix_plpl(X27,reverse(X27,X29),cons(X27,X28,X30)))
| ~ mem(X27,X31,reverse(X27,cons(X27,X28,X29))) )
| ~ spl11_277 ),
inference(avatar_component_clause,[],[f4788]) ).
tff(f8973,plain,
( spl11_385
| ~ spl11_33
| ~ spl11_277 ),
inference(avatar_split_clause,[],[f4926,f4788,f383,f8971]) ).
tff(f8971,plain,
( spl11_385
<=> ! [X24: uni,X23: uni] :
( mem(a1,X23,infix_plpl(a1,reverse(a1,X24),t2tb3(sK0)))
| ~ mem(a1,X23,reverse(a1,cons(a1,t2tb(sK2),X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_385])]) ).
tff(f4926,plain,
( ! [X24: uni,X23: uni] :
( mem(a1,X23,infix_plpl(a1,reverse(a1,X24),t2tb3(sK0)))
| ~ mem(a1,X23,reverse(a1,cons(a1,t2tb(sK2),X24))) )
| ~ spl11_33
| ~ spl11_277 ),
inference(superposition,[],[f4789,f385]) ).
tff(f8922,plain,
( spl11_124
| ~ spl11_44
| ~ spl11_45
| ~ spl11_338
| ~ spl11_349 ),
inference(avatar_split_clause,[],[f8224,f6782,f6663,f437,f433,f1238]) ).
tff(f6663,plain,
( spl11_338
<=> ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_338])]) ).
tff(f8224,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) )
| ~ spl11_44
| ~ spl11_45
| ~ spl11_338
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7713,f7355]) ).
tff(f7355,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,t2tb3(sK8)) )
| ~ spl11_45
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7323,f438]) ).
tff(f7323,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,infix_plpl(a1,nil(a1),t2tb3(sK8))) )
| ~ spl11_45
| ~ spl11_349 ),
inference(superposition,[],[f6783,f438]) ).
tff(f7713,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK1)) )
| ~ spl11_44
| ~ spl11_338 ),
inference(forward_demodulation,[],[f7689,f434]) ).
tff(f7689,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,infix_plpl(a1,t2tb3(sK0),nil(a1))) )
| ~ spl11_44
| ~ spl11_338 ),
inference(superposition,[],[f6664,f434]) ).
tff(f6664,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK0),X1)) )
| ~ spl11_338 ),
inference(avatar_component_clause,[],[f6663]) ).
tff(f8682,plain,
( spl11_384
| ~ spl11_38
| ~ spl11_275 ),
inference(avatar_split_clause,[],[f4882,f4780,f408,f8680]) ).
tff(f8680,plain,
( spl11_384
<=> ! [X41: ty,X40: ty,X44: uni,X42: uni,X43: uni] : ( tuple21(X40,X41,X42,X43) = match_list(tuple2(X40,X41),a1,t2tb3(sK5),X44,tuple21(X40,X41,X42,X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_384])]) ).
tff(f4780,plain,
( spl11_275
<=> ! [X48: ty,X51: uni,X54: uni,X53: uni,X50: uni,X49: ty,X52: uni,X47: ty] : ( tuple21(X47,X48,X53,X54) = match_list(tuple2(X47,X48),X49,cons(X49,X50,X51),X52,tuple21(X47,X48,X53,X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_275])]) ).
tff(f4882,plain,
( ! [X40: ty,X41: ty,X44: uni,X42: uni,X43: uni] : ( tuple21(X40,X41,X42,X43) = match_list(tuple2(X40,X41),a1,t2tb3(sK5),X44,tuple21(X40,X41,X42,X43)) )
| ~ spl11_38
| ~ spl11_275 ),
inference(superposition,[],[f4781,f410]) ).
tff(f4781,plain,
( ! [X50: uni,X51: uni,X48: ty,X49: ty,X47: ty,X54: uni,X52: uni,X53: uni] : ( tuple21(X47,X48,X53,X54) = match_list(tuple2(X47,X48),X49,cons(X49,X50,X51),X52,tuple21(X47,X48,X53,X54)) )
| ~ spl11_275 ),
inference(avatar_component_clause,[],[f4780]) ).
tff(f8678,plain,
( spl11_383
| ~ spl11_33
| ~ spl11_275 ),
inference(avatar_split_clause,[],[f4881,f4780,f383,f8676]) ).
tff(f8676,plain,
( spl11_383
<=> ! [X38: uni,X36: ty,X35: ty,X39: uni,X37: uni] : ( tuple21(X35,X36,X37,X38) = match_list(tuple2(X35,X36),a1,t2tb3(sK0),X39,tuple21(X35,X36,X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_383])]) ).
tff(f4881,plain,
( ! [X38: uni,X39: uni,X36: ty,X37: uni,X35: ty] : ( tuple21(X35,X36,X37,X38) = match_list(tuple2(X35,X36),a1,t2tb3(sK0),X39,tuple21(X35,X36,X37,X38)) )
| ~ spl11_33
| ~ spl11_275 ),
inference(superposition,[],[f4781,f385]) ).
tff(f8648,plain,
( spl11_110
| ~ spl11_45
| ~ spl11_349 ),
inference(avatar_split_clause,[],[f7355,f6782,f437,f1099]) ).
tff(f1099,plain,
( spl11_110
<=> ( length(a1,t2tb3(sK1)) = length(a1,t2tb3(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_110])]) ).
tff(f8647,plain,
( spl11_382
| ~ spl11_38
| ~ spl11_274 ),
inference(avatar_split_clause,[],[f4846,f4776,f408,f8645]) ).
tff(f8645,plain,
( spl11_382
<=> ! [X48: uni,X47: uni,X50: uni,X49: uni,X45: ty,X46: ty] : ( match_list(X45,X46,X47,X48,X49) = match_list(X45,a1,t2tb3(sK5),X50,match_list(X45,X46,X47,X48,X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_382])]) ).
tff(f4776,plain,
( spl11_274
<=> ! [X21: uni,X18: ty,X19: uni,X16: uni,X14: ty,X17: uni,X15: uni,X13: ty,X20: uni] : ( match_list(X13,X18,X19,X20,X21) = match_list(X13,X14,cons(X14,X15,X16),X17,match_list(X13,X18,X19,X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_274])]) ).
tff(f4846,plain,
( ! [X50: uni,X48: uni,X46: ty,X49: uni,X47: uni,X45: ty] : ( match_list(X45,X46,X47,X48,X49) = match_list(X45,a1,t2tb3(sK5),X50,match_list(X45,X46,X47,X48,X49)) )
| ~ spl11_38
| ~ spl11_274 ),
inference(superposition,[],[f4777,f410]) ).
tff(f4777,plain,
( ! [X21: uni,X18: ty,X19: uni,X16: uni,X14: ty,X17: uni,X15: uni,X13: ty,X20: uni] : ( match_list(X13,X18,X19,X20,X21) = match_list(X13,X14,cons(X14,X15,X16),X17,match_list(X13,X18,X19,X20,X21)) )
| ~ spl11_274 ),
inference(avatar_component_clause,[],[f4776]) ).
tff(f8643,plain,
( spl11_381
| ~ spl11_33
| ~ spl11_274 ),
inference(avatar_split_clause,[],[f4845,f4776,f383,f8641]) ).
tff(f8641,plain,
( spl11_381
<=> ! [X41: uni,X40: ty,X44: uni,X42: uni,X43: uni,X39: ty] : ( match_list(X39,X40,X41,X42,X43) = match_list(X39,a1,t2tb3(sK0),X44,match_list(X39,X40,X41,X42,X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_381])]) ).
tff(f4845,plain,
( ! [X40: ty,X41: uni,X39: ty,X44: uni,X42: uni,X43: uni] : ( match_list(X39,X40,X41,X42,X43) = match_list(X39,a1,t2tb3(sK0),X44,match_list(X39,X40,X41,X42,X43)) )
| ~ spl11_33
| ~ spl11_274 ),
inference(superposition,[],[f4777,f385]) ).
tff(f8639,plain,
( spl11_380
| ~ spl11_106
| ~ spl11_146 ),
inference(avatar_split_clause,[],[f1585,f1509,f1033,f8637]) ).
tff(f8637,plain,
( spl11_380
<=> ! [X1: uni] :
( ( 0 != length(a1,infix_plpl(a1,X1,t2tb3(sK8))) )
| ( nil(a1) = reverse(a1,infix_plpl(a1,X1,t2tb3(sK3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_380])]) ).
tff(f1509,plain,
( spl11_146
<=> ! [X2: uni,X1: ty] :
( ( 0 != length(X1,X2) )
| ( nil(X1) = reverse(X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_146])]) ).
tff(f1585,plain,
( ! [X1: uni] :
( ( 0 != length(a1,infix_plpl(a1,X1,t2tb3(sK8))) )
| ( nil(a1) = reverse(a1,infix_plpl(a1,X1,t2tb3(sK3))) ) )
| ~ spl11_106
| ~ spl11_146 ),
inference(superposition,[],[f1510,f1034]) ).
tff(f1510,plain,
( ! [X2: uni,X1: ty] :
( ( 0 != length(X1,X2) )
| ( nil(X1) = reverse(X1,X2) ) )
| ~ spl11_146 ),
inference(avatar_component_clause,[],[f1509]) ).
tff(f8635,plain,
( spl11_379
| ~ spl11_105
| ~ spl11_146 ),
inference(avatar_split_clause,[],[f1584,f1509,f1029,f8633]) ).
tff(f8633,plain,
( spl11_379
<=> ! [X0: uni] :
( ( 0 != length(a1,infix_plpl(a1,t2tb3(sK8),X0)) )
| ( nil(a1) = reverse(a1,infix_plpl(a1,t2tb3(sK3),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_379])]) ).
tff(f1584,plain,
( ! [X0: uni] :
( ( 0 != length(a1,infix_plpl(a1,t2tb3(sK8),X0)) )
| ( nil(a1) = reverse(a1,infix_plpl(a1,t2tb3(sK3),X0)) ) )
| ~ spl11_105
| ~ spl11_146 ),
inference(superposition,[],[f1510,f1030]) ).
tff(f8631,plain,
( spl11_378
| ~ spl11_38
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f974,f966,f408,f8629]) ).
tff(f8629,plain,
( spl11_378
<=> ! [X1: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK7)),cons(a1,t2tb(sK6),X1)) = infix_plpl(a1,reverse(a1,t2tb3(sK5)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_378])]) ).
tff(f974,plain,
( ! [X1: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK7)),cons(a1,t2tb(sK6),X1)) = infix_plpl(a1,reverse(a1,t2tb3(sK5)),X1) )
| ~ spl11_38
| ~ spl11_100 ),
inference(superposition,[],[f967,f410]) ).
tff(f8627,plain,
( spl11_377
| ~ spl11_33
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f973,f966,f383,f8625]) ).
tff(f8625,plain,
( spl11_377
<=> ! [X0: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK3)),cons(a1,t2tb(sK2),X0)) = infix_plpl(a1,reverse(a1,t2tb3(sK0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_377])]) ).
tff(f973,plain,
( ! [X0: uni] : ( infix_plpl(a1,reverse(a1,t2tb3(sK3)),cons(a1,t2tb(sK2),X0)) = infix_plpl(a1,reverse(a1,t2tb3(sK0)),X0) )
| ~ spl11_33
| ~ spl11_100 ),
inference(superposition,[],[f967,f385]) ).
tff(f8129,plain,
( spl11_376
| ~ spl11_111
| ~ spl11_159 ),
inference(avatar_split_clause,[],[f6690,f1867,f1103,f8127]) ).
tff(f6690,plain,
( ! [X0: $int] :
( ( length(a1,t2tb3(sK1)) = X0 )
| $less(X0,length(a1,t2tb3(sK1)))
| $less(length(a1,t2tb3(sK8)),X0) )
| ~ spl11_111
| ~ spl11_159 ),
inference(resolution,[],[f1105,f1868]) ).
tff(f7830,plain,
( spl11_375
| ~ spl11_38
| ~ spl11_268 ),
inference(avatar_split_clause,[],[f4636,f4474,f408,f7828]) ).
tff(f4474,plain,
( spl11_268
<=> ! [X6: ty,X10: bool,X9: uni,X11: uni,X12: uni,X5: ty,X8: uni,X7: uni] : ( match_bool(X5,X10,X11,X12) = match_list(X5,X6,cons(X6,X7,X8),X9,match_bool(X5,X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_268])]) ).
tff(f4636,plain,
( ! [X36: uni,X34: uni,X35: uni,X32: ty,X33: bool] : ( match_bool(X32,X33,X34,X35) = match_list(X32,a1,t2tb3(sK5),X36,match_bool(X32,X33,X34,X35)) )
| ~ spl11_38
| ~ spl11_268 ),
inference(superposition,[],[f4475,f410]) ).
tff(f4475,plain,
( ! [X10: bool,X11: uni,X8: uni,X6: ty,X9: uni,X7: uni,X5: ty,X12: uni] : ( match_bool(X5,X10,X11,X12) = match_list(X5,X6,cons(X6,X7,X8),X9,match_bool(X5,X10,X11,X12)) )
| ~ spl11_268 ),
inference(avatar_component_clause,[],[f4474]) ).
tff(f7826,plain,
( spl11_374
| ~ spl11_33
| ~ spl11_268 ),
inference(avatar_split_clause,[],[f4635,f4474,f383,f7824]) ).
tff(f4635,plain,
( ! [X31: uni,X28: bool,X29: uni,X27: ty,X30: uni] : ( match_bool(X27,X28,X29,X30) = match_list(X27,a1,t2tb3(sK0),X31,match_bool(X27,X28,X29,X30)) )
| ~ spl11_33
| ~ spl11_268 ),
inference(superposition,[],[f4475,f385]) ).
tff(f7822,plain,
( spl11_373
| ~ spl11_33
| ~ spl11_105
| ~ spl11_261 ),
inference(avatar_split_clause,[],[f4410,f4097,f1029,f383,f7820]) ).
tff(f7820,plain,
( spl11_373
<=> ! [X15: uni] : ( length(a1,infix_plpl(a1,X15,t2tb3(sK0))) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_373])]) ).
tff(f4410,plain,
( ! [X15: uni] : ( length(a1,infix_plpl(a1,X15,t2tb3(sK0))) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X15))) )
| ~ spl11_33
| ~ spl11_105
| ~ spl11_261 ),
inference(forward_demodulation,[],[f4377,f1030]) ).
tff(f4377,plain,
( ! [X15: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK3),X15))) = length(a1,infix_plpl(a1,X15,t2tb3(sK0))) )
| ~ spl11_33
| ~ spl11_261 ),
inference(superposition,[],[f4098,f385]) ).
tff(f7818,plain,
( spl11_372
| ~ spl11_38
| ~ spl11_261 ),
inference(avatar_split_clause,[],[f4378,f4097,f408,f7816]) ).
tff(f7816,plain,
( spl11_372
<=> ! [X16: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK7),X16))) = length(a1,infix_plpl(a1,X16,t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_372])]) ).
tff(f4378,plain,
( ! [X16: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK7),X16))) = length(a1,infix_plpl(a1,X16,t2tb3(sK5))) )
| ~ spl11_38
| ~ spl11_261 ),
inference(superposition,[],[f4098,f410]) ).
tff(f7814,plain,
( spl11_371
| ~ spl11_33
| ~ spl11_105
| ~ spl11_260 ),
inference(avatar_split_clause,[],[f4336,f4093,f1029,f383,f7812]) ).
tff(f4336,plain,
( ! [X15: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X15)) = $sum(1,length(a1,infix_plpl(a1,t2tb3(sK8),X15))) )
| ~ spl11_33
| ~ spl11_105
| ~ spl11_260 ),
inference(forward_demodulation,[],[f4307,f1030]) ).
tff(f4307,plain,
( ! [X15: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK3),X15))) = length(a1,infix_plpl(a1,t2tb3(sK0),X15)) )
| ~ spl11_33
| ~ spl11_260 ),
inference(superposition,[],[f4094,f385]) ).
tff(f7810,plain,
( spl11_370
| ~ spl11_38
| ~ spl11_260 ),
inference(avatar_split_clause,[],[f4308,f4093,f408,f7808]) ).
tff(f7808,plain,
( spl11_370
<=> ! [X16: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK7),X16))) = length(a1,infix_plpl(a1,t2tb3(sK5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_370])]) ).
tff(f4308,plain,
( ! [X16: uni] : ( $sum(1,length(a1,infix_plpl(a1,t2tb3(sK7),X16))) = length(a1,infix_plpl(a1,t2tb3(sK5),X16)) )
| ~ spl11_38
| ~ spl11_260 ),
inference(superposition,[],[f4094,f410]) ).
tff(f7806,plain,
( spl11_369
| ~ spl11_47
| ~ spl11_247 ),
inference(avatar_split_clause,[],[f3889,f3508,f445,f7804]) ).
tff(f7804,plain,
( spl11_369
<=> ! [X24: $int] :
( $less(length(a1,t2tb3(sK1)),$sum(X24,length(a1,t2tb3(sK5))))
| ~ $less(length(a1,t2tb3(sK8)),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_369])]) ).
tff(f3508,plain,
( spl11_247
<=> ! [X10: uni,X11: $int,X9: uni,X8: ty] :
( $less(length(X8,infix_plpl(X8,X9,X10)),$sum(X11,length(X8,X10)))
| ~ $less(length(X8,X9),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_247])]) ).
tff(f3889,plain,
( ! [X24: $int] :
( $less(length(a1,t2tb3(sK1)),$sum(X24,length(a1,t2tb3(sK5))))
| ~ $less(length(a1,t2tb3(sK8)),X24) )
| ~ spl11_47
| ~ spl11_247 ),
inference(superposition,[],[f3509,f447]) ).
tff(f3509,plain,
( ! [X10: uni,X11: $int,X8: ty,X9: uni] :
( $less(length(X8,infix_plpl(X8,X9,X10)),$sum(X11,length(X8,X10)))
| ~ $less(length(X8,X9),X11) )
| ~ spl11_247 ),
inference(avatar_component_clause,[],[f3508]) ).
tff(f7802,plain,
( spl11_368
| ~ spl11_47
| ~ spl11_246 ),
inference(avatar_split_clause,[],[f3841,f3504,f445,f7800]) ).
tff(f7800,plain,
( spl11_368
<=> ! [X24: $int] :
( $less($sum(X24,length(a1,t2tb3(sK5))),length(a1,t2tb3(sK1)))
| ~ $less(X24,length(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_368])]) ).
tff(f7798,plain,
( spl11_367
| ~ spl11_61
| ~ spl11_106 ),
inference(avatar_split_clause,[],[f1053,f1033,f527,f7796]) ).
tff(f7796,plain,
( spl11_367
<=> ! [X4: uni] :
( ( 0 != length(a1,infix_plpl(a1,X4,t2tb3(sK8))) )
| ( nil(a1) = infix_plpl(a1,X4,t2tb3(sK3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_367])]) ).
tff(f527,plain,
( spl11_61
<=> ! [X0: ty,X1: uni] :
( ( nil(X0) = X1 )
| ( 0 != length(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_61])]) ).
tff(f1053,plain,
( ! [X4: uni] :
( ( 0 != length(a1,infix_plpl(a1,X4,t2tb3(sK8))) )
| ( nil(a1) = infix_plpl(a1,X4,t2tb3(sK3)) ) )
| ~ spl11_61
| ~ spl11_106 ),
inference(superposition,[],[f528,f1034]) ).
tff(f528,plain,
( ! [X0: ty,X1: uni] :
( ( 0 != length(X0,X1) )
| ( nil(X0) = X1 ) )
| ~ spl11_61 ),
inference(avatar_component_clause,[],[f527]) ).
tff(f7794,plain,
( spl11_366
| ~ spl11_61
| ~ spl11_105 ),
inference(avatar_split_clause,[],[f1039,f1029,f527,f7792]) ).
tff(f7792,plain,
( spl11_366
<=> ! [X4: uni] :
( ( 0 != length(a1,infix_plpl(a1,t2tb3(sK8),X4)) )
| ( nil(a1) = infix_plpl(a1,t2tb3(sK3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_366])]) ).
tff(f1039,plain,
( ! [X4: uni] :
( ( 0 != length(a1,infix_plpl(a1,t2tb3(sK8),X4)) )
| ( nil(a1) = infix_plpl(a1,t2tb3(sK3),X4) ) )
| ~ spl11_61
| ~ spl11_105 ),
inference(superposition,[],[f528,f1030]) ).
tff(f7790,plain,
( spl11_365
| ~ spl11_118
| ~ spl11_255 ),
inference(avatar_split_clause,[],[f5924,f4004,f1182,f7788]) ).
tff(f7788,plain,
( spl11_365
<=> ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK0)))
| $less(length(a1,t2tb3(sK8)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_365])]) ).
tff(f5924,plain,
( ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK0)))
| $less(length(a1,t2tb3(sK8)),X2) )
| ~ spl11_118
| ~ spl11_255 ),
inference(superposition,[],[f1183,f4006]) ).
tff(f7786,plain,
( ~ spl11_222
| spl11_364
| ~ spl11_38
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f945,f932,f408,f7784,f2941]) ).
tff(f7784,plain,
( spl11_364
<=> ! [X1: uni] :
( mem(a1,X1,t2tb3(sK5))
| ~ sort(a1,X1)
| ~ mem(a1,X1,t2tb3(sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_364])]) ).
tff(f932,plain,
( spl11_97
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,cons(X0,X2,X3))
| ~ mem(X0,X1,X3)
| ~ sort(X0,X2)
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_97])]) ).
tff(f945,plain,
( ! [X1: uni] :
( mem(a1,X1,t2tb3(sK5))
| ~ mem(a1,X1,t2tb3(sK7))
| ~ sort(a1,t2tb(sK6))
| ~ sort(a1,X1) )
| ~ spl11_38
| ~ spl11_97 ),
inference(superposition,[],[f933,f410]) ).
tff(f933,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X2,X3))
| ~ mem(X0,X1,X3)
| ~ sort(X0,X2)
| ~ sort(X0,X1) )
| ~ spl11_97 ),
inference(avatar_component_clause,[],[f932]) ).
tff(f7782,plain,
( ~ spl11_203
| spl11_363
| ~ spl11_33
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f944,f932,f383,f7780,f2534]) ).
tff(f7780,plain,
( spl11_363
<=> ! [X0: uni] :
( mem(a1,X0,t2tb3(sK0))
| ~ sort(a1,X0)
| ~ mem(a1,X0,t2tb3(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_363])]) ).
tff(f944,plain,
( ! [X0: uni] :
( mem(a1,X0,t2tb3(sK0))
| ~ mem(a1,X0,t2tb3(sK3))
| ~ sort(a1,t2tb(sK2))
| ~ sort(a1,X0) )
| ~ spl11_33
| ~ spl11_97 ),
inference(superposition,[],[f933,f385]) ).
tff(f7762,plain,
( spl11_362
| ~ spl11_38
| ~ spl11_253 ),
inference(avatar_split_clause,[],[f4074,f3532,f408,f7760]) ).
tff(f7760,plain,
( spl11_362
<=> ! [X16: uni] :
( mem(a1,X16,reverse(a1,t2tb3(sK5)))
| ~ mem(a1,X16,cons(a1,t2tb(sK6),nil(a1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_362])]) ).
tff(f3532,plain,
( spl11_253
<=> ! [X13: uni,X14: uni,X12: ty,X15: uni] :
( mem(X12,X15,reverse(X12,cons(X12,X14,X13)))
| ~ mem(X12,X15,cons(X12,X14,nil(X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_253])]) ).
tff(f4074,plain,
( ! [X16: uni] :
( mem(a1,X16,reverse(a1,t2tb3(sK5)))
| ~ mem(a1,X16,cons(a1,t2tb(sK6),nil(a1))) )
| ~ spl11_38
| ~ spl11_253 ),
inference(superposition,[],[f3533,f410]) ).
tff(f3533,plain,
( ! [X14: uni,X15: uni,X12: ty,X13: uni] :
( mem(X12,X15,reverse(X12,cons(X12,X14,X13)))
| ~ mem(X12,X15,cons(X12,X14,nil(X12))) )
| ~ spl11_253 ),
inference(avatar_component_clause,[],[f3532]) ).
tff(f7758,plain,
( spl11_361
| ~ spl11_33
| ~ spl11_253 ),
inference(avatar_split_clause,[],[f4073,f3532,f383,f7756]) ).
tff(f7756,plain,
( spl11_361
<=> ! [X15: uni] :
( mem(a1,X15,reverse(a1,t2tb3(sK0)))
| ~ mem(a1,X15,cons(a1,t2tb(sK2),nil(a1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_361])]) ).
tff(f4073,plain,
( ! [X15: uni] :
( mem(a1,X15,reverse(a1,t2tb3(sK0)))
| ~ mem(a1,X15,cons(a1,t2tb(sK2),nil(a1))) )
| ~ spl11_33
| ~ spl11_253 ),
inference(superposition,[],[f3533,f385]) ).
tff(f7754,plain,
( spl11_360
| ~ spl11_47
| ~ spl11_251 ),
inference(avatar_split_clause,[],[f3990,f3524,f445,f7752]) ).
tff(f7752,plain,
( spl11_360
<=> ! [X30: uni,X31: uni] :
( mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK1)))
| ~ mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_360])]) ).
tff(f3524,plain,
( spl11_251
<=> ! [X17: uni,X13: ty,X14: uni,X16: uni,X15: uni] :
( mem(X13,X17,infix_plpl(X13,X14,infix_plpl(X13,X15,X16)))
| ~ mem(X13,X17,infix_plpl(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_251])]) ).
tff(f3990,plain,
( ! [X31: uni,X30: uni] :
( mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK1)))
| ~ mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK8))) )
| ~ spl11_47
| ~ spl11_251 ),
inference(superposition,[],[f3525,f447]) ).
tff(f3525,plain,
( ! [X16: uni,X14: uni,X17: uni,X15: uni,X13: ty] :
( mem(X13,X17,infix_plpl(X13,X14,infix_plpl(X13,X15,X16)))
| ~ mem(X13,X17,infix_plpl(X13,X14,X15)) )
| ~ spl11_251 ),
inference(avatar_component_clause,[],[f3524]) ).
tff(f7750,plain,
( spl11_108
| ~ spl11_44
| ~ spl11_338 ),
inference(avatar_split_clause,[],[f7713,f6663,f433,f1079]) ).
tff(f7748,plain,
( spl11_358
| ~ spl11_359
| ~ spl11_4
| ~ spl11_199 ),
inference(avatar_split_clause,[],[f2754,f2518,f254,f7745,f7742]) ).
tff(f7742,plain,
( spl11_358
<=> ! [X0: uni] : ( nil(a1) = cons(a1,X0,t2tb3(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_358])]) ).
tff(f7745,plain,
( spl11_359
<=> ( 0 = $sum(1,length(a1,t2tb3(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_359])]) ).
tff(f254,plain,
( spl11_4
<=> ( length(a1,t2tb3(sK3)) = length(a1,t2tb3(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
tff(f2754,plain,
( ! [X0: uni] :
( ( 0 != $sum(1,length(a1,t2tb3(sK8))) )
| ( nil(a1) = cons(a1,X0,t2tb3(sK3)) ) )
| ~ spl11_4
| ~ spl11_199 ),
inference(superposition,[],[f2519,f256]) ).
tff(f256,plain,
( ( length(a1,t2tb3(sK3)) = length(a1,t2tb3(sK8)) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f254]) ).
tff(f7678,plain,
( spl11_355
| ~ spl11_109
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f6815,f1505,f1083,f7561]) ).
tff(f7561,plain,
( spl11_355
<=> ! [X1: $int] :
( $less(length(a1,t2tb3(sK0)),$sum(X1,1))
| $less(X1,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_355])]) ).
tff(f6815,plain,
( ! [X1: $int] :
( $less(length(a1,t2tb3(sK0)),$sum(X1,1))
| $less(X1,length(a1,t2tb3(sK1))) )
| ~ spl11_109
| ~ spl11_145 ),
inference(resolution,[],[f1085,f1506]) ).
tff(f7670,plain,
( spl11_357
| ~ spl11_45
| ~ spl11_109
| ~ spl11_337 ),
inference(avatar_split_clause,[],[f7663,f6658,f1083,f437,f7667]) ).
tff(f7667,plain,
( spl11_357
<=> $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_357])]) ).
tff(f6658,plain,
( spl11_337
<=> ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK1))) = length(a1,infix_plpl(a1,X0,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_337])]) ).
tff(f7663,plain,
( $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK0)))
| ~ spl11_45
| ~ spl11_109
| ~ spl11_337 ),
inference(forward_demodulation,[],[f1085,f7103]) ).
tff(f7103,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK1)) )
| ~ spl11_45
| ~ spl11_337 ),
inference(forward_demodulation,[],[f7075,f438]) ).
tff(f7075,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,infix_plpl(a1,nil(a1),t2tb3(sK0))) )
| ~ spl11_45
| ~ spl11_337 ),
inference(superposition,[],[f6659,f438]) ).
tff(f6659,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK1))) = length(a1,infix_plpl(a1,X0,t2tb3(sK0))) )
| ~ spl11_337 ),
inference(avatar_component_clause,[],[f6658]) ).
tff(f7646,plain,
( spl11_356
| ~ spl11_112
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f1577,f1505,f1121,f7644]) ).
tff(f7644,plain,
( spl11_356
<=> ! [X20: $int] :
( $less(length(a1,t2tb3(sK8)),$sum(X20,1))
| $less(X20,length(a1,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_356])]) ).
tff(f1577,plain,
( ! [X20: $int] :
( $less(length(a1,t2tb3(sK8)),$sum(X20,1))
| $less(X20,length(a1,t2tb3(sK0))) )
| ~ spl11_112
| ~ spl11_145 ),
inference(resolution,[],[f1506,f1122]) ).
tff(f7640,plain,
( ~ spl11_117
| spl11_6
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1087,f1079,f264,f1165]) ).
tff(f1165,plain,
( spl11_117
<=> $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_117])]) ).
tff(f264,plain,
( spl11_6
<=> $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
tff(f1087,plain,
( ~ $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK8)))
| spl11_6
| ~ spl11_108 ),
inference(superposition,[],[f266,f1081]) ).
tff(f266,plain,
( ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK8)))
| spl11_6 ),
inference(avatar_component_clause,[],[f264]) ).
tff(f7634,plain,
( spl11_112
| ~ spl11_108
| ~ spl11_111 ),
inference(avatar_split_clause,[],[f1242,f1103,f1079,f1121]) ).
tff(f1242,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK0)))
| ~ spl11_108
| ~ spl11_111 ),
inference(forward_demodulation,[],[f1105,f1081]) ).
tff(f7585,plain,
( spl11_340
| ~ spl11_45
| ~ spl11_112
| ~ spl11_337
| ~ spl11_349 ),
inference(avatar_split_clause,[],[f7568,f6782,f6658,f1121,f437,f6683]) ).
tff(f7568,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_45
| ~ spl11_112
| ~ spl11_337
| ~ spl11_349 ),
inference(forward_demodulation,[],[f1122,f7496]) ).
tff(f7496,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) )
| ~ spl11_45
| ~ spl11_337
| ~ spl11_349 ),
inference(forward_demodulation,[],[f7103,f7355]) ).
tff(f7563,plain,
( spl11_355
| ~ spl11_109
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f6815,f1505,f1083,f7561]) ).
tff(f7487,plain,
( ~ spl11_8
| ~ spl11_340 ),
inference(avatar_contradiction_clause,[],[f7483]) ).
tff(f7483,plain,
( $false
| ~ spl11_8
| ~ spl11_340 ),
inference(resolution,[],[f6685,f275]) ).
tff(f275,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f274]) ).
tff(f274,plain,
( spl11_8
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
tff(f6685,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_340 ),
inference(avatar_component_clause,[],[f6683]) ).
tff(f7480,plain,
( spl11_340
| ~ spl11_110
| ~ spl11_111 ),
inference(avatar_split_clause,[],[f7418,f1103,f1099,f6683]) ).
tff(f7418,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_110
| ~ spl11_111 ),
inference(forward_demodulation,[],[f1105,f1101]) ).
tff(f1101,plain,
( ( length(a1,t2tb3(sK1)) = length(a1,t2tb3(sK8)) )
| ~ spl11_110 ),
inference(avatar_component_clause,[],[f1099]) ).
tff(f7433,plain,
( ~ spl11_110
| spl11_108
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f6786,f1238,f1079,f1099]) ).
tff(f6786,plain,
( ( length(a1,t2tb3(sK1)) != length(a1,t2tb3(sK8)) )
| spl11_108
| ~ spl11_124 ),
inference(forward_demodulation,[],[f1080,f1240]) ).
tff(f1080,plain,
( ( length(a1,t2tb3(sK0)) != length(a1,t2tb3(sK1)) )
| spl11_108 ),
inference(avatar_component_clause,[],[f1079]) ).
tff(f7402,plain,
( spl11_354
| ~ spl11_338
| ~ spl11_339 ),
inference(avatar_split_clause,[],[f6798,f6668,f6663,f7400]) ).
tff(f6798,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK0),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) )
| ~ spl11_338
| ~ spl11_339 ),
inference(forward_demodulation,[],[f6664,f6669]) ).
tff(f7303,plain,
( spl11_353
| ~ spl11_119
| ~ spl11_255 ),
inference(avatar_split_clause,[],[f5923,f4004,f1186,f7301]) ).
tff(f7301,plain,
( spl11_353
<=> ! [X1: $int] :
( ~ $less(X1,length(a1,t2tb3(sK0)))
| ~ $less(length(a1,t2tb3(sK8)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_353])]) ).
tff(f5923,plain,
( ! [X1: $int] :
( ~ $less(X1,length(a1,t2tb3(sK0)))
| ~ $less(length(a1,t2tb3(sK8)),X1) )
| ~ spl11_119
| ~ spl11_255 ),
inference(superposition,[],[f1187,f4006]) ).
tff(f6874,plain,
( spl11_352
| ~ spl11_58
| ~ spl11_109 ),
inference(avatar_split_clause,[],[f6816,f1083,f515,f6872]) ).
tff(f6872,plain,
( spl11_352
<=> ! [X2: $int] :
( ~ $less(X2,length(a1,t2tb3(sK0)))
| $less(X2,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_352])]) ).
tff(f6816,plain,
( ! [X2: $int] :
( ~ $less(X2,length(a1,t2tb3(sK0)))
| $less(X2,length(a1,t2tb3(sK1))) )
| ~ spl11_58
| ~ spl11_109 ),
inference(resolution,[],[f1085,f516]) ).
tff(f6867,plain,
( spl11_351
| ~ spl11_58
| ~ spl11_109
| ~ spl11_110 ),
inference(avatar_split_clause,[],[f6820,f1099,f1083,f515,f6865]) ).
tff(f6820,plain,
( ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK8)))
| ~ $less(X2,length(a1,t2tb3(sK0))) )
| ~ spl11_58
| ~ spl11_109
| ~ spl11_110 ),
inference(forward_demodulation,[],[f6816,f1101]) ).
tff(f6854,plain,
( spl11_117
| ~ spl11_109
| ~ spl11_110 ),
inference(avatar_split_clause,[],[f6821,f1099,f1083,f1165]) ).
tff(f6821,plain,
( $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK8)))
| ~ spl11_109
| ~ spl11_110 ),
inference(superposition,[],[f1085,f1101]) ).
tff(f6797,plain,
( spl11_350
| ~ spl11_111
| ~ spl11_145 ),
inference(avatar_split_clause,[],[f6691,f1505,f1103,f6795]) ).
tff(f6795,plain,
( spl11_350
<=> ! [X1: $int] :
( $less(length(a1,t2tb3(sK8)),$sum(X1,1))
| $less(X1,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_350])]) ).
tff(f6691,plain,
( ! [X1: $int] :
( $less(length(a1,t2tb3(sK8)),$sum(X1,1))
| $less(X1,length(a1,t2tb3(sK1))) )
| ~ spl11_111
| ~ spl11_145 ),
inference(resolution,[],[f1105,f1506]) ).
tff(f6784,plain,
( spl11_349
| ~ spl11_110
| ~ spl11_202 ),
inference(avatar_split_clause,[],[f6393,f2530,f1099,f6782]) ).
tff(f6393,plain,
( ! [X3: uni] : ( length(a1,infix_plpl(a1,X3,t2tb3(sK1))) = length(a1,infix_plpl(a1,X3,t2tb3(sK8))) )
| ~ spl11_110
| ~ spl11_202 ),
inference(forward_demodulation,[],[f6383,f2531]) ).
tff(f6383,plain,
( ! [X3: uni] : ( length(a1,infix_plpl(a1,X3,t2tb3(sK1))) = $sum(length(a1,t2tb3(sK8)),length(a1,X3)) )
| ~ spl11_110
| ~ spl11_202 ),
inference(superposition,[],[f2531,f1101]) ).
tff(f6780,plain,
( spl11_348
| ~ spl11_38
| ~ spl11_250 ),
inference(avatar_split_clause,[],[f3976,f3520,f408,f6778]) ).
tff(f6778,plain,
( spl11_348
<=> ! [X20: ty,X21: uni] : ( nil(tuple2(X20,a1)) = combine(a1,X20,nil(X20),infix_plpl(a1,t2tb3(sK5),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_348])]) ).
tff(f3520,plain,
( spl11_250
<=> ! [X4: ty,X0: ty,X3: uni,X2: uni,X1: uni] : ( nil(tuple2(X4,X0)) = combine(X0,X4,nil(X4),infix_plpl(X0,cons(X0,X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_250])]) ).
tff(f3976,plain,
( ! [X21: uni,X20: ty] : ( nil(tuple2(X20,a1)) = combine(a1,X20,nil(X20),infix_plpl(a1,t2tb3(sK5),X21)) )
| ~ spl11_38
| ~ spl11_250 ),
inference(superposition,[],[f3521,f410]) ).
tff(f3521,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni,X4: ty] : ( nil(tuple2(X4,X0)) = combine(X0,X4,nil(X4),infix_plpl(X0,cons(X0,X1,X2),X3)) )
| ~ spl11_250 ),
inference(avatar_component_clause,[],[f3520]) ).
tff(f6776,plain,
( spl11_347
| ~ spl11_118
| ~ spl11_254 ),
inference(avatar_split_clause,[],[f5691,f3619,f1182,f6774]) ).
tff(f6774,plain,
( spl11_347
<=> ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK5)))
| $less(length(a1,t2tb3(sK7)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_347])]) ).
tff(f5691,plain,
( ! [X2: $int] :
( $less(X2,length(a1,t2tb3(sK5)))
| $less(length(a1,t2tb3(sK7)),X2) )
| ~ spl11_118
| ~ spl11_254 ),
inference(superposition,[],[f1183,f3621]) ).
tff(f6772,plain,
( spl11_346
| ~ spl11_33
| ~ spl11_250 ),
inference(avatar_split_clause,[],[f3975,f3520,f383,f6770]) ).
tff(f6770,plain,
( spl11_346
<=> ! [X18: ty,X19: uni] : ( nil(tuple2(X18,a1)) = combine(a1,X18,nil(X18),infix_plpl(a1,t2tb3(sK0),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_346])]) ).
tff(f3975,plain,
( ! [X18: ty,X19: uni] : ( nil(tuple2(X18,a1)) = combine(a1,X18,nil(X18),infix_plpl(a1,t2tb3(sK0),X19)) )
| ~ spl11_33
| ~ spl11_250 ),
inference(superposition,[],[f3521,f385]) ).
tff(f6768,plain,
( spl11_345
| ~ spl11_38
| ~ spl11_249 ),
inference(avatar_split_clause,[],[f3961,f3516,f408,f6766]) ).
tff(f6766,plain,
( spl11_345
<=> ! [X31: uni,X29: ty,X28: ty,X30: uni] : ( tuple2_proj_2(X28,X29,X30) = match_list(X29,a1,t2tb3(sK5),X31,tuple2_proj_2(X28,X29,X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_345])]) ).
tff(f3516,plain,
( spl11_249
<=> ! [X38: uni,X41: uni,X40: ty,X36: ty,X35: ty,X39: uni,X37: uni] : ( tuple2_proj_2(X40,X35,X41) = match_list(X35,X36,cons(X36,X37,X38),X39,tuple2_proj_2(X40,X35,X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_249])]) ).
tff(f3961,plain,
( ! [X31: uni,X28: ty,X29: ty,X30: uni] : ( tuple2_proj_2(X28,X29,X30) = match_list(X29,a1,t2tb3(sK5),X31,tuple2_proj_2(X28,X29,X30)) )
| ~ spl11_38
| ~ spl11_249 ),
inference(superposition,[],[f3517,f410]) ).
tff(f3517,plain,
( ! [X40: ty,X38: uni,X41: uni,X39: uni,X36: ty,X37: uni,X35: ty] : ( tuple2_proj_2(X40,X35,X41) = match_list(X35,X36,cons(X36,X37,X38),X39,tuple2_proj_2(X40,X35,X41)) )
| ~ spl11_249 ),
inference(avatar_component_clause,[],[f3516]) ).
tff(f6764,plain,
( spl11_344
| ~ spl11_33
| ~ spl11_249 ),
inference(avatar_split_clause,[],[f3960,f3516,f383,f6762]) ).
tff(f6762,plain,
( spl11_344
<=> ! [X24: ty,X27: uni,X25: ty,X26: uni] : ( tuple2_proj_2(X24,X25,X26) = match_list(X25,a1,t2tb3(sK0),X27,tuple2_proj_2(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_344])]) ).
tff(f3960,plain,
( ! [X26: uni,X27: uni,X24: ty,X25: ty] : ( tuple2_proj_2(X24,X25,X26) = match_list(X25,a1,t2tb3(sK0),X27,tuple2_proj_2(X24,X25,X26)) )
| ~ spl11_33
| ~ spl11_249 ),
inference(superposition,[],[f3517,f385]) ).
tff(f6760,plain,
( spl11_343
| ~ spl11_38
| ~ spl11_248 ),
inference(avatar_split_clause,[],[f3946,f3512,f408,f6758]) ).
tff(f6758,plain,
( spl11_343
<=> ! [X31: uni,X29: ty,X28: ty,X30: uni] : ( tuple2_proj_1(X28,X29,X30) = match_list(X28,a1,t2tb3(sK5),X31,tuple2_proj_1(X28,X29,X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_343])]) ).
tff(f3512,plain,
( spl11_248
<=> ! [X28: ty,X31: uni,X34: uni,X29: ty,X33: ty,X32: uni,X30: uni] : ( tuple2_proj_1(X28,X33,X34) = match_list(X28,X29,cons(X29,X30,X31),X32,tuple2_proj_1(X28,X33,X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_248])]) ).
tff(f3946,plain,
( ! [X31: uni,X28: ty,X29: ty,X30: uni] : ( tuple2_proj_1(X28,X29,X30) = match_list(X28,a1,t2tb3(sK5),X31,tuple2_proj_1(X28,X29,X30)) )
| ~ spl11_38
| ~ spl11_248 ),
inference(superposition,[],[f3513,f410]) ).
tff(f3513,plain,
( ! [X31: uni,X28: ty,X29: ty,X34: uni,X32: uni,X30: uni,X33: ty] : ( tuple2_proj_1(X28,X33,X34) = match_list(X28,X29,cons(X29,X30,X31),X32,tuple2_proj_1(X28,X33,X34)) )
| ~ spl11_248 ),
inference(avatar_component_clause,[],[f3512]) ).
tff(f6756,plain,
( spl11_342
| ~ spl11_33
| ~ spl11_248 ),
inference(avatar_split_clause,[],[f3945,f3512,f383,f6754]) ).
tff(f6754,plain,
( spl11_342
<=> ! [X24: ty,X27: uni,X25: ty,X26: uni] : ( tuple2_proj_1(X24,X25,X26) = match_list(X24,a1,t2tb3(sK0),X27,tuple2_proj_1(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_342])]) ).
tff(f3945,plain,
( ! [X26: uni,X27: uni,X24: ty,X25: ty] : ( tuple2_proj_1(X24,X25,X26) = match_list(X24,a1,t2tb3(sK0),X27,tuple2_proj_1(X24,X25,X26)) )
| ~ spl11_33
| ~ spl11_248 ),
inference(superposition,[],[f3513,f385]) ).
tff(f6736,plain,
( spl11_111
| ~ spl11_109
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f6688,f1238,f1083,f1103]) ).
tff(f6688,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1)))
| ~ spl11_109
| ~ spl11_124 ),
inference(forward_demodulation,[],[f1085,f1240]) ).
tff(f6696,plain,
( spl11_341
| ~ spl11_58
| ~ spl11_111 ),
inference(avatar_split_clause,[],[f6692,f1103,f515,f6694]) ).
tff(f6694,plain,
( spl11_341
<=> ! [X2: $int] :
( ~ $less(X2,length(a1,t2tb3(sK8)))
| $less(X2,length(a1,t2tb3(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_341])]) ).
tff(f6692,plain,
( ! [X2: $int] :
( ~ $less(X2,length(a1,t2tb3(sK8)))
| $less(X2,length(a1,t2tb3(sK1))) )
| ~ spl11_58
| ~ spl11_111 ),
inference(resolution,[],[f1105,f516]) ).
tff(f6686,plain,
( spl11_340
| ~ spl11_112
| ~ spl11_124 ),
inference(avatar_split_clause,[],[f6677,f1238,f1121,f6683]) ).
tff(f6677,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK8)))
| ~ spl11_112
| ~ spl11_124 ),
inference(forward_demodulation,[],[f1122,f1240]) ).
tff(f6670,plain,
( spl11_339
| ~ spl11_87
| ~ spl11_110 ),
inference(avatar_split_clause,[],[f1119,f1099,f820,f6668]) ).
tff(f1119,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = length(a1,infix_plpl(a1,t2tb3(sK8),X1)) )
| ~ spl11_87
| ~ spl11_110 ),
inference(forward_demodulation,[],[f1114,f821]) ).
tff(f1114,plain,
( ! [X1: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK1),X1)) = $sum(length(a1,t2tb3(sK8)),length(a1,X1)) )
| ~ spl11_87
| ~ spl11_110 ),
inference(superposition,[],[f821,f1101]) ).
tff(f6665,plain,
( spl11_338
| ~ spl11_87
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1094,f1079,f820,f6663]) ).
tff(f6660,plain,
( spl11_337
| ~ spl11_87
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1093,f1079,f820,f6658]) ).
tff(f1093,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK1))) = length(a1,infix_plpl(a1,X0,t2tb3(sK0))) )
| ~ spl11_87
| ~ spl11_108 ),
inference(forward_demodulation,[],[f1089,f821]) ).
tff(f1089,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK1))) = $sum(length(a1,X0),length(a1,t2tb3(sK0))) )
| ~ spl11_87
| ~ spl11_108 ),
inference(superposition,[],[f821,f1081]) ).
tff(f6656,plain,
( spl11_336
| ~ spl11_47
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f1014,f873,f445,f6654]) ).
tff(f6654,plain,
( spl11_336
<=> ! [X2: uni] : ( infix_plpl(a1,cons(a1,X2,t2tb3(sK8)),t2tb3(sK5)) = cons(a1,X2,t2tb3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_336])]) ).
tff(f873,plain,
( spl11_90
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] : ( infix_plpl(X0,cons(X0,X2,X3),X1) = cons(X0,X2,infix_plpl(X0,X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_90])]) ).
tff(f1014,plain,
( ! [X2: uni] : ( infix_plpl(a1,cons(a1,X2,t2tb3(sK8)),t2tb3(sK5)) = cons(a1,X2,t2tb3(sK1)) )
| ~ spl11_47
| ~ spl11_90 ),
inference(superposition,[],[f874,f447]) ).
tff(f874,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,cons(X0,X2,X3),X1) = cons(X0,X2,infix_plpl(X0,X3,X1)) )
| ~ spl11_90 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f6652,plain,
( spl11_335
| ~ spl11_47
| ~ spl11_91 ),
inference(avatar_split_clause,[],[f1013,f877,f445,f6650]) ).
tff(f6650,plain,
( spl11_335
<=> ! [X1: uni] : ( infix_plpl(a1,t2tb3(sK8),infix_plpl(a1,t2tb3(sK5),X1)) = infix_plpl(a1,t2tb3(sK1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_335])]) ).
tff(f1013,plain,
( ! [X1: uni] : ( infix_plpl(a1,t2tb3(sK8),infix_plpl(a1,t2tb3(sK5),X1)) = infix_plpl(a1,t2tb3(sK1),X1) )
| ~ spl11_47
| ~ spl11_91 ),
inference(superposition,[],[f878,f447]) ).
tff(f6648,plain,
( spl11_334
| ~ spl11_47
| ~ spl11_92 ),
inference(avatar_split_clause,[],[f1012,f881,f445,f6646]) ).
tff(f6646,plain,
( spl11_334
<=> ! [X0: uni] :
( ~ mem(a1,X0,t2tb3(sK1))
| mem(a1,X0,t2tb3(sK8))
| mem(a1,X0,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_334])]) ).
tff(f881,plain,
( spl11_92
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,X3)
| mem(X0,X1,X2)
| ~ mem(X0,X1,infix_plpl(X0,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_92])]) ).
tff(f1012,plain,
( ! [X0: uni] :
( ~ mem(a1,X0,t2tb3(sK1))
| mem(a1,X0,t2tb3(sK8))
| mem(a1,X0,t2tb3(sK5)) )
| ~ spl11_47
| ~ spl11_92 ),
inference(superposition,[],[f882,f447]) ).
tff(f882,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( ~ mem(X0,X1,infix_plpl(X0,X2,X3))
| mem(X0,X1,X2)
| mem(X0,X1,X3) )
| ~ spl11_92 ),
inference(avatar_component_clause,[],[f881]) ).
tff(f6623,plain,
( spl11_333
| ~ spl11_119
| ~ spl11_254 ),
inference(avatar_split_clause,[],[f5690,f3619,f1186,f6621]) ).
tff(f6621,plain,
( spl11_333
<=> ! [X1: $int] :
( ~ $less(X1,length(a1,t2tb3(sK5)))
| ~ $less(length(a1,t2tb3(sK7)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_333])]) ).
tff(f5690,plain,
( ! [X1: $int] :
( ~ $less(X1,length(a1,t2tb3(sK5)))
| ~ $less(length(a1,t2tb3(sK7)),X1) )
| ~ spl11_119
| ~ spl11_254 ),
inference(superposition,[],[f1187,f3621]) ).
tff(f6610,plain,
( spl11_332
| ~ spl11_38
| ~ spl11_235 ),
inference(avatar_split_clause,[],[f3465,f3211,f408,f6608]) ).
tff(f6608,plain,
( spl11_332
<=> ! [X25: uni,X24: ty,X26: uni] : ( nil(tuple2(X24,a1)) != combine(a1,X24,cons(X24,X25,X26),t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_332])]) ).
tff(f3211,plain,
( spl11_235
<=> ! [X2: uni,X3: uni,X4: uni,X0: ty,X5: uni,X1: ty] : ( nil(tuple2(X0,X1)) != combine(X1,X0,cons(X0,X2,X4),cons(X1,X3,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_235])]) ).
tff(f3465,plain,
( ! [X26: uni,X24: ty,X25: uni] : ( nil(tuple2(X24,a1)) != combine(a1,X24,cons(X24,X25,X26),t2tb3(sK5)) )
| ~ spl11_38
| ~ spl11_235 ),
inference(superposition,[],[f3212,f410]) ).
tff(f3212,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] : ( nil(tuple2(X0,X1)) != combine(X1,X0,cons(X0,X2,X4),cons(X1,X3,X5)) )
| ~ spl11_235 ),
inference(avatar_component_clause,[],[f3211]) ).
tff(f6606,plain,
( spl11_331
| ~ spl11_33
| ~ spl11_235 ),
inference(avatar_split_clause,[],[f3464,f3211,f383,f6604]) ).
tff(f6604,plain,
( spl11_331
<=> ! [X22: uni,X21: ty,X23: uni] : ( nil(tuple2(X21,a1)) != combine(a1,X21,cons(X21,X22,X23),t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_331])]) ).
tff(f3464,plain,
( ! [X21: ty,X22: uni,X23: uni] : ( nil(tuple2(X21,a1)) != combine(a1,X21,cons(X21,X22,X23),t2tb3(sK0)) )
| ~ spl11_33
| ~ spl11_235 ),
inference(superposition,[],[f3212,f385]) ).
tff(f6602,plain,
( spl11_330
| ~ spl11_38
| ~ spl11_235 ),
inference(avatar_split_clause,[],[f3460,f3211,f408,f6600]) ).
tff(f6600,plain,
( spl11_330
<=> ! [X25: uni,X24: ty,X26: uni] : ( nil(tuple2(a1,X24)) != combine(X24,a1,t2tb3(sK5),cons(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_330])]) ).
tff(f3460,plain,
( ! [X26: uni,X24: ty,X25: uni] : ( nil(tuple2(a1,X24)) != combine(X24,a1,t2tb3(sK5),cons(X24,X25,X26)) )
| ~ spl11_38
| ~ spl11_235 ),
inference(superposition,[],[f3212,f410]) ).
tff(f6598,plain,
( spl11_329
| ~ spl11_33
| ~ spl11_235 ),
inference(avatar_split_clause,[],[f3459,f3211,f383,f6596]) ).
tff(f6596,plain,
( spl11_329
<=> ! [X22: uni,X21: ty,X23: uni] : ( nil(tuple2(a1,X21)) != combine(X21,a1,t2tb3(sK0),cons(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_329])]) ).
tff(f3459,plain,
( ! [X21: ty,X22: uni,X23: uni] : ( nil(tuple2(a1,X21)) != combine(X21,a1,t2tb3(sK0),cons(X21,X22,X23)) )
| ~ spl11_33
| ~ spl11_235 ),
inference(superposition,[],[f3212,f385]) ).
tff(f6594,plain,
( spl11_328
| ~ spl11_38
| ~ spl11_221 ),
inference(avatar_split_clause,[],[f3162,f2937,f408,f6592]) ).
tff(f6592,plain,
( spl11_328
<=> ! [X16: uni] :
( mem(a1,X16,reverse(a1,t2tb3(sK5)))
| ~ mem(a1,X16,reverse(a1,t2tb3(sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_328])]) ).
tff(f2937,plain,
( spl11_221
<=> ! [X18: uni,X17: uni,X16: ty,X19: uni] :
( mem(X16,X19,reverse(X16,cons(X16,X18,X17)))
| ~ mem(X16,X19,reverse(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_221])]) ).
tff(f3162,plain,
( ! [X16: uni] :
( mem(a1,X16,reverse(a1,t2tb3(sK5)))
| ~ mem(a1,X16,reverse(a1,t2tb3(sK7))) )
| ~ spl11_38
| ~ spl11_221 ),
inference(superposition,[],[f2938,f410]) ).
tff(f2938,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: uni] :
( mem(X16,X19,reverse(X16,cons(X16,X18,X17)))
| ~ mem(X16,X19,reverse(X16,X17)) )
| ~ spl11_221 ),
inference(avatar_component_clause,[],[f2937]) ).
tff(f6590,plain,
( spl11_327
| ~ spl11_33
| ~ spl11_221 ),
inference(avatar_split_clause,[],[f3161,f2937,f383,f6588]) ).
tff(f6588,plain,
( spl11_327
<=> ! [X15: uni] :
( mem(a1,X15,reverse(a1,t2tb3(sK0)))
| ~ mem(a1,X15,reverse(a1,t2tb3(sK3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_327])]) ).
tff(f3161,plain,
( ! [X15: uni] :
( mem(a1,X15,reverse(a1,t2tb3(sK0)))
| ~ mem(a1,X15,reverse(a1,t2tb3(sK3))) )
| ~ spl11_33
| ~ spl11_221 ),
inference(superposition,[],[f2938,f385]) ).
tff(f6569,plain,
( spl11_326
| ~ spl11_174
| ~ spl11_252 ),
inference(avatar_split_clause,[],[f4015,f3528,f2017,f6567]) ).
tff(f6567,plain,
( spl11_326
<=> ! [X2: uni] : ( nil(a1) != reverse(a1,cons(a1,X2,reverse(a1,t2tb3(sK5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_326])]) ).
tff(f2017,plain,
( spl11_174
<=> ! [X16: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK5),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_174])]) ).
tff(f3528,plain,
( spl11_252
<=> ! [X2: ty,X3: uni,X4: uni] : ( reverse(X2,cons(X2,X4,reverse(X2,X3))) = infix_plpl(X2,X3,cons(X2,X4,nil(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_252])]) ).
tff(f4015,plain,
( ! [X2: uni] : ( nil(a1) != reverse(a1,cons(a1,X2,reverse(a1,t2tb3(sK5)))) )
| ~ spl11_174
| ~ spl11_252 ),
inference(superposition,[],[f2018,f3529]) ).
tff(f3529,plain,
( ! [X2: ty,X3: uni,X4: uni] : ( reverse(X2,cons(X2,X4,reverse(X2,X3))) = infix_plpl(X2,X3,cons(X2,X4,nil(X2))) )
| ~ spl11_252 ),
inference(avatar_component_clause,[],[f3528]) ).
tff(f2018,plain,
( ! [X16: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK5),X16) )
| ~ spl11_174 ),
inference(avatar_component_clause,[],[f2017]) ).
tff(f6470,plain,
( spl11_325
| ~ spl11_38
| ~ spl11_220 ),
inference(avatar_split_clause,[],[f3149,f2933,f408,f6468]) ).
tff(f6468,plain,
( spl11_325
<=> ! [X20: lpa1cm_a1rp,X21: uni] : ( t2tb2(X20) = match_list(tuple2(a1,a1),a1,t2tb3(sK5),X21,t2tb2(X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_325])]) ).
tff(f2933,plain,
( spl11_220
<=> ! [X44: uni,X43: uni,X42: ty,X46: lpa1cm_a1rp,X45: uni] : ( t2tb2(X46) = match_list(tuple2(a1,a1),X42,cons(X42,X43,X44),X45,t2tb2(X46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_220])]) ).
tff(f3149,plain,
( ! [X21: uni,X20: lpa1cm_a1rp] : ( t2tb2(X20) = match_list(tuple2(a1,a1),a1,t2tb3(sK5),X21,t2tb2(X20)) )
| ~ spl11_38
| ~ spl11_220 ),
inference(superposition,[],[f2934,f410]) ).
tff(f2934,plain,
( ! [X46: lpa1cm_a1rp,X44: uni,X45: uni,X42: ty,X43: uni] : ( t2tb2(X46) = match_list(tuple2(a1,a1),X42,cons(X42,X43,X44),X45,t2tb2(X46)) )
| ~ spl11_220 ),
inference(avatar_component_clause,[],[f2933]) ).
tff(f6466,plain,
( spl11_324
| ~ spl11_33
| ~ spl11_220 ),
inference(avatar_split_clause,[],[f3148,f2933,f383,f6464]) ).
tff(f6464,plain,
( spl11_324
<=> ! [X18: lpa1cm_a1rp,X19: uni] : ( t2tb2(X18) = match_list(tuple2(a1,a1),a1,t2tb3(sK0),X19,t2tb2(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_324])]) ).
tff(f3148,plain,
( ! [X18: lpa1cm_a1rp,X19: uni] : ( t2tb2(X18) = match_list(tuple2(a1,a1),a1,t2tb3(sK0),X19,t2tb2(X18)) )
| ~ spl11_33
| ~ spl11_220 ),
inference(superposition,[],[f2934,f385]) ).
tff(f6462,plain,
( spl11_323
| ~ spl11_38
| ~ spl11_219 ),
inference(avatar_split_clause,[],[f3134,f2929,f408,f6460]) ).
tff(f6460,plain,
( spl11_323
<=> ! [X25: uni,X24: ty,X26: uni] : ( cons_proj_1(X24,X25) = match_list(X24,a1,t2tb3(sK5),X26,cons_proj_1(X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_323])]) ).
tff(f2929,plain,
( spl11_219
<=> ! [X24: uni,X23: ty,X27: uni,X25: uni,X22: ty,X26: uni] : ( cons_proj_1(X22,X27) = match_list(X22,X23,cons(X23,X24,X25),X26,cons_proj_1(X22,X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_219])]) ).
tff(f3134,plain,
( ! [X26: uni,X24: ty,X25: uni] : ( cons_proj_1(X24,X25) = match_list(X24,a1,t2tb3(sK5),X26,cons_proj_1(X24,X25)) )
| ~ spl11_38
| ~ spl11_219 ),
inference(superposition,[],[f2930,f410]) ).
tff(f2930,plain,
( ! [X26: uni,X27: uni,X24: uni,X22: ty,X25: uni,X23: ty] : ( cons_proj_1(X22,X27) = match_list(X22,X23,cons(X23,X24,X25),X26,cons_proj_1(X22,X27)) )
| ~ spl11_219 ),
inference(avatar_component_clause,[],[f2929]) ).
tff(f6458,plain,
( spl11_322
| ~ spl11_33
| ~ spl11_219 ),
inference(avatar_split_clause,[],[f3133,f2929,f383,f6456]) ).
tff(f6456,plain,
( spl11_322
<=> ! [X22: uni,X21: ty,X23: uni] : ( cons_proj_1(X21,X22) = match_list(X21,a1,t2tb3(sK0),X23,cons_proj_1(X21,X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_322])]) ).
tff(f3133,plain,
( ! [X21: ty,X22: uni,X23: uni] : ( cons_proj_1(X21,X22) = match_list(X21,a1,t2tb3(sK0),X23,cons_proj_1(X21,X22)) )
| ~ spl11_33
| ~ spl11_219 ),
inference(superposition,[],[f2930,f385]) ).
tff(f6454,plain,
( spl11_321
| ~ spl11_167
| ~ spl11_252 ),
inference(avatar_split_clause,[],[f4014,f3528,f1973,f6452]) ).
tff(f6452,plain,
( spl11_321
<=> ! [X1: uni] : ( nil(a1) != reverse(a1,cons(a1,X1,reverse(a1,t2tb3(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_321])]) ).
tff(f1973,plain,
( spl11_167
<=> ! [X15: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK0),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_167])]) ).
tff(f4014,plain,
( ! [X1: uni] : ( nil(a1) != reverse(a1,cons(a1,X1,reverse(a1,t2tb3(sK0)))) )
| ~ spl11_167
| ~ spl11_252 ),
inference(superposition,[],[f1974,f3529]) ).
tff(f1974,plain,
( ! [X15: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK0),X15) )
| ~ spl11_167 ),
inference(avatar_component_clause,[],[f1973]) ).
tff(f6450,plain,
( spl11_320
| ~ spl11_47
| ~ spl11_206 ),
inference(avatar_split_clause,[],[f2867,f2547,f445,f6448]) ).
tff(f6448,plain,
( spl11_320
<=> ! [X30: uni,X31: uni] :
( mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK1)))
| ~ mem(a1,X30,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_320])]) ).
tff(f2547,plain,
( spl11_206
<=> ! [X10: uni,X11: uni,X12: uni,X9: uni,X8: ty] :
( mem(X8,X12,infix_plpl(X8,X9,infix_plpl(X8,X10,X11)))
| ~ mem(X8,X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_206])]) ).
tff(f2867,plain,
( ! [X31: uni,X30: uni] :
( mem(a1,X30,infix_plpl(a1,X31,t2tb3(sK1)))
| ~ mem(a1,X30,t2tb3(sK5)) )
| ~ spl11_47
| ~ spl11_206 ),
inference(superposition,[],[f2548,f447]) ).
tff(f2548,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: uni,X12: uni] :
( mem(X8,X12,infix_plpl(X8,X9,infix_plpl(X8,X10,X11)))
| ~ mem(X8,X12,X11) )
| ~ spl11_206 ),
inference(avatar_component_clause,[],[f2547]) ).
tff(f6446,plain,
( spl11_319
| ~ spl11_38
| ~ spl11_205 ),
inference(avatar_split_clause,[],[f2851,f2543,f408,f6444]) ).
tff(f6444,plain,
( spl11_319
<=> ! [X16: uni] : ( infix_plpl(a1,t2tb3(sK7),X16) = cons_proj_2(a1,infix_plpl(a1,t2tb3(sK5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_319])]) ).
tff(f2543,plain,
( spl11_205
<=> ! [X10: uni,X11: uni,X12: uni,X9: ty] : ( infix_plpl(X9,X11,X12) = cons_proj_2(X9,infix_plpl(X9,cons(X9,X10,X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_205])]) ).
tff(f2851,plain,
( ! [X16: uni] : ( infix_plpl(a1,t2tb3(sK7),X16) = cons_proj_2(a1,infix_plpl(a1,t2tb3(sK5),X16)) )
| ~ spl11_38
| ~ spl11_205 ),
inference(superposition,[],[f2544,f410]) ).
tff(f2544,plain,
( ! [X10: uni,X11: uni,X9: ty,X12: uni] : ( infix_plpl(X9,X11,X12) = cons_proj_2(X9,infix_plpl(X9,cons(X9,X10,X11),X12)) )
| ~ spl11_205 ),
inference(avatar_component_clause,[],[f2543]) ).
tff(f6442,plain,
( spl11_318
| ~ spl11_33
| ~ spl11_205 ),
inference(avatar_split_clause,[],[f2850,f2543,f383,f6440]) ).
tff(f6440,plain,
( spl11_318
<=> ! [X15: uni] : ( infix_plpl(a1,t2tb3(sK3),X15) = cons_proj_2(a1,infix_plpl(a1,t2tb3(sK0),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_318])]) ).
tff(f2850,plain,
( ! [X15: uni] : ( infix_plpl(a1,t2tb3(sK3),X15) = cons_proj_2(a1,infix_plpl(a1,t2tb3(sK0),X15)) )
| ~ spl11_33
| ~ spl11_205 ),
inference(superposition,[],[f2544,f385]) ).
tff(f6362,plain,
( spl11_317
| ~ spl11_58
| ~ spl11_112 ),
inference(avatar_split_clause,[],[f1247,f1121,f515,f6360]) ).
tff(f6360,plain,
( spl11_317
<=> ! [X0: $int] :
( ~ $less(X0,length(a1,t2tb3(sK8)))
| $less(X0,length(a1,t2tb3(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_317])]) ).
tff(f1247,plain,
( ! [X0: $int] :
( ~ $less(X0,length(a1,t2tb3(sK8)))
| $less(X0,length(a1,t2tb3(sK0))) )
| ~ spl11_58
| ~ spl11_112 ),
inference(resolution,[],[f1122,f516]) ).
tff(f6358,plain,
( spl11_316
| ~ spl11_38
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f861,f824,f408,f6356]) ).
tff(f6356,plain,
( spl11_316
<=> ! [X1: ty] : ( nil(tuple2(X1,a1)) = combine(a1,X1,nil(X1),t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_316])]) ).
tff(f824,plain,
( spl11_88
<=> ! [X4: uni,X0: ty,X3: uni,X1: ty] : ( nil(tuple2(X0,X1)) = combine(X1,X0,nil(X0),cons(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_88])]) ).
tff(f861,plain,
( ! [X1: ty] : ( nil(tuple2(X1,a1)) = combine(a1,X1,nil(X1),t2tb3(sK5)) )
| ~ spl11_38
| ~ spl11_88 ),
inference(superposition,[],[f825,f410]) ).
tff(f825,plain,
( ! [X3: uni,X0: ty,X1: ty,X4: uni] : ( nil(tuple2(X0,X1)) = combine(X1,X0,nil(X0),cons(X1,X3,X4)) )
| ~ spl11_88 ),
inference(avatar_component_clause,[],[f824]) ).
tff(f6354,plain,
( spl11_315
| ~ spl11_33
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f860,f824,f383,f6352]) ).
tff(f6352,plain,
( spl11_315
<=> ! [X0: ty] : ( nil(tuple2(X0,a1)) = combine(a1,X0,nil(X0),t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_315])]) ).
tff(f860,plain,
( ! [X0: ty] : ( nil(tuple2(X0,a1)) = combine(a1,X0,nil(X0),t2tb3(sK0)) )
| ~ spl11_33
| ~ spl11_88 ),
inference(superposition,[],[f825,f385]) ).
tff(f6288,plain,
( spl11_314
| ~ spl11_101
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1010,f999,f989,f6286]) ).
tff(f6286,plain,
( spl11_314
<=> ! [X44: uni,X41: uni,X40: ty,X42: uni,X45: uni,X43: uni,X39: ty] :
( ~ mem(tuple2(X39,X40),X45,combine(X40,X39,cons(X39,X41,X43),cons(X40,X42,X44)))
| ( tuple21(X39,X40,X41,X42) = X45 )
| mem(tuple2(X39,X40),X45,combine(X40,X39,X43,X44))
| ~ sort(tuple2(X39,X40),tuple21(X39,X40,X41,X42))
| ~ sort(tuple2(X39,X40),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_314])]) ).
tff(f1010,plain,
( ! [X40: ty,X41: uni,X39: ty,X44: uni,X45: uni,X42: uni,X43: uni] :
( ~ mem(tuple2(X39,X40),X45,combine(X40,X39,cons(X39,X41,X43),cons(X40,X42,X44)))
| ( tuple21(X39,X40,X41,X42) = X45 )
| mem(tuple2(X39,X40),X45,combine(X40,X39,X43,X44))
| ~ sort(tuple2(X39,X40),tuple21(X39,X40,X41,X42))
| ~ sort(tuple2(X39,X40),X45) )
| ~ spl11_101
| ~ spl11_102 ),
inference(superposition,[],[f990,f1000]) ).
tff(f6186,plain,
( spl11_313
| ~ spl11_100
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1009,f999,f966,f6184]) ).
tff(f6184,plain,
( spl11_313
<=> ! [X38: uni,X34: uni,X36: uni,X33: ty,X35: uni,X32: ty,X37: uni] : ( infix_plpl(tuple2(X32,X33),reverse(tuple2(X32,X33),combine(X33,X32,X36,X37)),cons(tuple2(X32,X33),tuple21(X32,X33,X34,X35),X38)) = infix_plpl(tuple2(X32,X33),reverse(tuple2(X32,X33),combine(X33,X32,cons(X32,X34,X36),cons(X33,X35,X37))),X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_313])]) ).
tff(f1009,plain,
( ! [X38: uni,X36: uni,X37: uni,X34: uni,X35: uni,X32: ty,X33: ty] : ( infix_plpl(tuple2(X32,X33),reverse(tuple2(X32,X33),combine(X33,X32,X36,X37)),cons(tuple2(X32,X33),tuple21(X32,X33,X34,X35),X38)) = infix_plpl(tuple2(X32,X33),reverse(tuple2(X32,X33),combine(X33,X32,cons(X32,X34,X36),cons(X33,X35,X37))),X38) )
| ~ spl11_100
| ~ spl11_102 ),
inference(superposition,[],[f967,f1000]) ).
tff(f6157,plain,
( spl11_312
| ~ spl11_97
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1008,f999,f932,f6155]) ).
tff(f1008,plain,
( ! [X31: uni,X28: uni,X29: uni,X26: ty,X27: uni,X25: ty,X30: uni] :
( mem(tuple2(X25,X26),X31,combine(X26,X25,cons(X25,X27,X29),cons(X26,X28,X30)))
| ~ mem(tuple2(X25,X26),X31,combine(X26,X25,X29,X30))
| ~ sort(tuple2(X25,X26),tuple21(X25,X26,X27,X28))
| ~ sort(tuple2(X25,X26),X31) )
| ~ spl11_97
| ~ spl11_102 ),
inference(superposition,[],[f933,f1000]) ).
tff(f6091,plain,
( spl11_311
| ~ spl11_97
| ~ spl11_99 ),
inference(avatar_split_clause,[],[f972,f962,f932,f6089]) ).
tff(f6089,plain,
( spl11_311
<=> ! [X11: ty,X13: uni,X14: uni,X12: uni] :
( ( cons(X11,X13,X14) = infix_plpl(X11,sK9(X11,X12,cons(X11,X13,X14)),cons(X11,X12,sK10(X11,X12,cons(X11,X13,X14)))) )
| ~ mem(X11,X12,X14)
| ~ sort(X11,X13)
| ~ sort(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_311])]) ).
tff(f962,plain,
( spl11_99
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( infix_plpl(X0,sK9(X0,X1,X2),cons(X0,X1,sK10(X0,X1,X2))) = X2 )
| ~ mem(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_99])]) ).
tff(f972,plain,
( ! [X11: ty,X14: uni,X12: uni,X13: uni] :
( ( cons(X11,X13,X14) = infix_plpl(X11,sK9(X11,X12,cons(X11,X13,X14)),cons(X11,X12,sK10(X11,X12,cons(X11,X13,X14)))) )
| ~ mem(X11,X12,X14)
| ~ sort(X11,X13)
| ~ sort(X11,X12) )
| ~ spl11_97
| ~ spl11_99 ),
inference(resolution,[],[f963,f933]) ).
tff(f963,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ mem(X0,X1,X2)
| ( infix_plpl(X0,sK9(X0,X1,X2),cons(X0,X1,sK10(X0,X1,X2))) = X2 ) )
| ~ spl11_99 ),
inference(avatar_component_clause,[],[f962]) ).
tff(f6087,plain,
( spl11_310
| ~ spl11_56
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f956,f949,f492,f6085]) ).
tff(f6085,plain,
( spl11_310
<=> ! [X17: uni,X14: ty,X13: ty,X12: ty,X16: uni,X15: uni] : ( match_list(tuple2(X12,X13),X14,X15,X16,X17) = tuple21(X12,X13,tuple2_proj_1(X12,X13,match_list(tuple2(X12,X13),X14,X15,X16,X17)),tuple2_proj_2(X12,X13,match_list(tuple2(X12,X13),X14,X15,X16,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_310])]) ).
tff(f492,plain,
( spl11_56
<=> ! [X4: uni,X0: ty,X3: uni,X2: uni,X1: ty] : sort(X1,match_list(X1,X0,X2,X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_56])]) ).
tff(f949,plain,
( spl11_98
<=> ! [X2: uni,X0: ty,X1: ty] :
( ( tuple21(X1,X0,tuple2_proj_1(X1,X0,X2),tuple2_proj_2(X1,X0,X2)) = X2 )
| ~ sort(tuple2(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_98])]) ).
tff(f956,plain,
( ! [X16: uni,X14: ty,X17: uni,X15: uni,X12: ty,X13: ty] : ( match_list(tuple2(X12,X13),X14,X15,X16,X17) = tuple21(X12,X13,tuple2_proj_1(X12,X13,match_list(tuple2(X12,X13),X14,X15,X16,X17)),tuple2_proj_2(X12,X13,match_list(tuple2(X12,X13),X14,X15,X16,X17))) )
| ~ spl11_56
| ~ spl11_98 ),
inference(resolution,[],[f950,f493]) ).
tff(f493,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : sort(X1,match_list(X1,X0,X2,X3,X4))
| ~ spl11_56 ),
inference(avatar_component_clause,[],[f492]) ).
tff(f950,plain,
( ! [X2: uni,X0: ty,X1: ty] :
( ~ sort(tuple2(X1,X0),X2)
| ( tuple21(X1,X0,tuple2_proj_1(X1,X0,X2),tuple2_proj_2(X1,X0,X2)) = X2 ) )
| ~ spl11_98 ),
inference(avatar_component_clause,[],[f949]) ).
tff(f6055,plain,
( spl11_309
| ~ spl11_50
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f955,f949,f458,f6053]) ).
tff(f6053,plain,
( spl11_309
<=> ! [X10: uni,X11: uni,X9: bool,X8: ty,X7: ty] : ( match_bool(tuple2(X7,X8),X9,X10,X11) = tuple21(X7,X8,tuple2_proj_1(X7,X8,match_bool(tuple2(X7,X8),X9,X10,X11)),tuple2_proj_2(X7,X8,match_bool(tuple2(X7,X8),X9,X10,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_309])]) ).
tff(f458,plain,
( spl11_50
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool] : sort(X0,match_bool(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_50])]) ).
tff(f955,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: bool,X7: ty] : ( match_bool(tuple2(X7,X8),X9,X10,X11) = tuple21(X7,X8,tuple2_proj_1(X7,X8,match_bool(tuple2(X7,X8),X9,X10,X11)),tuple2_proj_2(X7,X8,match_bool(tuple2(X7,X8),X9,X10,X11))) )
| ~ spl11_50
| ~ spl11_98 ),
inference(resolution,[],[f950,f459]) ).
tff(f459,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: bool] : sort(X0,match_bool(X0,X1,X2,X3))
| ~ spl11_50 ),
inference(avatar_component_clause,[],[f458]) ).
tff(f6031,plain,
( spl11_308
| ~ spl11_88
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1003,f999,f824,f6029]) ).
tff(f1003,plain,
( ! [X10: uni,X8: uni,X6: ty,X9: uni,X7: uni,X5: ty] : ( combine(X5,X6,cons(X6,X9,nil(X6)),cons(X5,X10,cons(X5,X7,X8))) = cons(tuple2(X6,X5),tuple21(X6,X5,X9,X10),nil(tuple2(X6,X5))) )
| ~ spl11_88
| ~ spl11_102 ),
inference(superposition,[],[f1000,f825]) ).
tff(f5920,plain,
( spl11_307
| ~ spl11_77
| ~ spl11_99 ),
inference(avatar_split_clause,[],[f971,f962,f665,f5918]) ).
tff(f5918,plain,
( spl11_307
<=> ! [X10: uni,X7: ty,X9: uni,X8: uni] :
( ( infix_plpl(X7,X9,X10) = infix_plpl(X7,sK9(X7,X8,infix_plpl(X7,X9,X10)),cons(X7,X8,sK10(X7,X8,infix_plpl(X7,X9,X10)))) )
| ~ mem(X7,X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_307])]) ).
tff(f665,plain,
( spl11_77
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_77])]) ).
tff(f971,plain,
( ! [X10: uni,X8: uni,X9: uni,X7: ty] :
( ( infix_plpl(X7,X9,X10) = infix_plpl(X7,sK9(X7,X8,infix_plpl(X7,X9,X10)),cons(X7,X8,sK10(X7,X8,infix_plpl(X7,X9,X10)))) )
| ~ mem(X7,X8,X9) )
| ~ spl11_77
| ~ spl11_99 ),
inference(resolution,[],[f963,f666]) ).
tff(f666,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X2) )
| ~ spl11_77 ),
inference(avatar_component_clause,[],[f665]) ).
tff(f5916,plain,
( spl11_306
| ~ spl11_78
| ~ spl11_99 ),
inference(avatar_split_clause,[],[f970,f962,f669,f5914]) ).
tff(f5914,plain,
( spl11_306
<=> ! [X5: uni,X4: uni,X6: uni,X3: ty] :
( ( infix_plpl(X3,X5,X6) = infix_plpl(X3,sK9(X3,X4,infix_plpl(X3,X5,X6)),cons(X3,X4,sK10(X3,X4,infix_plpl(X3,X5,X6)))) )
| ~ mem(X3,X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_306])]) ).
tff(f669,plain,
( spl11_78
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_78])]) ).
tff(f970,plain,
( ! [X3: ty,X6: uni,X4: uni,X5: uni] :
( ( infix_plpl(X3,X5,X6) = infix_plpl(X3,sK9(X3,X4,infix_plpl(X3,X5,X6)),cons(X3,X4,sK10(X3,X4,infix_plpl(X3,X5,X6)))) )
| ~ mem(X3,X4,X6) )
| ~ spl11_78
| ~ spl11_99 ),
inference(resolution,[],[f963,f670]) ).
tff(f670,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X3) )
| ~ spl11_78 ),
inference(avatar_component_clause,[],[f669]) ).
tff(f5912,plain,
( spl11_305
| ~ spl11_37
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f959,f949,f400,f5910]) ).
tff(f5910,plain,
( spl11_305
<=> ! [X28: uni,X27: ty,X25: ty,X26: ty] : ( tuple2_proj_2(X27,tuple2(X25,X26),X28) = tuple21(X25,X26,tuple2_proj_1(X25,X26,tuple2_proj_2(X27,tuple2(X25,X26),X28)),tuple2_proj_2(X25,X26,tuple2_proj_2(X27,tuple2(X25,X26),X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_305])]) ).
tff(f400,plain,
( spl11_37
<=> ! [X2: uni,X0: ty,X1: ty] : sort(X0,tuple2_proj_2(X1,X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_37])]) ).
tff(f959,plain,
( ! [X28: uni,X26: ty,X27: ty,X25: ty] : ( tuple2_proj_2(X27,tuple2(X25,X26),X28) = tuple21(X25,X26,tuple2_proj_1(X25,X26,tuple2_proj_2(X27,tuple2(X25,X26),X28)),tuple2_proj_2(X25,X26,tuple2_proj_2(X27,tuple2(X25,X26),X28))) )
| ~ spl11_37
| ~ spl11_98 ),
inference(resolution,[],[f950,f401]) ).
tff(f401,plain,
( ! [X2: uni,X0: ty,X1: ty] : sort(X0,tuple2_proj_2(X1,X0,X2))
| ~ spl11_37 ),
inference(avatar_component_clause,[],[f400]) ).
tff(f5908,plain,
( spl11_304
| ~ spl11_36
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f958,f949,f396,f5906]) ).
tff(f5906,plain,
( spl11_304
<=> ! [X24: uni,X21: ty,X23: ty,X22: ty] : ( tuple2_proj_1(tuple2(X21,X22),X23,X24) = tuple21(X21,X22,tuple2_proj_1(X21,X22,tuple2_proj_1(tuple2(X21,X22),X23,X24)),tuple2_proj_2(X21,X22,tuple2_proj_1(tuple2(X21,X22),X23,X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_304])]) ).
tff(f396,plain,
( spl11_36
<=> ! [X2: uni,X0: ty,X1: ty] : sort(X1,tuple2_proj_1(X1,X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_36])]) ).
tff(f958,plain,
( ! [X21: ty,X24: uni,X22: ty,X23: ty] : ( tuple2_proj_1(tuple2(X21,X22),X23,X24) = tuple21(X21,X22,tuple2_proj_1(X21,X22,tuple2_proj_1(tuple2(X21,X22),X23,X24)),tuple2_proj_2(X21,X22,tuple2_proj_1(tuple2(X21,X22),X23,X24))) )
| ~ spl11_36
| ~ spl11_98 ),
inference(resolution,[],[f950,f397]) ).
tff(f397,plain,
( ! [X2: uni,X0: ty,X1: ty] : sort(X1,tuple2_proj_1(X1,X0,X2))
| ~ spl11_36 ),
inference(avatar_component_clause,[],[f396]) ).
tff(f5835,plain,
( spl11_303
| ~ spl11_79
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1006,f999,f722,f5833]) ).
tff(f1006,plain,
( ! [X16: uni,X14: uni,X17: uni,X15: uni,X12: ty,X13: ty] : ( $sum(1,length(tuple2(X12,X13),combine(X13,X12,X16,X17))) = length(tuple2(X12,X13),combine(X13,X12,cons(X12,X14,X16),cons(X13,X15,X17))) )
| ~ spl11_79
| ~ spl11_102 ),
inference(superposition,[],[f723,f1000]) ).
tff(f5831,plain,
( spl11_302
| ~ spl11_86
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f995,f989,f816,f5829]) ).
tff(f5829,plain,
( spl11_302
<=> ! [X4: uni,X2: ty,X3: uni] :
( ~ mem(X2,X4,X3)
| ( cons_proj_1(X2,X3) = X4 )
| mem(X2,X4,cons_proj_2(X2,X3))
| ~ sort(X2,cons_proj_1(X2,X3))
| ~ sort(X2,X4)
| ( nil(X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_302])]) ).
tff(f816,plain,
( spl11_86
<=> ! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_86])]) ).
tff(f995,plain,
( ! [X2: ty,X3: uni,X4: uni] :
( ~ mem(X2,X4,X3)
| ( cons_proj_1(X2,X3) = X4 )
| mem(X2,X4,cons_proj_2(X2,X3))
| ~ sort(X2,cons_proj_1(X2,X3))
| ~ sort(X2,X4)
| ( nil(X2) = X3 ) )
| ~ spl11_86
| ~ spl11_101 ),
inference(superposition,[],[f990,f817]) ).
tff(f817,plain,
( ! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) )
| ~ spl11_86 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f5687,plain,
( spl11_301
| ~ spl11_75
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1002,f999,f657,f5685]) ).
tff(f5685,plain,
( spl11_301
<=> ! [X2: uni,X4: uni,X0: ty,X3: uni,X1: ty] : ( combine(X0,X1,cons(X1,X3,X2),cons(X0,X4,nil(X0))) = cons(tuple2(X1,X0),tuple21(X1,X0,X3,X4),nil(tuple2(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_301])]) ).
tff(f657,plain,
( spl11_75
<=> ! [X2: uni,X0: ty,X1: ty] : ( nil(tuple2(X0,X1)) = combine(X1,X0,X2,nil(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_75])]) ).
tff(f1002,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : ( combine(X0,X1,cons(X1,X3,X2),cons(X0,X4,nil(X0))) = cons(tuple2(X1,X0),tuple21(X1,X0,X3,X4),nil(tuple2(X1,X0))) )
| ~ spl11_75
| ~ spl11_102 ),
inference(superposition,[],[f1000,f658]) ).
tff(f658,plain,
( ! [X2: uni,X0: ty,X1: ty] : ( nil(tuple2(X0,X1)) = combine(X1,X0,X2,nil(X1)) )
| ~ spl11_75 ),
inference(avatar_component_clause,[],[f657]) ).
tff(f5683,plain,
( spl11_300
| ~ spl11_90
| ~ spl11_101 ),
inference(avatar_split_clause,[],[f996,f989,f873,f5681]) ).
tff(f996,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] :
( ~ mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ( X6 = X9 )
| mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) )
| ~ spl11_90
| ~ spl11_101 ),
inference(superposition,[],[f990,f874]) ).
tff(f5303,plain,
( spl11_299
| ~ spl11_38
| ~ spl11_188 ),
inference(avatar_split_clause,[],[f2444,f2074,f408,f5301]) ).
tff(f5301,plain,
( spl11_299
<=> ! [X20: a,X21: uni] : ( t2tb(X20) = match_list(a1,a1,t2tb3(sK5),X21,t2tb(X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_299])]) ).
tff(f2074,plain,
( spl11_188
<=> ! [X55: ty,X59: a,X57: uni,X56: uni,X58: uni] : ( t2tb(X59) = match_list(a1,X55,cons(X55,X56,X57),X58,t2tb(X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_188])]) ).
tff(f2444,plain,
( ! [X21: uni,X20: a] : ( t2tb(X20) = match_list(a1,a1,t2tb3(sK5),X21,t2tb(X20)) )
| ~ spl11_38
| ~ spl11_188 ),
inference(superposition,[],[f2075,f410]) ).
tff(f2075,plain,
( ! [X58: uni,X59: a,X56: uni,X57: uni,X55: ty] : ( t2tb(X59) = match_list(a1,X55,cons(X55,X56,X57),X58,t2tb(X59)) )
| ~ spl11_188 ),
inference(avatar_component_clause,[],[f2074]) ).
tff(f5299,plain,
( spl11_298
| ~ spl11_88
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1007,f999,f824,f5297]) ).
tff(f1007,plain,
( ! [X21: uni,X18: ty,X19: ty,X24: ty,X22: uni,X23: uni,X20: uni] : ( nil(tuple2(X24,tuple2(X18,X19))) = combine(tuple2(X18,X19),X24,nil(X24),combine(X19,X18,cons(X18,X20,X22),cons(X19,X21,X23))) )
| ~ spl11_88
| ~ spl11_102 ),
inference(superposition,[],[f825,f1000]) ).
tff(f5295,plain,
( spl11_297
| ~ spl11_90
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f987,f966,f873,f5293]) ).
tff(f987,plain,
( ! [X21: uni,X18: uni,X19: uni,X17: ty,X20: uni] : ( infix_plpl(X17,cons(X17,X21,reverse(X17,cons(X17,X18,X19))),X20) = infix_plpl(X17,cons(X17,X21,reverse(X17,X19)),cons(X17,X18,X20)) )
| ~ spl11_90
| ~ spl11_100 ),
inference(forward_demodulation,[],[f983,f874]) ).
tff(f983,plain,
( ! [X21: uni,X18: uni,X19: uni,X17: ty,X20: uni] : ( infix_plpl(X17,cons(X17,X21,reverse(X17,cons(X17,X18,X19))),X20) = cons(X17,X21,infix_plpl(X17,reverse(X17,X19),cons(X17,X18,X20))) )
| ~ spl11_90
| ~ spl11_100 ),
inference(superposition,[],[f874,f967]) ).
tff(f5291,plain,
( spl11_296
| ~ spl11_91
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f986,f966,f877,f5289]) ).
tff(f986,plain,
( ! [X16: uni,X14: uni,X15: uni,X12: ty,X13: uni] : ( infix_plpl(X12,reverse(X12,cons(X12,X13,X14)),infix_plpl(X12,X15,X16)) = infix_plpl(X12,reverse(X12,X14),infix_plpl(X12,cons(X12,X13,X15),X16)) )
| ~ spl11_91
| ~ spl11_100 ),
inference(forward_demodulation,[],[f982,f878]) ).
tff(f982,plain,
( ! [X16: uni,X14: uni,X15: uni,X12: ty,X13: uni] : ( infix_plpl(X12,reverse(X12,cons(X12,X13,X14)),infix_plpl(X12,X15,X16)) = infix_plpl(X12,infix_plpl(X12,reverse(X12,X14),cons(X12,X13,X15)),X16) )
| ~ spl11_91
| ~ spl11_100 ),
inference(superposition,[],[f878,f967]) ).
tff(f5287,plain,
( spl11_295
| ~ spl11_92
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f981,f966,f881,f5285]) ).
tff(f981,plain,
( ! [X10: uni,X11: uni,X8: uni,X9: uni,X7: ty] :
( ~ mem(X7,X11,infix_plpl(X7,reverse(X7,X9),cons(X7,X8,X10)))
| mem(X7,X11,reverse(X7,cons(X7,X8,X9)))
| mem(X7,X11,X10) )
| ~ spl11_92
| ~ spl11_100 ),
inference(superposition,[],[f882,f967]) ).
tff(f5283,plain,
( spl11_294
| ~ spl11_90
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f976,f966,f873,f5281]) ).
tff(f976,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] : ( infix_plpl(X5,reverse(X5,infix_plpl(X5,X7,X8)),cons(X5,X6,X9)) = infix_plpl(X5,reverse(X5,infix_plpl(X5,cons(X5,X6,X7),X8)),X9) )
| ~ spl11_90
| ~ spl11_100 ),
inference(superposition,[],[f967,f874]) ).
tff(f5279,plain,
( spl11_293
| ~ spl11_70
| ~ spl11_99 ),
inference(avatar_split_clause,[],[f969,f962,f584,f5277]) ).
tff(f5277,plain,
( spl11_293
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( reverse(X0,X2) = infix_plpl(X0,sK9(X0,X1,reverse(X0,X2)),cons(X0,X1,sK10(X0,X1,reverse(X0,X2)))) )
| ~ mem(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_293])]) ).
tff(f584,plain,
( spl11_70
<=> ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X2,reverse(X0,X1))
| ~ mem(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).
tff(f969,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ( reverse(X0,X2) = infix_plpl(X0,sK9(X0,X1,reverse(X0,X2)),cons(X0,X1,sK10(X0,X1,reverse(X0,X2)))) )
| ~ mem(X0,X1,X2) )
| ~ spl11_70
| ~ spl11_99 ),
inference(resolution,[],[f963,f585]) ).
tff(f585,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X2,reverse(X0,X1))
| ~ mem(X0,X2,X1) )
| ~ spl11_70 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f5275,plain,
( spl11_292
| ~ spl11_27
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f957,f949,f352,f5273]) ).
tff(f5273,plain,
( spl11_292
<=> ! [X20: uni,X18: ty,X19: ty] : ( cons_proj_1(tuple2(X18,X19),X20) = tuple21(X18,X19,tuple2_proj_1(X18,X19,cons_proj_1(tuple2(X18,X19),X20)),tuple2_proj_2(X18,X19,cons_proj_1(tuple2(X18,X19),X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_292])]) ).
tff(f352,plain,
( spl11_27
<=> ! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).
tff(f957,plain,
( ! [X18: ty,X19: ty,X20: uni] : ( cons_proj_1(tuple2(X18,X19),X20) = tuple21(X18,X19,tuple2_proj_1(X18,X19,cons_proj_1(tuple2(X18,X19),X20)),tuple2_proj_2(X18,X19,cons_proj_1(tuple2(X18,X19),X20))) )
| ~ spl11_27
| ~ spl11_98 ),
inference(resolution,[],[f950,f353]) ).
tff(f353,plain,
( ! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1))
| ~ spl11_27 ),
inference(avatar_component_clause,[],[f352]) ).
tff(f5271,plain,
( spl11_291
| ~ spl11_63
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f953,f949,f535,f5269]) ).
tff(f5269,plain,
( spl11_291
<=> ! [X4: uni,X3: uni,X2: ty,X1: ty] : ( tuple21(X1,X2,X3,X4) = tuple21(X1,X2,tuple2_proj_1(X1,X2,tuple21(X1,X2,X3,X4)),tuple2_proj_2(X1,X2,tuple21(X1,X2,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_291])]) ).
tff(f535,plain,
( spl11_63
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] : sort(tuple2(X1,X0),tuple21(X1,X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).
tff(f953,plain,
( ! [X2: ty,X3: uni,X1: ty,X4: uni] : ( tuple21(X1,X2,X3,X4) = tuple21(X1,X2,tuple2_proj_1(X1,X2,tuple21(X1,X2,X3,X4)),tuple2_proj_2(X1,X2,tuple21(X1,X2,X3,X4))) )
| ~ spl11_63
| ~ spl11_98 ),
inference(resolution,[],[f950,f536]) ).
tff(f536,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty] : sort(tuple2(X1,X0),tuple21(X1,X0,X2,X3))
| ~ spl11_63 ),
inference(avatar_component_clause,[],[f535]) ).
tff(f5191,plain,
( spl11_290
| ~ spl11_86
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f975,f966,f816,f5189]) ).
tff(f5189,plain,
( spl11_290
<=> ! [X4: uni,X2: ty,X3: uni] :
( ( infix_plpl(X2,reverse(X2,cons_proj_2(X2,X3)),cons(X2,cons_proj_1(X2,X3),X4)) = infix_plpl(X2,reverse(X2,X3),X4) )
| ( nil(X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_290])]) ).
tff(f975,plain,
( ! [X2: ty,X3: uni,X4: uni] :
( ( infix_plpl(X2,reverse(X2,cons_proj_2(X2,X3)),cons(X2,cons_proj_1(X2,X3),X4)) = infix_plpl(X2,reverse(X2,X3),X4) )
| ( nil(X2) = X3 ) )
| ~ spl11_86
| ~ spl11_100 ),
inference(superposition,[],[f967,f817]) ).
tff(f5187,plain,
( spl11_289
| ~ spl11_33
| ~ spl11_188 ),
inference(avatar_split_clause,[],[f2443,f2074,f383,f5185]) ).
tff(f5185,plain,
( spl11_289
<=> ! [X18: a,X19: uni] : ( t2tb(X18) = match_list(a1,a1,t2tb3(sK0),X19,t2tb(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_289])]) ).
tff(f2443,plain,
( ! [X18: a,X19: uni] : ( t2tb(X18) = match_list(a1,a1,t2tb3(sK0),X19,t2tb(X18)) )
| ~ spl11_33
| ~ spl11_188 ),
inference(superposition,[],[f2075,f385]) ).
tff(f5043,plain,
( spl11_288
| ~ spl11_96
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f977,f966,f928,f5041]) ).
tff(f5041,plain,
( spl11_288
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] : ( reverse(X0,cons(X0,X3,cons(X0,X1,X2))) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,cons(X0,X3,nil(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_288])]) ).
tff(f928,plain,
( spl11_96
<=> ! [X2: uni,X0: ty,X1: uni] : ( reverse(X0,cons(X0,X1,X2)) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,nil(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_96])]) ).
tff(f977,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] : ( reverse(X0,cons(X0,X3,cons(X0,X1,X2))) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,cons(X0,X3,nil(X0)))) )
| ~ spl11_96
| ~ spl11_100 ),
inference(superposition,[],[f967,f929]) ).
tff(f929,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( reverse(X0,cons(X0,X1,X2)) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,nil(X0))) )
| ~ spl11_96 ),
inference(avatar_component_clause,[],[f928]) ).
tff(f5039,plain,
( spl11_287
| ~ spl11_90
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f947,f932,f873,f5037]) ).
tff(f947,plain,
( ! [X8: uni,X6: uni,X9: uni,X7: uni,X5: ty] :
( mem(X5,X9,infix_plpl(X5,cons(X5,X6,X7),X8))
| ~ mem(X5,X9,infix_plpl(X5,X7,X8))
| ~ sort(X5,X6)
| ~ sort(X5,X9) )
| ~ spl11_90
| ~ spl11_97 ),
inference(superposition,[],[f933,f874]) ).
tff(f5035,plain,
( spl11_286
| ~ spl11_90
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f939,f928,f873,f5033]) ).
tff(f5033,plain,
( spl11_286
<=> ! [X10: uni,X11: uni,X9: uni,X8: ty] : ( infix_plpl(X8,cons(X8,X11,reverse(X8,X9)),cons(X8,X10,nil(X8))) = cons(X8,X11,reverse(X8,cons(X8,X10,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_286])]) ).
tff(f939,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: uni] : ( infix_plpl(X8,cons(X8,X11,reverse(X8,X9)),cons(X8,X10,nil(X8))) = cons(X8,X11,reverse(X8,cons(X8,X10,X9))) )
| ~ spl11_90
| ~ spl11_96 ),
inference(superposition,[],[f874,f929]) ).
tff(f4984,plain,
( spl11_285
| ~ spl11_38
| ~ spl11_187 ),
inference(avatar_split_clause,[],[f2438,f2070,f408,f4982]) ).
tff(f4982,plain,
( spl11_285
<=> ! [X20: ty,X21: uni] : ( witness(X20) = match_list(X20,a1,t2tb3(sK5),X21,witness(X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_285])]) ).
tff(f2070,plain,
( spl11_187
<=> ! [X4: uni,X0: ty,X3: uni,X2: uni,X1: ty] : ( witness(X0) = match_list(X0,X1,cons(X1,X2,X3),X4,witness(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_187])]) ).
tff(f2438,plain,
( ! [X21: uni,X20: ty] : ( witness(X20) = match_list(X20,a1,t2tb3(sK5),X21,witness(X20)) )
| ~ spl11_38
| ~ spl11_187 ),
inference(superposition,[],[f2071,f410]) ).
tff(f2071,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : ( witness(X0) = match_list(X0,X1,cons(X1,X2,X3),X4,witness(X0)) )
| ~ spl11_187 ),
inference(avatar_component_clause,[],[f2070]) ).
tff(f4970,plain,
( spl11_284
| ~ spl11_11
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f954,f949,f288,f4968]) ).
tff(f4968,plain,
( spl11_284
<=> ! [X6: ty,X5: ty] : ( witness(tuple2(X5,X6)) = tuple21(X5,X6,tuple2_proj_1(X5,X6,witness(tuple2(X5,X6))),tuple2_proj_2(X5,X6,witness(tuple2(X5,X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_284])]) ).
tff(f288,plain,
( spl11_11
<=> ! [X0: ty] : sort(X0,witness(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
tff(f954,plain,
( ! [X6: ty,X5: ty] : ( witness(tuple2(X5,X6)) = tuple21(X5,X6,tuple2_proj_1(X5,X6,witness(tuple2(X5,X6))),tuple2_proj_2(X5,X6,witness(tuple2(X5,X6)))) )
| ~ spl11_11
| ~ spl11_98 ),
inference(resolution,[],[f950,f289]) ).
tff(f289,plain,
( ! [X0: ty] : sort(X0,witness(X0))
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f288]) ).
tff(f4966,plain,
( spl11_283
| ~ spl11_86
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f946,f932,f816,f4964]) ).
tff(f4964,plain,
( spl11_283
<=> ! [X4: uni,X2: ty,X3: uni] :
( mem(X2,X4,X3)
| ~ mem(X2,X4,cons_proj_2(X2,X3))
| ~ sort(X2,cons_proj_1(X2,X3))
| ~ sort(X2,X4)
| ( nil(X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_283])]) ).
tff(f946,plain,
( ! [X2: ty,X3: uni,X4: uni] :
( mem(X2,X4,X3)
| ~ mem(X2,X4,cons_proj_2(X2,X3))
| ~ sort(X2,cons_proj_1(X2,X3))
| ~ sort(X2,X4)
| ( nil(X2) = X3 ) )
| ~ spl11_86
| ~ spl11_97 ),
inference(superposition,[],[f933,f817]) ).
tff(f4962,plain,
( spl11_282
| ~ spl11_74
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f923,f913,f653,f4960]) ).
tff(f4960,plain,
( spl11_282
<=> ! [X11: $int,X13: $int,X14: $int,X12: $int,X15: $int] :
( ( $product(X11,$product(X12,X13)) != X14 )
| ( $product($product(X11,X12),X15) != X14 )
| ( 0 = $product(X11,X12) )
| ( X13 = X15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_282])]) ).
tff(f653,plain,
( spl11_74
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_74])]) ).
tff(f913,plain,
( spl11_94
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_94])]) ).
tff(f923,plain,
( ! [X11: $int,X14: $int,X15: $int,X12: $int,X13: $int] :
( ( $product(X11,$product(X12,X13)) != X14 )
| ( $product($product(X11,X12),X15) != X14 )
| ( 0 = $product(X11,X12) )
| ( X13 = X15 ) )
| ~ spl11_74
| ~ spl11_94 ),
inference(superposition,[],[f914,f654]) ).
tff(f654,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) )
| ~ spl11_74 ),
inference(avatar_component_clause,[],[f653]) ).
tff(f914,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $product(X0,X3) != X1 )
| ( $product(X0,X2) != X1 )
| ( 0 = X0 )
| ( X2 = X3 ) )
| ~ spl11_94 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f4958,plain,
( spl11_281
| ~ spl11_63
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f813,f761,f535,f4956]) ).
tff(f4956,plain,
( spl11_281
<=> ! [X38: uni,X33: ty,X34: ty,X36: uni,X35: ty,X37: uni] : ( tuple21(X33,X34,X36,X37) = tuple2_proj_1(tuple2(X33,X34),X35,tuple21(tuple2(X33,X34),X35,tuple21(X33,X34,X36,X37),X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_281])]) ).
tff(f761,plain,
( spl11_85
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] :
( ( tuple2_proj_1(X1,X0,tuple21(X1,X0,X2,X3)) = X2 )
| ~ sort(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_85])]) ).
tff(f813,plain,
( ! [X38: uni,X36: uni,X37: uni,X34: ty,X35: ty,X33: ty] : ( tuple21(X33,X34,X36,X37) = tuple2_proj_1(tuple2(X33,X34),X35,tuple21(tuple2(X33,X34),X35,tuple21(X33,X34,X36,X37),X38)) )
| ~ spl11_63
| ~ spl11_85 ),
inference(resolution,[],[f762,f536]) ).
tff(f762,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ~ sort(X1,X2)
| ( tuple2_proj_1(X1,X0,tuple21(X1,X0,X2,X3)) = X2 ) )
| ~ spl11_85 ),
inference(avatar_component_clause,[],[f761]) ).
tff(f4954,plain,
( spl11_280
| ~ spl11_63
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f804,f757,f535,f4952]) ).
tff(f4952,plain,
( spl11_280
<=> ! [X38: uni,X33: ty,X34: ty,X36: uni,X35: ty,X37: uni] : ( tuple21(X34,X35,X37,X38) = tuple2_proj_2(X33,tuple2(X34,X35),tuple21(X33,tuple2(X34,X35),X36,tuple21(X34,X35,X37,X38))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_280])]) ).
tff(f757,plain,
( spl11_84
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] :
( ( tuple2_proj_2(X1,X0,tuple21(X1,X0,X2,X3)) = X3 )
| ~ sort(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_84])]) ).
tff(f804,plain,
( ! [X38: uni,X36: uni,X37: uni,X34: ty,X35: ty,X33: ty] : ( tuple21(X34,X35,X37,X38) = tuple2_proj_2(X33,tuple2(X34,X35),tuple21(X33,tuple2(X34,X35),X36,tuple21(X34,X35,X37,X38))) )
| ~ spl11_63
| ~ spl11_84 ),
inference(resolution,[],[f758,f536]) ).
tff(f758,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ~ sort(X0,X3)
| ( tuple2_proj_2(X1,X0,tuple21(X1,X0,X2,X3)) = X3 ) )
| ~ spl11_84 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f4876,plain,
( spl11_279
| ~ spl11_33
| ~ spl11_187 ),
inference(avatar_split_clause,[],[f2437,f2070,f383,f4874]) ).
tff(f4874,plain,
( spl11_279
<=> ! [X18: ty,X19: uni] : ( witness(X18) = match_list(X18,a1,t2tb3(sK0),X19,witness(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_279])]) ).
tff(f2437,plain,
( ! [X18: ty,X19: uni] : ( witness(X18) = match_list(X18,a1,t2tb3(sK0),X19,witness(X18)) )
| ~ spl11_33
| ~ spl11_187 ),
inference(superposition,[],[f2071,f385]) ).
tff(f4794,plain,
( spl11_278
| ~ spl11_55
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1005,f999,f488,f4792]) ).
tff(f488,plain,
( spl11_55
<=> ! [X2: uni,X0: ty,X1: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_55])]) ).
tff(f1005,plain,
( ! [X10: uni,X11: uni,X8: uni,X6: ty,X9: uni,X7: ty] : ( combine(X7,X6,X10,X11) = cons_proj_2(tuple2(X6,X7),combine(X7,X6,cons(X6,X8,X10),cons(X7,X9,X11))) )
| ~ spl11_55
| ~ spl11_102 ),
inference(superposition,[],[f489,f1000]) ).
tff(f489,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 )
| ~ spl11_55 ),
inference(avatar_component_clause,[],[f488]) ).
tff(f4790,plain,
( spl11_277
| ~ spl11_77
| ~ spl11_100 ),
inference(avatar_split_clause,[],[f985,f966,f665,f4788]) ).
tff(f985,plain,
( ! [X31: uni,X28: uni,X29: uni,X27: ty,X30: uni] :
( mem(X27,X31,infix_plpl(X27,reverse(X27,X29),cons(X27,X28,X30)))
| ~ mem(X27,X31,reverse(X27,cons(X27,X28,X29))) )
| ~ spl11_77
| ~ spl11_100 ),
inference(superposition,[],[f666,f967]) ).
tff(f4786,plain,
( spl11_276
| ~ spl11_91
| ~ spl11_92 ),
inference(avatar_split_clause,[],[f906,f881,f877,f4784]) ).
tff(f906,plain,
( ! [X10: uni,X8: uni,X6: ty,X9: uni,X7: uni] :
( ~ mem(X6,X10,infix_plpl(X6,X7,infix_plpl(X6,X8,X9)))
| mem(X6,X10,infix_plpl(X6,X7,X8))
| mem(X6,X10,X9) )
| ~ spl11_91
| ~ spl11_92 ),
inference(superposition,[],[f882,f878]) ).
tff(f4782,plain,
( spl11_275
| ~ spl11_63
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f870,f828,f535,f4780]) ).
tff(f828,plain,
( spl11_89
<=> ! [X3: uni,X4: uni,X0: ty,X5: uni,X2: uni,X1: ty] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_89])]) ).
tff(f870,plain,
( ! [X50: uni,X51: uni,X48: ty,X49: ty,X47: ty,X54: uni,X52: uni,X53: uni] : ( tuple21(X47,X48,X53,X54) = match_list(tuple2(X47,X48),X49,cons(X49,X50,X51),X52,tuple21(X47,X48,X53,X54)) )
| ~ spl11_63
| ~ spl11_89 ),
inference(resolution,[],[f829,f536]) ).
tff(f829,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] :
( ~ sort(X1,X3)
| ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 ) )
| ~ spl11_89 ),
inference(avatar_component_clause,[],[f828]) ).
tff(f4778,plain,
( spl11_274
| ~ spl11_56
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f865,f828,f492,f4776]) ).
tff(f865,plain,
( ! [X21: uni,X18: ty,X19: uni,X16: uni,X14: ty,X17: uni,X15: uni,X13: ty,X20: uni] : ( match_list(X13,X18,X19,X20,X21) = match_list(X13,X14,cons(X14,X15,X16),X17,match_list(X13,X18,X19,X20,X21)) )
| ~ spl11_56
| ~ spl11_89 ),
inference(resolution,[],[f829,f493]) ).
tff(f4774,plain,
( spl11_273
| ~ spl11_55
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f831,f816,f488,f4772]) ).
tff(f4772,plain,
( spl11_273
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( cons(X0,X1,X2) = cons(X0,cons_proj_1(X0,cons(X0,X1,X2)),X2) )
| ( nil(X0) = cons(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_273])]) ).
tff(f831,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ( cons(X0,X1,X2) = cons(X0,cons_proj_1(X0,cons(X0,X1,X2)),X2) )
| ( nil(X0) = cons(X0,X1,X2) ) )
| ~ spl11_55
| ~ spl11_86 ),
inference(superposition,[],[f817,f489]) ).
tff(f4677,plain,
( spl11_272
| ~ spl11_56
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f808,f761,f492,f4675]) ).
tff(f4675,plain,
( spl11_272
<=> ! [X10: ty,X11: ty,X9: ty,X13: uni,X14: uni,X12: uni,X15: uni] : ( match_list(X9,X11,X12,X13,X14) = tuple2_proj_1(X9,X10,tuple21(X9,X10,match_list(X9,X11,X12,X13,X14),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_272])]) ).
tff(f808,plain,
( ! [X10: ty,X11: ty,X9: ty,X14: uni,X15: uni,X12: uni,X13: uni] : ( match_list(X9,X11,X12,X13,X14) = tuple2_proj_1(X9,X10,tuple21(X9,X10,match_list(X9,X11,X12,X13,X14),X15)) )
| ~ spl11_56
| ~ spl11_85 ),
inference(resolution,[],[f762,f493]) ).
tff(f4673,plain,
( spl11_271
| ~ spl11_56
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f799,f757,f492,f4671]) ).
tff(f4671,plain,
( spl11_271
<=> ! [X10: ty,X11: uni,X9: ty,X13: uni,X14: uni,X12: ty,X15: uni] : ( match_list(X10,X12,X13,X14,X15) = tuple2_proj_2(X9,X10,tuple21(X9,X10,X11,match_list(X10,X12,X13,X14,X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_271])]) ).
tff(f799,plain,
( ! [X10: ty,X11: uni,X9: ty,X14: uni,X15: uni,X12: ty,X13: uni] : ( match_list(X10,X12,X13,X14,X15) = tuple2_proj_2(X9,X10,tuple21(X9,X10,X11,match_list(X10,X12,X13,X14,X15))) )
| ~ spl11_56
| ~ spl11_84 ),
inference(resolution,[],[f758,f493]) ).
tff(f4669,plain,
( spl11_270
| ~ spl11_59
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f783,f748,f519,f4667]) ).
tff(f4667,plain,
( spl11_270
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,X2)
| $less($product(X2,X0),$product(X1,X0))
| ( $product(X1,X0) = $product(X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_270])]) ).
tff(f519,plain,
( spl11_59
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_59])]) ).
tff(f748,plain,
( spl11_82
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_82])]) ).
tff(f783,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,X2)
| $less($product(X2,X0),$product(X1,X0))
| ( $product(X1,X0) = $product(X2,X0) ) )
| ~ spl11_59
| ~ spl11_82 ),
inference(resolution,[],[f749,f520]) ).
tff(f520,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl11_59 ),
inference(avatar_component_clause,[],[f519]) ).
tff(f749,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) )
| ~ spl11_82 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f4665,plain,
( spl11_269
| ~ spl11_63
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f715,f661,f535,f4663]) ).
tff(f4663,plain,
( spl11_269
<=> ! [X26: ty,X29: uni,X27: ty,X28: uni,X30: uni] : ( tuple21(X26,X27,X28,X29) = cons_proj_1(tuple2(X26,X27),cons(tuple2(X26,X27),tuple21(X26,X27,X28,X29),X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_269])]) ).
tff(f715,plain,
( ! [X28: uni,X29: uni,X26: ty,X27: ty,X30: uni] : ( tuple21(X26,X27,X28,X29) = cons_proj_1(tuple2(X26,X27),cons(tuple2(X26,X27),tuple21(X26,X27,X28,X29),X30)) )
| ~ spl11_63
| ~ spl11_76 ),
inference(resolution,[],[f662,f536]) ).
tff(f4476,plain,
( spl11_268
| ~ spl11_50
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f864,f828,f458,f4474]) ).
tff(f864,plain,
( ! [X10: bool,X11: uni,X8: uni,X6: ty,X9: uni,X7: uni,X5: ty,X12: uni] : ( match_bool(X5,X10,X11,X12) = match_list(X5,X6,cons(X6,X7,X8),X9,match_bool(X5,X10,X11,X12)) )
| ~ spl11_50
| ~ spl11_89 ),
inference(resolution,[],[f829,f459]) ).
tff(f4472,plain,
( spl11_267
| ~ spl11_74
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f780,f744,f653,f4470]) ).
tff(f4470,plain,
( spl11_267
<=> ! [X10: $int,X11: $int,X9: $int,X8: $int] : ( $sum($product(X8,$product(X9,X10)),$product(X8,$product(X9,X11))) = $product(X8,$product(X9,$sum(X10,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_267])]) ).
tff(f744,plain,
( spl11_81
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_81])]) ).
tff(f780,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] : ( $sum($product(X8,$product(X9,X10)),$product(X8,$product(X9,X11))) = $product(X8,$product(X9,$sum(X10,X11))) )
| ~ spl11_74
| ~ spl11_81 ),
inference(forward_demodulation,[],[f779,f654]) ).
tff(f779,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] : ( $product($product(X8,X9),$sum(X10,X11)) = $sum($product(X8,$product(X9,X10)),$product(X8,$product(X9,X11))) )
| ~ spl11_74
| ~ spl11_81 ),
inference(forward_demodulation,[],[f767,f654]) ).
tff(f767,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] : ( $product($product(X8,X9),$sum(X10,X11)) = $sum($product(X8,$product(X9,X10)),$product($product(X8,X9),X11)) )
| ~ spl11_74
| ~ spl11_81 ),
inference(superposition,[],[f745,f654]) ).
tff(f745,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) )
| ~ spl11_81 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f4468,plain,
( spl11_266
| ~ spl11_63
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f741,f726,f535,f4466]) ).
tff(f4466,plain,
( spl11_266
<=> ! [X38: uni,X33: ty,X34: ty,X36: uni,X35: ty,X37: uni] : ( tuple21(X33,X34,X36,X37) = match_list(tuple2(X33,X34),X35,nil(X35),tuple21(X33,X34,X36,X37),X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_266])]) ).
tff(f741,plain,
( ! [X38: uni,X36: uni,X37: uni,X34: ty,X35: ty,X33: ty] : ( tuple21(X33,X34,X36,X37) = match_list(tuple2(X33,X34),X35,nil(X35),tuple21(X33,X34,X36,X37),X38) )
| ~ spl11_63
| ~ spl11_80 ),
inference(resolution,[],[f727,f536]) ).
tff(f4464,plain,
( spl11_265
| ~ spl11_56
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f736,f726,f492,f4462]) ).
tff(f4462,plain,
( spl11_265
<=> ! [X10: ty,X11: ty,X9: ty,X13: uni,X14: uni,X12: uni,X15: uni] : ( match_list(X9,X11,X12,X13,X14) = match_list(X9,X10,nil(X10),match_list(X9,X11,X12,X13,X14),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_265])]) ).
tff(f736,plain,
( ! [X10: ty,X11: ty,X9: ty,X14: uni,X15: uni,X12: uni,X13: uni] : ( match_list(X9,X11,X12,X13,X14) = match_list(X9,X10,nil(X10),match_list(X9,X11,X12,X13,X14),X15) )
| ~ spl11_56
| ~ spl11_80 ),
inference(resolution,[],[f727,f493]) ).
tff(f4460,plain,
( spl11_264
| ~ spl11_56
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f616,f567,f492,f4458]) ).
tff(f4458,plain,
( spl11_264
<=> ! [X9: uni,X7: uni,X6: ty,X8: uni] : ( match_list(tuple2(a1,a1),X6,X7,X8,X9) = t2tb2(tb2t2(match_list(tuple2(a1,a1),X6,X7,X8,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_264])]) ).
tff(f567,plain,
( spl11_66
<=> ! [X0: uni] :
( ( t2tb2(tb2t2(X0)) = X0 )
| ~ sort(tuple2(a1,a1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_66])]) ).
tff(f616,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( match_list(tuple2(a1,a1),X6,X7,X8,X9) = t2tb2(tb2t2(match_list(tuple2(a1,a1),X6,X7,X8,X9))) )
| ~ spl11_56
| ~ spl11_66 ),
inference(resolution,[],[f568,f493]) ).
tff(f568,plain,
( ! [X0: uni] :
( ~ sort(tuple2(a1,a1),X0)
| ( t2tb2(tb2t2(X0)) = X0 ) )
| ~ spl11_66 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f4161,plain,
( spl11_262
| ~ spl11_263
| ~ spl11_61
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1091,f1079,f527,f4158,f4154]) ).
tff(f4154,plain,
( spl11_262
<=> ( t2tb3(sK1) = nil(a1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_262])]) ).
tff(f4158,plain,
( spl11_263
<=> ( 0 = length(a1,t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_263])]) ).
tff(f1091,plain,
( ( 0 != length(a1,t2tb3(sK0)) )
| ( t2tb3(sK1) = nil(a1) )
| ~ spl11_61
| ~ spl11_108 ),
inference(superposition,[],[f528,f1081]) ).
tff(f4099,plain,
( spl11_261
| ~ spl11_39
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f859,f820,f722,f649,f413,f4097]) ).
tff(f4095,plain,
( spl11_260
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f855,f820,f722,f649,f4093]) ).
tff(f855,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,cons(X6,X7,X8),X9)) = $sum(1,length(X6,infix_plpl(X6,X8,X9))) )
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(forward_demodulation,[],[f854,f821]) ).
tff(f854,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,cons(X6,X7,X8),X9)) = $sum(1,$sum(length(X6,X8),length(X6,X9))) )
| ~ spl11_73
| ~ spl11_79
| ~ spl11_87 ),
inference(forward_demodulation,[],[f838,f650]) ).
tff(f838,plain,
( ! [X8: uni,X6: ty,X9: uni,X7: uni] : ( length(X6,infix_plpl(X6,cons(X6,X7,X8),X9)) = $sum($sum(1,length(X6,X8)),length(X6,X9)) )
| ~ spl11_79
| ~ spl11_87 ),
inference(superposition,[],[f821,f723]) ).
tff(f4091,plain,
( spl11_259
| ~ spl11_73
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f845,f820,f649,f4089]) ).
tff(f4089,plain,
( spl11_259
<=> ! [X0: ty,X3: $int,X2: uni,X1: uni] : ( $sum(length(X0,X1),$sum(length(X0,X2),X3)) = $sum(length(X0,infix_plpl(X0,X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_259])]) ).
tff(f845,plain,
( ! [X2: uni,X3: $int,X0: ty,X1: uni] : ( $sum(length(X0,X1),$sum(length(X0,X2),X3)) = $sum(length(X0,infix_plpl(X0,X1,X2)),X3) )
| ~ spl11_73
| ~ spl11_87 ),
inference(superposition,[],[f650,f821]) ).
tff(f4087,plain,
( spl11_258
| ~ spl11_50
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f807,f761,f458,f4085]) ).
tff(f4085,plain,
( spl11_258
<=> ! [X5: bool,X3: ty,X4: ty,X7: uni,X6: uni,X8: uni] : ( match_bool(X3,X5,X6,X7) = tuple2_proj_1(X3,X4,tuple21(X3,X4,match_bool(X3,X5,X6,X7),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_258])]) ).
tff(f807,plain,
( ! [X3: ty,X8: uni,X6: uni,X7: uni,X4: ty,X5: bool] : ( match_bool(X3,X5,X6,X7) = tuple2_proj_1(X3,X4,tuple21(X3,X4,match_bool(X3,X5,X6,X7),X8)) )
| ~ spl11_50
| ~ spl11_85 ),
inference(resolution,[],[f762,f459]) ).
tff(f4083,plain,
( spl11_257
| ~ spl11_50
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f798,f757,f458,f4081]) ).
tff(f4081,plain,
( spl11_257
<=> ! [X5: uni,X3: ty,X4: ty,X7: uni,X6: bool,X8: uni] : ( match_bool(X4,X6,X7,X8) = tuple2_proj_2(X3,X4,tuple21(X3,X4,X5,match_bool(X4,X6,X7,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_257])]) ).
tff(f798,plain,
( ! [X3: ty,X8: uni,X6: bool,X7: uni,X4: ty,X5: uni] : ( match_bool(X4,X6,X7,X8) = tuple2_proj_2(X3,X4,tuple21(X3,X4,X5,match_bool(X4,X6,X7,X8))) )
| ~ spl11_50
| ~ spl11_84 ),
inference(resolution,[],[f758,f459]) ).
tff(f4079,plain,
( spl11_256
| ~ spl11_56
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f710,f661,f492,f4077]) ).
tff(f4077,plain,
( spl11_256
<=> ! [X10: uni,X11: uni,X12: uni,X9: uni,X8: ty,X7: ty] : ( match_list(X7,X8,X9,X10,X11) = cons_proj_1(X7,cons(X7,match_list(X7,X8,X9,X10,X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_256])]) ).
tff(f710,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: uni,X7: ty,X12: uni] : ( match_list(X7,X8,X9,X10,X11) = cons_proj_1(X7,cons(X7,match_list(X7,X8,X9,X10,X11),X12)) )
| ~ spl11_56
| ~ spl11_76 ),
inference(resolution,[],[f662,f493]) ).
tff(f4007,plain,
( spl11_255
| ~ spl11_4
| ~ spl11_33
| ~ spl11_79 ),
inference(avatar_split_clause,[],[f733,f722,f383,f254,f4004]) ).
tff(f733,plain,
( ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK8))) )
| ~ spl11_4
| ~ spl11_33
| ~ spl11_79 ),
inference(forward_demodulation,[],[f729,f256]) ).
tff(f729,plain,
( ( length(a1,t2tb3(sK0)) = $sum(1,length(a1,t2tb3(sK3))) )
| ~ spl11_33
| ~ spl11_79 ),
inference(superposition,[],[f723,f385]) ).
tff(f3622,plain,
( spl11_254
| ~ spl11_38
| ~ spl11_79 ),
inference(avatar_split_clause,[],[f730,f722,f408,f3619]) ).
tff(f730,plain,
( ( $sum(1,length(a1,t2tb3(sK7))) = length(a1,t2tb3(sK5)) )
| ~ spl11_38
| ~ spl11_79 ),
inference(superposition,[],[f723,f410]) ).
tff(f3534,plain,
( spl11_253
| ~ spl11_78
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f940,f928,f669,f3532]) ).
tff(f940,plain,
( ! [X14: uni,X15: uni,X12: ty,X13: uni] :
( mem(X12,X15,reverse(X12,cons(X12,X14,X13)))
| ~ mem(X12,X15,cons(X12,X14,nil(X12))) )
| ~ spl11_78
| ~ spl11_96 ),
inference(superposition,[],[f670,f929]) ).
tff(f3530,plain,
( spl11_252
| ~ spl11_43
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f936,f928,f429,f3528]) ).
tff(f936,plain,
( ! [X2: ty,X3: uni,X4: uni] : ( reverse(X2,cons(X2,X4,reverse(X2,X3))) = infix_plpl(X2,X3,cons(X2,X4,nil(X2))) )
| ~ spl11_43
| ~ spl11_96 ),
inference(superposition,[],[f929,f430]) ).
tff(f3526,plain,
( spl11_251
| ~ spl11_77
| ~ spl11_91 ),
inference(avatar_split_clause,[],[f897,f877,f665,f3524]) ).
tff(f897,plain,
( ! [X16: uni,X14: uni,X17: uni,X15: uni,X13: ty] :
( mem(X13,X17,infix_plpl(X13,X14,infix_plpl(X13,X15,X16)))
| ~ mem(X13,X17,infix_plpl(X13,X14,X15)) )
| ~ spl11_77
| ~ spl11_91 ),
inference(superposition,[],[f666,f878]) ).
tff(f3522,plain,
( spl11_250
| ~ spl11_88
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f886,f873,f824,f3520]) ).
tff(f886,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni,X4: ty] : ( nil(tuple2(X4,X0)) = combine(X0,X4,nil(X4),infix_plpl(X0,cons(X0,X1,X2),X3)) )
| ~ spl11_88
| ~ spl11_90 ),
inference(superposition,[],[f825,f874]) ).
tff(f3518,plain,
( spl11_249
| ~ spl11_37
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f868,f828,f400,f3516]) ).
tff(f868,plain,
( ! [X40: ty,X38: uni,X41: uni,X39: uni,X36: ty,X37: uni,X35: ty] : ( tuple2_proj_2(X40,X35,X41) = match_list(X35,X36,cons(X36,X37,X38),X39,tuple2_proj_2(X40,X35,X41)) )
| ~ spl11_37
| ~ spl11_89 ),
inference(resolution,[],[f829,f401]) ).
tff(f3514,plain,
( spl11_248
| ~ spl11_36
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f867,f828,f396,f3512]) ).
tff(f867,plain,
( ! [X31: uni,X28: ty,X29: ty,X34: uni,X32: uni,X30: uni,X33: ty] : ( tuple2_proj_1(X28,X33,X34) = match_list(X28,X29,cons(X29,X30,X31),X32,tuple2_proj_1(X28,X33,X34)) )
| ~ spl11_36
| ~ spl11_89 ),
inference(resolution,[],[f829,f397]) ).
tff(f3510,plain,
( spl11_247
| ~ spl11_65
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f847,f820,f563,f3508]) ).
tff(f847,plain,
( ! [X10: uni,X11: $int,X8: ty,X9: uni] :
( $less(length(X8,infix_plpl(X8,X9,X10)),$sum(X11,length(X8,X10)))
| ~ $less(length(X8,X9),X11) )
| ~ spl11_65
| ~ spl11_87 ),
inference(superposition,[],[f564,f821]) ).
tff(f3506,plain,
( spl11_246
| ~ spl11_65
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f846,f820,f563,f3504]) ).
tff(f846,plain,
( ! [X6: uni,X7: $int,X4: ty,X5: uni] :
( $less($sum(X7,length(X4,X6)),length(X4,infix_plpl(X4,X5,X6)))
| ~ $less(X7,length(X4,X5)) )
| ~ spl11_65
| ~ spl11_87 ),
inference(superposition,[],[f564,f821]) ).
tff(f3502,plain,
( spl11_245
| ~ spl11_74
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f792,f748,f653,f3500]) ).
tff(f3500,plain,
( spl11_245
<=> ! [X10: $int,X11: $int,X9: $int,X8: $int] :
( ~ $less($product(X11,X10),$product(X8,$product(X9,X10)))
| $less(X10,0)
| $less(X11,$product(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_245])]) ).
tff(f792,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] :
( ~ $less($product(X11,X10),$product(X8,$product(X9,X10)))
| $less(X10,0)
| $less(X11,$product(X8,X9)) )
| ~ spl11_74
| ~ spl11_82 ),
inference(superposition,[],[f749,f654]) ).
tff(f3498,plain,
( spl11_244
| ~ spl11_74
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f788,f748,f653,f3496]) ).
tff(f3496,plain,
( spl11_244
<=> ! [X10: $int,X11: $int,X9: $int,X8: $int] :
( ~ $less($product(X8,$product(X9,X10)),$product(X11,X10))
| $less(X10,0)
| $less($product(X8,X9),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_244])]) ).
tff(f788,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] :
( ~ $less($product(X8,$product(X9,X10)),$product(X11,X10))
| $less(X10,0)
| $less($product(X8,X9),X11) )
| ~ spl11_74
| ~ spl11_82 ),
inference(superposition,[],[f749,f654]) ).
tff(f3494,plain,
( spl11_243
| ~ spl11_73
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f774,f744,f649,f3492]) ).
tff(f3492,plain,
( spl11_243
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($product(X0,X1),$sum($product(X0,X2),X3)) = $sum($product(X0,$sum(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_243])]) ).
tff(f774,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,X1),$sum($product(X0,X2),X3)) = $sum($product(X0,$sum(X1,X2)),X3) )
| ~ spl11_73
| ~ spl11_81 ),
inference(superposition,[],[f650,f745]) ).
tff(f3490,plain,
( spl11_242
| ~ spl11_50
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f735,f726,f458,f3488]) ).
tff(f3488,plain,
( spl11_242
<=> ! [X5: bool,X3: ty,X4: ty,X7: uni,X6: uni,X8: uni] : ( match_bool(X3,X5,X6,X7) = match_list(X3,X4,nil(X4),match_bool(X3,X5,X6,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_242])]) ).
tff(f735,plain,
( ! [X3: ty,X8: uni,X6: uni,X7: uni,X4: ty,X5: bool] : ( match_bool(X3,X5,X6,X7) = match_list(X3,X4,nil(X4),match_bool(X3,X5,X6,X7),X8) )
| ~ spl11_50
| ~ spl11_80 ),
inference(resolution,[],[f727,f459]) ).
tff(f3486,plain,
( spl11_241
| ~ spl11_63
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f636,f580,f535,f3484]) ).
tff(f3484,plain,
( spl11_241
<=> ! [X28: uni,X29: uni,X27: ty,X26: ty,X30: uni] : ( tuple21(X26,X27,X29,X30) = match_bool(tuple2(X26,X27),false,X28,tuple21(X26,X27,X29,X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_241])]) ).
tff(f636,plain,
( ! [X28: uni,X29: uni,X26: ty,X27: ty,X30: uni] : ( tuple21(X26,X27,X29,X30) = match_bool(tuple2(X26,X27),false,X28,tuple21(X26,X27,X29,X30)) )
| ~ spl11_63
| ~ spl11_69 ),
inference(resolution,[],[f581,f536]) ).
tff(f3482,plain,
( spl11_240
| ~ spl11_56
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f631,f580,f492,f3480]) ).
tff(f3480,plain,
( spl11_240
<=> ! [X10: uni,X11: uni,X12: uni,X9: ty,X8: uni,X7: ty] : ( match_list(X7,X9,X10,X11,X12) = match_bool(X7,false,X8,match_list(X7,X9,X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_240])]) ).
tff(f631,plain,
( ! [X10: uni,X11: uni,X8: uni,X9: ty,X7: ty,X12: uni] : ( match_list(X7,X9,X10,X11,X12) = match_bool(X7,false,X8,match_list(X7,X9,X10,X11,X12)) )
| ~ spl11_56
| ~ spl11_69 ),
inference(resolution,[],[f581,f493]) ).
tff(f3478,plain,
( spl11_239
| ~ spl11_63
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f627,f571,f535,f3476]) ).
tff(f3476,plain,
( spl11_239
<=> ! [X26: ty,X29: uni,X27: ty,X28: uni,X30: uni] : ( tuple21(X26,X27,X28,X29) = match_bool(tuple2(X26,X27),true,tuple21(X26,X27,X28,X29),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_239])]) ).
tff(f627,plain,
( ! [X28: uni,X29: uni,X26: ty,X27: ty,X30: uni] : ( tuple21(X26,X27,X28,X29) = match_bool(tuple2(X26,X27),true,tuple21(X26,X27,X28,X29),X30) )
| ~ spl11_63
| ~ spl11_67 ),
inference(resolution,[],[f572,f536]) ).
tff(f3473,plain,
( spl11_238
| ~ spl11_56
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f622,f571,f492,f3471]) ).
tff(f3471,plain,
( spl11_238
<=> ! [X10: uni,X11: uni,X12: uni,X9: uni,X8: ty,X7: ty] : ( match_list(X7,X8,X9,X10,X11) = match_bool(X7,true,match_list(X7,X8,X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_238])]) ).
tff(f622,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: uni,X7: ty,X12: uni] : ( match_list(X7,X8,X9,X10,X11) = match_bool(X7,true,match_list(X7,X8,X9,X10,X11),X12) )
| ~ spl11_56
| ~ spl11_67 ),
inference(resolution,[],[f572,f493]) ).
tff(f3469,plain,
( spl11_237
| ~ spl11_50
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f615,f567,f458,f3467]) ).
tff(f3467,plain,
( spl11_237
<=> ! [X4: uni,X5: uni,X3: bool] : ( match_bool(tuple2(a1,a1),X3,X4,X5) = t2tb2(tb2t2(match_bool(tuple2(a1,a1),X3,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_237])]) ).
tff(f615,plain,
( ! [X3: bool,X4: uni,X5: uni] : ( match_bool(tuple2(a1,a1),X3,X4,X5) = t2tb2(tb2t2(match_bool(tuple2(a1,a1),X3,X4,X5))) )
| ~ spl11_50
| ~ spl11_66 ),
inference(resolution,[],[f568,f459]) ).
tff(f3374,plain,
( spl11_236
| ~ spl11_141
| ~ spl11_223 ),
inference(avatar_split_clause,[],[f3188,f2945,f1392,f3371]) ).
tff(f3371,plain,
( spl11_236
<=> mem(a1,t2tb(sK6),t2tb3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_236])]) ).
tff(f1392,plain,
( spl11_141
<=> ! [X3: uni] :
( mem(a1,X3,t2tb3(sK1))
| ~ mem(a1,X3,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_141])]) ).
tff(f2945,plain,
( spl11_223
<=> mem(a1,t2tb(sK6),t2tb3(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_223])]) ).
tff(f3188,plain,
( mem(a1,t2tb(sK6),t2tb3(sK1))
| ~ spl11_141
| ~ spl11_223 ),
inference(resolution,[],[f2947,f1393]) ).
tff(f1393,plain,
( ! [X3: uni] :
( ~ mem(a1,X3,t2tb3(sK5))
| mem(a1,X3,t2tb3(sK1)) )
| ~ spl11_141 ),
inference(avatar_component_clause,[],[f1392]) ).
tff(f2947,plain,
( mem(a1,t2tb(sK6),t2tb3(sK5))
| ~ spl11_223 ),
inference(avatar_component_clause,[],[f2945]) ).
tff(f3213,plain,
( spl11_235
| ~ spl11_46
| ~ spl11_102 ),
inference(avatar_split_clause,[],[f1004,f999,f441,f3211]) ).
tff(f441,plain,
( spl11_46
<=> ! [X2: uni,X0: ty,X1: uni] : ( nil(X0) != cons(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_46])]) ).
tff(f1004,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] : ( nil(tuple2(X0,X1)) != combine(X1,X0,cons(X0,X2,X4),cons(X1,X3,X5)) )
| ~ spl11_46
| ~ spl11_102 ),
inference(superposition,[],[f442,f1000]) ).
tff(f442,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( nil(X0) != cons(X0,X1,X2) )
| ~ spl11_46 ),
inference(avatar_component_clause,[],[f441]) ).
tff(f3209,plain,
( spl11_234
| ~ spl11_30
| ~ spl11_98 ),
inference(avatar_split_clause,[],[f952,f949,f371,f3207]) ).
tff(f3207,plain,
( spl11_234
<=> ! [X0: lpa1cm_a1rp] : ( t2tb2(X0) = tuple21(a1,a1,tuple2_proj_1(a1,a1,t2tb2(X0)),tuple2_proj_2(a1,a1,t2tb2(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_234])]) ).
tff(f371,plain,
( spl11_30
<=> ! [X0: lpa1cm_a1rp] : sort(tuple2(a1,a1),t2tb2(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).
tff(f952,plain,
( ! [X0: lpa1cm_a1rp] : ( t2tb2(X0) = tuple21(a1,a1,tuple2_proj_1(a1,a1,t2tb2(X0)),tuple2_proj_2(a1,a1,t2tb2(X0))) )
| ~ spl11_30
| ~ spl11_98 ),
inference(resolution,[],[f950,f372]) ).
tff(f372,plain,
( ! [X0: lpa1cm_a1rp] : sort(tuple2(a1,a1),t2tb2(X0))
| ~ spl11_30 ),
inference(avatar_component_clause,[],[f371]) ).
tff(f3205,plain,
( spl11_233
| ~ spl11_40
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f921,f913,f417,f3203]) ).
tff(f3203,plain,
( spl11_233
<=> ! [X5: $int,X4: $int,X6: $int,X3: $int] :
( ( $product(X4,X3) != X5 )
| ( $product(X3,X6) != X5 )
| ( 0 = X3 )
| ( X4 = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_233])]) ).
tff(f417,plain,
( spl11_40
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_40])]) ).
tff(f921,plain,
( ! [X3: $int,X6: $int,X4: $int,X5: $int] :
( ( $product(X4,X3) != X5 )
| ( $product(X3,X6) != X5 )
| ( 0 = X3 )
| ( X4 = X6 ) )
| ~ spl11_40
| ~ spl11_94 ),
inference(superposition,[],[f914,f418]) ).
tff(f418,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl11_40 ),
inference(avatar_component_clause,[],[f417]) ).
tff(f3201,plain,
( spl11_232
| ~ spl11_30
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f812,f761,f371,f3199]) ).
tff(f3199,plain,
( spl11_232
<=> ! [X32: uni,X30: ty,X31: lpa1cm_a1rp] : ( t2tb2(X31) = tuple2_proj_1(tuple2(a1,a1),X30,tuple21(tuple2(a1,a1),X30,t2tb2(X31),X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_232])]) ).
tff(f812,plain,
( ! [X31: lpa1cm_a1rp,X32: uni,X30: ty] : ( t2tb2(X31) = tuple2_proj_1(tuple2(a1,a1),X30,tuple21(tuple2(a1,a1),X30,t2tb2(X31),X32)) )
| ~ spl11_30
| ~ spl11_85 ),
inference(resolution,[],[f762,f372]) ).
tff(f3197,plain,
( spl11_231
| ~ spl11_37
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f811,f761,f400,f3195]) ).
tff(f3195,plain,
( spl11_231
<=> ! [X28: uni,X29: uni,X27: ty,X25: ty,X26: ty] : ( tuple2_proj_2(X27,X25,X28) = tuple2_proj_1(X25,X26,tuple21(X25,X26,tuple2_proj_2(X27,X25,X28),X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_231])]) ).
tff(f811,plain,
( ! [X28: uni,X29: uni,X26: ty,X27: ty,X25: ty] : ( tuple2_proj_2(X27,X25,X28) = tuple2_proj_1(X25,X26,tuple21(X25,X26,tuple2_proj_2(X27,X25,X28),X29)) )
| ~ spl11_37
| ~ spl11_85 ),
inference(resolution,[],[f762,f401]) ).
tff(f3193,plain,
( spl11_230
| ~ spl11_36
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f810,f761,f396,f3191]) ).
tff(f3191,plain,
( spl11_230
<=> ! [X24: uni,X20: ty,X21: ty,X23: uni,X22: ty] : ( tuple2_proj_1(X20,X22,X23) = tuple2_proj_1(X20,X21,tuple21(X20,X21,tuple2_proj_1(X20,X22,X23),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_230])]) ).
tff(f810,plain,
( ! [X21: ty,X24: uni,X22: ty,X23: uni,X20: ty] : ( tuple2_proj_1(X20,X22,X23) = tuple2_proj_1(X20,X21,tuple21(X20,X21,tuple2_proj_1(X20,X22,X23),X24)) )
| ~ spl11_36
| ~ spl11_85 ),
inference(resolution,[],[f762,f397]) ).
tff(f3187,plain,
( spl11_229
| ~ spl11_30
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f803,f757,f371,f3185]) ).
tff(f3185,plain,
( spl11_229
<=> ! [X32: lpa1cm_a1rp,X30: ty,X31: uni] : ( t2tb2(X32) = tuple2_proj_2(X30,tuple2(a1,a1),tuple21(X30,tuple2(a1,a1),X31,t2tb2(X32))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_229])]) ).
tff(f803,plain,
( ! [X31: uni,X32: lpa1cm_a1rp,X30: ty] : ( t2tb2(X32) = tuple2_proj_2(X30,tuple2(a1,a1),tuple21(X30,tuple2(a1,a1),X31,t2tb2(X32))) )
| ~ spl11_30
| ~ spl11_84 ),
inference(resolution,[],[f758,f372]) ).
tff(f3183,plain,
( spl11_228
| ~ spl11_37
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f802,f757,f400,f3181]) ).
tff(f3181,plain,
( spl11_228
<=> ! [X29: uni,X27: uni,X25: ty,X28: ty,X26: ty] : ( tuple2_proj_2(X28,X26,X29) = tuple2_proj_2(X25,X26,tuple21(X25,X26,X27,tuple2_proj_2(X28,X26,X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_228])]) ).
tff(f802,plain,
( ! [X28: ty,X29: uni,X26: ty,X27: uni,X25: ty] : ( tuple2_proj_2(X28,X26,X29) = tuple2_proj_2(X25,X26,tuple21(X25,X26,X27,tuple2_proj_2(X28,X26,X29))) )
| ~ spl11_37
| ~ spl11_84 ),
inference(resolution,[],[f758,f401]) ).
tff(f3179,plain,
( spl11_227
| ~ spl11_36
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f801,f757,f396,f3177]) ).
tff(f3177,plain,
( spl11_227
<=> ! [X24: uni,X20: ty,X21: ty,X23: ty,X22: uni] : ( tuple2_proj_1(X21,X23,X24) = tuple2_proj_2(X20,X21,tuple21(X20,X21,X22,tuple2_proj_1(X21,X23,X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_227])]) ).
tff(f801,plain,
( ! [X21: ty,X24: uni,X22: uni,X23: ty,X20: ty] : ( tuple2_proj_1(X21,X23,X24) = tuple2_proj_2(X20,X21,tuple21(X20,X21,X22,tuple2_proj_1(X21,X23,X24))) )
| ~ spl11_36
| ~ spl11_84 ),
inference(resolution,[],[f758,f397]) ).
tff(f3175,plain,
( spl11_226
| ~ spl11_65
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f776,f744,f563,f3173]) ).
tff(f3173,plain,
( spl11_226
<=> ! [X10: $int,X11: $int,X9: $int,X8: $int] :
( $less($product(X8,$sum(X9,X10)),$sum(X11,$product(X8,X10)))
| ~ $less($product(X8,X9),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_226])]) ).
tff(f776,plain,
( ! [X10: $int,X11: $int,X8: $int,X9: $int] :
( $less($product(X8,$sum(X9,X10)),$sum(X11,$product(X8,X10)))
| ~ $less($product(X8,X9),X11) )
| ~ spl11_65
| ~ spl11_81 ),
inference(superposition,[],[f564,f745]) ).
tff(f3171,plain,
( spl11_225
| ~ spl11_65
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f775,f744,f563,f3169]) ).
tff(f3169,plain,
( spl11_225
<=> ! [X5: $int,X4: $int,X7: $int,X6: $int] :
( $less($sum(X7,$product(X4,X6)),$product(X4,$sum(X5,X6)))
| ~ $less(X7,$product(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_225])]) ).
tff(f775,plain,
( ! [X6: $int,X7: $int,X4: $int,X5: $int] :
( $less($sum(X7,$product(X4,X6)),$product(X4,$sum(X5,X6)))
| ~ $less(X7,$product(X4,X5)) )
| ~ spl11_65
| ~ spl11_81 ),
inference(superposition,[],[f564,f745]) ).
tff(f3167,plain,
( spl11_224
| ~ spl11_50
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f709,f661,f458,f3165]) ).
tff(f3165,plain,
( spl11_224
<=> ! [X5: uni,X4: uni,X2: ty,X6: uni,X3: bool] : ( match_bool(X2,X3,X4,X5) = cons_proj_1(X2,cons(X2,match_bool(X2,X3,X4,X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_224])]) ).
tff(f709,plain,
( ! [X2: ty,X3: bool,X6: uni,X4: uni,X5: uni] : ( match_bool(X2,X3,X4,X5) = cons_proj_1(X2,cons(X2,match_bool(X2,X3,X4,X5),X6)) )
| ~ spl11_50
| ~ spl11_76 ),
inference(resolution,[],[f662,f459]) ).
tff(f3128,plain,
( ~ spl11_12
| spl11_222 ),
inference(avatar_contradiction_clause,[],[f3127]) ).
tff(f3127,plain,
( $false
| ~ spl11_12
| spl11_222 ),
inference(resolution,[],[f2943,f293]) ).
tff(f293,plain,
( ! [X0: a] : sort(a1,t2tb(X0))
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f292]) ).
tff(f292,plain,
( spl11_12
<=> ! [X0: a] : sort(a1,t2tb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
tff(f2943,plain,
( ~ sort(a1,t2tb(sK6))
| spl11_222 ),
inference(avatar_component_clause,[],[f2941]) ).
tff(f2948,plain,
( ~ spl11_222
| spl11_223
| ~ spl11_38
| ~ spl11_140 ),
inference(avatar_split_clause,[],[f1489,f1388,f408,f2945,f2941]) ).
tff(f1388,plain,
( spl11_140
<=> ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X1,X2))
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_140])]) ).
tff(f1489,plain,
( mem(a1,t2tb(sK6),t2tb3(sK5))
| ~ sort(a1,t2tb(sK6))
| ~ spl11_38
| ~ spl11_140 ),
inference(superposition,[],[f1389,f410]) ).
tff(f1389,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X1,X2))
| ~ sort(X0,X1) )
| ~ spl11_140 ),
inference(avatar_component_clause,[],[f1388]) ).
tff(f2939,plain,
( spl11_221
| ~ spl11_77
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f941,f928,f665,f2937]) ).
tff(f941,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: uni] :
( mem(X16,X19,reverse(X16,cons(X16,X18,X17)))
| ~ mem(X16,X19,reverse(X16,X17)) )
| ~ spl11_77
| ~ spl11_96 ),
inference(superposition,[],[f666,f929]) ).
tff(f2935,plain,
( spl11_220
| ~ spl11_30
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f869,f828,f371,f2933]) ).
tff(f869,plain,
( ! [X46: lpa1cm_a1rp,X44: uni,X45: uni,X42: ty,X43: uni] : ( t2tb2(X46) = match_list(tuple2(a1,a1),X42,cons(X42,X43,X44),X45,t2tb2(X46)) )
| ~ spl11_30
| ~ spl11_89 ),
inference(resolution,[],[f829,f372]) ).
tff(f2931,plain,
( spl11_219
| ~ spl11_27
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f866,f828,f352,f2929]) ).
tff(f866,plain,
( ! [X26: uni,X27: uni,X24: uni,X22: ty,X25: uni,X23: ty] : ( cons_proj_1(X22,X27) = match_list(X22,X23,cons(X23,X24,X25),X26,cons_proj_1(X22,X27)) )
| ~ spl11_27
| ~ spl11_89 ),
inference(resolution,[],[f829,f353]) ).
tff(f2927,plain,
( spl11_218
| ~ spl11_86
| ~ spl11_88 ),
inference(avatar_split_clause,[],[f862,f824,f816,f2925]) ).
tff(f2925,plain,
( spl11_218
<=> ! [X4: ty,X2: ty,X3: uni] :
( ( nil(tuple2(X4,X2)) = combine(X2,X4,nil(X4),X3) )
| ( nil(X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_218])]) ).
tff(f862,plain,
( ! [X2: ty,X3: uni,X4: ty] :
( ( nil(tuple2(X4,X2)) = combine(X2,X4,nil(X4),X3) )
| ( nil(X2) = X3 ) )
| ~ spl11_86
| ~ spl11_88 ),
inference(superposition,[],[f825,f817]) ).
tff(f2923,plain,
( spl11_217
| ~ spl11_60
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f857,f820,f523,f2921]) ).
tff(f857,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,X5,reverse(X3,X4))) = length(X3,infix_plpl(X3,X5,X4)) )
| ~ spl11_60
| ~ spl11_87 ),
inference(forward_demodulation,[],[f841,f821]) ).
tff(f841,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( length(X3,infix_plpl(X3,X5,reverse(X3,X4))) = $sum(length(X3,X5),length(X3,X4)) )
| ~ spl11_60
| ~ spl11_87 ),
inference(superposition,[],[f821,f524]) ).
tff(f2919,plain,
( spl11_216
| ~ spl11_60
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f853,f820,f523,f2917]) ).
tff(f2915,plain,
( spl11_215
| ~ spl11_79
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f833,f816,f722,f2913]) ).
tff(f2913,plain,
( spl11_215
<=> ! [X0: ty,X1: uni] :
( ( length(X0,X1) = $sum(1,length(X0,cons_proj_2(X0,X1))) )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_215])]) ).
tff(f833,plain,
( ! [X0: ty,X1: uni] :
( ( length(X0,X1) = $sum(1,length(X0,cons_proj_2(X0,X1))) )
| ( nil(X0) = X1 ) )
| ~ spl11_79
| ~ spl11_86 ),
inference(superposition,[],[f723,f817]) ).
tff(f2911,plain,
( spl11_214
| ~ spl11_37
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f739,f726,f400,f2909]) ).
tff(f2909,plain,
( spl11_214
<=> ! [X28: uni,X29: uni,X27: ty,X25: ty,X26: ty] : ( tuple2_proj_2(X27,X25,X28) = match_list(X25,X26,nil(X26),tuple2_proj_2(X27,X25,X28),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_214])]) ).
tff(f739,plain,
( ! [X28: uni,X29: uni,X26: ty,X27: ty,X25: ty] : ( tuple2_proj_2(X27,X25,X28) = match_list(X25,X26,nil(X26),tuple2_proj_2(X27,X25,X28),X29) )
| ~ spl11_37
| ~ spl11_80 ),
inference(resolution,[],[f727,f401]) ).
tff(f2907,plain,
( spl11_213
| ~ spl11_36
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f738,f726,f396,f2905]) ).
tff(f2905,plain,
( spl11_213
<=> ! [X24: uni,X20: ty,X21: ty,X23: uni,X22: ty] : ( tuple2_proj_1(X20,X22,X23) = match_list(X20,X21,nil(X21),tuple2_proj_1(X20,X22,X23),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_213])]) ).
tff(f738,plain,
( ! [X21: ty,X24: uni,X22: ty,X23: uni,X20: ty] : ( tuple2_proj_1(X20,X22,X23) = match_list(X20,X21,nil(X21),tuple2_proj_1(X20,X22,X23),X24) )
| ~ spl11_36
| ~ spl11_80 ),
inference(resolution,[],[f727,f397]) ).
tff(f2903,plain,
( spl11_212
| ~ spl11_50
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f630,f580,f458,f2901]) ).
tff(f2901,plain,
( spl11_212
<=> ! [X5: uni,X3: uni,X4: bool,X6: uni,X2: ty] : ( match_bool(X2,X4,X5,X6) = match_bool(X2,false,X3,match_bool(X2,X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_212])]) ).
tff(f630,plain,
( ! [X2: ty,X3: uni,X6: uni,X4: bool,X5: uni] : ( match_bool(X2,X4,X5,X6) = match_bool(X2,false,X3,match_bool(X2,X4,X5,X6)) )
| ~ spl11_50
| ~ spl11_69 ),
inference(resolution,[],[f581,f459]) ).
tff(f2898,plain,
( spl11_211
| ~ spl11_50
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f621,f571,f458,f2896]) ).
tff(f2896,plain,
( spl11_211
<=> ! [X5: uni,X4: uni,X2: ty,X6: uni,X3: bool] : ( match_bool(X2,X3,X4,X5) = match_bool(X2,true,match_bool(X2,X3,X4,X5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_211])]) ).
tff(f621,plain,
( ! [X2: ty,X3: bool,X6: uni,X4: uni,X5: uni] : ( match_bool(X2,X3,X4,X5) = match_bool(X2,true,match_bool(X2,X3,X4,X5),X6) )
| ~ spl11_50
| ~ spl11_67 ),
inference(resolution,[],[f572,f459]) ).
tff(f2894,plain,
( spl11_210
| ~ spl11_37
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f619,f567,f400,f2892]) ).
tff(f2892,plain,
( spl11_210
<=> ! [X13: ty,X14: uni] : ( tuple2_proj_2(X13,tuple2(a1,a1),X14) = t2tb2(tb2t2(tuple2_proj_2(X13,tuple2(a1,a1),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_210])]) ).
tff(f619,plain,
( ! [X14: uni,X13: ty] : ( tuple2_proj_2(X13,tuple2(a1,a1),X14) = t2tb2(tb2t2(tuple2_proj_2(X13,tuple2(a1,a1),X14))) )
| ~ spl11_37
| ~ spl11_66 ),
inference(resolution,[],[f568,f401]) ).
tff(f2890,plain,
( spl11_209
| ~ spl11_36
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f618,f567,f396,f2888]) ).
tff(f2888,plain,
( spl11_209
<=> ! [X11: ty,X12: uni] : ( tuple2_proj_1(tuple2(a1,a1),X11,X12) = t2tb2(tb2t2(tuple2_proj_1(tuple2(a1,a1),X11,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_209])]) ).
tff(f618,plain,
( ! [X11: ty,X12: uni] : ( tuple2_proj_1(tuple2(a1,a1),X11,X12) = t2tb2(tb2t2(tuple2_proj_1(tuple2(a1,a1),X11,X12))) )
| ~ spl11_36
| ~ spl11_66 ),
inference(resolution,[],[f568,f397]) ).
tff(f2886,plain,
( spl11_208
| ~ spl11_53
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f513,f492,f480,f2884]) ).
tff(f2884,plain,
( spl11_208
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] : ( match_list(a1,X0,X1,X2,X3) = t2tb(tb2t(match_list(a1,X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_208])]) ).
tff(f480,plain,
( spl11_53
<=> ! [X0: uni] :
( ( t2tb(tb2t(X0)) = X0 )
| ~ sort(a1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_53])]) ).
tff(f513,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] : ( match_list(a1,X0,X1,X2,X3) = t2tb(tb2t(match_list(a1,X0,X1,X2,X3))) )
| ~ spl11_53
| ~ spl11_56 ),
inference(resolution,[],[f493,f481]) ).
tff(f481,plain,
( ! [X0: uni] :
( ~ sort(a1,X0)
| ( t2tb(tb2t(X0)) = X0 ) )
| ~ spl11_53 ),
inference(avatar_component_clause,[],[f480]) ).
tff(f2763,plain,
( ~ spl11_12
| spl11_203 ),
inference(avatar_contradiction_clause,[],[f2762]) ).
tff(f2762,plain,
( $false
| ~ spl11_12
| spl11_203 ),
inference(resolution,[],[f2536,f293]) ).
tff(f2536,plain,
( ~ sort(a1,t2tb(sK2))
| spl11_203 ),
inference(avatar_component_clause,[],[f2534]) ).
tff(f2553,plain,
( spl11_207
| ~ spl11_17
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f920,f913,f312,f2551]) ).
tff(f2551,plain,
( spl11_207
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( 0 != X1 )
| ( $product(X0,X2) != X1 )
| ( 0 = X0 )
| ( 0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_207])]) ).
tff(f312,plain,
( spl11_17
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
tff(f920,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( 0 != X1 )
| ( $product(X0,X2) != X1 )
| ( 0 = X0 )
| ( 0 = X2 ) )
| ~ spl11_17
| ~ spl11_94 ),
inference(superposition,[],[f914,f313]) ).
tff(f313,plain,
( ! [X0: $int] : ( 0 = $product(X0,0) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f312]) ).
tff(f2549,plain,
( spl11_206
| ~ spl11_78
| ~ spl11_91 ),
inference(avatar_split_clause,[],[f896,f877,f669,f2547]) ).
tff(f896,plain,
( ! [X10: uni,X11: uni,X8: ty,X9: uni,X12: uni] :
( mem(X8,X12,infix_plpl(X8,X9,infix_plpl(X8,X10,X11)))
| ~ mem(X8,X12,X11) )
| ~ spl11_78
| ~ spl11_91 ),
inference(superposition,[],[f670,f878]) ).
tff(f2545,plain,
( spl11_205
| ~ spl11_55
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f888,f873,f488,f2543]) ).
tff(f888,plain,
( ! [X10: uni,X11: uni,X9: ty,X12: uni] : ( infix_plpl(X9,X11,X12) = cons_proj_2(X9,infix_plpl(X9,cons(X9,X10,X11),X12)) )
| ~ spl11_55
| ~ spl11_90 ),
inference(superposition,[],[f489,f874]) ).
tff(f2541,plain,
( ~ spl11_203
| spl11_204
| ~ spl11_33
| ~ spl11_140 ),
inference(avatar_split_clause,[],[f1488,f1388,f383,f2538,f2534]) ).
tff(f2538,plain,
( spl11_204
<=> mem(a1,t2tb(sK2),t2tb3(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_204])]) ).
tff(f1488,plain,
( mem(a1,t2tb(sK2),t2tb3(sK0))
| ~ sort(a1,t2tb(sK2))
| ~ spl11_33
| ~ spl11_140 ),
inference(superposition,[],[f1389,f385]) ).
tff(f2532,plain,
( spl11_202
| ~ spl11_39
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f843,f820,f413,f2530]) ).
tff(f843,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( $sum(length(X3,X5),length(X3,X4)) = length(X3,infix_plpl(X3,X4,X5)) )
| ~ spl11_39
| ~ spl11_87 ),
inference(superposition,[],[f821,f414]) ).
tff(f2528,plain,
( spl11_201
| ~ spl11_27
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f809,f761,f352,f2526]) ).
tff(f2526,plain,
( spl11_201
<=> ! [X18: uni,X17: ty,X16: ty,X19: uni] : ( cons_proj_1(X16,X18) = tuple2_proj_1(X16,X17,tuple21(X16,X17,cons_proj_1(X16,X18),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_201])]) ).
tff(f809,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: ty] : ( cons_proj_1(X16,X18) = tuple2_proj_1(X16,X17,tuple21(X16,X17,cons_proj_1(X16,X18),X19)) )
| ~ spl11_27
| ~ spl11_85 ),
inference(resolution,[],[f762,f353]) ).
tff(f2524,plain,
( spl11_200
| ~ spl11_27
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f800,f757,f352,f2522]) ).
tff(f2522,plain,
( spl11_200
<=> ! [X18: uni,X17: ty,X16: ty,X19: uni] : ( cons_proj_1(X17,X19) = tuple2_proj_2(X16,X17,tuple21(X16,X17,X18,cons_proj_1(X17,X19))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_200])]) ).
tff(f800,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: ty] : ( cons_proj_1(X17,X19) = tuple2_proj_2(X16,X17,tuple21(X16,X17,X18,cons_proj_1(X17,X19))) )
| ~ spl11_27
| ~ spl11_84 ),
inference(resolution,[],[f758,f353]) ).
tff(f2520,plain,
( spl11_199
| ~ spl11_61
| ~ spl11_79 ),
inference(avatar_split_clause,[],[f731,f722,f527,f2518]) ).
tff(f731,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ( 0 != $sum(1,length(X0,X2)) )
| ( nil(X0) = cons(X0,X1,X2) ) )
| ~ spl11_61
| ~ spl11_79 ),
inference(superposition,[],[f528,f723]) ).
tff(f2516,plain,
( spl11_198
| ~ spl11_30
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f714,f661,f371,f2514]) ).
tff(f2514,plain,
( spl11_198
<=> ! [X25: uni,X24: lpa1cm_a1rp] : ( t2tb2(X24) = cons_proj_1(tuple2(a1,a1),cons(tuple2(a1,a1),t2tb2(X24),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_198])]) ).
tff(f714,plain,
( ! [X24: lpa1cm_a1rp,X25: uni] : ( t2tb2(X24) = cons_proj_1(tuple2(a1,a1),cons(tuple2(a1,a1),t2tb2(X24),X25)) )
| ~ spl11_30
| ~ spl11_76 ),
inference(resolution,[],[f662,f372]) ).
tff(f2512,plain,
( spl11_197
| ~ spl11_37
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f713,f661,f400,f2510]) ).
tff(f2510,plain,
( spl11_197
<=> ! [X20: ty,X21: ty,X23: uni,X22: uni] : ( tuple2_proj_2(X21,X20,X22) = cons_proj_1(X20,cons(X20,tuple2_proj_2(X21,X20,X22),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_197])]) ).
tff(f713,plain,
( ! [X21: ty,X22: uni,X23: uni,X20: ty] : ( tuple2_proj_2(X21,X20,X22) = cons_proj_1(X20,cons(X20,tuple2_proj_2(X21,X20,X22),X23)) )
| ~ spl11_37
| ~ spl11_76 ),
inference(resolution,[],[f662,f401]) ).
tff(f2508,plain,
( spl11_196
| ~ spl11_36
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f712,f661,f396,f2506]) ).
tff(f2506,plain,
( spl11_196
<=> ! [X18: uni,X17: ty,X16: ty,X19: uni] : ( tuple2_proj_1(X16,X17,X18) = cons_proj_1(X16,cons(X16,tuple2_proj_1(X16,X17,X18),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_196])]) ).
tff(f712,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: ty] : ( tuple2_proj_1(X16,X17,X18) = cons_proj_1(X16,cons(X16,tuple2_proj_1(X16,X17,X18),X19)) )
| ~ spl11_36
| ~ spl11_76 ),
inference(resolution,[],[f662,f397]) ).
tff(f2504,plain,
( spl11_195
| ~ spl11_65
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f682,f649,f563,f2502]) ).
tff(f682,plain,
( ! [X8: $int,X6: $int,X9: $int,X7: $int] :
( $less($sum(X6,$sum(X7,X8)),$sum(X9,X8))
| ~ $less($sum(X6,X7),X9) )
| ~ spl11_65
| ~ spl11_73 ),
inference(superposition,[],[f564,f650]) ).
tff(f2500,plain,
( spl11_194
| ~ spl11_65
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f681,f649,f563,f2498]) ).
tff(f681,plain,
( ! [X2: $int,X3: $int,X4: $int,X5: $int] :
( $less($sum(X5,X4),$sum(X2,$sum(X3,X4)))
| ~ $less(X5,$sum(X2,X3)) )
| ~ spl11_65
| ~ spl11_73 ),
inference(superposition,[],[f564,f650]) ).
tff(f2496,plain,
( spl11_193
| ~ spl11_64
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f675,f649,f559,f2494]) ).
tff(f675,plain,
( ! [X10: $int,X8: $int,X9: $int] : ( $sum($uminus(X8),$sum($uminus(X9),X10)) = $sum($uminus($sum(X9,X8)),X10) )
| ~ spl11_64
| ~ spl11_73 ),
inference(superposition,[],[f650,f560]) ).
tff(f2244,plain,
( spl11_192
| ~ spl11_47
| ~ spl11_77 ),
inference(avatar_split_clause,[],[f1016,f665,f445,f2242]) ).
tff(f2242,plain,
( spl11_192
<=> ! [X4: uni] :
( mem(a1,X4,t2tb3(sK1))
| ~ mem(a1,X4,t2tb3(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_192])]) ).
tff(f1016,plain,
( ! [X4: uni] :
( mem(a1,X4,t2tb3(sK1))
| ~ mem(a1,X4,t2tb3(sK8)) )
| ~ spl11_47
| ~ spl11_77 ),
inference(superposition,[],[f666,f447]) ).
tff(f2088,plain,
( spl11_191
| ~ spl11_42
| ~ spl11_45
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f942,f928,f437,f425,f2086]) ).
tff(f942,plain,
( ! [X0: ty,X1: uni] : ( cons(X0,X1,nil(X0)) = reverse(X0,cons(X0,X1,nil(X0))) )
| ~ spl11_42
| ~ spl11_45
| ~ spl11_96 ),
inference(forward_demodulation,[],[f935,f438]) ).
tff(f935,plain,
( ! [X0: ty,X1: uni] : ( reverse(X0,cons(X0,X1,nil(X0))) = infix_plpl(X0,nil(X0),cons(X0,X1,nil(X0))) )
| ~ spl11_42
| ~ spl11_96 ),
inference(superposition,[],[f929,f426]) ).
tff(f2084,plain,
( spl11_190
| ~ spl11_94 ),
inference(avatar_split_clause,[],[f924,f913,f2082]) ).
tff(f2082,plain,
( spl11_190
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X0,X1) != $product(X0,X2) )
| ( 0 = X0 )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_190])]) ).
tff(f924,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X0,X1) != $product(X0,X2) )
| ( 0 = X0 )
| ( X1 = X2 ) )
| ~ spl11_94 ),
inference(equality_resolution,[],[f914]) ).
tff(f2080,plain,
( spl11_189
| ~ spl11_45
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f885,f873,f437,f2078]) ).
tff(f885,plain,
( ! [X3: ty,X4: uni,X5: uni] : ( infix_plpl(X3,cons(X3,X5,nil(X3)),X4) = cons(X3,X5,X4) )
| ~ spl11_45
| ~ spl11_90 ),
inference(superposition,[],[f874,f438]) ).
tff(f2076,plain,
( spl11_188
| ~ spl11_12
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f871,f828,f292,f2074]) ).
tff(f871,plain,
( ! [X58: uni,X59: a,X56: uni,X57: uni,X55: ty] : ( t2tb(X59) = match_list(a1,X55,cons(X55,X56,X57),X58,t2tb(X59)) )
| ~ spl11_12
| ~ spl11_89 ),
inference(resolution,[],[f829,f293]) ).
tff(f2072,plain,
( spl11_187
| ~ spl11_11
| ~ spl11_89 ),
inference(avatar_split_clause,[],[f863,f828,f288,f2070]) ).
tff(f863,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : ( witness(X0) = match_list(X0,X1,cons(X1,X2,X3),X4,witness(X0)) )
| ~ spl11_11
| ~ spl11_89 ),
inference(resolution,[],[f829,f289]) ).
tff(f2068,plain,
( spl11_186
| ~ spl11_40
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f790,f748,f417,f2066]) ).
tff(f2066,plain,
( spl11_186
<=> ! [X2: $int,X4: $int,X3: $int] :
( ~ $less($product(X4,X3),$product(X3,X2))
| $less(X3,0)
| $less(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_186])]) ).
tff(f790,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( ~ $less($product(X4,X3),$product(X3,X2))
| $less(X3,0)
| $less(X4,X2) )
| ~ spl11_40
| ~ spl11_82 ),
inference(superposition,[],[f749,f418]) ).
tff(f2064,plain,
( spl11_185
| ~ spl11_40
| ~ spl11_82 ),
inference(avatar_split_clause,[],[f786,f748,f417,f2062]) ).
tff(f2062,plain,
( spl11_185
<=> ! [X4: $int,X2: $int,X3: $int] :
( ~ $less($product(X3,X2),$product(X4,X3))
| $less(X3,0)
| $less(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_185])]) ).
tff(f786,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( ~ $less($product(X3,X2),$product(X4,X3))
| $less(X3,0)
| $less(X2,X4) )
| ~ spl11_40
| ~ spl11_82 ),
inference(superposition,[],[f749,f418]) ).
tff(f2059,plain,
( spl11_184
| ~ spl11_39
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f772,f744,f413,f2057]) ).
tff(f2057,plain,
( spl11_184
<=> ! [X4: $int,X5: $int,X3: $int] : ( $sum($product(X3,X5),$product(X3,X4)) = $product(X3,$sum(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_184])]) ).
tff(f772,plain,
( ! [X3: $int,X4: $int,X5: $int] : ( $sum($product(X3,X5),$product(X3,X4)) = $product(X3,$sum(X4,X5)) )
| ~ spl11_39
| ~ spl11_81 ),
inference(superposition,[],[f745,f414]) ).
tff(f2055,plain,
( spl11_183
| ~ spl11_40
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f769,f744,f417,f2053]) ).
tff(f2053,plain,
( spl11_183
<=> ! [X2: $int,X4: $int,X3: $int] : ( $product(X2,$sum(X4,X3)) = $sum($product(X2,X4),$product(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_183])]) ).
tff(f769,plain,
( ! [X2: $int,X3: $int,X4: $int] : ( $product(X2,$sum(X4,X3)) = $sum($product(X2,X4),$product(X3,X2)) )
| ~ spl11_40
| ~ spl11_81 ),
inference(superposition,[],[f745,f418]) ).
tff(f2051,plain,
( spl11_182
| ~ spl11_40
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f765,f744,f417,f2049]) ).
tff(f2049,plain,
( spl11_182
<=> ! [X4: $int,X2: $int,X3: $int] : ( $product(X2,$sum(X3,X4)) = $sum($product(X3,X2),$product(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_182])]) ).
tff(f765,plain,
( ! [X2: $int,X3: $int,X4: $int] : ( $product(X2,$sum(X3,X4)) = $sum($product(X3,X2),$product(X2,X4)) )
| ~ spl11_40
| ~ spl11_81 ),
inference(superposition,[],[f745,f418]) ).
tff(f2047,plain,
( spl11_181
| ~ spl11_30
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f740,f726,f371,f2045]) ).
tff(f2045,plain,
( spl11_181
<=> ! [X32: uni,X30: ty,X31: lpa1cm_a1rp] : ( t2tb2(X31) = match_list(tuple2(a1,a1),X30,nil(X30),t2tb2(X31),X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_181])]) ).
tff(f740,plain,
( ! [X31: lpa1cm_a1rp,X32: uni,X30: ty] : ( t2tb2(X31) = match_list(tuple2(a1,a1),X30,nil(X30),t2tb2(X31),X32) )
| ~ spl11_30
| ~ spl11_80 ),
inference(resolution,[],[f727,f372]) ).
tff(f2043,plain,
( spl11_180
| ~ spl11_27
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f737,f726,f352,f2041]) ).
tff(f2041,plain,
( spl11_180
<=> ! [X18: uni,X17: ty,X16: ty,X19: uni] : ( cons_proj_1(X16,X18) = match_list(X16,X17,nil(X17),cons_proj_1(X16,X18),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_180])]) ).
tff(f737,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: ty] : ( cons_proj_1(X16,X18) = match_list(X16,X17,nil(X17),cons_proj_1(X16,X18),X19) )
| ~ spl11_27
| ~ spl11_80 ),
inference(resolution,[],[f727,f353]) ).
tff(f2039,plain,
( spl11_179
| ~ spl11_37
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f634,f580,f400,f2037]) ).
tff(f2037,plain,
( spl11_179
<=> ! [X20: ty,X21: uni,X23: uni,X22: ty] : ( tuple2_proj_2(X22,X20,X23) = match_bool(X20,false,X21,tuple2_proj_2(X22,X20,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_179])]) ).
tff(f634,plain,
( ! [X21: uni,X22: ty,X23: uni,X20: ty] : ( tuple2_proj_2(X22,X20,X23) = match_bool(X20,false,X21,tuple2_proj_2(X22,X20,X23)) )
| ~ spl11_37
| ~ spl11_69 ),
inference(resolution,[],[f581,f401]) ).
tff(f2035,plain,
( spl11_178
| ~ spl11_36
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f633,f580,f396,f2033]) ).
tff(f2033,plain,
( spl11_178
<=> ! [X18: ty,X17: uni,X16: ty,X19: uni] : ( tuple2_proj_1(X16,X18,X19) = match_bool(X16,false,X17,tuple2_proj_1(X16,X18,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_178])]) ).
tff(f633,plain,
( ! [X18: ty,X19: uni,X16: ty,X17: uni] : ( tuple2_proj_1(X16,X18,X19) = match_bool(X16,false,X17,tuple2_proj_1(X16,X18,X19)) )
| ~ spl11_36
| ~ spl11_69 ),
inference(resolution,[],[f581,f397]) ).
tff(f2031,plain,
( spl11_177
| ~ spl11_37
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f625,f571,f400,f2029]) ).
tff(f2029,plain,
( spl11_177
<=> ! [X20: ty,X21: ty,X23: uni,X22: uni] : ( tuple2_proj_2(X21,X20,X22) = match_bool(X20,true,tuple2_proj_2(X21,X20,X22),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_177])]) ).
tff(f625,plain,
( ! [X21: ty,X22: uni,X23: uni,X20: ty] : ( tuple2_proj_2(X21,X20,X22) = match_bool(X20,true,tuple2_proj_2(X21,X20,X22),X23) )
| ~ spl11_37
| ~ spl11_67 ),
inference(resolution,[],[f572,f401]) ).
tff(f2027,plain,
( spl11_176
| ~ spl11_36
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f624,f571,f396,f2025]) ).
tff(f2025,plain,
( spl11_176
<=> ! [X18: uni,X17: ty,X16: ty,X19: uni] : ( tuple2_proj_1(X16,X17,X18) = match_bool(X16,true,tuple2_proj_1(X16,X17,X18),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_176])]) ).
tff(f624,plain,
( ! [X18: uni,X19: uni,X16: ty,X17: ty] : ( tuple2_proj_1(X16,X17,X18) = match_bool(X16,true,tuple2_proj_1(X16,X17,X18),X19) )
| ~ spl11_36
| ~ spl11_67 ),
inference(resolution,[],[f572,f397]) ).
tff(f2023,plain,
( spl11_175
| ~ spl11_27
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f617,f567,f352,f2021]) ).
tff(f2021,plain,
( spl11_175
<=> ! [X10: uni] : ( cons_proj_1(tuple2(a1,a1),X10) = t2tb2(tb2t2(cons_proj_1(tuple2(a1,a1),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_175])]) ).
tff(f617,plain,
( ! [X10: uni] : ( cons_proj_1(tuple2(a1,a1),X10) = t2tb2(tb2t2(cons_proj_1(tuple2(a1,a1),X10))) )
| ~ spl11_27
| ~ spl11_66 ),
inference(resolution,[],[f568,f353]) ).
tff(f2019,plain,
( spl11_174
| ~ spl11_38
| ~ spl11_139 ),
inference(avatar_split_clause,[],[f1481,f1384,f408,f2017]) ).
tff(f1384,plain,
( spl11_139
<=> ! [X13: ty,X14: uni,X16: uni,X15: uni] : ( infix_plpl(X13,cons(X13,X14,X15),X16) != nil(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_139])]) ).
tff(f1481,plain,
( ! [X16: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK5),X16) )
| ~ spl11_38
| ~ spl11_139 ),
inference(superposition,[],[f1385,f410]) ).
tff(f1385,plain,
( ! [X16: uni,X14: uni,X15: uni,X13: ty] : ( infix_plpl(X13,cons(X13,X14,X15),X16) != nil(X13) )
| ~ spl11_139 ),
inference(avatar_component_clause,[],[f1384]) ).
tff(f2015,plain,
( spl11_173
| ~ spl11_63
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f613,f567,f535,f2013]) ).
tff(f2013,plain,
( spl11_173
<=> ! [X2: uni,X1: uni] : ( tuple21(a1,a1,X1,X2) = t2tb2(tb2t2(tuple21(a1,a1,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_173])]) ).
tff(f613,plain,
( ! [X2: uni,X1: uni] : ( tuple21(a1,a1,X1,X2) = t2tb2(tb2t2(tuple21(a1,a1,X1,X2))) )
| ~ spl11_63
| ~ spl11_66 ),
inference(resolution,[],[f568,f536]) ).
tff(f2011,plain,
( spl11_172
| ~ spl11_64
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f611,f563,f559,f2009]) ).
tff(f2009,plain,
( spl11_172
<=> ! [X9: $int,X8: $int,X10: $int] :
( $less($sum(X10,$uminus(X9)),$uminus($sum(X9,X8)))
| ~ $less(X10,$uminus(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_172])]) ).
tff(f611,plain,
( ! [X10: $int,X8: $int,X9: $int] :
( $less($sum(X10,$uminus(X9)),$uminus($sum(X9,X8)))
| ~ $less(X10,$uminus(X8)) )
| ~ spl11_64
| ~ spl11_65 ),
inference(superposition,[],[f564,f560]) ).
tff(f2007,plain,
( spl11_171
| ~ spl11_64
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f607,f563,f559,f2005]) ).
tff(f2005,plain,
( spl11_171
<=> ! [X9: $int,X8: $int,X10: $int] :
( $less($uminus($sum(X9,X8)),$sum(X10,$uminus(X9)))
| ~ $less($uminus(X8),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_171])]) ).
tff(f607,plain,
( ! [X10: $int,X8: $int,X9: $int] :
( $less($uminus($sum(X9,X8)),$sum(X10,$uminus(X9)))
| ~ $less($uminus(X8),X10) )
| ~ spl11_64
| ~ spl11_65 ),
inference(superposition,[],[f564,f560]) ).
tff(f2003,plain,
( spl11_170
| ~ spl11_58
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f603,f563,f515,f2001]) ).
tff(f2001,plain,
( spl11_170
<=> ! [X5: $int,X4: $int,X6: $int,X3: $int] :
( ~ $less(X3,X4)
| ~ $less(X5,$sum(X3,X6))
| $less(X5,$sum(X4,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_170])]) ).
tff(f603,plain,
( ! [X3: $int,X6: $int,X4: $int,X5: $int] :
( ~ $less(X3,X4)
| ~ $less(X5,$sum(X3,X6))
| $less(X5,$sum(X4,X6)) )
| ~ spl11_58
| ~ spl11_65 ),
inference(resolution,[],[f564,f516]) ).
tff(f1999,plain,
( spl11_169
| ~ spl11_52
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f544,f519,f476,f1997]) ).
tff(f1997,plain,
( spl11_169
<=> ! [X6: $int,X7: $int] :
( $less($sum(X7,1),X6)
| ( $sum(X7,1) = X6 )
| ~ $less(X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_169])]) ).
tff(f476,plain,
( spl11_52
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_52])]) ).
tff(f544,plain,
( ! [X6: $int,X7: $int] :
( $less($sum(X7,1),X6)
| ( $sum(X7,1) = X6 )
| ~ $less(X7,X6) )
| ~ spl11_52
| ~ spl11_59 ),
inference(resolution,[],[f520,f477]) ).
tff(f477,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl11_52 ),
inference(avatar_component_clause,[],[f476]) ).
tff(f1995,plain,
( spl11_168
| ~ spl11_50
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f508,f480,f458,f1993]) ).
tff(f1993,plain,
( spl11_168
<=> ! [X2: uni,X1: bool,X3: uni] : ( match_bool(a1,X1,X2,X3) = t2tb(tb2t(match_bool(a1,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_168])]) ).
tff(f508,plain,
( ! [X2: uni,X3: uni,X1: bool] : ( match_bool(a1,X1,X2,X3) = t2tb(tb2t(match_bool(a1,X1,X2,X3))) )
| ~ spl11_50
| ~ spl11_53 ),
inference(resolution,[],[f481,f459]) ).
tff(f1975,plain,
( spl11_167
| ~ spl11_33
| ~ spl11_139 ),
inference(avatar_split_clause,[],[f1480,f1384,f383,f1973]) ).
tff(f1480,plain,
( ! [X15: uni] : ( nil(a1) != infix_plpl(a1,t2tb3(sK0),X15) )
| ~ spl11_33
| ~ spl11_139 ),
inference(superposition,[],[f1385,f385]) ).
tff(f1903,plain,
( spl11_166
| ~ spl11_12
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f814,f761,f292,f1901]) ).
tff(f1901,plain,
( spl11_166
<=> ! [X41: uni,X40: a,X39: ty] : ( t2tb(X40) = tuple2_proj_1(a1,X39,tuple21(a1,X39,t2tb(X40),X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_166])]) ).
tff(f814,plain,
( ! [X40: a,X41: uni,X39: ty] : ( t2tb(X40) = tuple2_proj_1(a1,X39,tuple21(a1,X39,t2tb(X40),X41)) )
| ~ spl11_12
| ~ spl11_85 ),
inference(resolution,[],[f762,f293]) ).
tff(f1899,plain,
( spl11_165
| ~ spl11_11
| ~ spl11_85 ),
inference(avatar_split_clause,[],[f806,f761,f288,f1897]) ).
tff(f1897,plain,
( spl11_165
<=> ! [X2: uni,X0: ty,X1: ty] : ( witness(X0) = tuple2_proj_1(X0,X1,tuple21(X0,X1,witness(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_165])]) ).
tff(f806,plain,
( ! [X2: uni,X0: ty,X1: ty] : ( witness(X0) = tuple2_proj_1(X0,X1,tuple21(X0,X1,witness(X0),X2)) )
| ~ spl11_11
| ~ spl11_85 ),
inference(resolution,[],[f762,f289]) ).
tff(f1895,plain,
( spl11_164
| ~ spl11_12
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f805,f757,f292,f1893]) ).
tff(f1893,plain,
( spl11_164
<=> ! [X41: a,X40: uni,X39: ty] : ( t2tb(X41) = tuple2_proj_2(X39,a1,tuple21(X39,a1,X40,t2tb(X41))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_164])]) ).
tff(f805,plain,
( ! [X40: uni,X41: a,X39: ty] : ( t2tb(X41) = tuple2_proj_2(X39,a1,tuple21(X39,a1,X40,t2tb(X41))) )
| ~ spl11_12
| ~ spl11_84 ),
inference(resolution,[],[f758,f293]) ).
tff(f1891,plain,
( spl11_163
| ~ spl11_11
| ~ spl11_84 ),
inference(avatar_split_clause,[],[f797,f757,f288,f1889]) ).
tff(f1889,plain,
( spl11_163
<=> ! [X2: uni,X0: ty,X1: ty] : ( witness(X1) = tuple2_proj_2(X0,X1,tuple21(X0,X1,X2,witness(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_163])]) ).
tff(f797,plain,
( ! [X2: uni,X0: ty,X1: ty] : ( witness(X1) = tuple2_proj_2(X0,X1,tuple21(X0,X1,X2,witness(X1))) )
| ~ spl11_11
| ~ spl11_84 ),
inference(resolution,[],[f758,f289]) ).
tff(f1887,plain,
( spl11_162
| ~ spl11_27
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f711,f661,f352,f1885]) ).
tff(f1885,plain,
( spl11_162
<=> ! [X13: ty,X14: uni,X15: uni] : ( cons_proj_1(X13,X14) = cons_proj_1(X13,cons(X13,cons_proj_1(X13,X14),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_162])]) ).
tff(f711,plain,
( ! [X14: uni,X15: uni,X13: ty] : ( cons_proj_1(X13,X14) = cons_proj_1(X13,cons(X13,cons_proj_1(X13,X14),X15)) )
| ~ spl11_27
| ~ spl11_76 ),
inference(resolution,[],[f662,f353]) ).
tff(f1883,plain,
( spl11_161
| ~ spl11_51
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f686,f649,f472,f1881]) ).
tff(f472,plain,
( spl11_51
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_51])]) ).
tff(f686,plain,
( ! [X21: $int,X19: $int,X20: $int] :
( $less(X21,$sum(X19,$sum(X20,1)))
| $less($sum(X19,X20),X21) )
| ~ spl11_51
| ~ spl11_73 ),
inference(superposition,[],[f473,f650]) ).
tff(f473,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl11_51 ),
inference(avatar_component_clause,[],[f472]) ).
tff(f1873,plain,
( spl11_160
| ~ spl11_52
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f685,f649,f476,f1871]) ).
tff(f685,plain,
( ! [X18: $int,X16: $int,X17: $int] :
( ~ $less(X18,$sum(X16,$sum(X17,1)))
| ~ $less($sum(X16,X17),X18) )
| ~ spl11_52
| ~ spl11_73 ),
inference(superposition,[],[f477,f650]) ).
tff(f1869,plain,
( spl11_159
| ~ spl11_58
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f540,f519,f515,f1867]) ).
tff(f540,plain,
( ! [X2: $int,X3: $int,X1: $int] :
( $less(X2,X1)
| ( X1 = X2 )
| ~ $less(X3,X1)
| $less(X3,X2) )
| ~ spl11_58
| ~ spl11_59 ),
inference(resolution,[],[f520,f516]) ).
tff(f1561,plain,
( spl11_158
| ~ spl11_12
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f742,f726,f292,f1559]) ).
tff(f1559,plain,
( spl11_158
<=> ! [X41: uni,X40: a,X39: ty] : ( t2tb(X40) = match_list(a1,X39,nil(X39),t2tb(X40),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_158])]) ).
tff(f742,plain,
( ! [X40: a,X41: uni,X39: ty] : ( t2tb(X40) = match_list(a1,X39,nil(X39),t2tb(X40),X41) )
| ~ spl11_12
| ~ spl11_80 ),
inference(resolution,[],[f727,f293]) ).
tff(f1557,plain,
( spl11_157
| ~ spl11_11
| ~ spl11_80 ),
inference(avatar_split_clause,[],[f734,f726,f288,f1555]) ).
tff(f1555,plain,
( spl11_157
<=> ! [X2: uni,X0: ty,X1: ty] : ( witness(X0) = match_list(X0,X1,nil(X1),witness(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_157])]) ).
tff(f734,plain,
( ! [X2: uni,X0: ty,X1: ty] : ( witness(X0) = match_list(X0,X1,nil(X1),witness(X0),X2) )
| ~ spl11_11
| ~ spl11_80 ),
inference(resolution,[],[f727,f289]) ).
tff(f1553,plain,
( spl11_156
| ~ spl11_40
| ~ spl11_74 ),
inference(avatar_split_clause,[],[f695,f653,f417,f1551]) ).
tff(f1551,plain,
( spl11_156
<=> ! [X6: $int,X5: $int,X7: $int] : ( $product(X5,$product(X6,X7)) = $product(X7,$product(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_156])]) ).
tff(f695,plain,
( ! [X6: $int,X7: $int,X5: $int] : ( $product(X5,$product(X6,X7)) = $product(X7,$product(X5,X6)) )
| ~ spl11_40
| ~ spl11_74 ),
inference(superposition,[],[f654,f418]) ).
tff(f1549,plain,
( spl11_155
| ~ spl11_38
| ~ spl11_138 ),
inference(avatar_split_clause,[],[f1472,f1380,f408,f1546]) ).
tff(f1546,plain,
( spl11_155
<=> ( t2tb(sK6) = cons_proj_1(a1,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_155])]) ).
tff(f1380,plain,
( spl11_138
<=> ! [X32: uni,X31: a] : ( t2tb(X31) = cons_proj_1(a1,cons(a1,t2tb(X31),X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_138])]) ).
tff(f1472,plain,
( ( t2tb(sK6) = cons_proj_1(a1,t2tb3(sK5)) )
| ~ spl11_38
| ~ spl11_138 ),
inference(superposition,[],[f1381,f410]) ).
tff(f1381,plain,
( ! [X31: a,X32: uni] : ( t2tb(X31) = cons_proj_1(a1,cons(a1,t2tb(X31),X32)) )
| ~ spl11_138 ),
inference(avatar_component_clause,[],[f1380]) ).
tff(f1544,plain,
( spl11_154
| ~ spl11_40
| ~ spl11_74 ),
inference(avatar_split_clause,[],[f691,f653,f417,f1542]) ).
tff(f1542,plain,
( spl11_154
<=> ! [X4: $int,X2: $int,X3: $int] : ( $product(X2,$product(X3,X4)) = $product($product(X3,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_154])]) ).
tff(f691,plain,
( ! [X2: $int,X3: $int,X4: $int] : ( $product(X2,$product(X3,X4)) = $product($product(X3,X2),X4) )
| ~ spl11_40
| ~ spl11_74 ),
inference(superposition,[],[f654,f418]) ).
tff(f1540,plain,
( spl11_153
| ~ spl11_39
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f678,f649,f413,f1538]) ).
tff(f1536,plain,
( spl11_152
| ~ spl11_39
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f673,f649,f413,f1534]) ).
tff(f673,plain,
( ! [X2: $int,X3: $int,X4: $int] : ( $sum(X2,$sum(X3,X4)) = $sum($sum(X3,X2),X4) )
| ~ spl11_39
| ~ spl11_73 ),
inference(superposition,[],[f650,f414]) ).
tff(f1532,plain,
( spl11_151
| ~ spl11_30
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f635,f580,f371,f1530]) ).
tff(f1530,plain,
( spl11_151
<=> ! [X25: lpa1cm_a1rp,X24: uni] : ( t2tb2(X25) = match_bool(tuple2(a1,a1),false,X24,t2tb2(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_151])]) ).
tff(f635,plain,
( ! [X24: uni,X25: lpa1cm_a1rp] : ( t2tb2(X25) = match_bool(tuple2(a1,a1),false,X24,t2tb2(X25)) )
| ~ spl11_30
| ~ spl11_69 ),
inference(resolution,[],[f581,f372]) ).
tff(f1528,plain,
( spl11_150
| ~ spl11_27
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f632,f580,f352,f1526]) ).
tff(f1526,plain,
( spl11_150
<=> ! [X13: ty,X14: uni,X15: uni] : ( cons_proj_1(X13,X15) = match_bool(X13,false,X14,cons_proj_1(X13,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_150])]) ).
tff(f632,plain,
( ! [X14: uni,X15: uni,X13: ty] : ( cons_proj_1(X13,X15) = match_bool(X13,false,X14,cons_proj_1(X13,X15)) )
| ~ spl11_27
| ~ spl11_69 ),
inference(resolution,[],[f581,f353]) ).
tff(f1524,plain,
( spl11_149
| ~ spl11_30
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f626,f571,f371,f1522]) ).
tff(f1522,plain,
( spl11_149
<=> ! [X25: uni,X24: lpa1cm_a1rp] : ( t2tb2(X24) = match_bool(tuple2(a1,a1),true,t2tb2(X24),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_149])]) ).
tff(f626,plain,
( ! [X24: lpa1cm_a1rp,X25: uni] : ( t2tb2(X24) = match_bool(tuple2(a1,a1),true,t2tb2(X24),X25) )
| ~ spl11_30
| ~ spl11_67 ),
inference(resolution,[],[f572,f372]) ).
tff(f1520,plain,
( spl11_148
| ~ spl11_27
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f623,f571,f352,f1518]) ).
tff(f1518,plain,
( spl11_148
<=> ! [X13: ty,X14: uni,X15: uni] : ( cons_proj_1(X13,X14) = match_bool(X13,true,cons_proj_1(X13,X14),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_148])]) ).
tff(f623,plain,
( ! [X14: uni,X15: uni,X13: ty] : ( cons_proj_1(X13,X14) = match_bool(X13,true,cons_proj_1(X13,X14),X15) )
| ~ spl11_27
| ~ spl11_67 ),
inference(resolution,[],[f572,f353]) ).
tff(f1516,plain,
( spl11_147
| ~ spl11_11
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f614,f567,f288,f1513]) ).
tff(f1513,plain,
( spl11_147
<=> ( witness(tuple2(a1,a1)) = t2tb2(tb2t2(witness(tuple2(a1,a1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_147])]) ).
tff(f614,plain,
( ( witness(tuple2(a1,a1)) = t2tb2(tb2t2(witness(tuple2(a1,a1)))) )
| ~ spl11_11
| ~ spl11_66 ),
inference(resolution,[],[f568,f289]) ).
tff(f1511,plain,
( spl11_146
| ~ spl11_60
| ~ spl11_61 ),
inference(avatar_split_clause,[],[f556,f527,f523,f1509]) ).
tff(f556,plain,
( ! [X2: uni,X1: ty] :
( ( 0 != length(X1,X2) )
| ( nil(X1) = reverse(X1,X2) ) )
| ~ spl11_60
| ~ spl11_61 ),
inference(superposition,[],[f528,f524]) ).
tff(f1507,plain,
( spl11_145
| ~ spl11_51
| ~ spl11_58 ),
inference(avatar_split_clause,[],[f538,f515,f472,f1505]) ).
tff(f538,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl11_51
| ~ spl11_58 ),
inference(resolution,[],[f516,f473]) ).
tff(f1503,plain,
( spl11_144
| ~ spl11_33
| ~ spl11_138 ),
inference(avatar_split_clause,[],[f1471,f1380,f383,f1500]) ).
tff(f1500,plain,
( spl11_144
<=> ( t2tb(sK2) = cons_proj_1(a1,t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_144])]) ).
tff(f1471,plain,
( ( t2tb(sK2) = cons_proj_1(a1,t2tb3(sK0)) )
| ~ spl11_33
| ~ spl11_138 ),
inference(superposition,[],[f1381,f385]) ).
tff(f1498,plain,
( spl11_143
| ~ spl11_37
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f511,f480,f400,f1496]) ).
tff(f1496,plain,
( spl11_143
<=> ! [X8: uni,X7: ty] : ( tuple2_proj_2(X7,a1,X8) = t2tb(tb2t(tuple2_proj_2(X7,a1,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_143])]) ).
tff(f511,plain,
( ! [X8: uni,X7: ty] : ( tuple2_proj_2(X7,a1,X8) = t2tb(tb2t(tuple2_proj_2(X7,a1,X8))) )
| ~ spl11_37
| ~ spl11_53 ),
inference(resolution,[],[f481,f401]) ).
tff(f1494,plain,
( spl11_142
| ~ spl11_36
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f510,f480,f396,f1492]) ).
tff(f1492,plain,
( spl11_142
<=> ! [X6: uni,X5: ty] : ( tuple2_proj_1(a1,X5,X6) = t2tb(tb2t(tuple2_proj_1(a1,X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_142])]) ).
tff(f510,plain,
( ! [X6: uni,X5: ty] : ( tuple2_proj_1(a1,X5,X6) = t2tb(tb2t(tuple2_proj_1(a1,X5,X6))) )
| ~ spl11_36
| ~ spl11_53 ),
inference(resolution,[],[f481,f397]) ).
tff(f1394,plain,
( spl11_141
| ~ spl11_47
| ~ spl11_78 ),
inference(avatar_split_clause,[],[f1015,f669,f445,f1392]) ).
tff(f1015,plain,
( ! [X3: uni] :
( mem(a1,X3,t2tb3(sK1))
| ~ mem(a1,X3,t2tb3(sK5)) )
| ~ spl11_47
| ~ spl11_78 ),
inference(superposition,[],[f670,f447]) ).
tff(f1390,plain,
( spl11_140
| ~ spl11_95 ),
inference(avatar_split_clause,[],[f926,f917,f1388]) ).
tff(f917,plain,
( spl11_95
<=> ! [X0: ty,X3: uni,X2: uni,X1: uni] :
( mem(X0,X1,cons(X0,X2,X3))
| ( X1 != X2 )
| ~ sort(X0,X2)
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_95])]) ).
tff(f926,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X1,X2))
| ~ sort(X0,X1) )
| ~ spl11_95 ),
inference(duplicate_literal_removal,[],[f925]) ).
tff(f925,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X1,X2))
| ~ sort(X0,X1)
| ~ sort(X0,X1) )
| ~ spl11_95 ),
inference(equality_resolution,[],[f918]) ).
tff(f918,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: uni] :
( ( X1 != X2 )
| mem(X0,X1,cons(X0,X2,X3))
| ~ sort(X0,X2)
| ~ sort(X0,X1) )
| ~ spl11_95 ),
inference(avatar_component_clause,[],[f917]) ).
tff(f1386,plain,
( spl11_139
| ~ spl11_46
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f889,f873,f441,f1384]) ).
tff(f889,plain,
( ! [X16: uni,X14: uni,X15: uni,X13: ty] : ( infix_plpl(X13,cons(X13,X14,X15),X16) != nil(X13) )
| ~ spl11_46
| ~ spl11_90 ),
inference(superposition,[],[f442,f874]) ).
tff(f1382,plain,
( spl11_138
| ~ spl11_12
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f716,f661,f292,f1380]) ).
tff(f716,plain,
( ! [X31: a,X32: uni] : ( t2tb(X31) = cons_proj_1(a1,cons(a1,t2tb(X31),X32)) )
| ~ spl11_12
| ~ spl11_76 ),
inference(resolution,[],[f662,f293]) ).
tff(f1378,plain,
( spl11_137
| ~ spl11_11
| ~ spl11_76 ),
inference(avatar_split_clause,[],[f708,f661,f288,f1376]) ).
tff(f1376,plain,
( spl11_137
<=> ! [X0: ty,X1: uni] : ( witness(X0) = cons_proj_1(X0,cons(X0,witness(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_137])]) ).
tff(f708,plain,
( ! [X0: ty,X1: uni] : ( witness(X0) = cons_proj_1(X0,cons(X0,witness(X0),X1)) )
| ~ spl11_11
| ~ spl11_76 ),
inference(resolution,[],[f662,f289]) ).
tff(f1373,plain,
( spl11_136
| ~ spl11_29
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f677,f649,f367,f1371]) ).
tff(f1371,plain,
( spl11_136
<=> ! [X4: $int,X3: $int] : ( 0 = $sum(X3,$sum(X4,$uminus($sum(X3,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_136])]) ).
tff(f677,plain,
( ! [X3: $int,X4: $int] : ( 0 = $sum(X3,$sum(X4,$uminus($sum(X3,X4)))) )
| ~ spl11_29
| ~ spl11_73 ),
inference(superposition,[],[f650,f368]) ).
tff(f1369,plain,
( spl11_135
| ~ spl11_39
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f609,f563,f413,f1367]) ).
tff(f609,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( $less($sum(X4,X3),$sum(X3,X2))
| ~ $less(X4,X2) )
| ~ spl11_39
| ~ spl11_65 ),
inference(superposition,[],[f564,f414]) ).
tff(f1365,plain,
( spl11_134
| ~ spl11_39
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f605,f563,f413,f1363]) ).
tff(f605,plain,
( ! [X2: $int,X3: $int,X4: $int] :
( $less($sum(X3,X2),$sum(X4,X3))
| ~ $less(X2,X4) )
| ~ spl11_39
| ~ spl11_65 ),
inference(superposition,[],[f564,f414]) ).
tff(f1361,plain,
( spl11_133
| ~ spl11_39
| ~ spl11_64 ),
inference(avatar_split_clause,[],[f592,f559,f413,f1359]) ).
tff(f592,plain,
( ! [X3: $int,X4: $int] : ( $sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3)) )
| ~ spl11_39
| ~ spl11_64 ),
inference(superposition,[],[f560,f414]) ).
tff(f1357,plain,
( spl11_132
| ~ spl11_26
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f541,f519,f348,f1355]) ).
tff(f1355,plain,
( spl11_132
<=> ! [X4: ty,X5: uni] :
( $less(0,length(X4,X5))
| ( 0 = length(X4,X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_132])]) ).
tff(f348,plain,
( spl11_26
<=> ! [X0: ty,X1: uni] : ~ $less(length(X0,X1),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).
tff(f541,plain,
( ! [X4: ty,X5: uni] :
( $less(0,length(X4,X5))
| ( 0 = length(X4,X5) ) )
| ~ spl11_26
| ~ spl11_59 ),
inference(resolution,[],[f520,f349]) ).
tff(f349,plain,
( ! [X0: ty,X1: uni] : ~ $less(length(X0,X1),0)
| ~ spl11_26 ),
inference(avatar_component_clause,[],[f348]) ).
tff(f1351,plain,
( spl11_131
| ~ spl11_23
| ~ spl11_72 ),
inference(avatar_split_clause,[],[f647,f644,f336,f1349]) ).
tff(f336,plain,
( spl11_23
<=> ! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).
tff(f644,plain,
( spl11_72
<=> ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(sK7))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_72])]) ).
tff(f647,plain,
( ! [X0: uni] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) != tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,X0))) )
| ( length(a1,t2tb3(sK0)) != length(a1,X0) )
| ( sK1 != tb2t3(infix_plpl(a1,X0,t2tb3(sK7))) ) )
| ~ spl11_23
| ~ spl11_72 ),
inference(superposition,[],[f645,f337]) ).
tff(f337,plain,
( ! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 )
| ~ spl11_23 ),
inference(avatar_component_clause,[],[f336]) ).
tff(f645,plain,
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(sK7))) ) )
| ~ spl11_72 ),
inference(avatar_component_clause,[],[f644]) ).
tff(f1271,plain,
( spl11_130
| ~ spl11_45
| ~ spl11_77 ),
inference(avatar_split_clause,[],[f718,f665,f437,f1269]) ).
tff(f1269,plain,
( spl11_130
<=> ! [X4: uni,X5: uni,X3: ty] :
( mem(X3,X5,X4)
| ~ mem(X3,X5,nil(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_130])]) ).
tff(f718,plain,
( ! [X3: ty,X4: uni,X5: uni] :
( mem(X3,X5,X4)
| ~ mem(X3,X5,nil(X3)) )
| ~ spl11_45
| ~ spl11_77 ),
inference(superposition,[],[f666,f438]) ).
tff(f1267,plain,
( spl11_129
| ~ spl11_12
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f637,f580,f292,f1265]) ).
tff(f1265,plain,
( spl11_129
<=> ! [X32: a,X31: uni] : ( t2tb(X32) = match_bool(a1,false,X31,t2tb(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_129])]) ).
tff(f637,plain,
( ! [X31: uni,X32: a] : ( t2tb(X32) = match_bool(a1,false,X31,t2tb(X32)) )
| ~ spl11_12
| ~ spl11_69 ),
inference(resolution,[],[f581,f293]) ).
tff(f1263,plain,
( spl11_128
| ~ spl11_11
| ~ spl11_69 ),
inference(avatar_split_clause,[],[f629,f580,f288,f1261]) ).
tff(f1261,plain,
( spl11_128
<=> ! [X0: ty,X1: uni] : ( witness(X0) = match_bool(X0,false,X1,witness(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_128])]) ).
tff(f629,plain,
( ! [X0: ty,X1: uni] : ( witness(X0) = match_bool(X0,false,X1,witness(X0)) )
| ~ spl11_11
| ~ spl11_69 ),
inference(resolution,[],[f581,f289]) ).
tff(f1259,plain,
( spl11_127
| ~ spl11_12
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f628,f571,f292,f1257]) ).
tff(f1257,plain,
( spl11_127
<=> ! [X32: uni,X31: a] : ( t2tb(X31) = match_bool(a1,true,t2tb(X31),X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_127])]) ).
tff(f628,plain,
( ! [X31: a,X32: uni] : ( t2tb(X31) = match_bool(a1,true,t2tb(X31),X32) )
| ~ spl11_12
| ~ spl11_67 ),
inference(resolution,[],[f572,f293]) ).
tff(f1255,plain,
( spl11_126
| ~ spl11_11
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f620,f571,f288,f1253]) ).
tff(f1253,plain,
( spl11_126
<=> ! [X0: ty,X1: uni] : ( witness(X0) = match_bool(X0,true,witness(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_126])]) ).
tff(f620,plain,
( ! [X0: ty,X1: uni] : ( witness(X0) = match_bool(X0,true,witness(X0),X1) )
| ~ spl11_11
| ~ spl11_67 ),
inference(resolution,[],[f572,f289]) ).
tff(f1251,plain,
( spl11_125
| ~ spl11_29
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f608,f563,f367,f1249]) ).
tff(f608,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl11_29
| ~ spl11_65 ),
inference(superposition,[],[f564,f368]) ).
tff(f1246,plain,
( spl11_112
| ~ spl11_108
| ~ spl11_111 ),
inference(avatar_split_clause,[],[f1242,f1103,f1079,f1121]) ).
tff(f1241,plain,
( spl11_124
| ~ spl11_108
| ~ spl11_110 ),
inference(avatar_split_clause,[],[f1108,f1099,f1079,f1238]) ).
tff(f1108,plain,
( ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK8)) )
| ~ spl11_108
| ~ spl11_110 ),
inference(superposition,[],[f1101,f1081]) ).
tff(f1236,plain,
( spl11_123
| ~ spl11_29
| ~ spl11_65 ),
inference(avatar_split_clause,[],[f604,f563,f367,f1234]) ).
tff(f604,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl11_29
| ~ spl11_65 ),
inference(superposition,[],[f564,f368]) ).
tff(f1232,plain,
( spl11_122
| ~ spl11_27
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f509,f480,f352,f1230]) ).
tff(f1230,plain,
( spl11_122
<=> ! [X4: uni] : ( cons_proj_1(a1,X4) = t2tb(tb2t(cons_proj_1(a1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_122])]) ).
tff(f509,plain,
( ! [X4: uni] : ( cons_proj_1(a1,X4) = t2tb(tb2t(cons_proj_1(a1,X4))) )
| ~ spl11_27
| ~ spl11_53 ),
inference(resolution,[],[f481,f353]) ).
tff(f1228,plain,
( spl11_121
| ~ spl11_32 ),
inference(avatar_split_clause,[],[f404,f379,f1226]) ).
tff(f1226,plain,
( spl11_121
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( true = X1 )
| ( true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_121])]) ).
tff(f379,plain,
( spl11_32
<=> ! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
tff(f404,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( true = X1 )
| ( true = X0 ) )
| ~ spl11_32 ),
inference(superposition,[],[f380,f380]) ).
tff(f380,plain,
( ! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) )
| ~ spl11_32 ),
inference(avatar_component_clause,[],[f379]) ).
tff(f1192,plain,
( spl11_120
| ~ spl11_29
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f687,f649,f367,f1190]) ).
tff(f687,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl11_29
| ~ spl11_73 ),
inference(evaluation,[],[f672]) ).
tff(f672,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl11_29
| ~ spl11_73 ),
inference(superposition,[],[f650,f368]) ).
tff(f1188,plain,
( spl11_119
| ~ spl11_39
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f499,f476,f413,f1186]) ).
tff(f499,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl11_39
| ~ spl11_52 ),
inference(superposition,[],[f477,f414]) ).
tff(f1184,plain,
( spl11_118
| ~ spl11_39
| ~ spl11_51 ),
inference(avatar_split_clause,[],[f496,f472,f413,f1182]) ).
tff(f496,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl11_39
| ~ spl11_51 ),
inference(superposition,[],[f473,f414]) ).
tff(f1168,plain,
( ~ spl11_117
| spl11_6
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f1087,f1079,f264,f1165]) ).
tff(f1162,plain,
( spl11_116
| ~ spl11_26
| ~ spl11_79 ),
inference(avatar_split_clause,[],[f732,f722,f348,f1160]) ).
tff(f732,plain,
( ! [X3: ty,X5: uni] : ~ $less($sum(1,length(X3,X5)),0)
| ~ spl11_26
| ~ spl11_79 ),
inference(superposition,[],[f349,f723]) ).
tff(f1158,plain,
( spl11_115
| ~ spl11_11
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f507,f480,f288,f1155]) ).
tff(f1155,plain,
( spl11_115
<=> ( witness(a1) = t2tb(tb2t(witness(a1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_115])]) ).
tff(f507,plain,
( ( witness(a1) = t2tb(tb2t(witness(a1))) )
| ~ spl11_11
| ~ spl11_53 ),
inference(resolution,[],[f481,f289]) ).
tff(f1133,plain,
( spl11_114
| ~ spl11_8
| ~ spl11_51 ),
inference(avatar_split_clause,[],[f495,f472,f274,f1131]) ).
tff(f495,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl11_8
| ~ spl11_51 ),
inference(resolution,[],[f473,f275]) ).
tff(f1129,plain,
( spl11_113
| ~ spl11_17
| ~ spl11_40 ),
inference(avatar_split_clause,[],[f461,f417,f312,f1127]) ).
tff(f1127,plain,
( spl11_113
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_113])]) ).
tff(f461,plain,
( ! [X0: $int] : ( 0 = $product(0,X0) )
| ~ spl11_17
| ~ spl11_40 ),
inference(superposition,[],[f418,f313]) ).
tff(f1124,plain,
( ~ spl11_112
| ~ spl11_108
| spl11_111 ),
inference(avatar_split_clause,[],[f1107,f1103,f1079,f1121]) ).
tff(f1107,plain,
( ~ $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK0)))
| ~ spl11_108
| spl11_111 ),
inference(forward_demodulation,[],[f1104,f1081]) ).
tff(f1104,plain,
( ~ $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1)))
| spl11_111 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f1106,plain,
( spl11_110
| spl11_111
| spl11_6
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f543,f519,f264,f1103,f1099]) ).
tff(f543,plain,
( $less(length(a1,t2tb3(sK8)),length(a1,t2tb3(sK1)))
| ( length(a1,t2tb3(sK1)) = length(a1,t2tb3(sK8)) )
| spl11_6
| ~ spl11_59 ),
inference(resolution,[],[f520,f266]) ).
tff(f1086,plain,
( spl11_108
| spl11_109
| spl11_1
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f542,f519,f239,f1083,f1079]) ).
tff(f542,plain,
( $less(length(a1,t2tb3(sK0)),length(a1,t2tb3(sK1)))
| ( length(a1,t2tb3(sK0)) = length(a1,t2tb3(sK1)) )
| spl11_1
| ~ spl11_59 ),
inference(resolution,[],[f520,f241]) ).
tff(f241,plain,
( ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0)))
| spl11_1 ),
inference(avatar_component_clause,[],[f239]) ).
tff(f1070,plain,
( spl11_107
| ~ spl11_35
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f468,f429,f392,f1068]) ).
tff(f392,plain,
( spl11_35
<=> ! [X0: ty,X1: uni] : sort(list(X0),reverse(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_35])]) ).
tff(f468,plain,
( ! [X0: ty,X1: uni] : sort(list(X0),X1)
| ~ spl11_35
| ~ spl11_43 ),
inference(superposition,[],[f393,f430]) ).
tff(f393,plain,
( ! [X0: ty,X1: uni] : sort(list(X0),reverse(X0,X1))
| ~ spl11_35 ),
inference(avatar_component_clause,[],[f392]) ).
tff(f1035,plain,
( spl11_106
| ~ spl11_4
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f856,f820,f254,f1033]) ).
tff(f856,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK3))) = length(a1,infix_plpl(a1,X0,t2tb3(sK8))) )
| ~ spl11_4
| ~ spl11_87 ),
inference(forward_demodulation,[],[f839,f821]) ).
tff(f839,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,X0,t2tb3(sK3))) = $sum(length(a1,X0),length(a1,t2tb3(sK8))) )
| ~ spl11_4
| ~ spl11_87 ),
inference(superposition,[],[f821,f256]) ).
tff(f1031,plain,
( spl11_105
| ~ spl11_4
| ~ spl11_87 ),
inference(avatar_split_clause,[],[f852,f820,f254,f1029]) ).
tff(f852,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK3),X0)) = length(a1,infix_plpl(a1,t2tb3(sK8),X0)) )
| ~ spl11_4
| ~ spl11_87 ),
inference(forward_demodulation,[],[f835,f821]) ).
tff(f835,plain,
( ! [X0: uni] : ( length(a1,infix_plpl(a1,t2tb3(sK3),X0)) = $sum(length(a1,t2tb3(sK8)),length(a1,X0)) )
| ~ spl11_4
| ~ spl11_87 ),
inference(superposition,[],[f821,f256]) ).
tff(f1025,plain,
( spl11_103
| ~ spl11_104
| ~ spl11_4
| ~ spl11_61 ),
inference(avatar_split_clause,[],[f554,f527,f254,f1022,f1018]) ).
tff(f1018,plain,
( spl11_103
<=> ( t2tb3(sK3) = nil(a1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_103])]) ).
tff(f1022,plain,
( spl11_104
<=> ( 0 = length(a1,t2tb3(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_104])]) ).
tff(f554,plain,
( ( 0 != length(a1,t2tb3(sK8)) )
| ( t2tb3(sK3) = nil(a1) )
| ~ spl11_4
| ~ spl11_61 ),
inference(superposition,[],[f528,f256]) ).
tff(f1001,plain,
spl11_102,
inference(avatar_split_clause,[],[f213,f999]) ).
tff(f213,plain,
! [X3: uni,X0: ty,X1: ty,X6: uni,X4: uni,X5: uni] : ( combine(X1,X0,cons(X0,X5,X6),cons(X1,X3,X4)) = cons(tuple2(X0,X1),tuple21(X0,X1,X5,X3),combine(X1,X0,X6,X4)) ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: ty,X1: ty,X2: uni] :
( ! [X3: uni,X4: uni] :
( ! [X5: uni,X6: uni] : ( combine(X1,X0,cons(X0,X5,X6),cons(X1,X3,X4)) = cons(tuple2(X0,X1),tuple21(X0,X1,X5,X3),combine(X1,X0,X6,X4)) )
& ( nil(tuple2(X0,X1)) = combine(X1,X0,nil(X0),cons(X1,X3,X4)) ) )
& ( nil(tuple2(X0,X1)) = combine(X1,X0,X2,nil(X1)) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: ty,X16: ty,X1: uni] :
( ! [X2: uni,X3: uni] :
( ! [X17: uni,X18: uni] : ( combine(X16,X0,cons(X0,X17,X18),cons(X16,X2,X3)) = cons(tuple2(X0,X16),tuple21(X0,X16,X17,X2),combine(X16,X0,X18,X3)) )
& ( nil(tuple2(X0,X16)) = combine(X16,X0,nil(X0),cons(X16,X2,X3)) ) )
& ( combine(X16,X0,X1,nil(X16)) = nil(tuple2(X0,X16)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',combine_def) ).
tff(f991,plain,
spl11_101,
inference(avatar_split_clause,[],[f198,f989]) ).
tff(f198,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,X3)
| ( X1 = X2 )
| ~ mem(X0,X1,cons(X0,X2,X3))
| ~ sort(X0,X2)
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: ty,X1: uni] :
( ( ! [X2: uni,X3: uni] :
( ( ( mem(X0,X1,cons(X0,X2,X3))
| ( ~ mem(X0,X1,X3)
& ( X1 != X2 ) ) )
& ( mem(X0,X1,X3)
| ( X1 = X2 )
| ~ mem(X0,X1,cons(X0,X2,X3)) ) )
| ~ sort(X0,X2) )
& ~ mem(X0,X1,nil(X0)) )
| ~ sort(X0,X1) ),
inference(flattening,[],[f150]) ).
tff(f150,plain,
! [X0: ty,X1: uni] :
( ( ! [X2: uni,X3: uni] :
( ( ( mem(X0,X1,cons(X0,X2,X3))
| ( ~ mem(X0,X1,X3)
& ( X1 != X2 ) ) )
& ( mem(X0,X1,X3)
| ( X1 = X2 )
| ~ mem(X0,X1,cons(X0,X2,X3)) ) )
| ~ sort(X0,X2) )
& ~ mem(X0,X1,nil(X0)) )
| ~ sort(X0,X1) ),
inference(nnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: ty,X1: uni] :
( ( ! [X2: uni,X3: uni] :
( ( mem(X0,X1,cons(X0,X2,X3))
<=> ( mem(X0,X1,X3)
| ( X1 = X2 ) ) )
| ~ sort(X0,X2) )
& ~ mem(X0,X1,nil(X0)) )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
tff(f28,axiom,
! [X0: ty,X1: uni] :
( sort(X0,X1)
=> ( ! [X2: uni,X3: uni] :
( sort(X0,X2)
=> ( mem(X0,X1,cons(X0,X2,X3))
<=> ( mem(X0,X1,X3)
| ( X1 = X2 ) ) ) )
& ~ mem(X0,X1,nil(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',mem_def) ).
tff(f968,plain,
spl11_100,
inference(avatar_split_clause,[],[f228,f966]) ).
tff(f228,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,reverse(X0,cons(X0,X3,X1)),X2) = infix_plpl(X0,reverse(X0,X1),cons(X0,X3,X2)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] : ( infix_plpl(X0,reverse(X0,cons(X0,X3,X1)),X2) = infix_plpl(X0,reverse(X0,X1),cons(X0,X3,X2)) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: ty,X14: uni,X13: uni,X1: uni] : ( infix_plpl(X0,reverse(X0,cons(X0,X1,X14)),X13) = infix_plpl(X0,reverse(X0,X14),cons(X0,X1,X13)) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_append) ).
tff(f964,plain,
spl11_99,
inference(avatar_split_clause,[],[f220,f962]) ).
tff(f220,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( infix_plpl(X0,sK9(X0,X1,X2),cons(X0,X1,sK10(X0,X1,X2))) = X2 )
| ~ mem(X0,X1,X2) ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( ( infix_plpl(X0,sK9(X0,X1,X2),cons(X0,X1,sK10(X0,X1,X2))) = X2 )
& sort(list(X0),sK10(X0,X1,X2))
& sort(list(X0),sK9(X0,X1,X2)) )
| ~ mem(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f137,f153]) ).
tff(f153,plain,
! [X0: ty,X1: uni,X2: uni] :
( ? [X3: uni,X4: uni] :
( ( infix_plpl(X0,X3,cons(X0,X1,X4)) = X2 )
& sort(list(X0),X4)
& sort(list(X0),X3) )
=> ( ( infix_plpl(X0,sK9(X0,X1,X2),cons(X0,X1,sK10(X0,X1,X2))) = X2 )
& sort(list(X0),sK10(X0,X1,X2))
& sort(list(X0),sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f137,plain,
! [X0: ty,X1: uni,X2: uni] :
( ? [X3: uni,X4: uni] :
( ( infix_plpl(X0,X3,cons(X0,X1,X4)) = X2 )
& sort(list(X0),X4)
& sort(list(X0),X3) )
| ~ mem(X0,X1,X2) ),
inference(ennf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: ty,X1: uni,X2: uni] :
( mem(X0,X1,X2)
=> ? [X3: uni,X4: uni] :
( ( infix_plpl(X0,X3,cons(X0,X1,X4)) = X2 )
& sort(list(X0),X4)
& sort(list(X0),X3) ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: ty,X1: uni,X12: uni] :
( mem(X0,X1,X12)
=> ? [X14: uni,X13: uni] :
( ( infix_plpl(X0,X14,cons(X0,X1,X13)) = X12 )
& sort(list(X0),X13)
& sort(list(X0),X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',mem_decomp) ).
tff(f951,plain,
spl11_98,
inference(avatar_split_clause,[],[f221,f949]) ).
tff(f221,plain,
! [X2: uni,X0: ty,X1: ty] :
( ( tuple21(X1,X0,tuple2_proj_1(X1,X0,X2),tuple2_proj_2(X1,X0,X2)) = X2 )
| ~ sort(tuple2(X1,X0),X2) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: ty,X1: ty,X2: uni] :
( ( tuple21(X1,X0,tuple2_proj_1(X1,X0,X2),tuple2_proj_2(X1,X0,X2)) = X2 )
| ~ sort(tuple2(X1,X0),X2) ),
inference(ennf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: ty,X1: ty,X2: uni] :
( sort(tuple2(X1,X0),X2)
=> ( tuple21(X1,X0,tuple2_proj_1(X1,X0,X2),tuple2_proj_2(X1,X0,X2)) = X2 ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: ty,X8: ty,X6: uni] :
( sort(tuple2(X8,X0),X6)
=> ( tuple21(X8,X0,tuple2_proj_1(X8,X0,X6),tuple2_proj_2(X8,X0,X6)) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_inversion) ).
tff(f934,plain,
spl11_97,
inference(avatar_split_clause,[],[f200,f932]) ).
tff(f200,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X2,X3))
| ~ mem(X0,X1,X3)
| ~ sort(X0,X2)
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tff(f930,plain,
spl11_96,
inference(avatar_split_clause,[],[f183,f928]) ).
tff(f183,plain,
! [X2: uni,X0: ty,X1: uni] : ( reverse(X0,cons(X0,X1,X2)) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,nil(X0))) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,axiom,
! [X0: ty] :
( ! [X1: uni,X2: uni] : ( reverse(X0,cons(X0,X1,X2)) = infix_plpl(X0,reverse(X0,X2),cons(X0,X1,nil(X0))) )
& ( nil(X0) = reverse(X0,nil(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_def) ).
tff(f919,plain,
spl11_95,
inference(avatar_split_clause,[],[f199,f917]) ).
tff(f199,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,cons(X0,X2,X3))
| ( X1 != X2 )
| ~ sort(X0,X2)
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tff(f915,plain,
spl11_94,
inference(avatar_split_clause,[],[f79,f913]) ).
tff(f79,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_154,[]) ).
tff(f911,plain,
( spl11_93
| ~ spl11_38
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f706,f488,f408,f908]) ).
tff(f908,plain,
( spl11_93
<=> ( t2tb3(sK7) = cons_proj_2(a1,t2tb3(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_93])]) ).
tff(f706,plain,
( ( t2tb3(sK7) = cons_proj_2(a1,t2tb3(sK5)) )
| ~ spl11_38
| ~ spl11_55 ),
inference(superposition,[],[f489,f410]) ).
tff(f883,plain,
spl11_92,
inference(avatar_split_clause,[],[f232,f881]) ).
tff(f232,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,X3)
| mem(X0,X1,X2)
| ~ mem(X0,X1,infix_plpl(X0,X2,X3)) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( ( mem(X0,X1,infix_plpl(X0,X2,X3))
| ( ~ mem(X0,X1,X3)
& ~ mem(X0,X1,X2) ) )
& ( mem(X0,X1,X3)
| mem(X0,X1,X2)
| ~ mem(X0,X1,infix_plpl(X0,X2,X3)) ) ),
inference(flattening,[],[f156]) ).
tff(f156,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( ( mem(X0,X1,infix_plpl(X0,X2,X3))
| ( ~ mem(X0,X1,X3)
& ~ mem(X0,X1,X2) ) )
& ( mem(X0,X1,X3)
| mem(X0,X1,X2)
| ~ mem(X0,X1,infix_plpl(X0,X2,X3)) ) ),
inference(nnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
<=> ( mem(X0,X1,X3)
| mem(X0,X1,X2) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: ty,X1: uni,X14: uni,X13: uni] :
( mem(X0,X1,infix_plpl(X0,X14,X13))
<=> ( mem(X0,X1,X13)
| mem(X0,X1,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',mem_append) ).
tff(f879,plain,
spl11_91,
inference(avatar_split_clause,[],[f227,f877]) ).
tff(f227,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,X1,infix_plpl(X0,X2,X3)) = infix_plpl(X0,infix_plpl(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] : ( infix_plpl(X0,X1,infix_plpl(X0,X2,X3)) = infix_plpl(X0,infix_plpl(X0,X1,X2),X3) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: ty,X14: uni,X13: uni,X15: uni] : ( infix_plpl(X0,X14,infix_plpl(X0,X13,X15)) = infix_plpl(X0,infix_plpl(X0,X14,X13),X15) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',append_assoc) ).
tff(f875,plain,
spl11_90,
inference(avatar_split_clause,[],[f195,f873]) ).
tff(f195,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] : ( infix_plpl(X0,cons(X0,X2,X3),X1) = cons(X0,X2,infix_plpl(X0,X3,X1)) ),
inference(cnf_transformation,[],[f100]) ).
tff(f100,plain,
! [X0: ty,X1: uni] :
( ! [X2: uni,X3: uni] : ( infix_plpl(X0,cons(X0,X2,X3),X1) = cons(X0,X2,infix_plpl(X0,X3,X1)) )
& ( infix_plpl(X0,nil(X0),X1) = X1 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: ty,X13: uni] :
( ! [X1: uni,X2: uni] : ( infix_plpl(X0,cons(X0,X1,X2),X13) = cons(X0,X1,infix_plpl(X0,X2,X13)) )
& ( infix_plpl(X0,nil(X0),X13) = X13 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',infix_plpl_def) ).
tff(f830,plain,
spl11_89,
inference(avatar_split_clause,[],[f236,f828]) ).
tff(f236,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( sort(X1,X3)
=> ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: ty,X8: ty,X4: uni,X5: uni,X6: uni,X9: uni] :
( sort(X8,X5)
=> ( match_list(X8,X0,cons(X0,X6,X9),X4,X5) = X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_list_Cons) ).
tff(f826,plain,
spl11_88,
inference(avatar_split_clause,[],[f212,f824]) ).
tff(f212,plain,
! [X3: uni,X0: ty,X1: ty,X4: uni] : ( nil(tuple2(X0,X1)) = combine(X1,X0,nil(X0),cons(X1,X3,X4)) ),
inference(cnf_transformation,[],[f109]) ).
tff(f822,plain,
spl11_87,
inference(avatar_split_clause,[],[f209,f820]) ).
tff(f209,plain,
! [X2: uni,X0: ty,X1: uni] : ( length(X0,infix_plpl(X0,X1,X2)) = $sum(length(X0,X1),length(X0,X2)) ),
inference(cnf_transformation,[],[f107]) ).
tff(f107,plain,
! [X0: ty,X1: uni,X2: uni] : ( length(X0,infix_plpl(X0,X1,X2)) = $sum(length(X0,X1),length(X0,X2)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: ty,X14: uni,X13: uni] : ( length(X0,infix_plpl(X0,X14,X13)) = $sum(length(X0,X14),length(X0,X13)) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',append_length) ).
tff(f818,plain,
spl11_86,
inference(avatar_split_clause,[],[f196,f816]) ).
tff(f196,plain,
! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f101]) ).
tff(f101,plain,
! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: ty,X6: uni] :
( ( cons(X0,cons_proj_1(X0,X6),cons_proj_2(X0,X6)) = X6 )
| ( nil(X0) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',list_inversion) ).
tff(f763,plain,
spl11_85,
inference(avatar_split_clause,[],[f231,f761]) ).
tff(f231,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ( tuple2_proj_1(X1,X0,tuple21(X1,X0,X2,X3)) = X2 )
| ~ sort(X1,X2) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( ( tuple2_proj_1(X1,X0,tuple21(X1,X0,X2,X3)) = X2 )
| ~ sort(X1,X2) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( sort(X1,X2)
=> ( tuple2_proj_1(X1,X0,tuple21(X1,X0,X2,X3)) = X2 ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: ty,X8: ty,X6: uni,X9: uni] :
( sort(X8,X6)
=> ( tuple2_proj_1(X8,X0,tuple21(X8,X0,X6,X9)) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_proj_1_def) ).
tff(f759,plain,
spl11_84,
inference(avatar_split_clause,[],[f230,f757]) ).
tff(f230,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ( tuple2_proj_2(X1,X0,tuple21(X1,X0,X2,X3)) = X3 )
| ~ sort(X0,X3) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( ( tuple2_proj_2(X1,X0,tuple21(X1,X0,X2,X3)) = X3 )
| ~ sort(X0,X3) ),
inference(ennf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( sort(X0,X3)
=> ( tuple2_proj_2(X1,X0,tuple21(X1,X0,X2,X3)) = X3 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: ty,X8: ty,X6: uni,X9: uni] :
( sort(X0,X9)
=> ( tuple2_proj_2(X8,X0,tuple21(X8,X0,X6,X9)) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_proj_2_def) ).
tff(f755,plain,
( ~ spl11_83
| ~ spl11_38
| ~ spl11_46 ),
inference(avatar_split_clause,[],[f707,f441,f408,f752]) ).
tff(f752,plain,
( spl11_83
<=> ( t2tb3(sK5) = nil(a1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_83])]) ).
tff(f707,plain,
( ( t2tb3(sK5) != nil(a1) )
| ~ spl11_38
| ~ spl11_46 ),
inference(superposition,[],[f442,f410]) ).
tff(f750,plain,
spl11_82,
inference(avatar_split_clause,[],[f214,f748]) ).
tff(f214,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(flattening,[],[f132]) ).
tff(f132,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X1,X0)
=> ( ~ $less(X2,0)
=> ~ $less($product(X1,X2),$product(X0,X2)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,plain,
! [X1: $int,X7: $int,X4: $int] :
( ~ $less(X7,X1)
=> ( ~ $less(X4,0)
=> ~ $less($product(X7,X4),$product(X1,X4)) ) ),
inference(theory_normalization,[],[f8]) ).
tff(f8,axiom,
! [X1: $int,X7: $int,X4: $int] :
( $lesseq(X1,X7)
=> ( $lesseq(0,X4)
=> $lesseq($product(X1,X4),$product(X7,X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',compatOrderMult) ).
tff(f746,plain,
spl11_81,
inference(avatar_split_clause,[],[f78,f744]) ).
tff(f78,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_153,[]) ).
tff(f728,plain,
spl11_80,
inference(avatar_split_clause,[],[f229,f726]) ).
tff(f229,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ),
inference(ennf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( sort(X1,X2)
=> ( match_list(X1,X0,nil(X0),X2,X3) = X2 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: ty,X8: ty,X4: uni,X5: uni] :
( sort(X8,X4)
=> ( match_list(X8,X0,nil(X0),X4,X5) = X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_list_Nil) ).
tff(f724,plain,
spl11_79,
inference(avatar_split_clause,[],[f181,f722]) ).
tff(f181,plain,
! [X2: uni,X0: ty,X1: uni] : ( length(X0,cons(X0,X1,X2)) = $sum(1,length(X0,X2)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
! [X0: ty] :
( ! [X1: uni,X2: uni] : ( length(X0,cons(X0,X1,X2)) = $sum(1,length(X0,X2)) )
& ( 0 = length(X0,nil(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',length_def) ).
tff(f671,plain,
spl11_78,
inference(avatar_split_clause,[],[f234,f669]) ).
tff(f234,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X3) ),
inference(cnf_transformation,[],[f157]) ).
tff(f667,plain,
spl11_77,
inference(avatar_split_clause,[],[f233,f665]) ).
tff(f233,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,infix_plpl(X0,X2,X3))
| ~ mem(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tff(f663,plain,
spl11_76,
inference(avatar_split_clause,[],[f217,f661]) ).
tff(f217,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X1)
=> ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: ty,X6: uni,X9: uni] :
( sort(X0,X6)
=> ( cons_proj_1(X0,cons(X0,X6,X9)) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',cons_proj_1_def) ).
tff(f659,plain,
spl11_75,
inference(avatar_split_clause,[],[f211,f657]) ).
tff(f211,plain,
! [X2: uni,X0: ty,X1: ty] : ( nil(tuple2(X0,X1)) = combine(X1,X0,X2,nil(X1)) ),
inference(cnf_transformation,[],[f109]) ).
tff(f655,plain,
spl11_74,
inference(avatar_split_clause,[],[f75,f653]) ).
tff(f75,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f651,plain,
spl11_73,
inference(avatar_split_clause,[],[f64,f649]) ).
tff(f64,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f646,plain,
spl11_72,
inference(avatar_split_clause,[],[f165,f644]) ).
tff(f165,plain,
! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(sK7))) ) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(sK7))) ) )
& ( sK5 = tb2t3(cons(a1,t2tb(sK6),t2tb3(sK7))) )
& ( sK4 = tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8)))) )
& ( length(a1,t2tb3(sK3)) = length(a1,t2tb3(sK8)) )
& ( sK1 = tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK3)))
& ( sK0 = tb2t3(cons(a1,t2tb(sK2),t2tb3(sK3))) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f143,f148,f147,f146,f145,f144]) ).
tff(f144,plain,
( ? [X0: list_a1,X1: list_a1] :
( ? [X2: a,X3: list_a1] :
( ? [X4: list_lpa1cm_a1rp,X5: list_a1] :
( ? [X6: a,X7: list_a1] :
( ! [X8: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X6)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(X0),reverse(a1,t2tb3(X8)))) )
| ( length(a1,t2tb3(X0)) != length(a1,t2tb3(X8)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != X1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X9)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = X1 ) ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X0 ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X0))) )
=> ( ? [X3: list_a1,X2: a] :
( ? [X5: list_a1,X4: list_lpa1cm_a1rp] :
( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X6)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X9)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = sK1 ) ) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = sK0 ) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0))) ) ),
introduced(choice_axiom,[]) ).
tff(f145,plain,
( ? [X3: list_a1,X2: a] :
( ? [X5: list_a1,X4: list_lpa1cm_a1rp] :
( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X6)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X9)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = sK1 ) ) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = sK0 ) )
=> ( ? [X5: list_a1,X4: list_lpa1cm_a1rp] :
( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(X6)),t2tb1(X4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X9)) = length(a1,t2tb3(sK3)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = sK1 ) ) )
& ~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK3)))
& ( sK0 = tb2t3(cons(a1,t2tb(sK2),t2tb3(sK3))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f146,plain,
( ? [X5: list_a1,X4: list_lpa1cm_a1rp] :
( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(X6)),t2tb1(X4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X9)) = length(a1,t2tb3(sK3)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = sK1 ) ) )
=> ( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(X6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = sK5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(X9)))) = sK4 )
& ( length(a1,t2tb3(X9)) = length(a1,t2tb3(sK3)) )
& ( sK1 = tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(sK5))) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f147,plain,
( ? [X7: list_a1,X6: a] :
( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(X6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != sK1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = sK5 ) )
=> ( ! [X8: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK0),reverse(a1,t2tb3(X8)))) != tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(sK2),t2tb(sK6)),t2tb1(sK4))) )
| ( length(a1,t2tb3(X8)) != length(a1,t2tb3(sK0)) )
| ( sK1 != tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(sK7))) ) )
& ( sK5 = tb2t3(cons(a1,t2tb(sK6),t2tb3(sK7))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f148,plain,
( ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(X9)))) = sK4 )
& ( length(a1,t2tb3(X9)) = length(a1,t2tb3(sK3)) )
& ( sK1 = tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(sK5))) ) )
=> ( ( sK4 = tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8)))) )
& ( length(a1,t2tb3(sK3)) = length(a1,t2tb3(sK8)) )
& ( sK1 = tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f143,plain,
? [X0: list_a1,X1: list_a1] :
( ? [X2: a,X3: list_a1] :
( ? [X4: list_lpa1cm_a1rp,X5: list_a1] :
( ? [X6: a,X7: list_a1] :
( ! [X8: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X6)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(X0),reverse(a1,t2tb3(X8)))) )
| ( length(a1,t2tb3(X0)) != length(a1,t2tb3(X8)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X8),t2tb3(X7))) != X1 ) )
& ( tb2t3(cons(a1,t2tb(X6),t2tb3(X7))) = X5 ) )
& ? [X9: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X9)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X9)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X5))) = X1 ) ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X0 ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X0))) ),
inference(rectify,[],[f128]) ).
tff(f128,plain,
? [X0: list_a1,X1: list_a1] :
( ? [X2: a,X3: list_a1] :
( ? [X4: list_lpa1cm_a1rp,X5: list_a1] :
( ? [X7: a,X8: list_a1] :
( ! [X9: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X7)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(X0),reverse(a1,t2tb3(X9)))) )
| ( length(a1,t2tb3(X0)) != length(a1,t2tb3(X9)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X8))) != X1 ) )
& ( tb2t3(cons(a1,t2tb(X7),t2tb3(X8))) = X5 ) )
& ? [X6: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X6)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X6)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X6),t2tb3(X5))) = X1 ) ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X0 ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X0))) ),
inference(flattening,[],[f127]) ).
tff(f127,plain,
? [X0: list_a1,X1: list_a1] :
( ? [X2: a,X3: list_a1] :
( ? [X4: list_lpa1cm_a1rp,X5: list_a1] :
( ? [X7: a,X8: list_a1] :
( ! [X9: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X7)),t2tb1(X4))) != tb2t1(combine(a1,a1,t2tb3(X0),reverse(a1,t2tb3(X9)))) )
| ( length(a1,t2tb3(X0)) != length(a1,t2tb3(X9)) )
| ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X8))) != X1 ) )
& ( tb2t3(cons(a1,t2tb(X7),t2tb3(X8))) = X5 ) )
& ? [X6: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X6)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X6)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X6),t2tb3(X5))) = X1 ) ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X3)))
& ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X0 ) )
& ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X0))) ),
inference(ennf_transformation,[],[f81]) ).
tff(f81,plain,
~ ! [X0: list_a1,X1: list_a1] :
( ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X0)))
=> ! [X2: a,X3: list_a1] :
( ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X0 )
=> ( ~ $less(length(a1,t2tb3(X1)),length(a1,t2tb3(X3)))
=> ! [X4: list_lpa1cm_a1rp,X5: list_a1] :
( ? [X6: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X6)))) = X4 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X6)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X6),t2tb3(X5))) = X1 ) )
=> ! [X7: a,X8: list_a1] :
( ( tb2t3(cons(a1,t2tb(X7),t2tb3(X8))) = X5 )
=> ? [X9: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X7)),t2tb1(X4))) = tb2t1(combine(a1,a1,t2tb3(X0),reverse(a1,t2tb3(X9)))) )
& ( length(a1,t2tb3(X0)) = length(a1,t2tb3(X9)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X9),t2tb3(X8))) = X1 ) ) ) ) ) ) ),
inference(rectify,[],[f60]) ).
tff(f60,plain,
~ ! [X1: list_a1,X7: list_a1] :
( ~ $less(length(a1,t2tb3(X7)),length(a1,t2tb3(X1)))
=> ! [X2: a,X3: list_a1] :
( ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X1 )
=> ( ~ $less(length(a1,t2tb3(X7)),length(a1,t2tb3(X3)))
=> ! [X21: list_lpa1cm_a1rp,X22: list_a1] :
( ? [X23: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X23)))) = X21 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X22))) = X7 ) )
=> ! [X17: a,X18: list_a1] :
( ( tb2t3(cons(a1,t2tb(X17),t2tb3(X18))) = X22 )
=> ? [X23: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X17)),t2tb1(X21))) = tb2t1(combine(a1,a1,t2tb3(X1),reverse(a1,t2tb3(X23)))) )
& ( length(a1,t2tb3(X1)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X18))) = X7 ) ) ) ) ) ) ),
inference(theory_normalization,[],[f59]) ).
tff(f59,negated_conjecture,
~ ! [X1: list_a1,X7: list_a1] :
( $lesseq(length(a1,t2tb3(X1)),length(a1,t2tb3(X7)))
=> ! [X2: a,X3: list_a1] :
( ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X1 )
=> ( $lesseq(length(a1,t2tb3(X3)),length(a1,t2tb3(X7)))
=> ! [X21: list_lpa1cm_a1rp,X22: list_a1] :
( ? [X23: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X23)))) = X21 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X22))) = X7 ) )
=> ! [X17: a,X18: list_a1] :
( ( tb2t3(cons(a1,t2tb(X17),t2tb3(X18))) = X22 )
=> ? [X23: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X17)),t2tb1(X21))) = tb2t1(combine(a1,a1,t2tb3(X1),reverse(a1,t2tb3(X23)))) )
& ( length(a1,t2tb3(X1)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X18))) = X7 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f58]) ).
tff(f58,conjecture,
! [X1: list_a1,X7: list_a1] :
( $lesseq(length(a1,t2tb3(X1)),length(a1,t2tb3(X7)))
=> ! [X2: a,X3: list_a1] :
( ( tb2t3(cons(a1,t2tb(X2),t2tb3(X3))) = X1 )
=> ( $lesseq(length(a1,t2tb3(X3)),length(a1,t2tb3(X7)))
=> ! [X21: list_lpa1cm_a1rp,X22: list_a1] :
( ? [X23: list_a1] :
( ( tb2t1(combine(a1,a1,t2tb3(X3),reverse(a1,t2tb3(X23)))) = X21 )
& ( length(a1,t2tb3(X3)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X22))) = X7 ) )
=> ! [X17: a,X18: list_a1] :
( ( tb2t3(cons(a1,t2tb(X17),t2tb3(X18))) = X22 )
=> ? [X23: list_a1] :
( ( tb2t1(cons(tuple2(a1,a1),tuple21(a1,a1,t2tb(X2),t2tb(X17)),t2tb1(X21))) = tb2t1(combine(a1,a1,t2tb3(X1),reverse(a1,t2tb3(X23)))) )
& ( length(a1,t2tb3(X1)) = length(a1,t2tb3(X23)) )
& ( tb2t3(infix_plpl(a1,t2tb3(X23),t2tb3(X18))) = X7 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',wP_parameter_convolution_rec) ).
tff(f590,plain,
spl11_71,
inference(avatar_split_clause,[],[f223,f588]) ).
tff(f588,plain,
( spl11_71
<=> ! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X2,X1)
| ~ mem(X0,X2,reverse(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_71])]) ).
tff(f223,plain,
! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X2,X1)
| ~ mem(X0,X2,reverse(X0,X1)) ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( mem(X0,X2,X1)
| ~ mem(X0,X2,reverse(X0,X1)) )
& ( mem(X0,X2,reverse(X0,X1))
| ~ mem(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: ty,X1: uni,X2: uni] :
( mem(X0,X2,X1)
<=> mem(X0,X2,reverse(X0,X1)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: ty,X12: uni,X1: uni] :
( mem(X0,X1,X12)
<=> mem(X0,X1,reverse(X0,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_mem) ).
tff(f586,plain,
spl11_70,
inference(avatar_split_clause,[],[f222,f584]) ).
tff(f222,plain,
! [X2: uni,X0: ty,X1: uni] :
( mem(X0,X2,reverse(X0,X1))
| ~ mem(X0,X2,X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f582,plain,
spl11_69,
inference(avatar_split_clause,[],[f216,f580]) ).
tff(f216,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X2)
=> ( match_bool(X0,false,X1,X2) = X2 ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort(X0,X5)
=> ( match_bool(X0,false,X4,X5) = X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_bool_False) ).
tff(f578,plain,
( spl11_68
| ~ spl11_33
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f512,f488,f383,f575]) ).
tff(f575,plain,
( spl11_68
<=> ( t2tb3(sK3) = cons_proj_2(a1,t2tb3(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_68])]) ).
tff(f512,plain,
( ( t2tb3(sK3) = cons_proj_2(a1,t2tb3(sK0)) )
| ~ spl11_33
| ~ spl11_55 ),
inference(superposition,[],[f489,f385]) ).
tff(f573,plain,
spl11_67,
inference(avatar_split_clause,[],[f215,f571]) ).
tff(f215,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X1)
=> ( match_bool(X0,true,X1,X2) = X1 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort(X0,X4)
=> ( match_bool(X0,true,X4,X5) = X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_bool_True) ).
tff(f569,plain,
spl11_66,
inference(avatar_split_clause,[],[f186,f567]) ).
tff(f186,plain,
! [X0: uni] :
( ( t2tb2(tb2t2(X0)) = X0 )
| ~ sort(tuple2(a1,a1),X0) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: uni] :
( ( t2tb2(tb2t2(X0)) = X0 )
| ~ sort(tuple2(a1,a1),X0) ),
inference(ennf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0: uni] :
( sort(tuple2(a1,a1),X0)
=> ( t2tb2(tb2t2(X0)) = X0 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X20: uni] :
( sort(tuple2(a1,a1),X20)
=> ( t2tb2(tb2t2(X20)) = X20 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeR2) ).
tff(f565,plain,
spl11_65,
inference(avatar_split_clause,[],[f71,f563]) ).
tff(f71,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_148,[]) ).
tff(f561,plain,
spl11_64,
inference(avatar_split_clause,[],[f66,f559]) ).
tff(f66,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_142,[]) ).
tff(f537,plain,
spl11_63,
inference(avatar_split_clause,[],[f225,f535]) ).
tff(f225,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] : sort(tuple2(X1,X0),tuple21(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] : sort(tuple2(X1,X0),tuple21(X1,X0,X2,X3)),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: ty,X8: ty,X1: uni,X2: uni] : sort(tuple2(X8,X0),tuple21(X8,X0,X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_sort) ).
tff(f533,plain,
spl11_62,
inference(avatar_split_clause,[],[f202,f531]) ).
tff(f531,plain,
( spl11_62
<=> ! [X0: ty,X1: uni] :
( ( 0 = length(X0,X1) )
| ( nil(X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).
tff(f202,plain,
! [X0: ty,X1: uni] :
( ( 0 = length(X0,X1) )
| ( nil(X0) != X1 ) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: ty,X1: uni] :
( ( ( 0 = length(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( 0 != length(X0,X1) ) ) ),
inference(nnf_transformation,[],[f102]) ).
tff(f102,plain,
! [X0: ty,X1: uni] :
( ( 0 = length(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: ty,X12: uni] :
( ( 0 = length(X0,X12) )
<=> ( nil(X0) = X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',length_nil) ).
tff(f529,plain,
spl11_61,
inference(avatar_split_clause,[],[f201,f527]) ).
tff(f201,plain,
! [X0: ty,X1: uni] :
( ( nil(X0) = X1 )
| ( 0 != length(X0,X1) ) ),
inference(cnf_transformation,[],[f152]) ).
tff(f525,plain,
spl11_60,
inference(avatar_split_clause,[],[f193,f523]) ).
tff(f193,plain,
! [X0: ty,X1: uni] : ( length(X0,X1) = length(X0,reverse(X0,X1)) ),
inference(cnf_transformation,[],[f99]) ).
tff(f99,plain,
! [X0: ty,X1: uni] : ( length(X0,X1) = length(X0,reverse(X0,X1)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: ty,X12: uni] : ( length(X0,X12) = length(X0,reverse(X0,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_length) ).
tff(f521,plain,
spl11_59,
inference(avatar_split_clause,[],[f70,f519]) ).
tff(f70,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_147,[]) ).
tff(f517,plain,
spl11_58,
inference(avatar_split_clause,[],[f69,f515]) ).
tff(f69,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_146,[]) ).
tff(f505,plain,
( ~ spl11_57
| ~ spl11_33
| ~ spl11_46 ),
inference(avatar_split_clause,[],[f470,f441,f383,f502]) ).
tff(f502,plain,
( spl11_57
<=> ( t2tb3(sK0) = nil(a1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_57])]) ).
tff(f470,plain,
( ( t2tb3(sK0) != nil(a1) )
| ~ spl11_33
| ~ spl11_46 ),
inference(superposition,[],[f442,f385]) ).
tff(f494,plain,
spl11_56,
inference(avatar_split_clause,[],[f235,f492]) ).
tff(f235,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : sort(X1,match_list(X1,X0,X2,X3,X4)),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni] : sort(X1,match_list(X1,X0,X2,X3,X4)),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: ty,X8: ty,X1: uni,X2: uni,X3: uni] : sort(X8,match_list(X8,X0,X1,X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_list_sort) ).
tff(f490,plain,
spl11_55,
inference(avatar_split_clause,[],[f208,f488]) ).
tff(f208,plain,
! [X2: uni,X0: ty,X1: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f106]) ).
tff(f106,plain,
! [X0: ty,X1: uni,X2: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: ty,X6: uni,X9: uni] : ( cons_proj_2(X0,cons(X0,X6,X9)) = X9 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',cons_proj_2_def) ).
tff(f486,plain,
spl11_54,
inference(avatar_split_clause,[],[f197,f484]) ).
tff(f484,plain,
( spl11_54
<=> ! [X0: ty,X1: uni] :
( ~ mem(X0,X1,nil(X0))
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_54])]) ).
tff(f197,plain,
! [X0: ty,X1: uni] :
( ~ mem(X0,X1,nil(X0))
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tff(f482,plain,
spl11_53,
inference(avatar_split_clause,[],[f185,f480]) ).
tff(f185,plain,
! [X0: uni] :
( ( t2tb(tb2t(X0)) = X0 )
| ~ sort(a1,X0) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: uni] :
( ( t2tb(tb2t(X0)) = X0 )
| ~ sort(a1,X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,plain,
! [X0: uni] :
( sort(a1,X0)
=> ( t2tb(tb2t(X0)) = X0 ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X20: uni] :
( sort(a1,X20)
=> ( t2tb(tb2t(X20)) = X20 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeR) ).
tff(f478,plain,
spl11_52,
inference(avatar_split_clause,[],[f80,f476]) ).
tff(f80,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_164,[]) ).
tff(f474,plain,
spl11_51,
inference(avatar_split_clause,[],[f72,f472]) ).
tff(f72,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_150,[]) ).
tff(f460,plain,
spl11_50,
inference(avatar_split_clause,[],[f224,f458]) ).
tff(f224,plain,
! [X2: uni,X3: uni,X0: ty,X1: bool] : sort(X0,match_bool(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: ty,X1: bool,X2: uni,X3: uni] : sort(X0,match_bool(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',match_bool_sort) ).
tff(f456,plain,
spl11_49,
inference(avatar_split_clause,[],[f207,f454]) ).
tff(f454,plain,
( spl11_49
<=> ! [X2: uni,X0: ty,X1: uni] : sort(list(X0),cons(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).
tff(f207,plain,
! [X2: uni,X0: ty,X1: uni] : sort(list(X0),cons(X0,X1,X2)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: ty,X1: uni,X2: uni] : sort(list(X0),cons(X0,X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',cons_sort) ).
tff(f452,plain,
spl11_48,
inference(avatar_split_clause,[],[f206,f450]) ).
tff(f450,plain,
( spl11_48
<=> ! [X2: uni,X0: ty,X1: uni] : sort(list(X0),infix_plpl(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).
tff(f206,plain,
! [X2: uni,X0: ty,X1: uni] : sort(list(X0),infix_plpl(X0,X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
! [X0: ty,X1: uni,X2: uni] : sort(list(X0),infix_plpl(X0,X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',infix_plpl_sort) ).
tff(f448,plain,
( spl11_47
| ~ spl11_3
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f363,f336,f249,f445]) ).
tff(f249,plain,
( spl11_3
<=> ( sK1 = tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
tff(f363,plain,
( ( t2tb3(sK1) = infix_plpl(a1,t2tb3(sK8),t2tb3(sK5)) )
| ~ spl11_3
| ~ spl11_23 ),
inference(superposition,[],[f337,f251]) ).
tff(f251,plain,
( ( sK1 = tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f249]) ).
tff(f443,plain,
spl11_46,
inference(avatar_split_clause,[],[f205,f441]) ).
tff(f205,plain,
! [X2: uni,X0: ty,X1: uni] : ( nil(X0) != cons(X0,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0: ty,X1: uni,X2: uni] : ( nil(X0) != cons(X0,X1,X2) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: ty,X10: uni,X11: uni] : ( nil(X0) != cons(X0,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',nil_Cons) ).
tff(f439,plain,
spl11_45,
inference(avatar_split_clause,[],[f194,f437]) ).
tff(f194,plain,
! [X0: ty,X1: uni] : ( infix_plpl(X0,nil(X0),X1) = X1 ),
inference(cnf_transformation,[],[f100]) ).
tff(f435,plain,
spl11_44,
inference(avatar_split_clause,[],[f192,f433]) ).
tff(f192,plain,
! [X0: ty,X1: uni] : ( infix_plpl(X0,X1,nil(X0)) = X1 ),
inference(cnf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: ty,X1: uni] : ( infix_plpl(X0,X1,nil(X0)) = X1 ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: ty,X12: uni] : ( infix_plpl(X0,X12,nil(X0)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',append_l_nil) ).
tff(f431,plain,
spl11_43,
inference(avatar_split_clause,[],[f191,f429]) ).
tff(f191,plain,
! [X0: ty,X1: uni] : ( reverse(X0,reverse(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f97]) ).
tff(f97,plain,
! [X0: ty,X1: uni] : ( reverse(X0,reverse(X0,X1)) = X1 ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: ty,X12: uni] : ( reverse(X0,reverse(X0,X12)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_reverse) ).
tff(f427,plain,
spl11_42,
inference(avatar_split_clause,[],[f182,f425]) ).
tff(f182,plain,
! [X0: ty] : ( nil(X0) = reverse(X0,nil(X0)) ),
inference(cnf_transformation,[],[f32]) ).
tff(f423,plain,
spl11_41,
inference(avatar_split_clause,[],[f179,f421]) ).
tff(f421,plain,
( spl11_41
<=> ! [X0: list_lpa1cm_a1rp] : sort(list(tuple2(a1,a1)),t2tb1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_41])]) ).
tff(f179,plain,
! [X0: list_lpa1cm_a1rp] : sort(list(tuple2(a1,a1)),t2tb1(X0)),
inference(cnf_transformation,[],[f92]) ).
tff(f92,plain,
! [X0: list_lpa1cm_a1rp] : sort(list(tuple2(a1,a1)),t2tb1(X0)),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X1: list_lpa1cm_a1rp] : sort(list(tuple2(a1,a1)),t2tb1(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',t2tb_sort1) ).
tff(f419,plain,
spl11_40,
inference(avatar_split_clause,[],[f74,f417]) ).
tff(f74,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f415,plain,
spl11_39,
inference(avatar_split_clause,[],[f63,f413]) ).
tff(f63,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f411,plain,
( spl11_38
| ~ spl11_5
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f362,f336,f259,f408]) ).
tff(f259,plain,
( spl11_5
<=> ( sK5 = tb2t3(cons(a1,t2tb(sK6),t2tb3(sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
tff(f362,plain,
( ( t2tb3(sK5) = cons(a1,t2tb(sK6),t2tb3(sK7)) )
| ~ spl11_5
| ~ spl11_23 ),
inference(superposition,[],[f337,f261]) ).
tff(f261,plain,
( ( sK5 = tb2t3(cons(a1,t2tb(sK6),t2tb3(sK7))) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f259]) ).
tff(f402,plain,
spl11_37,
inference(avatar_split_clause,[],[f204,f400]) ).
tff(f204,plain,
! [X2: uni,X0: ty,X1: ty] : sort(X0,tuple2_proj_2(X1,X0,X2)),
inference(cnf_transformation,[],[f104]) ).
tff(f104,plain,
! [X0: ty,X1: ty,X2: uni] : sort(X0,tuple2_proj_2(X1,X0,X2)),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: ty,X8: ty,X1: uni] : sort(X0,tuple2_proj_2(X8,X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_proj_2_sort) ).
tff(f398,plain,
spl11_36,
inference(avatar_split_clause,[],[f203,f396]) ).
tff(f203,plain,
! [X2: uni,X0: ty,X1: ty] : sort(X1,tuple2_proj_1(X1,X0,X2)),
inference(cnf_transformation,[],[f103]) ).
tff(f103,plain,
! [X0: ty,X1: ty,X2: uni] : sort(X1,tuple2_proj_1(X1,X0,X2)),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: ty,X8: ty,X1: uni] : sort(X8,tuple2_proj_1(X8,X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple2_proj_1_sort) ).
tff(f394,plain,
spl11_35,
inference(avatar_split_clause,[],[f190,f392]) ).
tff(f190,plain,
! [X0: ty,X1: uni] : sort(list(X0),reverse(X0,X1)),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
! [X0: ty,X1: uni] : sort(list(X0),reverse(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',reverse_sort) ).
tff(f390,plain,
spl11_34,
inference(avatar_split_clause,[],[f189,f388]) ).
tff(f388,plain,
( spl11_34
<=> ! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).
tff(f189,plain,
! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',cons_proj_2_sort) ).
tff(f386,plain,
( spl11_33
| ~ spl11_2
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f361,f336,f244,f383]) ).
tff(f244,plain,
( spl11_2
<=> ( sK0 = tb2t3(cons(a1,t2tb(sK2),t2tb3(sK3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
tff(f361,plain,
( ( t2tb3(sK0) = cons(a1,t2tb(sK2),t2tb3(sK3)) )
| ~ spl11_2
| ~ spl11_23 ),
inference(superposition,[],[f337,f246]) ).
tff(f246,plain,
( ( sK0 = tb2t3(cons(a1,t2tb(sK2),t2tb3(sK3))) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f244]) ).
tff(f381,plain,
spl11_32,
inference(avatar_split_clause,[],[f184,f379]) ).
tff(f184,plain,
! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ),
inference(cnf_transformation,[],[f93]) ).
tff(f93,plain,
! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X6: bool] :
( ( false = X6 )
| ( true = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bool_inversion) ).
tff(f377,plain,
spl11_31,
inference(avatar_split_clause,[],[f180,f375]) ).
tff(f180,plain,
! [X0: ty] : ( 0 = length(X0,nil(X0)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f373,plain,
spl11_30,
inference(avatar_split_clause,[],[f178,f371]) ).
tff(f178,plain,
! [X0: lpa1cm_a1rp] : sort(tuple2(a1,a1),t2tb2(X0)),
inference(cnf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: lpa1cm_a1rp] : sort(tuple2(a1,a1),t2tb2(X0)),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X1: lpa1cm_a1rp] : sort(tuple2(a1,a1),t2tb2(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',t2tb_sort2) ).
tff(f369,plain,
spl11_29,
inference(avatar_split_clause,[],[f67,f367]) ).
tff(f67,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_143,[]) ).
tff(f360,plain,
( spl11_28
| ~ spl11_7
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f355,f324,f269,f357]) ).
tff(f269,plain,
( spl11_7
<=> ( sK4 = tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
tff(f324,plain,
( spl11_20
<=> ! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).
tff(f355,plain,
( ( t2tb1(sK4) = combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8))) )
| ~ spl11_7
| ~ spl11_20 ),
inference(superposition,[],[f325,f271]) ).
tff(f271,plain,
( ( sK4 = tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8)))) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f269]) ).
tff(f325,plain,
( ! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f324]) ).
tff(f354,plain,
spl11_27,
inference(avatar_split_clause,[],[f188,f352]) ).
tff(f188,plain,
! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',cons_proj_1_sort) ).
tff(f350,plain,
spl11_26,
inference(avatar_split_clause,[],[f187,f348]) ).
tff(f187,plain,
! [X0: ty,X1: uni] : ~ $less(length(X0,X1),0),
inference(cnf_transformation,[],[f96]) ).
tff(f96,plain,
! [X0: ty,X1: uni] : ~ $less(length(X0,X1),0),
inference(rectify,[],[f61]) ).
tff(f61,plain,
! [X0: ty,X12: uni] : ~ $less(length(X0,X12),0),
inference(theory_normalization,[],[f21]) ).
tff(f21,axiom,
! [X0: ty,X12: uni] : $lesseq(0,length(X0,X12)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',length_nonnegative) ).
tff(f346,plain,
spl11_25,
inference(avatar_split_clause,[],[f177,f344]) ).
tff(f344,plain,
( spl11_25
<=> ! [X0: ty] : sort(list(X0),nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).
tff(f177,plain,
! [X0: ty] : sort(list(X0),nil(X0)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: ty] : sort(list(X0),nil(X0)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',nil_sort) ).
tff(f342,plain,
spl11_24,
inference(avatar_split_clause,[],[f176,f340]) ).
tff(f340,plain,
( spl11_24
<=> ! [X0: list_a1] : sort(list(a1),t2tb3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).
tff(f176,plain,
! [X0: list_a1] : sort(list(a1),t2tb3(X0)),
inference(cnf_transformation,[],[f90]) ).
tff(f90,plain,
! [X0: list_a1] : sort(list(a1),t2tb3(X0)),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X1: list_a1] : sort(list(a1),t2tb3(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',t2tb_sort3) ).
tff(f338,plain,
spl11_23,
inference(avatar_split_clause,[],[f175,f336]) ).
tff(f175,plain,
! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
inference(cnf_transformation,[],[f89]) ).
tff(f89,plain,
! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X20: uni] : ( t2tb3(tb2t3(X20)) = X20 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeR3) ).
tff(f334,plain,
spl11_22,
inference(avatar_split_clause,[],[f174,f332]) ).
tff(f174,plain,
! [X0: list_a1] : ( tb2t3(t2tb3(X0)) = X0 ),
inference(cnf_transformation,[],[f88]) ).
tff(f88,plain,
! [X0: list_a1] : ( tb2t3(t2tb3(X0)) = X0 ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X19: list_a1] : ( tb2t3(t2tb3(X19)) = X19 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeL3) ).
tff(f330,plain,
spl11_21,
inference(avatar_split_clause,[],[f173,f328]) ).
tff(f328,plain,
( spl11_21
<=> ! [X0: list_lpa1cm_a1rp] : ( tb2t1(t2tb1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).
tff(f173,plain,
! [X0: list_lpa1cm_a1rp] : ( tb2t1(t2tb1(X0)) = X0 ),
inference(cnf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0: list_lpa1cm_a1rp] : ( tb2t1(t2tb1(X0)) = X0 ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X19: list_lpa1cm_a1rp] : ( tb2t1(t2tb1(X19)) = X19 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeL1) ).
tff(f326,plain,
spl11_20,
inference(avatar_split_clause,[],[f172,f324]) ).
tff(f172,plain,
! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ),
inference(cnf_transformation,[],[f86]) ).
tff(f86,plain,
! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X20: uni] : ( t2tb1(tb2t1(X20)) = X20 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeR1) ).
tff(f322,plain,
spl11_19,
inference(avatar_split_clause,[],[f171,f320]) ).
tff(f320,plain,
( spl11_19
<=> ! [X0: a] : ( tb2t(t2tb(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).
tff(f171,plain,
! [X0: a] : ( tb2t(t2tb(X0)) = X0 ),
inference(cnf_transformation,[],[f85]) ).
tff(f85,plain,
! [X0: a] : ( tb2t(t2tb(X0)) = X0 ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X19: a] : ( tb2t(t2tb(X19)) = X19 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeL) ).
tff(f318,plain,
spl11_18,
inference(avatar_split_clause,[],[f170,f316]) ).
tff(f316,plain,
( spl11_18
<=> ! [X0: lpa1cm_a1rp] : ( tb2t2(t2tb2(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
tff(f170,plain,
! [X0: lpa1cm_a1rp] : ( tb2t2(t2tb2(X0)) = X0 ),
inference(cnf_transformation,[],[f84]) ).
tff(f84,plain,
! [X0: lpa1cm_a1rp] : ( tb2t2(t2tb2(X0)) = X0 ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X19: lpa1cm_a1rp] : ( tb2t2(t2tb2(X19)) = X19 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',bridgeL2) ).
tff(f314,plain,
spl11_17,
inference(avatar_split_clause,[],[f77,f312]) ).
tff(f77,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_152,[]) ).
tff(f310,plain,
spl11_16,
inference(avatar_split_clause,[],[f76,f308]) ).
tff(f308,plain,
( spl11_16
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
tff(f76,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f306,plain,
spl11_15,
inference(avatar_split_clause,[],[f73,f304]) ).
tff(f304,plain,
( spl11_15
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
tff(f73,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_151,[]) ).
tff(f302,plain,
spl11_14,
inference(avatar_split_clause,[],[f65,f300]) ).
tff(f300,plain,
( spl11_14
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
tff(f65,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f298,plain,
( spl11_13
| ~ spl11_10 ),
inference(avatar_split_clause,[],[f286,f283,f296]) ).
tff(f296,plain,
( spl11_13
<=> ! [X0: tuple0,X1: tuple0] : ( X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
tff(f283,plain,
( spl11_10
<=> ! [X0: tuple0] : ( tuple02 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
tff(f286,plain,
( ! [X0: tuple0,X1: tuple0] : ( X0 = X1 )
| ~ spl11_10 ),
inference(superposition,[],[f284,f284]) ).
tff(f284,plain,
( ! [X0: tuple0] : ( tuple02 = X0 )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f283]) ).
tff(f294,plain,
spl11_12,
inference(avatar_split_clause,[],[f169,f292]) ).
tff(f169,plain,
! [X0: a] : sort(a1,t2tb(X0)),
inference(cnf_transformation,[],[f83]) ).
tff(f83,plain,
! [X0: a] : sort(a1,t2tb(X0)),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X1: a] : sort(a1,t2tb(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',t2tb_sort) ).
tff(f290,plain,
spl11_11,
inference(avatar_split_clause,[],[f168,f288]) ).
tff(f168,plain,
! [X0: ty] : sort(X0,witness(X0)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: ty] : sort(X0,witness(X0)),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',witness_sort) ).
tff(f285,plain,
spl11_10,
inference(avatar_split_clause,[],[f167,f283]) ).
tff(f167,plain,
! [X0: tuple0] : ( tuple02 = X0 ),
inference(cnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0: tuple0] : ( tuple02 = X0 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: tuple0] : ( tuple02 = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',tuple0_inversion) ).
tff(f281,plain,
~ spl11_9,
inference(avatar_split_clause,[],[f166,f278]) ).
tff(f278,plain,
( spl11_9
<=> ( true = false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
tff(f166,plain,
true != false,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
true != false,
file('/export/starexec/sandbox2/tmp/tmp.1vkwhmdYfX/Vampire---4.8_6334',true_False) ).
tff(f276,plain,
spl11_8,
inference(avatar_split_clause,[],[f68,f274]) ).
tff(f68,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
tff(f272,plain,
spl11_7,
inference(avatar_split_clause,[],[f163,f269]) ).
tff(f163,plain,
sK4 = tb2t1(combine(a1,a1,t2tb3(sK3),reverse(a1,t2tb3(sK8)))),
inference(cnf_transformation,[],[f149]) ).
tff(f267,plain,
~ spl11_6,
inference(avatar_split_clause,[],[f237,f264]) ).
tff(f237,plain,
~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK8))),
inference(forward_demodulation,[],[f160,f162]) ).
tff(f162,plain,
length(a1,t2tb3(sK3)) = length(a1,t2tb3(sK8)),
inference(cnf_transformation,[],[f149]) ).
tff(f160,plain,
~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK3))),
inference(cnf_transformation,[],[f149]) ).
tff(f262,plain,
spl11_5,
inference(avatar_split_clause,[],[f164,f259]) ).
tff(f164,plain,
sK5 = tb2t3(cons(a1,t2tb(sK6),t2tb3(sK7))),
inference(cnf_transformation,[],[f149]) ).
tff(f257,plain,
spl11_4,
inference(avatar_split_clause,[],[f162,f254]) ).
tff(f252,plain,
spl11_3,
inference(avatar_split_clause,[],[f161,f249]) ).
tff(f161,plain,
sK1 = tb2t3(infix_plpl(a1,t2tb3(sK8),t2tb3(sK5))),
inference(cnf_transformation,[],[f149]) ).
tff(f247,plain,
spl11_2,
inference(avatar_split_clause,[],[f159,f244]) ).
tff(f159,plain,
sK0 = tb2t3(cons(a1,t2tb(sK2),t2tb3(sK3))),
inference(cnf_transformation,[],[f149]) ).
tff(f242,plain,
~ spl11_1,
inference(avatar_split_clause,[],[f158,f239]) ).
tff(f158,plain,
~ $less(length(a1,t2tb3(sK1)),length(a1,t2tb3(sK0))),
inference(cnf_transformation,[],[f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW648_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 30 17:01:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.39 % (6442)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (6445)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.40 % (6447)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.40 % (6451)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.40 % (6449)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.40 % (6452)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.40 % (6454)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.40 % (6456)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.40 % (6451)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (6447)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (6445)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (6451)Terminated due to inappropriate strategy.
% 0.21/0.40 % (6451)------------------------------
% 0.21/0.40 % (6451)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.40 % (6447)Terminated due to inappropriate strategy.
% 0.21/0.40 % (6447)------------------------------
% 0.21/0.40 % (6447)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.40 % (6445)Terminated due to inappropriate strategy.
% 0.21/0.40 % (6445)------------------------------
% 0.21/0.40 % (6445)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.40 % (6451)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.40 % (6451)Termination reason: Inappropriate
% 0.21/0.40
% 0.21/0.40 % (6447)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.40 % (6445)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.40 % (6447)Termination reason: Inappropriate
% 0.21/0.40 % (6445)Termination reason: Inappropriate
% 0.21/0.40
% 0.21/0.40 % (6451)Memory used [KB]: 1023
% 0.21/0.40
% 0.21/0.40 % (6451)Time elapsed: 0.003 s
% 0.21/0.40 % (6451)------------------------------
% 0.21/0.40 % (6451)------------------------------
% 0.21/0.40 % (6447)Memory used [KB]: 1023
% 0.21/0.40 % (6445)Memory used [KB]: 1023
% 0.21/0.40 % (6447)Time elapsed: 0.004 s
% 0.21/0.40 % (6445)Time elapsed: 0.004 s
% 0.21/0.40 % (6447)------------------------------
% 0.21/0.40 % (6447)------------------------------
% 0.21/0.40 % (6445)------------------------------
% 0.21/0.40 % (6445)------------------------------
% 0.21/0.40 % (6457)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on Vampire---4 for (411ds/0Mi)
% 0.21/0.40 % (6458)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on Vampire---4 for (382ds/0Mi)
% 0.21/0.40 % (6459)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 0.21/0.41 % (6457)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.41 % (6457)Terminated due to inappropriate strategy.
% 0.21/0.41 % (6457)------------------------------
% 0.21/0.41 % (6457)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.41 % (6457)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.41 % (6457)Termination reason: Inappropriate
% 0.21/0.41
% 0.21/0.41 % (6457)Memory used [KB]: 1023
% 0.21/0.41 % (6457)Time elapsed: 0.004 s
% 0.21/0.41 % (6457)------------------------------
% 0.21/0.41 % (6457)------------------------------
% 0.21/0.41 % (6460)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on Vampire---4 for (354ds/0Mi)
% 3.13/0.84 % (6452)First to succeed.
% 3.13/0.86 % (6452)Refutation found. Thanks to Tanya!
% 3.13/0.86 % SZS status Theorem for Vampire---4
% 3.13/0.86 % SZS output start Proof for Vampire---4
% See solution above
% 3.13/0.87 % (6452)------------------------------
% 3.13/0.87 % (6452)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 3.13/0.87 % (6452)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 3.13/0.87 % (6452)Termination reason: Refutation
% 3.13/0.87
% 3.13/0.87 % (6452)Memory used [KB]: 18549
% 3.13/0.87 % (6452)Time elapsed: 0.463 s
% 3.13/0.87 % (6452)------------------------------
% 3.13/0.87 % (6452)------------------------------
% 3.13/0.87 % (6442)Success in time 0.51 s
% 3.13/0.88 % Vampire---4.8 exiting
%------------------------------------------------------------------------------