TSTP Solution File: LCL799_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL799_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:28 EDT 2024
% Result : Theorem 1.35s 0.55s
% Output : Refutation 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL799_5 : TPTP v8.1.2. Released v6.0.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:27:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (4025)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39 % (4032)WARNING: value z3 for option sas not known
% 0.22/0.39 % (4030)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (4033)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (4032)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39 % (4031)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (4034)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (4036)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39 % (4035)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.40 % (4036)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.22/0.40
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (4049)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (4050)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.42 % (4051)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.42 % (4049)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (4050)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % Exception at run slice level
% 0.22/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44 % (4058)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 theBenchmark for (354ds/0Mi)
% 1.21/0.53 % (4034)First to succeed.
% 1.35/0.55 % (4034)Refutation found. Thanks to Tanya!
% 1.35/0.55 % SZS status Theorem for theBenchmark
% 1.35/0.55 % SZS output start Proof for theBenchmark
% 1.35/0.55 tff(type_def_5, type, bool: $tType).
% 1.35/0.55 tff(type_def_6, type, dB: $tType).
% 1.35/0.55 tff(type_def_7, type, list: $tType > $tType).
% 1.35/0.55 tff(type_def_8, type, nat: $tType).
% 1.35/0.55 tff(type_def_9, type, type: $tType).
% 1.35/0.55 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 1.35/0.55 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))))).
% 1.35/0.55 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * X1) > fun(X0,X2))).
% 1.35/0.55 tff(func_def_2, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 1.35/0.55 tff(func_def_3, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.35/0.55 tff(func_def_4, type, it: fun(dB,bool)).
% 1.35/0.55 tff(func_def_5, type, beta: fun(dB,fun(dB,bool))).
% 1.35/0.55 tff(func_def_6, type, abs: dB > dB).
% 1.35/0.55 tff(func_def_7, type, app: fun(dB,fun(dB,dB))).
% 1.35/0.55 tff(func_def_8, type, var: nat > dB).
% 1.35/0.55 tff(func_def_9, type, dB_size: dB > nat).
% 1.35/0.55 tff(func_def_10, type, lift: fun(dB,fun(nat,dB))).
% 1.35/0.55 tff(func_def_11, type, subst: (dB * dB * nat) > dB).
% 1.35/0.55 tff(func_def_12, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 1.35/0.55 tff(func_def_13, type, foldr: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * list(X0) * X1) > X1)).
% 1.35/0.55 tff(func_def_14, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 1.35/0.55 tff(func_def_15, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 1.35/0.55 tff(func_def_16, type, map: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * list(X0)) > list(X1))).
% 1.35/0.55 tff(func_def_17, type, size_size: !>[X0: $tType]:((X0) > nat)).
% 1.35/0.55 tff(func_def_18, type, shift: !>[X0: $tType]:((fun(nat,X0) * nat * X0) > fun(nat,X0))).
% 1.35/0.55 tff(func_def_19, type, fun1: fun(type,fun(type,type))).
% 1.35/0.55 tff(func_def_20, type, type_case: !>[X0: $tType]:((fun(nat,X0) * fun(type,fun(type,X0)) * type) > X0)).
% 1.35/0.55 tff(func_def_21, type, typing: (fun(nat,type) * dB) > fun(type,bool)).
% 1.35/0.55 tff(func_def_22, type, typings: (fun(nat,type) * list(dB)) > fun(list(type),bool)).
% 1.35/0.55 tff(func_def_23, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 1.35/0.55 tff(func_def_24, type, fFalse: bool).
% 1.35/0.55 tff(func_def_25, type, fTrue: bool).
% 1.35/0.55 tff(func_def_26, type, fconj: fun(bool,fun(bool,bool))).
% 1.35/0.55 tff(func_def_27, type, t: type).
% 1.35/0.55 tff(func_def_28, type, t2: type).
% 1.35/0.55 tff(func_def_29, type, t_a: type).
% 1.35/0.55 tff(func_def_30, type, t1: type).
% 1.35/0.55 tff(func_def_31, type, ts: list(type)).
% 1.35/0.55 tff(func_def_32, type, a: dB).
% 1.35/0.55 tff(func_def_33, type, as: list(dB)).
% 1.35/0.55 tff(func_def_34, type, e: fun(nat,type)).
% 1.35/0.55 tff(func_def_35, type, ea: fun(nat,type)).
% 1.35/0.55 tff(func_def_36, type, i: nat).
% 1.35/0.55 tff(func_def_37, type, ia: nat).
% 1.35/0.55 tff(func_def_38, type, n: nat).
% 1.35/0.55 tff(func_def_39, type, rs: list(dB)).
% 1.35/0.55 tff(func_def_40, type, t3: dB).
% 1.35/0.55 tff(func_def_41, type, u: dB).
% 1.35/0.55 tff(func_def_42, type, ua: dB).
% 1.35/0.55 tff(func_def_43, type, sK5: type).
% 1.35/0.55 tff(func_def_44, type, sK6: list(type)).
% 1.35/0.55 tff(func_def_45, type, sK7: dB > dB).
% 1.35/0.55 tff(func_def_46, type, sK8: dB > list(dB)).
% 1.35/0.55 tff(func_def_47, type, sK9: dB > nat).
% 1.35/0.55 tff(func_def_48, type, sK10: dB > dB).
% 1.35/0.55 tff(func_def_49, type, sK11: dB > dB).
% 1.35/0.55 tff(func_def_50, type, sK12: dB > list(dB)).
% 1.35/0.55 tff(func_def_51, type, sK13: (dB * dB) > dB).
% 1.35/0.55 tff(func_def_52, type, sK14: (dB * fun(nat,type)) > type).
% 1.35/0.55 tff(func_def_53, type, sK15: (dB * fun(nat,type)) > type).
% 1.35/0.55 tff(func_def_54, type, sK16: (type * dB * fun(nat,type)) > type).
% 1.35/0.55 tff(func_def_55, type, sK17: (type * dB * fun(nat,type)) > type).
% 1.35/0.55 tff(func_def_56, type, sK18: (dB * list(dB) * dB) > dB).
% 1.35/0.55 tff(func_def_57, type, sK19: (dB * list(dB) * dB) > dB).
% 1.35/0.55 tff(func_def_58, type, sK20: (dB * list(dB) * dB) > list(dB)).
% 1.35/0.55 tff(func_def_59, type, sK21: (dB * list(dB) * dB) > list(dB)).
% 1.35/0.55 tff(func_def_60, type, sK22: (dB * list(dB) * dB) > dB).
% 1.35/0.55 tff(func_def_61, type, sK23: (dB * list(dB) * nat) > list(dB)).
% 1.35/0.55 tff(func_def_62, type, sK24: (dB * dB * dB) > dB).
% 1.35/0.55 tff(func_def_63, type, sK25: (dB * dB * dB) > dB).
% 1.35/0.55 tff(func_def_64, type, sK26: (dB * dB * dB) > dB).
% 1.35/0.55 tff(func_def_65, type, sK27: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 1.35/0.55 tff(func_def_66, type, sK28: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 1.35/0.55 tff(func_def_67, type, sK29: (type * list(dB) * nat * fun(nat,type)) > list(type)).
% 1.35/0.55 tff(func_def_68, type, sK30: (type * dB * dB * fun(nat,type)) > type).
% 1.35/0.55 tff(func_def_69, type, sK31: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 1.35/0.55 tff(func_def_70, type, sK32: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > list(X0))).
% 1.35/0.55 tff(func_def_71, type, sK33: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > X0)).
% 1.35/0.55 tff(func_def_72, type, sK34: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.35/0.55 tff(func_def_73, type, sK35: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.35/0.55 tff(func_def_74, type, sK36: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 1.35/0.55 tff(func_def_75, type, sK37: (type * type * list(dB) * fun(nat,type)) > list(type)).
% 1.35/0.55 tff(pred_def_1, type, zero: !>[X0: $tType]:($o)).
% 1.35/0.55 tff(pred_def_2, type, step1: !>[X0: $tType]:((fun(X0,fun(X0,bool)) * list(X0) * list(X0)) > $o)).
% 1.35/0.55 tff(pred_def_3, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.35/0.55 tff(pred_def_4, type, pp: bool > $o).
% 1.35/0.55 tff(pred_def_5, type, sP0: dB > $o).
% 1.35/0.55 tff(pred_def_6, type, sP1: dB > $o).
% 1.35/0.55 tff(pred_def_7, type, sP2: (dB * list(dB) * dB) > $o).
% 1.35/0.55 tff(pred_def_8, type, sP3: (dB * dB * dB) > $o).
% 1.35/0.55 tff(pred_def_9, type, sP4: !>[X0: $tType]:((list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0) > $o)).
% 1.35/0.55 tff(f3391,plain,(
% 1.35/0.55 $false),
% 1.35/0.55 inference(avatar_sat_refutation,[],[f558,f563,f568,f573,f577,f581,f586,f591,f596,f600,f604,f616,f620,f624,f628,f632,f636,f643,f648,f653,f657,f661,f665,f669,f684,f690,f694,f698,f714,f718,f722,f727,f733,f738,f742,f746,f753,f758,f763,f767,f771,f776,f781,f785,f790,f804,f808,f813,f818,f823,f828,f832,f836,f840,f844,f852,f856,f860,f865,f872,f876,f880,f885,f889,f893,f897,f901,f917,f926,f932,f939,f944,f948,f953,f957,f961,f965,f969,f974,f979,f983,f989,f1003,f1008,f1013,f1017,f1023,f1027,f1031,f1043,f1049,f1053,f1058,f1065,f1083,f1088,f1096,f1100,f1116,f1121,f1125,f1140,f1144,f1150,f1157,f1161,f1166,f1171,f1175,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1211,f1313,f1319,f1328,f1334,f1343,f1348,f1359,f1363,f1368,f1427,f1432,f1437,f1441,f1446,f1456,f1462,f1467,f1474,f1481,f1488,f1499,f1505,f1519,f1524,f1531,f1539,f1544,f1551,f1557,f1569,f1573,f1577,f1581,f1586,f1594,f1599,f1605,f1630,f1634,f1660,f1665,f1685,f1690,f1700,f1704,f1715,f1721,f1735,f1739,f1745,f1757,f1776,f1781,f1792,f1821,f1825,f1830,f1839,f1844,f1856,f1862,f1879,f1887,f1899,f1904,f1913,f1918,f1931,f1939,f1944,f1952,f1960,f1968,f1976,f1984,f1990,f2002,f2006,f2010,f2014,f2020,f2032,f2038,f2052,f2060,f2068,f2086,f2090,f2094,f2104,f2113,f2121,f2130,f2138,f2147,f2156,f2160,f2169,f2177,f2186,f2254,f2258,f2266,f2273,f2809,f2813,f2840,f2844,f2849,f2854,f2859,f2875,f2879,f2884,f2888,f2892,f2897,f2926,f2930,f2934,f2938,f2943,f2948,f2952,f2956,f2960,f2964,f2968,f2996,f3009,f3013,f3017,f3022,f3033,f3037,f3041,f3045,f3055,f3059,f3064,f3079,f3083,f3087,f3091,f3095,f3102,f3106,f3110,f3245,f3249,f3253,f3257,f3261,f3265,f3297,f3336,f3340,f3344,f3390])).
% 1.35/0.55 tff(f3390,plain,(
% 1.35/0.55 ~spl38_3 | spl38_4 | ~spl38_13 | ~spl38_20 | ~spl38_271),
% 1.35/0.55 inference(avatar_split_clause,[],[f3324,f3259,f650,f618,f570,f565])).
% 1.35/0.55 tff(f565,plain,(
% 1.35/0.55 spl38_3 <=> pp(fTrue)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_3])])).
% 1.35/0.55 tff(f570,plain,(
% 1.35/0.55 spl38_4 <=> pp(aa(type,bool,typing(e,subst(a,u,i)),t))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_4])])).
% 1.35/0.55 tff(f618,plain,(
% 1.35/0.55 spl38_13 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_13])])).
% 1.35/0.55 tff(f650,plain,(
% 1.35/0.55 spl38_20 <=> pp(aa(type,bool,typing(e,u),t1))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_20])])).
% 1.35/0.55 tff(f3259,plain,(
% 1.35/0.55 spl38_271 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t1)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),t)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_271])])).
% 1.35/0.55 tff(f3324,plain,(
% 1.35/0.55 ~pp(fTrue) | (spl38_4 | ~spl38_13 | ~spl38_20 | ~spl38_271)),
% 1.35/0.55 inference(forward_demodulation,[],[f3315,f1398])).
% 1.35/0.55 tff(f1398,plain,(
% 1.35/0.55 aa(type,bool,typing(e,u),t1) = fTrue | (~spl38_13 | ~spl38_20)),
% 1.35/0.55 inference(resolution,[],[f619,f652])).
% 1.35/0.55 tff(f652,plain,(
% 1.35/0.55 pp(aa(type,bool,typing(e,u),t1)) | ~spl38_20),
% 1.35/0.55 inference(avatar_component_clause,[],[f650])).
% 1.35/0.55 tff(f619,plain,(
% 1.35/0.55 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl38_13),
% 1.35/0.55 inference(avatar_component_clause,[],[f618])).
% 1.35/0.55 tff(f3315,plain,(
% 1.35/0.55 ~pp(aa(type,bool,typing(e,u),t1)) | (spl38_4 | ~spl38_271)),
% 1.35/0.55 inference(resolution,[],[f3260,f572])).
% 1.35/0.55 tff(f572,plain,(
% 1.35/0.55 ~pp(aa(type,bool,typing(e,subst(a,u,i)),t)) | spl38_4),
% 1.35/0.55 inference(avatar_component_clause,[],[f570])).
% 1.35/0.55 tff(f3260,plain,(
% 1.35/0.55 ( ! [X0 : dB] : (pp(aa(type,bool,typing(e,subst(a,X0,i)),t)) | ~pp(aa(type,bool,typing(e,X0),t1))) ) | ~spl38_271),
% 1.35/0.55 inference(avatar_component_clause,[],[f3259])).
% 1.35/0.55 tff(f3344,plain,(
% 1.35/0.55 spl38_276 | ~spl38_48 | ~spl38_167),
% 1.35/0.55 inference(avatar_split_clause,[],[f1748,f1743,f811,f3342])).
% 1.35/0.55 tff(f3342,plain,(
% 1.35/0.55 spl38_276 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK32(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_276])])).
% 1.35/0.55 tff(f811,plain,(
% 1.35/0.55 spl38_48 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_48])])).
% 1.35/0.55 tff(f1743,plain,(
% 1.35/0.55 spl38_167 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (pp(aa(X0,bool,combc(X0,X0,bool,X4,X2),sK33(X0,X1,X2,X3,X4))) | step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_167])])).
% 1.35/0.55 tff(f1748,plain,(
% 1.35/0.55 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK32(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0)) ) | (~spl38_48 | ~spl38_167)),
% 1.35/0.55 inference(resolution,[],[f1744,f812])).
% 1.35/0.55 tff(f812,plain,(
% 1.35/0.55 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl38_48),
% 1.35/0.55 inference(avatar_component_clause,[],[f811])).
% 1.35/0.55 tff(f1744,plain,(
% 1.35/0.55 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (pp(aa(X0,bool,combc(X0,X0,bool,X4,X2),sK33(X0,X1,X2,X3,X4))) | step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl38_167),
% 1.35/0.55 inference(avatar_component_clause,[],[f1743])).
% 1.35/0.55 tff(f3340,plain,(
% 1.35/0.55 spl38_275 | ~spl38_81 | ~spl38_104),
% 1.35/0.55 inference(avatar_split_clause,[],[f1152,f1148,f981,f3338])).
% 1.35/0.55 tff(f3338,plain,(
% 1.35/0.55 spl38_275 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP4(dB,X2,X2,beta,abs(X1),abs(X0)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_275])])).
% 1.35/0.55 tff(f981,plain,(
% 1.35/0.55 spl38_81 <=> ! [X3 : $tType,X4 : X3,X5 : X3,X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (~pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | sP4(X3,X1,X1,X2,X4,X5))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_81])])).
% 1.35/0.55 tff(f1148,plain,(
% 1.35/0.55 spl38_104 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,abs(X0)),abs(X1))))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_104])])).
% 1.35/0.55 tff(f1152,plain,(
% 1.35/0.55 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP4(dB,X2,X2,beta,abs(X1),abs(X0))) ) | (~spl38_81 | ~spl38_104)),
% 1.35/0.55 inference(resolution,[],[f1149,f982])).
% 1.35/0.55 tff(f982,plain,(
% 1.35/0.55 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X1 : list(X3),X4 : X3,X5 : X3] : (~pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | sP4(X3,X1,X1,X2,X4,X5)) ) | ~spl38_81),
% 1.35/0.55 inference(avatar_component_clause,[],[f981])).
% 1.35/0.55 tff(f1149,plain,(
% 1.35/0.55 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,abs(X0)),abs(X1))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | ~spl38_104),
% 1.35/0.55 inference(avatar_component_clause,[],[f1148])).
% 1.35/0.55 tff(f3336,plain,(
% 1.35/0.55 spl38_274 | ~spl38_12 | ~spl38_97),
% 1.35/0.55 inference(avatar_split_clause,[],[f1101,f1094,f613,f3334])).
% 1.35/0.55 tff(f3334,plain,(
% 1.35/0.55 spl38_274 <=> ! [X0 : $tType,X2 : fun(dB,fun(list(dB),X0)),X1 : X0] : aa(list(dB),X0,aa(dB,fun(list(dB),X0),X2,a),as) = list_case(X0,dB,X1,X2,rs)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_274])])).
% 1.35/0.55 tff(f613,plain,(
% 1.35/0.55 spl38_12 <=> rs = cons(dB,a,as)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_12])])).
% 1.35/0.55 tff(f1094,plain,(
% 1.35/0.55 spl38_97 <=> ! [X1 : $tType,X0 : $tType,X5 : X0,X4 : fun(X1,fun(list(X1),X0)),X3 : X1,X2 : list(X1)] : list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_97])])).
% 1.35/0.55 tff(f1101,plain,(
% 1.35/0.55 ( ! [X0 : $tType,X2 : fun(dB,fun(list(dB),X0)),X1 : X0] : (aa(list(dB),X0,aa(dB,fun(list(dB),X0),X2,a),as) = list_case(X0,dB,X1,X2,rs)) ) | (~spl38_12 | ~spl38_97)),
% 1.35/0.55 inference(superposition,[],[f1095,f615])).
% 1.35/0.55 tff(f615,plain,(
% 1.35/0.55 rs = cons(dB,a,as) | ~spl38_12),
% 1.35/0.55 inference(avatar_component_clause,[],[f613])).
% 1.35/0.55 tff(f1095,plain,(
% 1.35/0.55 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : (list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)) ) | ~spl38_97),
% 1.35/0.55 inference(avatar_component_clause,[],[f1094])).
% 1.35/0.55 tff(f3297,plain,(
% 1.35/0.55 spl38_172 | ~spl38_273 | ~spl38_260),
% 1.35/0.55 inference(avatar_split_clause,[],[f3226,f3081,f3294,f1815])).
% 1.35/0.55 tff(f1815,plain,(
% 1.35/0.55 spl38_172 <=> ! [X0 : bool] : fTrue = X0),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_172])])).
% 1.35/0.55 tff(f3294,plain,(
% 1.35/0.55 spl38_273 <=> fTrue = aa(type,bool,typing(e,subst(a,u,i)),t)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_273])])).
% 1.35/0.55 tff(f3081,plain,(
% 1.35/0.55 spl38_260 <=> ! [X0 : bool] : (aa(type,bool,typing(e,subst(a,u,i)),t) = X0 | fTrue = X0)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_260])])).
% 1.35/0.55 tff(f3226,plain,(
% 1.35/0.55 ( ! [X0 : bool] : (fTrue != aa(type,bool,typing(e,subst(a,u,i)),t) | fTrue = X0) ) | ~spl38_260),
% 1.35/0.55 inference(equality_factoring,[],[f3082])).
% 1.35/0.55 tff(f3082,plain,(
% 1.35/0.55 ( ! [X0 : bool] : (aa(type,bool,typing(e,subst(a,u,i)),t) = X0 | fTrue = X0) ) | ~spl38_260),
% 1.35/0.55 inference(avatar_component_clause,[],[f3081])).
% 1.35/0.55 tff(f3265,plain,(
% 1.35/0.55 spl38_272 | ~spl38_34 | ~spl38_156),
% 1.35/0.55 inference(avatar_split_clause,[],[f1651,f1632,f735,f3263])).
% 1.35/0.55 tff(f3263,plain,(
% 1.35/0.55 spl38_272 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t1)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),sK5)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_272])])).
% 1.35/0.55 tff(f735,plain,(
% 1.35/0.55 spl38_34 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),a),sK5))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_34])])).
% 1.35/0.55 tff(f1632,plain,(
% 1.35/0.55 spl38_156 <=> ! [X3 : fun(nat,type),X4 : type,X0 : nat,X5 : dB,X2 : dB,X1 : type] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(shift(type,X3,X0,X1),X5),X4)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_156])])).
% 1.35/0.55 tff(f1651,plain,(
% 1.35/0.55 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t1)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),sK5))) ) | (~spl38_34 | ~spl38_156)),
% 1.35/0.55 inference(resolution,[],[f1633,f737])).
% 1.35/0.55 tff(f737,plain,(
% 1.35/0.55 pp(aa(type,bool,typing(shift(type,e,i,t1),a),sK5)) | ~spl38_34),
% 1.35/0.55 inference(avatar_component_clause,[],[f735])).
% 1.35/0.55 tff(f1633,plain,(
% 1.35/0.55 ( ! [X2 : dB,X3 : fun(nat,type),X0 : nat,X1 : type,X4 : type,X5 : dB] : (~pp(aa(type,bool,typing(shift(type,X3,X0,X1),X5),X4)) | ~pp(aa(type,bool,typing(X3,X2),X1)) | pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4))) ) | ~spl38_156),
% 1.35/0.55 inference(avatar_component_clause,[],[f1632])).
% 1.35/0.55 tff(f3261,plain,(
% 1.35/0.55 spl38_271 | ~spl38_33 | ~spl38_156),
% 1.35/0.55 inference(avatar_split_clause,[],[f1648,f1632,f730,f3259])).
% 1.35/0.55 tff(f730,plain,(
% 1.35/0.55 spl38_33 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),a),t))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_33])])).
% 1.35/0.55 tff(f1648,plain,(
% 1.35/0.55 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t1)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),t))) ) | (~spl38_33 | ~spl38_156)),
% 1.35/0.55 inference(resolution,[],[f1633,f732])).
% 1.35/0.55 tff(f732,plain,(
% 1.35/0.55 pp(aa(type,bool,typing(shift(type,e,i,t1),a),t)) | ~spl38_33),
% 1.35/0.55 inference(avatar_component_clause,[],[f730])).
% 1.35/0.55 tff(f3257,plain,(
% 1.35/0.55 spl38_270 | ~spl38_107 | ~spl38_123),
% 1.35/0.55 inference(avatar_split_clause,[],[f1349,f1346,f1164,f3255])).
% 1.35/0.55 tff(f3255,plain,(
% 1.35/0.55 spl38_270 <=> ! [X2 : nat,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | step1(dB,beta,X0,sK23(foldl(dB,dB,app,var(X2),X1),X0,X2)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_270])])).
% 1.35/0.55 tff(f1164,plain,(
% 1.35/0.55 spl38_107 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,var(X2),X1))) | step1(dB,beta,X1,sK23(X0,X1,X2)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_107])])).
% 1.35/0.55 tff(f1346,plain,(
% 1.35/0.55 spl38_123 <=> ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,X1)),foldl(dB,dB,app,X0,X2))) | ~step1(dB,beta,X2,X1))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_123])])).
% 1.35/0.55 tff(f1349,plain,(
% 1.35/0.55 ( ! [X2 : nat,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | step1(dB,beta,X0,sK23(foldl(dB,dB,app,var(X2),X1),X0,X2))) ) | (~spl38_107 | ~spl38_123)),
% 1.35/0.55 inference(resolution,[],[f1347,f1165])).
% 1.35/0.55 tff(f1165,plain,(
% 1.35/0.55 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,var(X2),X1))) | step1(dB,beta,X1,sK23(X0,X1,X2))) ) | ~spl38_107),
% 1.35/0.55 inference(avatar_component_clause,[],[f1164])).
% 1.35/0.55 tff(f1347,plain,(
% 1.35/0.55 ( ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,X1)),foldl(dB,dB,app,X0,X2))) | ~step1(dB,beta,X2,X1)) ) | ~spl38_123),
% 1.35/0.55 inference(avatar_component_clause,[],[f1346])).
% 1.35/0.55 tff(f3253,plain,(
% 1.35/0.55 spl38_269 | ~spl38_89 | ~spl38_116),
% 1.35/0.55 inference(avatar_split_clause,[],[f1298,f1201,f1029,f3251])).
% 1.35/0.55 tff(f3251,plain,(
% 1.35/0.55 spl38_269 <=> ! [X2 : nat,X0 : dB,X1 : fun(dB,dB),X3 : list(dB)] : foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combs(dB,dB,dB,app,X1),abs(X0))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_269])])).
% 1.35/0.55 tff(f1029,plain,(
% 1.35/0.55 spl38_89 <=> ! [X2 : dB,X0 : list(dB),X1 : nat,X3 : dB] : foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_89])])).
% 1.35/0.55 tff(f1201,plain,(
% 1.35/0.55 spl38_116 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X2,fun(X1,X0)),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_116])])).
% 1.35/0.55 tff(f1298,plain,(
% 1.35/0.55 ( ! [X2 : nat,X3 : list(dB),X0 : dB,X1 : fun(dB,dB)] : (foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combs(dB,dB,dB,app,X1),abs(X0))) ) | (~spl38_89 | ~spl38_116)),
% 1.35/0.55 inference(superposition,[],[f1030,f1202])).
% 1.35/0.55 tff(f1202,plain,(
% 1.35/0.55 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) ) | ~spl38_116),
% 1.35/0.55 inference(avatar_component_clause,[],[f1201])).
% 1.35/0.55 tff(f1030,plain,(
% 1.35/0.55 ( ! [X2 : dB,X3 : dB,X0 : list(dB),X1 : nat] : (foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2)) ) | ~spl38_89),
% 1.35/0.55 inference(avatar_component_clause,[],[f1029])).
% 1.35/0.55 tff(f3249,plain,(
% 1.35/0.55 spl38_268 | ~spl38_84 | ~spl38_104),
% 1.35/0.55 inference(avatar_split_clause,[],[f1151,f1148,f1006,f3247])).
% 1.35/0.55 tff(f3247,plain,(
% 1.35/0.55 spl38_268 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | abs(X0) = abs(sK13(abs(X0),X1)))),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_268])])).
% 1.35/0.55 tff(f1006,plain,(
% 1.35/0.55 spl38_84 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0)),
% 1.35/0.55 introduced(avatar_definition,[new_symbols(naming,[spl38_84])])).
% 1.35/0.55 tff(f1151,plain,(
% 1.35/0.55 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | abs(X0) = abs(sK13(abs(X0),X1))) ) | (~spl38_84 | ~spl38_104)),
% 1.35/0.55 inference(resolution,[],[f1149,f1007])).
% 1.35/0.55 tff(f1007,plain,(
% 1.35/0.55 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0) ) | ~spl38_84),
% 1.35/0.55 inference(avatar_component_clause,[],[f1006])).
% 1.35/0.55 tff(f3245,plain,(
% 1.35/0.55 spl38_267 | ~spl38_97),
% 1.35/0.55 inference(avatar_split_clause,[],[f1107,f1094,f3243])).
% 1.35/0.55 tff(f3243,plain,(
% 1.35/0.56 spl38_267 <=> ! [X1 : $tType,X0 : $tType,X5 : X1,X6 : X1,X4 : list(X0),X3 : X0,X2 : fun(X0,fun(list(X0),X1))] : list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_267])])).
% 1.35/0.56 tff(f1107,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X0,X6 : X1,X4 : list(X0),X5 : X1] : (list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4))) ) | ~spl38_97),
% 1.35/0.56 inference(superposition,[],[f1095,f1095])).
% 1.35/0.56 tff(f3110,plain,(
% 1.35/0.56 spl38_266 | ~spl38_28 | ~spl38_96),
% 1.35/0.56 inference(avatar_split_clause,[],[f1090,f1086,f696,f3108])).
% 1.35/0.56 tff(f3108,plain,(
% 1.35/0.56 spl38_266 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_266])])).
% 1.35/0.56 tff(f696,plain,(
% 1.35/0.56 spl38_28 <=> ! [X1 : dB] : (sP1(abs(X1)) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_28])])).
% 1.35/0.56 tff(f1086,plain,(
% 1.35/0.56 spl38_96 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_96])])).
% 1.35/0.56 tff(f1090,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)))) ) | (~spl38_28 | ~spl38_96)),
% 1.35/0.56 inference(resolution,[],[f1087,f697])).
% 1.35/0.56 tff(f697,plain,(
% 1.35/0.56 ( ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | sP1(abs(X1))) ) | ~spl38_28),
% 1.35/0.56 inference(avatar_component_clause,[],[f696])).
% 1.35/0.56 tff(f1087,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1))) | ~pp(aa(dB,bool,it,X1))) ) | ~spl38_96),
% 1.35/0.56 inference(avatar_component_clause,[],[f1086])).
% 1.35/0.56 tff(f3106,plain,(
% 1.35/0.56 spl38_265 | ~spl38_89 | ~spl38_94),
% 1.35/0.56 inference(avatar_split_clause,[],[f1077,f1063,f1029,f3104])).
% 1.35/0.56 tff(f3104,plain,(
% 1.35/0.56 spl38_265 <=> ! [X2 : nat,X0 : dB,X1 : dB,X3 : list(dB)] : foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_265])])).
% 1.35/0.56 tff(f1063,plain,(
% 1.35/0.56 spl38_94 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_94])])).
% 1.35/0.56 tff(f1077,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : list(dB),X0 : dB,X1 : dB] : (foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0))) ) | (~spl38_89 | ~spl38_94)),
% 1.35/0.56 inference(superposition,[],[f1030,f1064])).
% 1.35/0.56 tff(f1064,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) ) | ~spl38_94),
% 1.35/0.56 inference(avatar_component_clause,[],[f1063])).
% 1.35/0.56 tff(f3102,plain,(
% 1.35/0.56 spl38_264 | ~spl38_28 | ~spl38_91),
% 1.35/0.56 inference(avatar_split_clause,[],[f1066,f1047,f696,f3100])).
% 1.35/0.56 tff(f3100,plain,(
% 1.35/0.56 spl38_264 <=> ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(abs(sK7(X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_264])])).
% 1.35/0.56 tff(f1047,plain,(
% 1.35/0.56 spl38_91 <=> ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_91])])).
% 1.35/0.56 tff(f1066,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(abs(sK7(X0)))) ) | (~spl38_28 | ~spl38_91)),
% 1.35/0.56 inference(resolution,[],[f1048,f697])).
% 1.35/0.56 tff(f1048,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK7(X0))) | sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) ) | ~spl38_91),
% 1.35/0.56 inference(avatar_component_clause,[],[f1047])).
% 1.35/0.56 tff(f3095,plain,(
% 1.35/0.56 spl38_263 | ~spl38_89 | ~spl38_114),
% 1.35/0.56 inference(avatar_split_clause,[],[f1249,f1193,f1029,f3093])).
% 1.35/0.56 tff(f3093,plain,(
% 1.35/0.56 spl38_263 <=> ! [X4 : list(dB),X0 : dB,X3 : nat,X2 : dB,X1 : list(dB)] : foldr(dB,dB,app,cons(dB,abs(X0),X1),X2) != foldl(dB,dB,app,var(X3),X4)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_263])])).
% 1.35/0.56 tff(f1193,plain,(
% 1.35/0.56 spl38_114 <=> ! [X1 : $tType,X0 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1)),X2 : X1] : foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_114])])).
% 1.35/0.56 tff(f1249,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : nat,X0 : dB,X1 : list(dB),X4 : list(dB)] : (foldr(dB,dB,app,cons(dB,abs(X0),X1),X2) != foldl(dB,dB,app,var(X3),X4)) ) | (~spl38_89 | ~spl38_114)),
% 1.35/0.56 inference(superposition,[],[f1030,f1194])).
% 1.35/0.56 tff(f1194,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))) ) | ~spl38_114),
% 1.35/0.56 inference(avatar_component_clause,[],[f1193])).
% 1.35/0.56 tff(f3091,plain,(
% 1.35/0.56 spl38_262 | ~spl38_21 | ~spl38_96),
% 1.35/0.56 inference(avatar_split_clause,[],[f1091,f1086,f655,f3089])).
% 1.35/0.56 tff(f3089,plain,(
% 1.35/0.56 spl38_262 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_262])])).
% 1.35/0.56 tff(f655,plain,(
% 1.35/0.56 spl38_21 <=> ! [X0 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_21])])).
% 1.35/0.56 tff(f1091,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) ) | (~spl38_21 | ~spl38_96)),
% 1.35/0.56 inference(resolution,[],[f1087,f656])).
% 1.35/0.56 tff(f656,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(X0)) ) | ~spl38_21),
% 1.35/0.56 inference(avatar_component_clause,[],[f655])).
% 1.35/0.56 tff(f3087,plain,(
% 1.35/0.56 spl38_261 | ~spl38_21 | ~spl38_91),
% 1.35/0.56 inference(avatar_split_clause,[],[f1067,f1047,f655,f3085])).
% 1.35/0.56 tff(f3085,plain,(
% 1.35/0.56 spl38_261 <=> ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(sK7(X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_261])])).
% 1.35/0.56 tff(f1067,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(sK7(X0))) ) | (~spl38_21 | ~spl38_91)),
% 1.35/0.56 inference(resolution,[],[f1048,f656])).
% 1.35/0.56 tff(f3083,plain,(
% 1.35/0.56 spl38_260 | ~spl38_3 | spl38_4 | ~spl38_222),
% 1.35/0.56 inference(avatar_split_clause,[],[f2591,f2271,f570,f565,f3081])).
% 1.35/0.56 tff(f2271,plain,(
% 1.35/0.56 spl38_222 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_222])])).
% 1.35/0.56 tff(f2591,plain,(
% 1.35/0.56 ( ! [X0 : bool] : (~pp(fTrue) | aa(type,bool,typing(e,subst(a,u,i)),t) = X0 | fTrue = X0) ) | (spl38_4 | ~spl38_222)),
% 1.35/0.56 inference(superposition,[],[f572,f2272])).
% 1.35/0.56 tff(f2272,plain,(
% 1.35/0.56 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl38_222),
% 1.35/0.56 inference(avatar_component_clause,[],[f2271])).
% 1.35/0.56 tff(f3079,plain,(
% 1.35/0.56 spl38_259 | ~spl38_28 | ~spl38_93),
% 1.35/0.56 inference(avatar_split_clause,[],[f1059,f1056,f696,f3077])).
% 1.35/0.56 tff(f3077,plain,(
% 1.35/0.56 spl38_259 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_259])])).
% 1.35/0.56 tff(f1056,plain,(
% 1.35/0.56 spl38_93 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_93])])).
% 1.35/0.56 tff(f1059,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)))) ) | (~spl38_28 | ~spl38_93)),
% 1.35/0.56 inference(resolution,[],[f1057,f697])).
% 1.35/0.56 tff(f1057,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))) | ~pp(aa(dB,bool,it,X1))) ) | ~spl38_93),
% 1.35/0.56 inference(avatar_component_clause,[],[f1056])).
% 1.35/0.56 tff(f3064,plain,(
% 1.35/0.56 spl38_258 | ~spl38_72 | ~spl38_94),
% 1.35/0.56 inference(avatar_split_clause,[],[f1073,f1063,f941,f3061])).
% 1.35/0.56 tff(f3061,plain,(
% 1.35/0.56 spl38_258 <=> t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),t)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_258])])).
% 1.35/0.56 tff(f941,plain,(
% 1.35/0.56 spl38_72 <=> t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_72])])).
% 1.35/0.56 tff(f1073,plain,(
% 1.35/0.56 t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),t) | (~spl38_72 | ~spl38_94)),
% 1.35/0.56 inference(superposition,[],[f1064,f943])).
% 1.35/0.56 tff(f943,plain,(
% 1.35/0.56 t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)) | ~spl38_72),
% 1.35/0.56 inference(avatar_component_clause,[],[f941])).
% 1.35/0.56 tff(f3059,plain,(
% 1.35/0.56 spl38_257 | ~spl38_21 | ~spl38_93),
% 1.35/0.56 inference(avatar_split_clause,[],[f1060,f1056,f655,f3057])).
% 1.35/0.56 tff(f3057,plain,(
% 1.35/0.56 spl38_257 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_257])])).
% 1.35/0.56 tff(f1060,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) ) | (~spl38_21 | ~spl38_93)),
% 1.35/0.56 inference(resolution,[],[f1057,f656])).
% 1.35/0.56 tff(f3055,plain,(
% 1.35/0.56 spl38_256 | ~spl38_28 | ~spl38_88),
% 1.35/0.56 inference(avatar_split_clause,[],[f1037,f1025,f696,f3053])).
% 1.35/0.56 tff(f3053,plain,(
% 1.35/0.56 spl38_256 <=> ! [X0 : dB] : (~sP0(X0) | sP1(abs(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_256])])).
% 1.35/0.56 tff(f1025,plain,(
% 1.35/0.56 spl38_88 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_88])])).
% 1.35/0.56 tff(f1037,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~sP0(X0) | sP1(abs(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0))))) ) | (~spl38_28 | ~spl38_88)),
% 1.35/0.56 inference(resolution,[],[f1026,f697])).
% 1.35/0.56 tff(f1026,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0)) ) | ~spl38_88),
% 1.35/0.56 inference(avatar_component_clause,[],[f1025])).
% 1.35/0.56 tff(f3045,plain,(
% 1.35/0.56 spl38_255 | ~spl38_51 | ~spl38_158),
% 1.35/0.56 inference(avatar_split_clause,[],[f1676,f1663,f826,f3043])).
% 1.35/0.56 tff(f3043,plain,(
% 1.35/0.56 spl38_255 <=> ! [X4 : dB,X0 : dB,X3 : dB,X2 : nat,X1 : dB] : abs(X4) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_255])])).
% 1.35/0.56 tff(f826,plain,(
% 1.35/0.56 spl38_51 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_51])])).
% 1.35/0.56 tff(f1663,plain,(
% 1.35/0.56 spl38_158 <=> ! [X0 : nat,X3 : dB,X2 : dB,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0)) = subst(aa(dB,dB,combc(dB,dB,dB,app,X2),X3),X1,X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_158])])).
% 1.35/0.56 tff(f1676,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB,X4 : dB] : (abs(X4) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2)) ) | (~spl38_51 | ~spl38_158)),
% 1.35/0.56 inference(superposition,[],[f827,f1664])).
% 1.35/0.56 tff(f1664,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0)) = subst(aa(dB,dB,combc(dB,dB,dB,app,X2),X3),X1,X0)) ) | ~spl38_158),
% 1.35/0.56 inference(avatar_component_clause,[],[f1663])).
% 1.35/0.56 tff(f827,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) ) | ~spl38_51),
% 1.35/0.56 inference(avatar_component_clause,[],[f826])).
% 1.35/0.56 tff(f3041,plain,(
% 1.35/0.56 spl38_254 | ~spl38_52 | ~spl38_158),
% 1.35/0.56 inference(avatar_split_clause,[],[f1675,f1663,f830,f3039])).
% 1.35/0.56 tff(f3039,plain,(
% 1.35/0.56 spl38_254 <=> ! [X4 : nat,X0 : dB,X3 : dB,X2 : nat,X1 : dB] : var(X4) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_254])])).
% 1.35/0.56 tff(f830,plain,(
% 1.35/0.56 spl38_52 <=> ! [X2 : nat,X0 : dB,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_52])])).
% 1.35/0.56 tff(f1675,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB,X4 : nat] : (var(X4) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2)) ) | (~spl38_52 | ~spl38_158)),
% 1.35/0.56 inference(superposition,[],[f831,f1664])).
% 1.35/0.56 tff(f831,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2)) ) | ~spl38_52),
% 1.35/0.56 inference(avatar_component_clause,[],[f830])).
% 1.35/0.56 tff(f3037,plain,(
% 1.35/0.56 spl38_253 | ~spl38_72 | ~spl38_110),
% 1.35/0.56 inference(avatar_split_clause,[],[f1215,f1177,f941,f3035])).
% 1.35/0.56 tff(f3035,plain,(
% 1.35/0.56 spl38_253 <=> ! [X0 : type,X1 : type] : (t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | t = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_253])])).
% 1.35/0.56 tff(f1177,plain,(
% 1.35/0.56 spl38_110 <=> ! [X0 : type,X3 : type,X2 : type,X1 : type] : (X1 = X3 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_110])])).
% 1.35/0.56 tff(f1215,plain,(
% 1.35/0.56 ( ! [X0 : type,X1 : type] : (t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | t = X0) ) | (~spl38_72 | ~spl38_110)),
% 1.35/0.56 inference(superposition,[],[f1178,f943])).
% 1.35/0.56 tff(f1178,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) | X1 = X3) ) | ~spl38_110),
% 1.35/0.56 inference(avatar_component_clause,[],[f1177])).
% 1.35/0.56 tff(f3033,plain,(
% 1.35/0.56 spl38_252 | ~spl38_21 | ~spl38_88),
% 1.35/0.56 inference(avatar_split_clause,[],[f1038,f1025,f655,f3031])).
% 1.35/0.56 tff(f3031,plain,(
% 1.35/0.56 spl38_252 <=> ! [X0 : dB] : (~sP0(X0) | sP1(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_252])])).
% 1.35/0.56 tff(f1038,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~sP0(X0) | sP1(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) ) | (~spl38_21 | ~spl38_88)),
% 1.35/0.56 inference(resolution,[],[f1026,f656])).
% 1.35/0.56 tff(f3022,plain,(
% 1.35/0.56 spl38_251 | ~spl38_12 | ~spl38_78),
% 1.35/0.56 inference(avatar_split_clause,[],[f995,f967,f613,f3020])).
% 1.35/0.56 tff(f3020,plain,(
% 1.35/0.56 spl38_251 <=> ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (step1(dB,X0,cons(dB,X1,X2),rs) | ~sP4(dB,as,X2,X0,X1,a))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_251])])).
% 1.35/0.56 tff(f967,plain,(
% 1.35/0.56 spl38_78 <=> ! [X0 : $tType,X5 : fun(X0,fun(X0,bool)),X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) | ~sP4(X0,X1,X3,X5,X4,X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_78])])).
% 1.35/0.56 tff(f995,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (step1(dB,X0,cons(dB,X1,X2),rs) | ~sP4(dB,as,X2,X0,X1,a)) ) | (~spl38_12 | ~spl38_78)),
% 1.35/0.56 inference(superposition,[],[f968,f615])).
% 1.35/0.56 tff(f968,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) | ~sP4(X0,X1,X3,X5,X4,X2)) ) | ~spl38_78),
% 1.35/0.56 inference(avatar_component_clause,[],[f967])).
% 1.35/0.56 tff(f3017,plain,(
% 1.35/0.56 spl38_250 | ~spl38_12 | ~spl38_78),
% 1.35/0.56 inference(avatar_split_clause,[],[f994,f967,f613,f3015])).
% 1.35/0.56 tff(f3015,plain,(
% 1.35/0.56 spl38_250 <=> ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (step1(dB,X0,rs,cons(dB,X1,X2)) | ~sP4(dB,X2,as,X0,a,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_250])])).
% 1.35/0.56 tff(f994,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (step1(dB,X0,rs,cons(dB,X1,X2)) | ~sP4(dB,X2,as,X0,a,X1)) ) | (~spl38_12 | ~spl38_78)),
% 1.35/0.56 inference(superposition,[],[f968,f615])).
% 1.35/0.56 tff(f3013,plain,(
% 1.35/0.56 spl38_249 | ~spl38_12 | ~spl38_77),
% 1.35/0.56 inference(avatar_split_clause,[],[f992,f963,f613,f3011])).
% 1.35/0.56 tff(f3011,plain,(
% 1.35/0.56 spl38_249 <=> ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (~step1(dB,X0,cons(dB,X1,X2),rs) | sP4(dB,as,X2,X0,X1,a))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_249])])).
% 1.35/0.56 tff(f963,plain,(
% 1.35/0.56 spl38_77 <=> ! [X0 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool)),X2 : X0,X1 : list(X0)] : (sP4(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_77])])).
% 1.35/0.56 tff(f992,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (~step1(dB,X0,cons(dB,X1,X2),rs) | sP4(dB,as,X2,X0,X1,a)) ) | (~spl38_12 | ~spl38_77)),
% 1.35/0.56 inference(superposition,[],[f964,f615])).
% 1.35/0.56 tff(f964,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) | sP4(X0,X1,X3,X5,X4,X2)) ) | ~spl38_77),
% 1.35/0.56 inference(avatar_component_clause,[],[f963])).
% 1.35/0.56 tff(f3009,plain,(
% 1.35/0.56 spl38_248 | ~spl38_12 | ~spl38_77),
% 1.35/0.56 inference(avatar_split_clause,[],[f991,f963,f613,f3007])).
% 1.35/0.56 tff(f3007,plain,(
% 1.35/0.56 spl38_248 <=> ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (~step1(dB,X0,rs,cons(dB,X1,X2)) | sP4(dB,X2,as,X0,a,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_248])])).
% 1.35/0.56 tff(f991,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : fun(dB,fun(dB,bool)),X1 : dB] : (~step1(dB,X0,rs,cons(dB,X1,X2)) | sP4(dB,X2,as,X0,a,X1)) ) | (~spl38_12 | ~spl38_77)),
% 1.35/0.56 inference(superposition,[],[f964,f615])).
% 1.35/0.56 tff(f2996,plain,(
% 1.35/0.56 spl38_247 | ~spl38_11 | ~spl38_31),
% 1.35/0.56 inference(avatar_split_clause,[],[f728,f720,f602,f2994])).
% 1.35/0.56 tff(f2994,plain,(
% 1.35/0.56 spl38_247 <=> ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_247])])).
% 1.35/0.56 tff(f602,plain,(
% 1.35/0.56 spl38_11 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_11])])).
% 1.35/0.56 tff(f720,plain,(
% 1.35/0.56 spl38_31 <=> ! [X0 : $tType,X2 : fun(nat,X0),X4 : nat,X1 : X0] : aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_31])])).
% 1.35/0.56 tff(f728,plain,(
% 1.35/0.56 ( ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1)) ) | (~spl38_11 | ~spl38_31)),
% 1.35/0.56 inference(superposition,[],[f721,f603])).
% 1.35/0.56 tff(f603,plain,(
% 1.35/0.56 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl38_11),
% 1.35/0.56 inference(avatar_component_clause,[],[f602])).
% 1.35/0.56 tff(f721,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) ) | ~spl38_31),
% 1.35/0.56 inference(avatar_component_clause,[],[f720])).
% 1.35/0.56 tff(f2968,plain,(
% 1.35/0.56 spl38_246 | ~spl38_42 | ~spl38_121),
% 1.35/0.56 inference(avatar_split_clause,[],[f1335,f1332,f774,f2966])).
% 1.35/0.56 tff(f2966,plain,(
% 1.35/0.56 spl38_246 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_246])])).
% 1.35/0.56 tff(f774,plain,(
% 1.35/0.56 spl38_42 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_42])])).
% 1.35/0.56 tff(f1332,plain,(
% 1.35/0.56 spl38_121 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK13(X0,X1)),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_121])])).
% 1.35/0.56 tff(f1335,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))) ) | (~spl38_42 | ~spl38_121)),
% 1.35/0.56 inference(resolution,[],[f1333,f775])).
% 1.35/0.56 tff(f775,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl38_42),
% 1.35/0.56 inference(avatar_component_clause,[],[f774])).
% 1.35/0.56 tff(f1333,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK13(X0,X1)),X1)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1)))) ) | ~spl38_121),
% 1.35/0.56 inference(avatar_component_clause,[],[f1332])).
% 1.35/0.56 tff(f2964,plain,(
% 1.35/0.56 spl38_245 | ~spl38_51 | ~spl38_116),
% 1.35/0.56 inference(avatar_split_clause,[],[f1297,f1201,f826,f2962])).
% 1.35/0.56 tff(f2962,plain,(
% 1.35/0.56 spl38_245 <=> ! [X2 : dB,X0 : dB,X1 : fun(dB,dB)] : abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_245])])).
% 1.35/0.56 tff(f1297,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : fun(dB,dB)] : (abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)) ) | (~spl38_51 | ~spl38_116)),
% 1.35/0.56 inference(superposition,[],[f827,f1202])).
% 1.35/0.56 tff(f2960,plain,(
% 1.35/0.56 spl38_244 | ~spl38_52 | ~spl38_116),
% 1.35/0.56 inference(avatar_split_clause,[],[f1296,f1201,f830,f2958])).
% 1.35/0.56 tff(f2958,plain,(
% 1.35/0.56 spl38_244 <=> ! [X2 : nat,X0 : dB,X1 : fun(dB,dB)] : var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_244])])).
% 1.35/0.56 tff(f1296,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : fun(dB,dB)] : (var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)) ) | (~spl38_52 | ~spl38_116)),
% 1.35/0.56 inference(superposition,[],[f831,f1202])).
% 1.35/0.56 tff(f2956,plain,(
% 1.35/0.56 spl38_243 | ~spl38_51 | ~spl38_94),
% 1.35/0.56 inference(avatar_split_clause,[],[f1076,f1063,f826,f2954])).
% 1.35/0.56 tff(f2954,plain,(
% 1.35/0.56 spl38_243 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_243])])).
% 1.35/0.56 tff(f1076,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl38_51 | ~spl38_94)),
% 1.35/0.56 inference(superposition,[],[f827,f1064])).
% 1.35/0.56 tff(f2952,plain,(
% 1.35/0.56 spl38_242 | ~spl38_52 | ~spl38_94),
% 1.35/0.56 inference(avatar_split_clause,[],[f1075,f1063,f830,f2950])).
% 1.35/0.56 tff(f2950,plain,(
% 1.35/0.56 spl38_242 <=> ! [X2 : nat,X0 : dB,X1 : dB] : var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_242])])).
% 1.35/0.56 tff(f1075,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : dB] : (var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl38_52 | ~spl38_94)),
% 1.35/0.56 inference(superposition,[],[f831,f1064])).
% 1.35/0.56 tff(f2948,plain,(
% 1.35/0.56 spl38_241 | ~spl38_8 | ~spl38_223),
% 1.35/0.56 inference(avatar_split_clause,[],[f2827,f2807,f588,f2945])).
% 1.35/0.56 tff(f2945,plain,(
% 1.35/0.56 spl38_241 <=> sP1(abs(abs(ua)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_241])])).
% 1.35/0.56 tff(f588,plain,(
% 1.35/0.56 spl38_8 <=> pp(aa(dB,bool,it,ua))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_8])])).
% 1.35/0.56 tff(f2807,plain,(
% 1.35/0.56 spl38_223 <=> ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_223])])).
% 1.35/0.56 tff(f2827,plain,(
% 1.35/0.56 sP1(abs(abs(ua))) | (~spl38_8 | ~spl38_223)),
% 1.35/0.56 inference(resolution,[],[f2808,f590])).
% 1.35/0.56 tff(f590,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,ua)) | ~spl38_8),
% 1.35/0.56 inference(avatar_component_clause,[],[f588])).
% 1.35/0.56 tff(f2808,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0)))) ) | ~spl38_223),
% 1.35/0.56 inference(avatar_component_clause,[],[f2807])).
% 1.35/0.56 tff(f2943,plain,(
% 1.35/0.56 spl38_240 | ~spl38_28 | ~spl38_70),
% 1.35/0.56 inference(avatar_split_clause,[],[f933,f929,f696,f2940])).
% 1.35/0.56 tff(f2940,plain,(
% 1.35/0.56 spl38_240 <=> sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_240])])).
% 1.35/0.56 tff(f929,plain,(
% 1.35/0.56 spl38_70 <=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_70])])).
% 1.35/0.56 tff(f933,plain,(
% 1.35/0.56 sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | (~spl38_28 | ~spl38_70)),
% 1.35/0.56 inference(resolution,[],[f931,f697])).
% 1.35/0.56 tff(f931,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | ~spl38_70),
% 1.35/0.56 inference(avatar_component_clause,[],[f929])).
% 1.35/0.56 tff(f2938,plain,(
% 1.35/0.56 spl38_239 | ~spl38_28 | ~spl38_64),
% 1.35/0.56 inference(avatar_split_clause,[],[f908,f887,f696,f2936])).
% 1.35/0.56 tff(f2936,plain,(
% 1.35/0.56 spl38_239 <=> ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(subst(X0,var(X1),X2))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_239])])).
% 1.35/0.56 tff(f887,plain,(
% 1.35/0.56 spl38_64 <=> ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_64])])).
% 1.35/0.56 tff(f908,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(subst(X0,var(X1),X2)))) ) | (~spl38_28 | ~spl38_64)),
% 1.35/0.56 inference(resolution,[],[f888,f697])).
% 1.35/0.56 tff(f888,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2))) ) | ~spl38_64),
% 1.35/0.56 inference(avatar_component_clause,[],[f887])).
% 1.35/0.56 tff(f2934,plain,(
% 1.35/0.56 spl38_238 | ~spl38_28 | ~spl38_60),
% 1.35/0.56 inference(avatar_split_clause,[],[f905,f870,f696,f2932])).
% 1.35/0.56 tff(f2932,plain,(
% 1.35/0.56 spl38_238 <=> ! [X0 : list(dB),X1 : nat] : (~listsp(dB,it,X0) | sP1(abs(foldl(dB,dB,app,var(X1),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_238])])).
% 1.35/0.56 tff(f870,plain,(
% 1.35/0.56 spl38_60 <=> ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_60])])).
% 1.35/0.56 tff(f905,plain,(
% 1.35/0.56 ( ! [X0 : list(dB),X1 : nat] : (~listsp(dB,it,X0) | sP1(abs(foldl(dB,dB,app,var(X1),X0)))) ) | (~spl38_28 | ~spl38_60)),
% 1.35/0.56 inference(resolution,[],[f871,f697])).
% 1.35/0.56 tff(f871,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) ) | ~spl38_60),
% 1.35/0.56 inference(avatar_component_clause,[],[f870])).
% 1.35/0.56 tff(f2930,plain,(
% 1.35/0.56 spl38_237 | ~spl38_28 | ~spl38_57),
% 1.35/0.56 inference(avatar_split_clause,[],[f902,f854,f696,f2928])).
% 1.35/0.56 tff(f2928,plain,(
% 1.35/0.56 spl38_237 <=> ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(abs(sK7(X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_237])])).
% 1.35/0.56 tff(f854,plain,(
% 1.35/0.56 spl38_57 <=> ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | listsp(dB,it,sK8(X0)) | ~sP1(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_57])])).
% 1.35/0.56 tff(f902,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(abs(sK7(X0)))) ) | (~spl38_28 | ~spl38_57)),
% 1.35/0.56 inference(resolution,[],[f855,f697])).
% 1.35/0.56 tff(f855,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK7(X0))) | sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0)) ) | ~spl38_57),
% 1.35/0.56 inference(avatar_component_clause,[],[f854])).
% 1.35/0.56 tff(f2926,plain,(
% 1.35/0.56 spl38_236 | ~spl38_31 | ~spl38_44),
% 1.35/0.56 inference(avatar_split_clause,[],[f799,f783,f720,f2924])).
% 1.35/0.56 tff(f2924,plain,(
% 1.35/0.56 spl38_236 <=> ! [X2 : type,X0 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_236])])).
% 1.35/0.56 tff(f783,plain,(
% 1.35/0.56 spl38_44 <=> ! [X2 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_44])])).
% 1.35/0.56 tff(f799,plain,(
% 1.35/0.56 ( ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))) ) | (~spl38_31 | ~spl38_44)),
% 1.35/0.56 inference(superposition,[],[f784,f721])).
% 1.35/0.56 tff(f784,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) ) | ~spl38_44),
% 1.35/0.56 inference(avatar_component_clause,[],[f783])).
% 1.35/0.56 tff(f2897,plain,(
% 1.35/0.56 spl38_235 | ~spl38_9 | ~spl38_223),
% 1.35/0.56 inference(avatar_split_clause,[],[f2826,f2807,f593,f2894])).
% 1.35/0.56 tff(f2894,plain,(
% 1.35/0.56 spl38_235 <=> sP1(abs(abs(u)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_235])])).
% 1.35/0.56 tff(f593,plain,(
% 1.35/0.56 spl38_9 <=> pp(aa(dB,bool,it,u))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_9])])).
% 1.35/0.56 tff(f2826,plain,(
% 1.35/0.56 sP1(abs(abs(u))) | (~spl38_9 | ~spl38_223)),
% 1.35/0.56 inference(resolution,[],[f2808,f595])).
% 1.35/0.56 tff(f595,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,u)) | ~spl38_9),
% 1.35/0.56 inference(avatar_component_clause,[],[f593])).
% 1.35/0.56 tff(f2892,plain,(
% 1.35/0.56 spl38_234 | ~spl38_51 | ~spl38_114),
% 1.35/0.56 inference(avatar_split_clause,[],[f1248,f1193,f826,f2890])).
% 1.35/0.56 tff(f2890,plain,(
% 1.35/0.56 spl38_234 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : dB] : abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_234])])).
% 1.35/0.56 tff(f1248,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : list(dB)] : (abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl38_51 | ~spl38_114)),
% 1.35/0.56 inference(superposition,[],[f827,f1194])).
% 1.35/0.56 tff(f2888,plain,(
% 1.35/0.56 spl38_233 | ~spl38_52 | ~spl38_114),
% 1.35/0.56 inference(avatar_split_clause,[],[f1247,f1193,f830,f2886])).
% 1.35/0.56 tff(f2886,plain,(
% 1.35/0.56 spl38_233 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : nat] : var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_233])])).
% 1.35/0.56 tff(f1247,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : nat,X0 : dB,X1 : list(dB)] : (var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl38_52 | ~spl38_114)),
% 1.35/0.56 inference(superposition,[],[f831,f1194])).
% 1.35/0.56 tff(f2884,plain,(
% 1.35/0.56 spl38_232 | ~spl38_21 | ~spl38_70),
% 1.35/0.56 inference(avatar_split_clause,[],[f934,f929,f655,f2881])).
% 1.35/0.56 tff(f2881,plain,(
% 1.35/0.56 spl38_232 <=> sP1(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_232])])).
% 1.35/0.56 tff(f934,plain,(
% 1.35/0.56 sP1(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)) | (~spl38_21 | ~spl38_70)),
% 1.35/0.56 inference(resolution,[],[f931,f656])).
% 1.35/0.56 tff(f2879,plain,(
% 1.35/0.56 spl38_231 | ~spl38_21 | ~spl38_64),
% 1.35/0.56 inference(avatar_split_clause,[],[f909,f887,f655,f2877])).
% 1.35/0.56 tff(f2877,plain,(
% 1.35/0.56 spl38_231 <=> ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(subst(X0,var(X1),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_231])])).
% 1.35/0.56 tff(f909,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(subst(X0,var(X1),X2))) ) | (~spl38_21 | ~spl38_64)),
% 1.35/0.56 inference(resolution,[],[f888,f656])).
% 1.35/0.56 tff(f2875,plain,(
% 1.35/0.56 spl38_230 | ~spl38_21 | ~spl38_57),
% 1.35/0.56 inference(avatar_split_clause,[],[f903,f854,f655,f2873])).
% 1.35/0.56 tff(f2873,plain,(
% 1.35/0.56 spl38_230 <=> ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(sK7(X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_230])])).
% 1.35/0.56 tff(f903,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(sK7(X0))) ) | (~spl38_21 | ~spl38_57)),
% 1.35/0.56 inference(resolution,[],[f855,f656])).
% 1.35/0.56 tff(f2859,plain,(
% 1.35/0.56 spl38_229 | ~spl38_31 | ~spl38_65 | ~spl38_137),
% 1.35/0.56 inference(avatar_split_clause,[],[f1492,f1485,f891,f720,f2856])).
% 1.35/0.56 tff(f2856,plain,(
% 1.35/0.56 spl38_229 <=> t1 = foldr(type,type,fun1,cons(type,sK5,ts),t2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_229])])).
% 1.35/0.56 tff(f891,plain,(
% 1.35/0.56 spl38_65 <=> ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_65])])).
% 1.35/0.56 tff(f1485,plain,(
% 1.35/0.56 spl38_137 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_137])])).
% 1.35/0.56 tff(f1492,plain,(
% 1.35/0.56 t1 = foldr(type,type,fun1,cons(type,sK5,ts),t2) | (~spl38_31 | ~spl38_65 | ~spl38_137)),
% 1.35/0.56 inference(forward_demodulation,[],[f1489,f721])).
% 1.35/0.56 tff(f1489,plain,(
% 1.35/0.56 foldr(type,type,fun1,cons(type,sK5,ts),t2) = aa(nat,type,shift(type,e,i,t1),i) | (~spl38_65 | ~spl38_137)),
% 1.35/0.56 inference(resolution,[],[f1487,f892])).
% 1.35/0.56 tff(f892,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (~pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) = X0) ) | ~spl38_65),
% 1.35/0.56 inference(avatar_component_clause,[],[f891])).
% 1.35/0.56 tff(f1487,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t2))) | ~spl38_137),
% 1.35/0.56 inference(avatar_component_clause,[],[f1485])).
% 1.35/0.56 tff(f2854,plain,(
% 1.35/0.56 spl38_228 | ~spl38_7 | ~spl38_223),
% 1.35/0.56 inference(avatar_split_clause,[],[f2825,f2807,f583,f2851])).
% 1.35/0.56 tff(f2851,plain,(
% 1.35/0.56 spl38_228 <=> sP1(abs(abs(t3)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_228])])).
% 1.35/0.56 tff(f583,plain,(
% 1.35/0.56 spl38_7 <=> pp(aa(dB,bool,it,t3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_7])])).
% 1.35/0.56 tff(f2825,plain,(
% 1.35/0.56 sP1(abs(abs(t3))) | (~spl38_7 | ~spl38_223)),
% 1.35/0.56 inference(resolution,[],[f2808,f585])).
% 1.35/0.56 tff(f585,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,t3)) | ~spl38_7),
% 1.35/0.56 inference(avatar_component_clause,[],[f583])).
% 1.35/0.56 tff(f2849,plain,(
% 1.35/0.56 spl38_227 | ~spl38_72 | ~spl38_114),
% 1.35/0.56 inference(avatar_split_clause,[],[f1237,f1193,f941,f2846])).
% 1.35/0.56 tff(f2846,plain,(
% 1.35/0.56 spl38_227 <=> t1 = foldr(type,type,fun1,cons(type,t,ts),t2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_227])])).
% 1.35/0.56 tff(f1237,plain,(
% 1.35/0.56 t1 = foldr(type,type,fun1,cons(type,t,ts),t2) | (~spl38_72 | ~spl38_114)),
% 1.35/0.56 inference(superposition,[],[f1194,f943])).
% 1.35/0.56 tff(f2844,plain,(
% 1.35/0.56 spl38_226 | ~spl38_59 | ~spl38_81),
% 1.35/0.56 inference(avatar_split_clause,[],[f998,f981,f863,f2842])).
% 1.35/0.56 tff(f2842,plain,(
% 1.35/0.56 spl38_226 <=> ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP4(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_226])])).
% 1.35/0.56 tff(f863,plain,(
% 1.35/0.56 spl38_59 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_59])])).
% 1.35/0.56 tff(f998,plain,(
% 1.35/0.56 ( ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP4(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1)) ) | (~spl38_59 | ~spl38_81)),
% 1.35/0.56 inference(resolution,[],[f982,f864])).
% 1.35/0.56 tff(f864,plain,(
% 1.35/0.56 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_59),
% 1.35/0.56 inference(avatar_component_clause,[],[f863])).
% 1.35/0.56 tff(f2840,plain,(
% 1.35/0.56 spl38_225 | ~spl38_12 | ~spl38_54),
% 1.35/0.56 inference(avatar_split_clause,[],[f845,f838,f613,f2838])).
% 1.35/0.56 tff(f2838,plain,(
% 1.35/0.56 spl38_225 <=> ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | as = X1)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_225])])).
% 1.35/0.56 tff(f838,plain,(
% 1.35/0.56 spl38_54 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : list(X0),X1 : list(X0)] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_54])])).
% 1.35/0.56 tff(f845,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | as = X1) ) | (~spl38_12 | ~spl38_54)),
% 1.35/0.56 inference(superposition,[],[f839,f615])).
% 1.35/0.56 tff(f839,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X1 = X3) ) | ~spl38_54),
% 1.35/0.56 inference(avatar_component_clause,[],[f838])).
% 1.35/0.56 tff(f2813,plain,(
% 1.35/0.56 spl38_224 | ~spl38_12 | ~spl38_43),
% 1.35/0.56 inference(avatar_split_clause,[],[f796,f779,f613,f2811])).
% 1.35/0.56 tff(f2811,plain,(
% 1.35/0.56 spl38_224 <=> ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | a = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_224])])).
% 1.35/0.56 tff(f779,plain,(
% 1.35/0.56 spl38_43 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_43])])).
% 1.35/0.56 tff(f796,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | a = X0) ) | (~spl38_12 | ~spl38_43)),
% 1.35/0.56 inference(superposition,[],[f780,f615])).
% 1.35/0.56 tff(f780,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X2 = X4) ) | ~spl38_43),
% 1.35/0.56 inference(avatar_component_clause,[],[f779])).
% 1.35/0.56 tff(f2809,plain,(
% 1.35/0.56 spl38_223 | ~spl38_28 | ~spl38_40),
% 1.35/0.56 inference(avatar_split_clause,[],[f793,f765,f696,f2807])).
% 1.35/0.56 tff(f765,plain,(
% 1.35/0.56 spl38_40 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_40])])).
% 1.35/0.56 tff(f793,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0)))) ) | (~spl38_28 | ~spl38_40)),
% 1.35/0.56 inference(resolution,[],[f766,f697])).
% 1.35/0.56 tff(f766,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0))) ) | ~spl38_40),
% 1.35/0.56 inference(avatar_component_clause,[],[f765])).
% 1.35/0.56 tff(f2273,plain,(
% 1.35/0.56 spl38_222 | ~spl38_11),
% 1.35/0.56 inference(avatar_split_clause,[],[f605,f602,f2271])).
% 1.35/0.56 tff(f605,plain,(
% 1.35/0.56 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl38_11),
% 1.35/0.56 inference(superposition,[],[f603,f603])).
% 1.35/0.56 tff(f2266,plain,(
% 1.35/0.56 spl38_221 | ~spl38_9 | ~spl38_13),
% 1.35/0.56 inference(avatar_split_clause,[],[f1382,f618,f593,f2263])).
% 1.35/0.56 tff(f2263,plain,(
% 1.35/0.56 spl38_221 <=> aa(dB,bool,it,u) = fTrue),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_221])])).
% 1.35/0.56 tff(f1382,plain,(
% 1.35/0.56 aa(dB,bool,it,u) = fTrue | (~spl38_9 | ~spl38_13)),
% 1.35/0.56 inference(resolution,[],[f619,f595])).
% 1.35/0.56 tff(f2258,plain,(
% 1.35/0.56 spl38_220),
% 1.35/0.56 inference(avatar_split_clause,[],[f467,f2256])).
% 1.35/0.56 tff(f2256,plain,(
% 1.35/0.56 spl38_220 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) | ~pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_220])])).
% 1.35/0.56 tff(f467,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : list(type),X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) | ~pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f320])).
% 1.35/0.56 tff(f320,plain,(
% 1.35/0.56 ! [X0 : list(type),X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) | ~pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0))) & (pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0)) | ~pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))))),
% 1.35/0.56 inference(nnf_transformation,[],[f174])).
% 1.35/0.56 tff(f174,plain,(
% 1.35/0.56 ! [X0 : list(type),X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) <=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0)))),
% 1.35/0.56 inference(rectify,[],[f59])).
% 1.35/0.56 tff(f59,axiom,(
% 1.35/0.56 ! [X31 : list(type),X30 : list(dB),X13 : dB,X14 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X14,cons(dB,X13,X30)),X31)) <=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X14,X13))),typings(X14,X30)),X31)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_typings_Osimps_I2_J)).
% 1.35/0.56 tff(f2254,plain,(
% 1.35/0.56 spl38_219),
% 1.35/0.56 inference(avatar_split_clause,[],[f466,f2252])).
% 1.35/0.56 tff(f2252,plain,(
% 1.35/0.56 spl38_219 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0)) | ~pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_219])])).
% 1.35/0.56 tff(f466,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : list(type),X1 : list(dB)] : (pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),typing(X3,X2))),typings(X3,X1)),X0)) | ~pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f320])).
% 1.35/0.56 tff(f2186,plain,(
% 1.35/0.56 spl38_218),
% 1.35/0.56 inference(avatar_split_clause,[],[f548,f2184])).
% 1.35/0.56 tff(f2184,plain,(
% 1.35/0.56 spl38_218 <=> ! [X1 : $tType,X0 : $tType,X5 : fun(X0,fun(X1,X0)),X4 : X0,X3 : list(X1),X2 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,X4,cons(X1,X2,X3)) | aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK34(X0,X1,X5))),sK35(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK35(X0,X1,X5))),sK34(X0,X1,X5)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_218])])).
% 1.35/0.56 tff(f548,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,X4,cons(X1,X2,X3)) | aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK34(X0,X1,X5))),sK35(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK35(X0,X1,X5))),sK34(X0,X1,X5))) )),
% 1.35/0.56 inference(forward_demodulation,[],[f502,f499])).
% 1.35/0.56 tff(f499,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f191])).
% 1.35/0.56 tff(f191,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)),
% 1.35/0.56 inference(rectify,[],[f48])).
% 1.35/0.56 tff(f48,axiom,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X58 : list(X1),X22 : X1,X57 : X0,X59 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X59,X57,cons(X1,X22,X58)) = foldl(X0,X1,X59,aa(X1,X0,aa(X0,fun(X1,X0),X59,X57),X22),X58)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_foldl__Cons)).
% 1.35/0.56 tff(f502,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) | aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK34(X0,X1,X5))),sK35(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK35(X0,X1,X5))),sK34(X0,X1,X5))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f338])).
% 1.35/0.56 tff(f338,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) | aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK34(X0,X1,X5))),sK35(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK35(X0,X1,X5))),sK34(X0,X1,X5)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f248,f337])).
% 1.35/0.56 tff(f337,plain,(
% 1.35/0.56 ! [X1 : $tType,X0 : $tType,X5 : fun(X0,fun(X1,X0))] : (? [X6 : X1,X7 : X1,X8 : X0] : aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) => aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK34(X0,X1,X5))),sK35(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK36(X0,X1,X5)),sK35(X0,X1,X5))),sK34(X0,X1,X5)))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f248,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) | ? [X6 : X1,X7 : X1,X8 : X0] : aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6))),
% 1.35/0.56 inference(ennf_transformation,[],[f194])).
% 1.35/0.56 tff(f194,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (! [X6 : X1,X7 : X1,X8 : X0] : aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) = aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) => aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3))),
% 1.35/0.56 inference(rectify,[],[f98])).
% 1.35/0.56 tff(f98,axiom,(
% 1.35/0.56 ! [X1 : $tType,X0 : $tType,X22 : X0,X58 : list(X0),X24 : X1,X59 : fun(X1,fun(X0,X1))] : (! [X71 : X0,X92 : X0,X83 : X1] : aa(X0,X1,aa(X1,fun(X0,X1),X59,aa(X0,X1,aa(X1,fun(X0,X1),X59,X83),X71)),X92) = aa(X0,X1,aa(X1,fun(X0,X1),X59,aa(X0,X1,aa(X1,fun(X0,X1),X59,X83),X92)),X71) => aa(X0,X1,aa(X1,fun(X0,X1),X59,foldl(X1,X0,X59,X24,X58)),X22) = foldl(X1,X0,X59,aa(X0,X1,aa(X1,fun(X0,X1),X59,X24),X22),X58))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_foldl__fun__comm)).
% 1.35/0.56 tff(f2177,plain,(
% 1.35/0.56 spl38_217 | ~spl38_94 | ~spl38_216),
% 1.35/0.56 inference(avatar_split_clause,[],[f2173,f2167,f1063,f2175])).
% 1.35/0.56 tff(f2175,plain,(
% 1.35/0.56 spl38_217 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_217])])).
% 1.35/0.56 tff(f2167,plain,(
% 1.35/0.56 spl38_216 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_216])])).
% 1.35/0.56 tff(f2173,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_216)),
% 1.35/0.56 inference(forward_demodulation,[],[f2172,f1064])).
% 1.35/0.56 tff(f2172,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_216)),
% 1.35/0.56 inference(forward_demodulation,[],[f2171,f1064])).
% 1.35/0.56 tff(f2171,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_216)),
% 1.35/0.56 inference(forward_demodulation,[],[f2170,f1064])).
% 1.35/0.56 tff(f2170,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_216)),
% 1.35/0.56 inference(forward_demodulation,[],[f2168,f1064])).
% 1.35/0.56 tff(f2168,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_216),
% 1.35/0.56 inference(avatar_component_clause,[],[f2167])).
% 1.35/0.56 tff(f2169,plain,(
% 1.35/0.56 spl38_216),
% 1.35/0.56 inference(avatar_split_clause,[],[f444,f2167])).
% 1.35/0.56 tff(f444,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f308])).
% 1.35/0.56 tff(f308,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : ((pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0) | (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f305,f307,f306])).
% 1.35/0.56 tff(f306,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X3)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f307,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X4 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f305,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X3)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0) | ? [X4 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(rectify,[],[f263])).
% 1.35/0.56 tff(f263,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0) | ? [X4 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(definition_folding,[],[f226,f262])).
% 1.35/0.56 tff(f262,plain,(
% 1.35/0.56 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP3(X2,X0,X1))),
% 1.35/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])).
% 1.35/0.56 tff(f226,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0) | ? [X4 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0) | ? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(flattening,[],[f225])).
% 1.35/0.56 tff(f225,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (((? [X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0) | ? [X4 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) & aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0)) | ? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f160])).
% 1.35/0.56 tff(f160,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) => (! [X3 : dB] : (subst(X3,X1,zero_zero(nat)) = X0 => abs(X3) != X2) => (! [X4 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))) => ~! [X5 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5))))))),
% 1.35/0.56 inference(rectify,[],[f90])).
% 1.35/0.56 tff(f90,axiom,(
% 1.35/0.56 ! [X43 : dB,X28 : dB,X42 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X28)),X43)) => (! [X83 : dB] : (subst(X83,X28,zero_zero(nat)) = X43 => abs(X83) != X42) => (! [X82 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X82),X28) = X43 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X42),X82))) => ~! [X82 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X82) = X43 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X28),X82))))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_beta__cases_I3_J)).
% 1.35/0.56 tff(f2160,plain,(
% 1.35/0.56 spl38_215 | ~spl38_94 | ~spl38_213),
% 1.35/0.56 inference(avatar_split_clause,[],[f2151,f2145,f1063,f2158])).
% 1.35/0.56 tff(f2158,plain,(
% 1.35/0.56 spl38_215 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_215])])).
% 1.35/0.56 tff(f2145,plain,(
% 1.35/0.56 spl38_213 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_213])])).
% 1.35/0.56 tff(f2151,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_213)),
% 1.35/0.56 inference(forward_demodulation,[],[f2150,f1064])).
% 1.35/0.56 tff(f2150,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_213)),
% 1.35/0.56 inference(forward_demodulation,[],[f2149,f1064])).
% 1.35/0.56 tff(f2149,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,X1),sK26(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_213)),
% 1.35/0.56 inference(forward_demodulation,[],[f2148,f1064])).
% 1.35/0.56 tff(f2148,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_213)),
% 1.35/0.56 inference(forward_demodulation,[],[f2146,f1064])).
% 1.35/0.56 tff(f2146,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_213),
% 1.35/0.56 inference(avatar_component_clause,[],[f2145])).
% 1.35/0.56 tff(f2156,plain,(
% 1.35/0.56 spl38_214 | ~spl38_7 | ~spl38_13),
% 1.35/0.56 inference(avatar_split_clause,[],[f1381,f618,f583,f2153])).
% 1.35/0.56 tff(f2153,plain,(
% 1.35/0.56 spl38_214 <=> aa(dB,bool,it,t3) = fTrue),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_214])])).
% 1.35/0.56 tff(f1381,plain,(
% 1.35/0.56 aa(dB,bool,it,t3) = fTrue | (~spl38_7 | ~spl38_13)),
% 1.35/0.56 inference(resolution,[],[f619,f585])).
% 1.35/0.56 tff(f2147,plain,(
% 1.35/0.56 spl38_213),
% 1.35/0.56 inference(avatar_split_clause,[],[f446,f2145])).
% 1.35/0.56 tff(f446,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK26(X0,X1,X2)),X1) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f308])).
% 1.35/0.56 tff(f2138,plain,(
% 1.35/0.56 spl38_212 | ~spl38_94 | ~spl38_211),
% 1.35/0.56 inference(avatar_split_clause,[],[f2134,f2128,f1063,f2136])).
% 1.35/0.56 tff(f2136,plain,(
% 1.35/0.56 spl38_212 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_212])])).
% 1.35/0.56 tff(f2128,plain,(
% 1.35/0.56 spl38_211 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_211])])).
% 1.35/0.56 tff(f2134,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_211)),
% 1.35/0.56 inference(forward_demodulation,[],[f2133,f1064])).
% 1.35/0.56 tff(f2133,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_211)),
% 1.35/0.56 inference(forward_demodulation,[],[f2132,f1064])).
% 1.35/0.56 tff(f2132,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_211)),
% 1.35/0.56 inference(forward_demodulation,[],[f2131,f1064])).
% 1.35/0.56 tff(f2131,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,sK25(X0,X1,X2)),X2) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_211)),
% 1.35/0.56 inference(forward_demodulation,[],[f2129,f1064])).
% 1.35/0.56 tff(f2129,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_211),
% 1.35/0.56 inference(avatar_component_clause,[],[f2128])).
% 1.35/0.56 tff(f2130,plain,(
% 1.35/0.56 spl38_211),
% 1.35/0.56 inference(avatar_split_clause,[],[f445,f2128])).
% 1.35/0.56 tff(f445,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK25(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f308])).
% 1.35/0.56 tff(f2121,plain,(
% 1.35/0.56 spl38_210 | ~spl38_94 | ~spl38_209),
% 1.35/0.56 inference(avatar_split_clause,[],[f2117,f2111,f1063,f2119])).
% 1.35/0.56 tff(f2119,plain,(
% 1.35/0.56 spl38_210 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_210])])).
% 1.35/0.56 tff(f2111,plain,(
% 1.35/0.56 spl38_209 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_209])])).
% 1.35/0.56 tff(f2117,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_209)),
% 1.35/0.56 inference(forward_demodulation,[],[f2116,f1064])).
% 1.35/0.56 tff(f2116,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1)) ) | (~spl38_94 | ~spl38_209)),
% 1.35/0.56 inference(forward_demodulation,[],[f2115,f1064])).
% 1.35/0.56 tff(f2115,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK26(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_209)),
% 1.35/0.56 inference(forward_demodulation,[],[f2114,f1064])).
% 1.35/0.56 tff(f2114,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_209)),
% 1.35/0.56 inference(forward_demodulation,[],[f2112,f1064])).
% 1.35/0.56 tff(f2112,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_209),
% 1.35/0.56 inference(avatar_component_clause,[],[f2111])).
% 1.35/0.56 tff(f2113,plain,(
% 1.35/0.56 spl38_209),
% 1.35/0.56 inference(avatar_split_clause,[],[f447,f2111])).
% 1.35/0.56 tff(f447,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK25(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK26(X0,X1,X2))) | sP3(X2,X0,X1) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f308])).
% 1.35/0.56 tff(f2104,plain,(
% 1.35/0.56 spl38_208),
% 1.35/0.56 inference(avatar_split_clause,[],[f515,f2102])).
% 1.35/0.56 tff(f2102,plain,(
% 1.35/0.56 spl38_208 <=> ! [X5 : nat,X3 : list(dB),X4 : list(dB),X0 : type,X6 : fun(nat,type),X2 : type,X1 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),sK37(X0,X2,X3,X6))) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_208])])).
% 1.35/0.56 tff(f515,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : list(dB),X0 : type,X1 : list(type),X6 : fun(nat,type),X4 : list(dB),X5 : nat] : (pp(aa(list(type),bool,typings(X6,X3),sK37(X0,X2,X3,X6))) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f344])).
% 1.35/0.56 tff(f344,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X6,X3),sK37(X0,X2,X3,X6))) & foldr(type,type,fun1,sK37(X0,X2,X3,X6),X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f256,f343])).
% 1.35/0.56 tff(f343,plain,(
% 1.35/0.56 ! [X0 : type,X2 : type,X3 : list(dB),X6 : fun(nat,type)] : (? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) => (pp(aa(list(type),bool,typings(X6,X3),sK37(X0,X2,X3,X6))) & foldr(type,type,fun1,sK37(X0,X2,X3,X6),X2) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f256,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 1.35/0.56 inference(flattening,[],[f255])).
% 1.35/0.56 tff(f255,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (((? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0))) | ~pp(aa(list(type),bool,typings(X6,X4),X1))) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 1.35/0.56 inference(ennf_transformation,[],[f199])).
% 1.35/0.56 tff(f199,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) => (pp(aa(list(type),bool,typings(X6,X4),X1)) => (pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) => ? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0))))),
% 1.35/0.56 inference(rectify,[],[f34])).
% 1.35/0.56 tff(f34,axiom,(
% 1.35/0.56 ! [X9 : type,X31 : list(type),X12 : type,X35 : list(dB),X30 : list(dB),X8 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,foldl(dB,dB,app,var(X8),X30),X35)),X12)) => (pp(aa(list(type),bool,typings(X14,X30),X31)) => (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X8),X30)),X9)) => ? [X36 : list(type)] : (pp(aa(list(type),bool,typings(X14,X35),X36)) & foldr(type,type,fun1,X36,X12) = X9))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_var__app__types)).
% 1.35/0.56 tff(f2094,plain,(
% 1.35/0.56 spl38_207),
% 1.35/0.56 inference(avatar_split_clause,[],[f514,f2092])).
% 1.35/0.56 tff(f2092,plain,(
% 1.35/0.56 spl38_207 <=> ! [X5 : nat,X3 : list(dB),X4 : list(dB),X0 : type,X6 : fun(nat,type),X2 : type,X1 : list(type)] : (foldr(type,type,fun1,sK37(X0,X2,X3,X6),X2) = X0 | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_207])])).
% 1.35/0.56 tff(f514,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : list(dB),X0 : type,X1 : list(type),X6 : fun(nat,type),X4 : list(dB),X5 : nat] : (foldr(type,type,fun1,sK37(X0,X2,X3,X6),X2) = X0 | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f344])).
% 1.35/0.56 tff(f2090,plain,(
% 1.35/0.56 spl38_206),
% 1.35/0.56 inference(avatar_split_clause,[],[f553,f2088])).
% 1.35/0.56 tff(f2088,plain,(
% 1.35/0.56 spl38_206 <=> ! [X5 : type,X3 : fun(nat,type),X4 : dB,X0 : dB,X6 : type,X2 : nat,X1 : type] : (t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) | pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_206])])).
% 1.35/0.56 tff(f553,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) | pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4))) )),
% 1.35/0.56 inference(forward_demodulation,[],[f513,f496])).
% 1.35/0.56 tff(f496,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f188])).
% 1.35/0.56 tff(f188,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 1.35/0.56 inference(rectify,[],[f104])).
% 1.35/0.56 tff(f104,axiom,(
% 1.35/0.56 ! [X0 : $tType,X2 : $tType,X1 : $tType,X94 : X0,X95 : X1,X96 : fun(X0,fun(X1,X2))] : aa(X0,X2,combc(X0,X1,X2,X96,X95),X94) = aa(X1,X2,aa(X0,fun(X1,X2),X96,X94),X95)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 1.35/0.56 tff(f513,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f254])).
% 1.35/0.56 tff(f254,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.35/0.56 inference(flattening,[],[f253])).
% 1.35/0.56 tff(f253,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (((((pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5))) | ~pp(aa(dB,bool,it,X0))) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1))) | ~pp(aa(dB,bool,it,X4))) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.35/0.56 inference(ennf_transformation,[],[f198])).
% 1.35/0.56 tff(f198,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) => (pp(aa(dB,bool,it,X4)) => (pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) => (pp(aa(dB,bool,it,X0)) => (pp(aa(type,bool,typing(X3,X0),X5)) => pp(aa(dB,bool,it,subst(X4,X0,X2))))))))),
% 1.35/0.56 inference(rectify,[],[f15])).
% 1.35/0.56 tff(f15,axiom,(
% 1.35/0.56 ! [X10 : dB,X12 : type,X8 : nat,X14 : fun(nat,type),X13 : dB,X15 : type,X16 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X16),X15) => (pp(aa(dB,bool,it,X13)) => (pp(aa(type,bool,typing(shift(type,X14,X8,X15),X13),X12)) => (pp(aa(dB,bool,it,X10)) => (pp(aa(type,bool,typing(X14,X10),X15)) => pp(aa(dB,bool,it,subst(X13,X10,X8))))))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_MI2)).
% 1.35/0.56 tff(f2086,plain,(
% 1.35/0.56 spl38_205),
% 1.35/0.56 inference(avatar_split_clause,[],[f552,f2084])).
% 1.35/0.56 tff(f2084,plain,(
% 1.35/0.56 spl38_205 <=> ! [X5 : type,X3 : fun(nat,type),X4 : dB,X0 : dB,X6 : type,X2 : nat,X1 : type] : (t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) | pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~pp(aa(dB,bool,it,X4)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_205])])).
% 1.35/0.56 tff(f552,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) | pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~pp(aa(dB,bool,it,X4))) )),
% 1.35/0.56 inference(forward_demodulation,[],[f512,f496])).
% 1.35/0.56 tff(f512,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f252])).
% 1.35/0.56 tff(f252,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.35/0.56 inference(flattening,[],[f251])).
% 1.35/0.56 tff(f251,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (((((pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X6))) | ~pp(aa(dB,bool,it,X0))) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1))) | ~pp(aa(dB,bool,it,X4))) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.35/0.56 inference(ennf_transformation,[],[f197])).
% 1.35/0.56 tff(f197,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) => (pp(aa(dB,bool,it,X4)) => (pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) => (pp(aa(dB,bool,it,X0)) => (pp(aa(type,bool,typing(X3,X0),X6)) => pp(aa(dB,bool,it,subst(X4,X0,X2))))))))),
% 1.35/0.56 inference(rectify,[],[f14])).
% 1.35/0.56 tff(f14,axiom,(
% 1.35/0.56 ! [X10 : dB,X12 : type,X8 : nat,X14 : fun(nat,type),X13 : dB,X15 : type,X16 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X16),X15) => (pp(aa(dB,bool,it,X13)) => (pp(aa(type,bool,typing(shift(type,X14,X8,X16),X13),X12)) => (pp(aa(dB,bool,it,X10)) => (pp(aa(type,bool,typing(X14,X10),X16)) => pp(aa(dB,bool,it,subst(X13,X10,X8))))))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_MI1)).
% 1.35/0.56 tff(f2068,plain,(
% 1.35/0.56 spl38_204 | ~spl38_94 | ~spl38_203),
% 1.35/0.56 inference(avatar_split_clause,[],[f2064,f2058,f1063,f2066])).
% 1.35/0.56 tff(f2066,plain,(
% 1.35/0.56 spl38_204 <=> ! [X2 : dB,X0 : nat,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_204])])).
% 1.35/0.56 tff(f2058,plain,(
% 1.35/0.56 spl38_203 <=> ! [X2 : dB,X0 : nat,X1 : dB] : aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_203])])).
% 1.35/0.56 tff(f2064,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) ) | (~spl38_94 | ~spl38_203)),
% 1.35/0.56 inference(forward_demodulation,[],[f2063,f1064])).
% 1.35/0.56 tff(f2063,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1))) ) | (~spl38_94 | ~spl38_203)),
% 1.35/0.56 inference(forward_demodulation,[],[f2062,f1064])).
% 1.35/0.56 tff(f2062,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))) ) | (~spl38_94 | ~spl38_203)),
% 1.35/0.56 inference(forward_demodulation,[],[f2061,f1064])).
% 1.35/0.56 tff(f2061,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))) ) | (~spl38_94 | ~spl38_203)),
% 1.35/0.56 inference(forward_demodulation,[],[f2059,f1064])).
% 1.35/0.56 tff(f2059,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ) | ~spl38_203),
% 1.35/0.56 inference(avatar_component_clause,[],[f2058])).
% 1.35/0.56 tff(f2060,plain,(
% 1.35/0.56 spl38_203),
% 1.35/0.56 inference(avatar_split_clause,[],[f420,f2058])).
% 1.35/0.56 tff(f420,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f146])).
% 1.35/0.56 tff(f146,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB] : aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))),
% 1.35/0.56 inference(rectify,[],[f53])).
% 1.35/0.56 tff(f53,axiom,(
% 1.35/0.56 ! [X41 : nat,X28 : dB,X42 : dB] : aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X28)),X41) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X42),X41)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X28),X41))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_lift_Osimps_I2_J)).
% 1.35/0.56 tff(f2052,plain,(
% 1.35/0.56 spl38_202),
% 1.35/0.56 inference(avatar_split_clause,[],[f482,f2050])).
% 1.35/0.56 tff(f2050,plain,(
% 1.35/0.56 spl38_202 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_202])])).
% 1.35/0.56 tff(f482,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f330])).
% 1.35/0.56 tff(f330,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3)) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)))),
% 1.35/0.56 inference(flattening,[],[f329])).
% 1.35/0.56 tff(f329,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | (~listsp(X0,X1,X3) | ~listsp(X0,X2,X3))) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)))),
% 1.35/0.56 inference(nnf_transformation,[],[f179])).
% 1.35/0.56 tff(f179,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) <=> (listsp(X0,X1,X3) & listsp(X0,X2,X3)))),
% 1.35/0.56 inference(rectify,[],[f78])).
% 1.35/0.56 tff(f78,axiom,(
% 1.35/0.56 ! [X0 : $tType,X73 : fun(X0,bool),X74 : fun(X0,bool),X75 : list(X0)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X74),X73),X75) <=> (listsp(X0,X73,X75) & listsp(X0,X74,X75)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_listsp__conj__eq)).
% 1.35/0.56 tff(f2038,plain,(
% 1.35/0.56 spl38_201 | ~spl38_94 | ~spl38_200),
% 1.35/0.56 inference(avatar_split_clause,[],[f2034,f2030,f1063,f2036])).
% 1.35/0.56 tff(f2036,plain,(
% 1.35/0.56 spl38_201 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_201])])).
% 1.35/0.56 tff(f2030,plain,(
% 1.35/0.56 spl38_200 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_200])])).
% 1.35/0.56 tff(f2034,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0) ) | (~spl38_94 | ~spl38_200)),
% 1.35/0.56 inference(forward_demodulation,[],[f2033,f1064])).
% 1.35/0.56 tff(f2033,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | (~spl38_94 | ~spl38_200)),
% 1.35/0.56 inference(forward_demodulation,[],[f2031,f1064])).
% 1.35/0.56 tff(f2031,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl38_200),
% 1.35/0.56 inference(avatar_component_clause,[],[f2030])).
% 1.35/0.56 tff(f2032,plain,(
% 1.35/0.56 spl38_200),
% 1.35/0.56 inference(avatar_split_clause,[],[f438,f2030])).
% 1.35/0.56 tff(f438,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f298])).
% 1.35/0.56 tff(f298,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP2(X0,X1,X2) | (foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK21(X0,X1,X2))) | (foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f295,f297,f296])).
% 1.35/0.56 tff(f296,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X3 : list(dB)] : (foldl(dB,dB,app,X2,X3) = X0 & step1(dB,beta,X1,X3)) => (foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK21(X0,X1,X2))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f297,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X4 : dB] : (foldl(dB,dB,app,X4,X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))) => (foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f295,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP2(X0,X1,X2) | ? [X3 : list(dB)] : (foldl(dB,dB,app,X2,X3) = X0 & step1(dB,beta,X1,X3)) | ? [X4 : dB] : (foldl(dB,dB,app,X4,X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(rectify,[],[f261])).
% 1.35/0.56 tff(f261,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP2(X0,X1,X2) | ? [X4 : list(dB)] : (foldl(dB,dB,app,X2,X4) = X0 & step1(dB,beta,X1,X4)) | ? [X3 : dB] : (foldl(dB,dB,app,X3,X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(definition_folding,[],[f223,f260])).
% 1.35/0.56 tff(f260,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X5 : dB] : (? [X6 : dB,X7 : list(dB)] : (foldl(dB,dB,app,subst(X5,X6,zero_zero(nat)),X7) = X0 & cons(dB,X6,X7) = X1) & abs(X5) = X2) | ~sP2(X0,X1,X2))),
% 1.35/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 1.35/0.56 tff(f223,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X5 : dB] : (? [X6 : dB,X7 : list(dB)] : (foldl(dB,dB,app,subst(X5,X6,zero_zero(nat)),X7) = X0 & cons(dB,X6,X7) = X1) & abs(X5) = X2) | ? [X4 : list(dB)] : (foldl(dB,dB,app,X2,X4) = X0 & step1(dB,beta,X1,X4)) | ? [X3 : dB] : (foldl(dB,dB,app,X3,X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(flattening,[],[f222])).
% 1.35/0.56 tff(f222,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (((? [X5 : dB] : (? [X6 : dB,X7 : list(dB)] : (foldl(dB,dB,app,subst(X5,X6,zero_zero(nat)),X7) = X0 & cons(dB,X6,X7) = X1) & abs(X5) = X2) | ? [X4 : list(dB)] : (foldl(dB,dB,app,X2,X4) = X0 & step1(dB,beta,X1,X4))) | ? [X3 : dB] : (foldl(dB,dB,app,X3,X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3)))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f158])).
% 1.35/0.56 tff(f158,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) => (! [X3 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3)) => foldl(dB,dB,app,X3,X1) != X0) => (! [X4 : list(dB)] : (step1(dB,beta,X1,X4) => foldl(dB,dB,app,X2,X4) != X0) => ~! [X5 : dB] : (abs(X5) = X2 => ! [X6 : dB,X7 : list(dB)] : (cons(dB,X6,X7) = X1 => foldl(dB,dB,app,subst(X5,X6,zero_zero(nat)),X7) != X0)))))),
% 1.35/0.56 inference(rectify,[],[f92])).
% 1.35/0.56 tff(f92,axiom,(
% 1.35/0.56 ! [X24 : dB,X39 : list(dB),X44 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X44,X39)),X24)) => (! [X84 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X44),X84)) => foldl(dB,dB,app,X84,X39) != X24) => (! [X85 : list(dB)] : (step1(dB,beta,X39,X85) => foldl(dB,dB,app,X44,X85) != X24) => ~! [X82 : dB] : (abs(X82) = X44 => ! [X86 : dB,X87 : list(dB)] : (cons(dB,X86,X87) = X39 => foldl(dB,dB,app,subst(X82,X86,zero_zero(nat)),X87) != X24)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_apps__betasE)).
% 1.35/0.56 tff(f2020,plain,(
% 1.35/0.56 spl38_199 | ~spl38_94 | ~spl38_198),
% 1.35/0.56 inference(avatar_split_clause,[],[f2016,f2012,f1063,f2018])).
% 1.35/0.56 tff(f2018,plain,(
% 1.35/0.56 spl38_199 <=> ! [X4 : fun(nat,type),X0 : dB,X3 : dB,X2 : type,X1 : type] : (~pp(aa(type,bool,typing(X4,X3),aa(type,type,combc(type,type,type,fun1,X1),X2))) | pp(aa(type,bool,typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_199])])).
% 1.35/0.56 tff(f2012,plain,(
% 1.35/0.56 spl38_198 <=> ! [X2 : type,X4 : fun(nat,type),X0 : dB,X3 : dB,X1 : type] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_198])])).
% 1.35/0.56 tff(f2016,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (~pp(aa(type,bool,typing(X4,X3),aa(type,type,combc(type,type,type,fun1,X1),X2))) | pp(aa(type,bool,typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2))) ) | (~spl38_94 | ~spl38_198)),
% 1.35/0.56 inference(forward_demodulation,[],[f2015,f1064])).
% 1.35/0.56 tff(f2015,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) ) | (~spl38_94 | ~spl38_198)),
% 1.35/0.56 inference(forward_demodulation,[],[f2013,f1064])).
% 1.35/0.56 tff(f2013,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) ) | ~spl38_198),
% 1.35/0.56 inference(avatar_component_clause,[],[f2012])).
% 1.35/0.56 tff(f2014,plain,(
% 1.35/0.56 spl38_198),
% 1.35/0.56 inference(avatar_split_clause,[],[f492,f2012])).
% 1.35/0.56 tff(f492,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f247])).
% 1.35/0.56 tff(f247,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 1.35/0.56 inference(flattening,[],[f246])).
% 1.35/0.56 tff(f246,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : ((pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2))) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 1.35/0.56 inference(ennf_transformation,[],[f186])).
% 1.35/0.56 tff(f186,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) => (pp(aa(type,bool,typing(X4,X0),X2)) => pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))))),
% 1.35/0.56 inference(rectify,[],[f24])).
% 1.35/0.56 tff(f24,axiom,(
% 1.35/0.56 ! [X13 : dB,X9 : type,X12 : type,X24 : dB,X23 : fun(nat,type)] : (pp(aa(type,bool,typing(X23,X24),aa(type,type,aa(type,fun(type,type),fun1,X12),X9))) => (pp(aa(type,bool,typing(X23,X13),X12)) => pp(aa(type,bool,typing(X23,aa(dB,dB,aa(dB,fun(dB,dB),app,X24),X13)),X9))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_App)).
% 1.35/0.56 tff(f2010,plain,(
% 1.35/0.56 spl38_197),
% 1.35/0.56 inference(avatar_split_clause,[],[f481,f2008])).
% 1.35/0.56 tff(f2008,plain,(
% 1.35/0.56 spl38_197 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,X1,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_197])])).
% 1.35/0.56 tff(f481,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,X1,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f330])).
% 1.35/0.56 tff(f2006,plain,(
% 1.35/0.56 spl38_196),
% 1.35/0.56 inference(avatar_split_clause,[],[f480,f2004])).
% 1.35/0.56 tff(f2004,plain,(
% 1.35/0.56 spl38_196 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,X2,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_196])])).
% 1.35/0.56 tff(f480,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,X2,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f330])).
% 1.35/0.56 tff(f2002,plain,(
% 1.35/0.56 spl38_195 | ~spl38_27 | ~spl38_28),
% 1.35/0.56 inference(avatar_split_clause,[],[f709,f696,f692,f2000])).
% 1.35/0.56 tff(f2000,plain,(
% 1.35/0.56 spl38_195 <=> ! [X0 : dB] : (sP1(abs(sK11(X0))) | ~sP0(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_195])])).
% 1.35/0.56 tff(f692,plain,(
% 1.35/0.56 spl38_27 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_27])])).
% 1.35/0.56 tff(f709,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP1(abs(sK11(X0))) | ~sP0(X0)) ) | (~spl38_27 | ~spl38_28)),
% 1.35/0.56 inference(resolution,[],[f697,f693])).
% 1.35/0.56 tff(f693,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0)) ) | ~spl38_27),
% 1.35/0.56 inference(avatar_component_clause,[],[f692])).
% 1.35/0.56 tff(f1990,plain,(
% 1.35/0.56 spl38_194 | ~spl38_94 | ~spl38_193),
% 1.35/0.56 inference(avatar_split_clause,[],[f1986,f1982,f1063,f1988])).
% 1.35/0.56 tff(f1988,plain,(
% 1.35/0.56 spl38_194 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_194])])).
% 1.35/0.56 tff(f1982,plain,(
% 1.35/0.56 spl38_193 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_193])])).
% 1.35/0.56 tff(f1986,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2))) ) | (~spl38_94 | ~spl38_193)),
% 1.35/0.56 inference(forward_demodulation,[],[f1985,f1064])).
% 1.35/0.56 tff(f1985,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK22(X0,X1,X2)),X2)) | sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | (~spl38_94 | ~spl38_193)),
% 1.35/0.56 inference(forward_demodulation,[],[f1983,f1064])).
% 1.35/0.56 tff(f1983,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl38_193),
% 1.35/0.56 inference(avatar_component_clause,[],[f1982])).
% 1.35/0.56 tff(f1984,plain,(
% 1.35/0.56 spl38_193),
% 1.35/0.56 inference(avatar_split_clause,[],[f436,f1982])).
% 1.35/0.56 tff(f436,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f298])).
% 1.35/0.56 tff(f1976,plain,(
% 1.35/0.56 spl38_192 | ~spl38_94 | ~spl38_191),
% 1.35/0.56 inference(avatar_split_clause,[],[f1972,f1966,f1063,f1974])).
% 1.35/0.56 tff(f1974,plain,(
% 1.35/0.56 spl38_192 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X1)),aa(dB,dB,combc(dB,dB,dB,app,X0),X2))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_192])])).
% 1.35/0.56 tff(f1966,plain,(
% 1.35/0.56 spl38_191 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_191])])).
% 1.35/0.56 tff(f1972,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X1)),aa(dB,dB,combc(dB,dB,dB,app,X0),X2)))) ) | (~spl38_94 | ~spl38_191)),
% 1.35/0.56 inference(forward_demodulation,[],[f1971,f1064])).
% 1.35/0.56 tff(f1971,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X1)),aa(dB,dB,combc(dB,dB,dB,app,X0),X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_191)),
% 1.35/0.56 inference(forward_demodulation,[],[f1970,f1064])).
% 1.35/0.56 tff(f1970,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),aa(dB,dB,combc(dB,dB,dB,app,X0),X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_191)),
% 1.35/0.56 inference(forward_demodulation,[],[f1969,f1064])).
% 1.35/0.56 tff(f1969,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_191)),
% 1.35/0.56 inference(forward_demodulation,[],[f1967,f1064])).
% 1.35/0.56 tff(f1967,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | ~spl38_191),
% 1.35/0.56 inference(avatar_component_clause,[],[f1966])).
% 1.35/0.56 tff(f1968,plain,(
% 1.35/0.56 spl38_191),
% 1.35/0.56 inference(avatar_split_clause,[],[f431,f1966])).
% 1.35/0.56 tff(f431,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f219])).
% 1.35/0.56 tff(f219,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f156])).
% 1.35/0.56 tff(f156,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))))),
% 1.35/0.56 inference(rectify,[],[f82])).
% 1.35/0.56 tff(f82,axiom,(
% 1.35/0.56 ! [X43 : dB,X28 : dB,X42 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X42),X28)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X43)),aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X43))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_appL)).
% 1.35/0.56 tff(f1960,plain,(
% 1.35/0.56 spl38_190 | ~spl38_94 | ~spl38_189),
% 1.35/0.56 inference(avatar_split_clause,[],[f1956,f1950,f1063,f1958])).
% 1.35/0.56 tff(f1958,plain,(
% 1.35/0.56 spl38_190 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),aa(dB,dB,combc(dB,dB,dB,app,X2),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_190])])).
% 1.35/0.56 tff(f1950,plain,(
% 1.35/0.56 spl38_189 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_189])])).
% 1.35/0.56 tff(f1956,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),aa(dB,dB,combc(dB,dB,dB,app,X2),X0)))) ) | (~spl38_94 | ~spl38_189)),
% 1.35/0.56 inference(forward_demodulation,[],[f1955,f1064])).
% 1.35/0.56 tff(f1955,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),aa(dB,dB,combc(dB,dB,dB,app,X2),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_189)),
% 1.35/0.56 inference(forward_demodulation,[],[f1954,f1064])).
% 1.35/0.56 tff(f1954,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)),aa(dB,dB,combc(dB,dB,dB,app,X2),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_189)),
% 1.35/0.56 inference(forward_demodulation,[],[f1953,f1064])).
% 1.35/0.56 tff(f1953,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_189)),
% 1.35/0.56 inference(forward_demodulation,[],[f1951,f1064])).
% 1.35/0.56 tff(f1951,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | ~spl38_189),
% 1.35/0.56 inference(avatar_component_clause,[],[f1950])).
% 1.35/0.56 tff(f1952,plain,(
% 1.35/0.56 spl38_189),
% 1.35/0.56 inference(avatar_split_clause,[],[f430,f1950])).
% 1.35/0.56 tff(f430,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f218])).
% 1.35/0.56 tff(f218,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f155])).
% 1.35/0.56 tff(f155,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))))),
% 1.35/0.56 inference(rectify,[],[f81])).
% 1.35/0.56 tff(f81,axiom,(
% 1.35/0.56 ! [X43 : dB,X28 : dB,X42 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X42),X28)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X43),X42)),aa(dB,dB,aa(dB,fun(dB,dB),app,X43),X28))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_appR)).
% 1.35/0.56 tff(f1944,plain,(
% 1.35/0.56 spl38_188 | ~spl38_26 | ~spl38_28),
% 1.35/0.56 inference(avatar_split_clause,[],[f705,f696,f687,f1941])).
% 1.35/0.56 tff(f1941,plain,(
% 1.35/0.56 spl38_188 <=> sP1(abs(subst(a,u,i)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_188])])).
% 1.35/0.56 tff(f687,plain,(
% 1.35/0.56 spl38_26 <=> pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_26])])).
% 1.35/0.56 tff(f705,plain,(
% 1.35/0.56 sP1(abs(subst(a,u,i))) | (~spl38_26 | ~spl38_28)),
% 1.35/0.56 inference(resolution,[],[f697,f689])).
% 1.35/0.56 tff(f689,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,subst(a,u,i))) | ~spl38_26),
% 1.35/0.56 inference(avatar_component_clause,[],[f687])).
% 1.35/0.56 tff(f1939,plain,(
% 1.35/0.56 spl38_187 | ~spl38_94 | ~spl38_186),
% 1.35/0.56 inference(avatar_split_clause,[],[f1935,f1929,f1063,f1937])).
% 1.35/0.56 tff(f1937,plain,(
% 1.35/0.56 spl38_187 <=> ! [X2 : dB,X0 : nat,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X2))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_187])])).
% 1.35/0.56 tff(f1929,plain,(
% 1.35/0.56 spl38_186 <=> ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_186])])).
% 1.35/0.56 tff(f1935,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)))) ) | (~spl38_94 | ~spl38_186)),
% 1.35/0.56 inference(forward_demodulation,[],[f1934,f1064])).
% 1.35/0.56 tff(f1934,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_186)),
% 1.35/0.56 inference(forward_demodulation,[],[f1933,f1064])).
% 1.35/0.56 tff(f1933,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_186)),
% 1.35/0.56 inference(forward_demodulation,[],[f1932,f1064])).
% 1.35/0.56 tff(f1932,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_186)),
% 1.35/0.56 inference(forward_demodulation,[],[f1930,f1064])).
% 1.35/0.56 tff(f1930,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | ~spl38_186),
% 1.35/0.56 inference(avatar_component_clause,[],[f1929])).
% 1.35/0.56 tff(f1931,plain,(
% 1.35/0.56 spl38_186),
% 1.35/0.56 inference(avatar_split_clause,[],[f429,f1929])).
% 1.35/0.56 tff(f429,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f217])).
% 1.35/0.56 tff(f217,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f154])).
% 1.35/0.56 tff(f154,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))))),
% 1.35/0.56 inference(rectify,[],[f87])).
% 1.35/0.56 tff(f87,axiom,(
% 1.35/0.56 ! [X27 : nat,X42 : dB,X33 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X33),X42)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X33),X27)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X42),X27))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_lift__preserves__beta)).
% 1.35/0.56 tff(f1918,plain,(
% 1.35/0.56 spl38_185 | ~spl38_94 | ~spl38_184),
% 1.35/0.56 inference(avatar_split_clause,[],[f1914,f1911,f1063,f1916])).
% 1.35/0.56 tff(f1916,plain,(
% 1.35/0.56 spl38_185 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_185])])).
% 1.35/0.56 tff(f1911,plain,(
% 1.35/0.56 spl38_184 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_184])])).
% 1.35/0.56 tff(f1914,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0) ) | (~spl38_94 | ~spl38_184)),
% 1.35/0.56 inference(forward_demodulation,[],[f1912,f1064])).
% 1.35/0.56 tff(f1912,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl38_184),
% 1.35/0.56 inference(avatar_component_clause,[],[f1911])).
% 1.35/0.56 tff(f1913,plain,(
% 1.35/0.56 spl38_184),
% 1.35/0.56 inference(avatar_split_clause,[],[f439,f1911])).
% 1.35/0.56 tff(f439,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | foldl(dB,dB,app,X2,sK21(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f298])).
% 1.35/0.56 tff(f1904,plain,(
% 1.35/0.56 spl38_183 | ~spl38_115 | ~spl38_182),
% 1.35/0.56 inference(avatar_split_clause,[],[f1900,f1897,f1197,f1902])).
% 1.35/0.56 tff(f1902,plain,(
% 1.35/0.56 spl38_183 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,abs(X2),cons(dB,X1,X0)))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_183])])).
% 1.35/0.56 tff(f1197,plain,(
% 1.35/0.56 spl38_115 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0)),X2 : list(X1)] : foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_115])])).
% 1.35/0.56 tff(f1897,plain,(
% 1.35/0.56 spl38_182 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_182])])).
% 1.35/0.56 tff(f1900,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,abs(X2),cons(dB,X1,X0)))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))) ) | (~spl38_115 | ~spl38_182)),
% 1.35/0.56 inference(forward_demodulation,[],[f1898,f1198])).
% 1.35/0.56 tff(f1198,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)) ) | ~spl38_115),
% 1.35/0.56 inference(avatar_component_clause,[],[f1197])).
% 1.35/0.56 tff(f1898,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))) ) | ~spl38_182),
% 1.35/0.56 inference(avatar_component_clause,[],[f1897])).
% 1.35/0.56 tff(f1899,plain,(
% 1.35/0.56 spl38_182),
% 1.35/0.56 inference(avatar_split_clause,[],[f432,f1897])).
% 1.35/0.56 tff(f432,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f221])).
% 1.35/0.56 tff(f221,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) | ~pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))))),
% 1.35/0.56 inference(flattening,[],[f220])).
% 1.35/0.56 tff(f220,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : dB] : ((pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) | ~pp(aa(dB,bool,it,X1))) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))))),
% 1.35/0.56 inference(ennf_transformation,[],[f157])).
% 1.35/0.56 tff(f157,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))) => (pp(aa(dB,bool,it,X1)) => pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))))),
% 1.35/0.56 inference(rectify,[],[f72])).
% 1.35/0.56 tff(f72,axiom,(
% 1.35/0.56 ! [X37 : list(dB),X24 : dB,X44 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X44,X24,zero_zero(nat)),X37))) => (pp(aa(dB,bool,it,X24)) => pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X44)),X24),X37)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Beta)).
% 1.35/0.56 tff(f1887,plain,(
% 1.35/0.56 spl38_181 | ~spl38_94 | ~spl38_180),
% 1.35/0.56 inference(avatar_split_clause,[],[f1881,f1876,f1063,f1884])).
% 1.35/0.56 tff(f1884,plain,(
% 1.35/0.56 spl38_181 <=> pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_181])])).
% 1.35/0.56 tff(f1876,plain,(
% 1.35/0.56 spl38_180 <=> pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_180])])).
% 1.35/0.56 tff(f1881,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),foldr(type,type,fun1,ts,t2))) | (~spl38_94 | ~spl38_180)),
% 1.35/0.56 inference(forward_demodulation,[],[f1880,f1064])).
% 1.35/0.56 tff(f1880,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))),foldr(type,type,fun1,ts,t2))) | (~spl38_94 | ~spl38_180)),
% 1.35/0.56 inference(forward_demodulation,[],[f1878,f1064])).
% 1.35/0.56 tff(f1878,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun1,ts,t2))) | ~spl38_180),
% 1.35/0.56 inference(avatar_component_clause,[],[f1876])).
% 1.35/0.56 tff(f1879,plain,(
% 1.35/0.56 spl38_180),
% 1.35/0.56 inference(avatar_split_clause,[],[f369,f1876])).
% 1.35/0.56 tff(f369,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 inference(cnf_transformation,[],[f45])).
% 1.35/0.56 tff(f45,axiom,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t),aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44__096e_0600_058T_H_H_062_A_092_060turnstile_062_Alift_Au_A0_A_092_060degree_062_AVar_A0_A_058_ATs_A_061_062_062_AT_H_096)).
% 1.35/0.56 tff(f1862,plain,(
% 1.35/0.56 spl38_179 | ~spl38_94 | ~spl38_178),
% 1.35/0.56 inference(avatar_split_clause,[],[f1858,f1854,f1063,f1860])).
% 1.35/0.56 tff(f1860,plain,(
% 1.35/0.56 spl38_179 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0)) | pp(aa(type,bool,typing(X3,X2),aa(type,type,combc(type,type,type,fun1,X0),sK30(X0,X1,X2,X3)))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_179])])).
% 1.35/0.56 tff(f1854,plain,(
% 1.35/0.56 spl38_178 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_178])])).
% 1.35/0.56 tff(f1858,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0)) | pp(aa(type,bool,typing(X3,X2),aa(type,type,combc(type,type,type,fun1,X0),sK30(X0,X1,X2,X3))))) ) | (~spl38_94 | ~spl38_178)),
% 1.35/0.56 inference(forward_demodulation,[],[f1857,f1064])).
% 1.35/0.56 tff(f1857,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,combc(type,type,type,fun1,X0),sK30(X0,X1,X2,X3)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl38_94 | ~spl38_178)),
% 1.35/0.56 inference(forward_demodulation,[],[f1855,f1064])).
% 1.35/0.56 tff(f1855,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_178),
% 1.35/0.56 inference(avatar_component_clause,[],[f1854])).
% 1.35/0.56 tff(f1856,plain,(
% 1.35/0.56 spl38_178),
% 1.35/0.56 inference(avatar_split_clause,[],[f463,f1854])).
% 1.35/0.56 tff(f463,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f317])).
% 1.35/0.56 tff(f317,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : ((pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f236,f316])).
% 1.35/0.56 tff(f316,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (? [X4 : type] : (pp(aa(type,bool,typing(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))) => (pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f236,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (? [X4 : type] : (pp(aa(type,bool,typing(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f172])).
% 1.35/0.56 tff(f172,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) => ~! [X4 : type] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) => ~pp(aa(type,bool,typing(X3,X1),X4))))),
% 1.35/0.56 inference(rectify,[],[f32])).
% 1.35/0.56 tff(f32,axiom,(
% 1.35/0.56 ! [X12 : type,X10 : dB,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,aa(dB,dB,aa(dB,fun(dB,dB),app,X13),X10)),X12)) => ~! [X34 : type] : (pp(aa(type,bool,typing(X14,X13),aa(type,type,aa(type,fun(type,type),fun1,X34),X12))) => ~pp(aa(type,bool,typing(X14,X10),X34))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_typing__elims_I2_J)).
% 1.35/0.56 tff(f1844,plain,(
% 1.35/0.56 spl38_177 | ~spl38_94 | ~spl38_176),
% 1.35/0.56 inference(avatar_split_clause,[],[f1840,f1837,f1063,f1842])).
% 1.35/0.56 tff(f1842,plain,(
% 1.35/0.56 spl38_177 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_177])])).
% 1.35/0.56 tff(f1837,plain,(
% 1.35/0.56 spl38_176 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_176])])).
% 1.35/0.56 tff(f1840,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0) ) | (~spl38_94 | ~spl38_176)),
% 1.35/0.56 inference(forward_demodulation,[],[f1838,f1064])).
% 1.35/0.56 tff(f1838,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl38_176),
% 1.35/0.56 inference(avatar_component_clause,[],[f1837])).
% 1.35/0.56 tff(f1839,plain,(
% 1.35/0.56 spl38_176),
% 1.35/0.56 inference(avatar_split_clause,[],[f437,f1837])).
% 1.35/0.56 tff(f437,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP2(X0,X1,X2) | step1(dB,beta,X1,sK21(X0,X1,X2)) | foldl(dB,dB,app,sK22(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f298])).
% 1.35/0.56 tff(f1830,plain,(
% 1.35/0.56 spl38_175 | ~spl38_115 | ~spl38_174),
% 1.35/0.56 inference(avatar_split_clause,[],[f1826,f1823,f1197,f1828])).
% 1.35/0.56 tff(f1828,plain,(
% 1.35/0.56 spl38_175 <=> ! [X2 : dB,X1 : dB,X3 : list(dB)] : (sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3))) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_175])])).
% 1.35/0.56 tff(f1823,plain,(
% 1.35/0.56 spl38_174 <=> ! [X2 : dB,X1 : dB,X3 : list(dB)] : (sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_174])])).
% 1.35/0.56 tff(f1826,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : list(dB),X1 : dB] : (sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3))) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))) ) | (~spl38_115 | ~spl38_174)),
% 1.35/0.56 inference(forward_demodulation,[],[f1824,f1198])).
% 1.35/0.56 tff(f1824,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : list(dB),X1 : dB] : (sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))) ) | ~spl38_174),
% 1.35/0.56 inference(avatar_component_clause,[],[f1823])).
% 1.35/0.56 tff(f1825,plain,(
% 1.35/0.56 spl38_174),
% 1.35/0.56 inference(avatar_split_clause,[],[f527,f1823])).
% 1.35/0.56 tff(f527,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : list(dB),X1 : dB] : (sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))) )),
% 1.35/0.56 inference(equality_resolution,[],[f392])).
% 1.35/0.56 tff(f392,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : list(dB),X0 : dB,X1 : dB] : (sP0(X0) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) | foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0) )),
% 1.35/0.56 inference(cnf_transformation,[],[f280])).
% 1.35/0.56 tff(f280,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP0(X0) | ! [X1 : dB,X2 : dB,X3 : list(dB)] : (~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) | foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0)) & ((pp(aa(dB,bool,it,sK11(X0))) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0) | ~sP0(X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f278,f279])).
% 1.35/0.56 tff(f279,plain,(
% 1.35/0.56 ! [X0 : dB] : (? [X4 : dB,X5 : dB,X6 : list(dB)] : (pp(aa(dB,bool,it,X5)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0) => (pp(aa(dB,bool,it,sK11(X0))) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f278,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP0(X0) | ! [X1 : dB,X2 : dB,X3 : list(dB)] : (~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) | foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0)) & (? [X4 : dB,X5 : dB,X6 : list(dB)] : (pp(aa(dB,bool,it,X5)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0) | ~sP0(X0)))),
% 1.35/0.56 inference(rectify,[],[f277])).
% 1.35/0.56 tff(f277,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP0(X0) | ! [X1 : dB,X2 : dB,X3 : list(dB)] : (~pp(aa(dB,bool,it,X2)) | ~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) | foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0)) & (? [X1 : dB,X2 : dB,X3 : list(dB)] : (pp(aa(dB,bool,it,X2)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0) | ~sP0(X0)))),
% 1.35/0.56 inference(nnf_transformation,[],[f257])).
% 1.35/0.56 tff(f257,plain,(
% 1.35/0.56 ! [X0 : dB] : (sP0(X0) <=> ? [X1 : dB,X2 : dB,X3 : list(dB)] : (pp(aa(dB,bool,it,X2)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0))),
% 1.35/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 1.35/0.56 tff(f1821,plain,(
% 1.35/0.56 spl38_172 | ~spl38_173 | ~spl38_11),
% 1.35/0.56 inference(avatar_split_clause,[],[f611,f602,f1818,f1815])).
% 1.35/0.56 tff(f1818,plain,(
% 1.35/0.56 spl38_173 <=> fFalse = fTrue),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_173])])).
% 1.35/0.56 tff(f611,plain,(
% 1.35/0.56 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl38_11),
% 1.35/0.56 inference(equality_factoring,[],[f603])).
% 1.35/0.56 tff(f1792,plain,(
% 1.35/0.56 spl38_171),
% 1.35/0.56 inference(avatar_split_clause,[],[f501,f1790])).
% 1.35/0.56 tff(f1790,plain,(
% 1.35/0.56 spl38_171 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X1,X0),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_171])])).
% 1.35/0.56 tff(f501,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f193])).
% 1.35/0.56 tff(f193,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 1.35/0.56 inference(rectify,[],[f103])).
% 1.35/0.56 tff(f103,axiom,(
% 1.35/0.56 ! [X2 : $tType,X1 : $tType,X0 : $tType,X94 : X0,X95 : fun(X0,X1),X96 : fun(X1,X2)] : aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X96),X95),X94) = aa(X1,X2,X96,aa(X0,X1,X95,X94))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 1.35/0.56 tff(f1781,plain,(
% 1.35/0.56 spl38_170 | ~spl38_94 | ~spl38_169),
% 1.35/0.56 inference(avatar_split_clause,[],[f1777,f1774,f1063,f1779])).
% 1.35/0.56 tff(f1779,plain,(
% 1.35/0.56 spl38_170 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (pp(aa(X0,bool,combc(X0,X0,bool,X4,X2),sK33(X0,X1,X2,X3,X4))) | cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_170])])).
% 1.35/0.56 tff(f1774,plain,(
% 1.35/0.56 spl38_169 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_169])])).
% 1.35/0.56 tff(f1777,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (pp(aa(X0,bool,combc(X0,X0,bool,X4,X2),sK33(X0,X1,X2,X3,X4))) | cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | (~spl38_94 | ~spl38_169)),
% 1.35/0.56 inference(forward_demodulation,[],[f1775,f1064])).
% 1.35/0.56 tff(f1775,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl38_169),
% 1.35/0.56 inference(avatar_component_clause,[],[f1774])).
% 1.35/0.56 tff(f1776,plain,(
% 1.35/0.56 spl38_169),
% 1.35/0.56 inference(avatar_split_clause,[],[f487,f1774])).
% 1.35/0.56 tff(f487,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f334])).
% 1.35/0.56 tff(f334,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : ((step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) & cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3) | (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) & cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f331,f333,f332])).
% 1.35/0.56 tff(f332,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : (? [X5 : list(X0)] : (step1(X0,X4,X5,X1) & cons(X0,X2,X5) = X3) => (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) & cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f333,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : (? [X6 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,X6),X2)) & cons(X0,X6,X1) = X3) => (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) & cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f331,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : (? [X5 : list(X0)] : (step1(X0,X4,X5,X1) & cons(X0,X2,X5) = X3) | ? [X6 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,X6),X2)) & cons(X0,X6,X1) = X3) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 inference(rectify,[],[f241])).
% 1.35/0.56 tff(f241,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : (? [X6 : list(X0)] : (step1(X0,X4,X6,X1) & cons(X0,X2,X6) = X3) | ? [X5 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,X5),X2)) & cons(X0,X5,X1) = X3) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 inference(flattening,[],[f240])).
% 1.35/0.56 tff(f240,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : ((? [X6 : list(X0)] : (step1(X0,X4,X6,X1) & cons(X0,X2,X6) = X3) | ? [X5 : X0] : (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,X5),X2)) & cons(X0,X5,X1) = X3)) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f183])).
% 1.35/0.56 tff(f183,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,X3,cons(X0,X2,X1)) => (! [X5 : X0] : (cons(X0,X5,X1) = X3 => ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,X5),X2))) => ~! [X6 : list(X0)] : (cons(X0,X2,X6) = X3 => ~step1(X0,X4,X6,X1))))),
% 1.35/0.56 inference(rectify,[],[f97])).
% 1.35/0.56 tff(f97,axiom,(
% 1.35/0.56 ! [X0 : $tType,X58 : list(X0),X22 : X0,X90 : list(X0),X44 : fun(X0,fun(X0,bool))] : (step1(X0,X44,X90,cons(X0,X22,X58)) => (! [X92 : X0] : (cons(X0,X92,X58) = X90 => ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X44,X92),X22))) => ~! [X93 : list(X0)] : (cons(X0,X22,X93) = X90 => ~step1(X0,X44,X93,X58))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Cons__step1E)).
% 1.35/0.56 tff(f1757,plain,(
% 1.35/0.56 spl38_168),
% 1.35/0.56 inference(avatar_split_clause,[],[f490,f1755])).
% 1.35/0.56 tff(f1755,plain,(
% 1.35/0.56 spl38_168 <=> ! [X2 : list(type),X4 : fun(nat,type),X0 : list(dB),X3 : dB,X1 : type] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_168])])).
% 1.35/0.56 tff(f490,plain,(
% 1.35/0.56 ( ! [X2 : list(type),X3 : dB,X0 : list(dB),X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1)))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f243])).
% 1.35/0.56 tff(f243,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 1.35/0.56 inference(flattening,[],[f242])).
% 1.35/0.56 tff(f242,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : ((pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2))) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 1.35/0.56 inference(ennf_transformation,[],[f184])).
% 1.35/0.56 tff(f184,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))) => (pp(aa(list(type),bool,typings(X4,X0),X2)) => pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1))))),
% 1.35/0.56 inference(rectify,[],[f29])).
% 1.35/0.56 tff(f29,axiom,(
% 1.35/0.56 ! [X30 : list(dB),X12 : type,X31 : list(type),X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X13),foldr(type,type,fun1,X31,X12))) => (pp(aa(list(type),bool,typings(X14,X30),X31)) => pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X13,X30)),X12))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_list__app__typeI)).
% 1.35/0.56 tff(f1745,plain,(
% 1.35/0.56 spl38_167 | ~spl38_94 | ~spl38_166),
% 1.35/0.56 inference(avatar_split_clause,[],[f1740,f1737,f1063,f1743])).
% 1.35/0.56 tff(f1737,plain,(
% 1.35/0.56 spl38_166 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_166])])).
% 1.35/0.56 tff(f1740,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (pp(aa(X0,bool,combc(X0,X0,bool,X4,X2),sK33(X0,X1,X2,X3,X4))) | step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | (~spl38_94 | ~spl38_166)),
% 1.35/0.56 inference(forward_demodulation,[],[f1738,f1064])).
% 1.35/0.56 tff(f1738,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl38_166),
% 1.35/0.56 inference(avatar_component_clause,[],[f1737])).
% 1.35/0.56 tff(f1739,plain,(
% 1.35/0.56 spl38_166),
% 1.35/0.56 inference(avatar_split_clause,[],[f489,f1737])).
% 1.35/0.56 tff(f489,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK33(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f334])).
% 1.35/0.56 tff(f1735,plain,(
% 1.35/0.56 spl38_165),
% 1.35/0.56 inference(avatar_split_clause,[],[f455,f1733])).
% 1.35/0.56 tff(f1733,plain,(
% 1.35/0.56 spl38_165 <=> ! [X0 : fun(nat,type),X3 : nat,X2 : dB,X1 : type] : (pp(aa(dB,bool,it,subst(a,X2,X3))) | ~pp(aa(type,bool,typing(X0,X2),t1)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t1),a),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_165])])).
% 1.35/0.56 tff(f455,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : nat,X0 : fun(nat,type),X1 : type] : (pp(aa(dB,bool,it,subst(a,X2,X3))) | ~pp(aa(type,bool,typing(X0,X2),t1)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t1),a),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f231])).
% 1.35/0.56 tff(f231,plain,(
% 1.35/0.56 ! [X0 : fun(nat,type),X1 : type,X2 : dB,X3 : nat] : (pp(aa(dB,bool,it,subst(a,X2,X3))) | ~pp(aa(type,bool,typing(X0,X2),t1)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t1),a),X1)))),
% 1.35/0.56 inference(flattening,[],[f230])).
% 1.35/0.56 tff(f230,plain,(
% 1.35/0.56 ! [X0 : fun(nat,type),X1 : type,X2 : dB,X3 : nat] : (((pp(aa(dB,bool,it,subst(a,X2,X3))) | ~pp(aa(type,bool,typing(X0,X2),t1))) | ~pp(aa(dB,bool,it,X2))) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t1),a),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f167])).
% 1.35/0.56 tff(f167,plain,(
% 1.35/0.56 ! [X0 : fun(nat,type),X1 : type,X2 : dB,X3 : nat] : (pp(aa(type,bool,typing(shift(type,X0,X3,t1),a),X1)) => (pp(aa(dB,bool,it,X2)) => (pp(aa(type,bool,typing(X0,X2),t1)) => pp(aa(dB,bool,it,subst(a,X2,X3))))))),
% 1.35/0.56 inference(rectify,[],[f7])).
% 1.35/0.56 tff(f7,axiom,(
% 1.35/0.56 ! [X4 : fun(nat,type),X5 : type,X6 : dB,X7 : nat] : (pp(aa(type,bool,typing(shift(type,X4,X7,t1),a),X5)) => (pp(aa(dB,bool,it,X6)) => (pp(aa(type,bool,typing(X4,X6),t1)) => pp(aa(dB,bool,it,subst(a,X6,X7))))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096ALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_Ia_091u_Pi_093_J_096)).
% 1.35/0.56 tff(f1721,plain,(
% 1.35/0.56 spl38_164 | ~spl38_94 | ~spl38_163),
% 1.35/0.56 inference(avatar_split_clause,[],[f1717,f1713,f1063,f1719])).
% 1.35/0.56 tff(f1719,plain,(
% 1.35/0.56 spl38_164 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X1,X0)),foldl(dB,dB,app,X2,X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_164])])).
% 1.35/0.56 tff(f1713,plain,(
% 1.35/0.56 spl38_163 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_163])])).
% 1.35/0.56 tff(f1717,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X1,X0)),foldl(dB,dB,app,X2,X0)))) ) | (~spl38_94 | ~spl38_163)),
% 1.35/0.56 inference(forward_demodulation,[],[f1716,f1064])).
% 1.35/0.56 tff(f1716,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X1,X0)),foldl(dB,dB,app,X2,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | (~spl38_94 | ~spl38_163)),
% 1.35/0.56 inference(forward_demodulation,[],[f1714,f1064])).
% 1.35/0.56 tff(f1714,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) ) | ~spl38_163),
% 1.35/0.56 inference(avatar_component_clause,[],[f1713])).
% 1.35/0.56 tff(f1715,plain,(
% 1.35/0.56 spl38_163),
% 1.35/0.56 inference(avatar_split_clause,[],[f428,f1713])).
% 1.35/0.56 tff(f428,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f216])).
% 1.35/0.56 tff(f216,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f153])).
% 1.35/0.56 tff(f153,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))))),
% 1.35/0.56 inference(rectify,[],[f89])).
% 1.35/0.56 tff(f89,axiom,(
% 1.35/0.56 ! [X37 : list(dB),X24 : dB,X44 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X44),X24)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X44,X37)),foldl(dB,dB,app,X24,X37))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_apps__preserves__beta)).
% 1.35/0.56 tff(f1704,plain,(
% 1.35/0.56 spl38_162),
% 1.35/0.56 inference(avatar_split_clause,[],[f486,f1702])).
% 1.35/0.56 tff(f1702,plain,(
% 1.35/0.56 spl38_162 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_162])])).
% 1.35/0.56 tff(f486,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK32(X0,X1,X2,X3,X4)) = X3 | cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f334])).
% 1.35/0.56 tff(f1700,plain,(
% 1.35/0.56 spl38_161),
% 1.35/0.56 inference(avatar_split_clause,[],[f461,f1698])).
% 1.35/0.56 tff(f1698,plain,(
% 1.35/0.56 spl38_161 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_161])])).
% 1.35/0.56 tff(f461,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f315])).
% 1.35/0.56 tff(f315,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK29(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f235,f314])).
% 1.35/0.56 tff(f314,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK29(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f235,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f171])).
% 1.35/0.56 tff(f171,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)) => ~! [X4 : list(type)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0))) => ~pp(aa(list(type),bool,typings(X3,X1),X4))))),
% 1.35/0.56 inference(rectify,[],[f33])).
% 1.35/0.56 tff(f33,axiom,(
% 1.35/0.56 ! [X12 : type,X30 : list(dB),X8 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X8),X30)),X12)) => ~! [X25 : list(type)] : (pp(aa(type,bool,typing(X14,var(X8)),foldr(type,type,fun1,X25,X12))) => ~pp(aa(list(type),bool,typings(X14,X30),X25))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_var__app__typesE)).
% 1.35/0.56 tff(f1690,plain,(
% 1.35/0.56 spl38_160 | ~spl38_94 | ~spl38_159),
% 1.35/0.56 inference(avatar_split_clause,[],[f1686,f1683,f1063,f1688])).
% 1.35/0.56 tff(f1688,plain,(
% 1.35/0.56 spl38_160 <=> ! [X0 : type,X3 : fun(nat,type),X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,combc(type,type,type,fun1,X0),X2))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_160])])).
% 1.35/0.56 tff(f1683,plain,(
% 1.35/0.56 spl38_159 <=> ! [X0 : type,X3 : fun(nat,type),X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_159])])).
% 1.35/0.56 tff(f1686,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,combc(type,type,type,fun1,X0),X2))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0))) ) | (~spl38_94 | ~spl38_159)),
% 1.35/0.56 inference(forward_demodulation,[],[f1684,f1064])).
% 1.35/0.56 tff(f1684,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0))) ) | ~spl38_159),
% 1.35/0.56 inference(avatar_component_clause,[],[f1683])).
% 1.35/0.56 tff(f1685,plain,(
% 1.35/0.56 spl38_159),
% 1.35/0.56 inference(avatar_split_clause,[],[f460,f1683])).
% 1.35/0.56 tff(f460,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f234])).
% 1.35/0.56 tff(f234,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : type,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f170])).
% 1.35/0.56 tff(f170,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : type,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0)) => pp(aa(type,bool,typing(X3,abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))))),
% 1.35/0.56 inference(rectify,[],[f61])).
% 1.35/0.56 tff(f61,axiom,(
% 1.35/0.56 ! [X9 : type,X13 : dB,X12 : type,X23 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X23,zero_zero(nat),X12),X13),X9)) => pp(aa(type,bool,typing(X23,abs(X13)),aa(type,type,aa(type,fun(type,type),fun1,X12),X9))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Abs)).
% 1.35/0.56 tff(f1665,plain,(
% 1.35/0.56 spl38_158 | ~spl38_94 | ~spl38_157),
% 1.35/0.56 inference(avatar_split_clause,[],[f1661,f1658,f1063,f1663])).
% 1.35/0.56 tff(f1658,plain,(
% 1.35/0.56 spl38_157 <=> ! [X0 : nat,X3 : dB,X2 : dB,X1 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_157])])).
% 1.35/0.56 tff(f1661,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0)) = subst(aa(dB,dB,combc(dB,dB,dB,app,X2),X3),X1,X0)) ) | (~spl38_94 | ~spl38_157)),
% 1.35/0.56 inference(forward_demodulation,[],[f1659,f1064])).
% 1.35/0.56 tff(f1659,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))) ) | ~spl38_157),
% 1.35/0.56 inference(avatar_component_clause,[],[f1658])).
% 1.35/0.56 tff(f1660,plain,(
% 1.35/0.56 spl38_157),
% 1.35/0.56 inference(avatar_split_clause,[],[f452,f1658])).
% 1.35/0.56 tff(f452,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f164])).
% 1.35/0.56 tff(f164,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB,X3 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))),
% 1.35/0.56 inference(rectify,[],[f38])).
% 1.35/0.56 tff(f38,axiom,(
% 1.35/0.56 ! [X41 : nat,X42 : dB,X43 : dB,X28 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X43),X42,X41) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X28,X42,X41)),subst(X43,X42,X41))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_subst__App)).
% 1.35/0.56 tff(f1634,plain,(
% 1.35/0.56 spl38_156),
% 1.35/0.56 inference(avatar_split_clause,[],[f545,f1632])).
% 1.35/0.56 tff(f545,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : nat,X1 : type,X4 : type,X5 : dB] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(shift(type,X3,X0,X1),X5),X4))) )),
% 1.35/0.56 inference(equality_resolution,[],[f511])).
% 1.35/0.56 tff(f511,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : nat,X1 : type,X6 : fun(nat,type),X4 : type,X5 : dB] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6 | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(X6,X5),X4))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f250])).
% 1.35/0.56 tff(f250,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6 | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(X6,X5),X4)))),
% 1.35/0.56 inference(flattening,[],[f249])).
% 1.35/0.56 tff(f249,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (((pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6) | ~pp(aa(type,bool,typing(X3,X2),X1))) | ~pp(aa(type,bool,typing(X6,X5),X4)))),
% 1.35/0.56 inference(ennf_transformation,[],[f196])).
% 1.35/0.56 tff(f196,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X6,X5),X4)) => (pp(aa(type,bool,typing(X3,X2),X1)) => (shift(type,X3,X0,X1) = X6 => pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)))))),
% 1.35/0.56 inference(rectify,[],[f9])).
% 1.35/0.56 tff(f9,axiom,(
% 1.35/0.56 ! [X8 : nat,X9 : type,X10 : dB,X11 : fun(nat,type),X12 : type,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X13),X12)) => (pp(aa(type,bool,typing(X11,X10),X9)) => (shift(type,X11,X8,X9) = X14 => pp(aa(type,bool,typing(X11,subst(X13,X10,X8)),X12)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_subst__lemma)).
% 1.35/0.56 tff(f1630,plain,(
% 1.35/0.56 spl38_155),
% 1.35/0.56 inference(avatar_split_clause,[],[f491,f1628])).
% 1.35/0.56 tff(f1628,plain,(
% 1.35/0.56 spl38_155 <=> ! [X4 : fun(nat,type),X0 : type,X3 : nat,X2 : list(dB),X1 : type] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_155])])).
% 1.35/0.56 tff(f491,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X3 : nat,X0 : type,X1 : type,X4 : fun(nat,type)] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f245])).
% 1.35/0.56 tff(f245,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 1.35/0.56 inference(flattening,[],[f244])).
% 1.35/0.56 tff(f244,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : ((X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0))) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f185])).
% 1.35/0.56 tff(f185,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)) => (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) => X0 = X1))),
% 1.35/0.56 inference(rectify,[],[f30])).
% 1.35/0.56 tff(f30,axiom,(
% 1.35/0.56 ! [X9 : type,X12 : type,X30 : list(dB),X8 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X8),X30)),X12)) => (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X8),X30)),X9)) => X9 = X12))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_var__app__type__eq)).
% 1.35/0.56 tff(f1605,plain,(
% 1.35/0.56 spl38_154),
% 1.35/0.56 inference(avatar_split_clause,[],[f488,f1603])).
% 1.35/0.56 tff(f1603,plain,(
% 1.35/0.56 spl38_154 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_154])])).
% 1.35/0.56 tff(f488,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK32(X0,X1,X2,X3,X4),X1) | cons(X0,sK33(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f334])).
% 1.35/0.56 tff(f1599,plain,(
% 1.35/0.56 spl38_153 | ~spl38_94 | ~spl38_152),
% 1.35/0.56 inference(avatar_split_clause,[],[f1595,f1592,f1063,f1597])).
% 1.35/0.56 tff(f1597,plain,(
% 1.35/0.56 spl38_153 <=> ! [X4 : fun(nat,type),X0 : type,X3 : dB,X2 : type,X1 : nat] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_153])])).
% 1.35/0.56 tff(f1592,plain,(
% 1.35/0.56 spl38_152 <=> ! [X4 : fun(nat,type),X0 : type,X3 : dB,X2 : type,X1 : nat] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_152])])).
% 1.35/0.56 tff(f1595,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : type,X1 : nat,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2))) ) | (~spl38_94 | ~spl38_152)),
% 1.35/0.56 inference(forward_demodulation,[],[f1593,f1064])).
% 1.35/0.56 tff(f1593,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : type,X1 : nat,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2))) ) | ~spl38_152),
% 1.35/0.56 inference(avatar_component_clause,[],[f1592])).
% 1.35/0.56 tff(f1594,plain,(
% 1.35/0.56 spl38_152),
% 1.35/0.56 inference(avatar_split_clause,[],[f485,f1592])).
% 1.35/0.56 tff(f485,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : dB,X0 : type,X1 : nat,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f239])).
% 1.35/0.56 tff(f239,plain,(
% 1.35/0.56 ! [X0 : type,X1 : nat,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) | ~pp(aa(type,bool,typing(X4,X3),X2)))),
% 1.35/0.56 inference(ennf_transformation,[],[f182])).
% 1.35/0.56 tff(f182,plain,(
% 1.35/0.56 ! [X0 : type,X1 : nat,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,X3),X2)) => pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)))),
% 1.35/0.56 inference(rectify,[],[f55])).
% 1.35/0.56 tff(f55,axiom,(
% 1.35/0.56 ! [X9 : type,X8 : nat,X12 : type,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X13),X12)) => pp(aa(type,bool,typing(shift(type,X14,X8,X9),aa(nat,dB,aa(dB,fun(nat,dB),lift,X13),X8)),X12)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_lift__type)).
% 1.35/0.56 tff(f1586,plain,(
% 1.35/0.56 spl38_151 | ~spl38_94 | ~spl38_150),
% 1.35/0.56 inference(avatar_split_clause,[],[f1582,f1579,f1063,f1584])).
% 1.35/0.56 tff(f1584,plain,(
% 1.35/0.56 spl38_151 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0)) | pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_151])])).
% 1.35/0.56 tff(f1579,plain,(
% 1.35/0.56 spl38_150 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_150])])).
% 1.35/0.56 tff(f1582,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0)) | pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3)))) ) | (~spl38_94 | ~spl38_150)),
% 1.35/0.56 inference(forward_demodulation,[],[f1580,f1064])).
% 1.35/0.56 tff(f1580,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl38_150),
% 1.35/0.56 inference(avatar_component_clause,[],[f1579])).
% 1.35/0.56 tff(f1581,plain,(
% 1.35/0.56 spl38_150),
% 1.35/0.56 inference(avatar_split_clause,[],[f464,f1579])).
% 1.35/0.56 tff(f464,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK30(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f317])).
% 1.35/0.56 tff(f1577,plain,(
% 1.35/0.56 spl38_149),
% 1.35/0.56 inference(avatar_split_clause,[],[f458,f1575])).
% 1.35/0.56 tff(f1575,plain,(
% 1.35/0.56 spl38_149 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_149])])).
% 1.35/0.56 tff(f458,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f313])).
% 1.35/0.56 tff(f313,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK28(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f233,f312])).
% 1.35/0.56 tff(f312,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK28(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f233,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f169])).
% 1.35/0.56 tff(f169,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) => ? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))))),
% 1.35/0.56 inference(rectify,[],[f36])).
% 1.35/0.56 tff(f36,axiom,(
% 1.35/0.56 ! [X12 : type,X30 : list(dB),X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X13,X30)),X12)) => ? [X25 : list(type)] : (pp(aa(list(type),bool,typings(X14,X30),X25)) & pp(aa(type,bool,typing(X14,X13),foldr(type,type,fun1,X25,X12)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_list__app__typeD)).
% 1.35/0.56 tff(f1573,plain,(
% 1.35/0.56 spl38_148 | ~spl38_22 | ~spl38_28),
% 1.35/0.56 inference(avatar_split_clause,[],[f703,f696,f659,f1571])).
% 1.35/0.56 tff(f1571,plain,(
% 1.35/0.56 spl38_148 <=> ! [X0 : dB] : (sP1(abs(X0)) | ~sP1(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_148])])).
% 1.35/0.56 tff(f659,plain,(
% 1.35/0.56 spl38_22 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_22])])).
% 1.35/0.56 tff(f703,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP1(abs(X0)) | ~sP1(X0)) ) | (~spl38_22 | ~spl38_28)),
% 1.35/0.56 inference(resolution,[],[f697,f660])).
% 1.35/0.56 tff(f660,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0)) ) | ~spl38_22),
% 1.35/0.56 inference(avatar_component_clause,[],[f659])).
% 1.35/0.56 tff(f1569,plain,(
% 1.35/0.56 spl38_147),
% 1.35/0.56 inference(avatar_split_clause,[],[f456,f1567])).
% 1.35/0.56 tff(f1567,plain,(
% 1.35/0.56 spl38_147 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_147])])).
% 1.35/0.56 tff(f456,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f311])).
% 1.35/0.56 tff(f311,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK27(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f232,f310])).
% 1.35/0.56 tff(f310,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK27(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f232,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f168])).
% 1.35/0.56 tff(f168,plain,(
% 1.35/0.56 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) => ~! [X4 : list(type)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0))) => ~pp(aa(list(type),bool,typings(X3,X1),X4))))),
% 1.35/0.56 inference(rectify,[],[f37])).
% 1.35/0.56 tff(f37,axiom,(
% 1.35/0.56 ! [X12 : type,X30 : list(dB),X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X13,X30)),X12)) => ~! [X25 : list(type)] : (pp(aa(type,bool,typing(X14,X13),foldr(type,type,fun1,X25,X12))) => ~pp(aa(list(type),bool,typings(X14,X30),X25))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_list__app__typeE)).
% 1.35/0.56 tff(f1557,plain,(
% 1.35/0.56 spl38_146 | ~spl38_94 | ~spl38_145),
% 1.35/0.56 inference(avatar_split_clause,[],[f1553,f1549,f1063,f1555])).
% 1.35/0.56 tff(f1555,plain,(
% 1.35/0.56 spl38_146 <=> ! [X0 : nat,X3 : dB,X2 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X2),X3)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X2,X1,X0)),subst(X3,X1,X0))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_146])])).
% 1.35/0.56 tff(f1549,plain,(
% 1.35/0.56 spl38_145 <=> ! [X0 : nat,X3 : dB,X2 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X3,X1,X0)),subst(X2,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_145])])).
% 1.35/0.56 tff(f1553,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X2),X3)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X2,X1,X0)),subst(X3,X1,X0)))) ) | (~spl38_94 | ~spl38_145)),
% 1.35/0.56 inference(forward_demodulation,[],[f1552,f1064])).
% 1.35/0.56 tff(f1552,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X2,X1,X0)),subst(X3,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2))) ) | (~spl38_94 | ~spl38_145)),
% 1.35/0.56 inference(forward_demodulation,[],[f1550,f1064])).
% 1.35/0.56 tff(f1550,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X3,X1,X0)),subst(X2,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2))) ) | ~spl38_145),
% 1.35/0.56 inference(avatar_component_clause,[],[f1549])).
% 1.35/0.56 tff(f1551,plain,(
% 1.35/0.56 spl38_145),
% 1.35/0.56 inference(avatar_split_clause,[],[f454,f1549])).
% 1.35/0.56 tff(f454,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X3,X1,X0)),subst(X2,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f229])).
% 1.35/0.56 tff(f229,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB,X3 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X3,X1,X0)),subst(X2,X1,X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)))),
% 1.35/0.56 inference(ennf_transformation,[],[f166])).
% 1.35/0.56 tff(f166,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB,X2 : dB,X3 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X3,X1,X0)),subst(X2,X1,X0))))),
% 1.35/0.56 inference(rectify,[],[f85])).
% 1.35/0.56 tff(f85,axiom,(
% 1.35/0.56 ! [X27 : nat,X28 : dB,X42 : dB,X33 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X33),X42)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X33,X28,X27)),subst(X42,X28,X27))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_subst__preserves__beta)).
% 1.35/0.56 tff(f1544,plain,(
% 1.35/0.56 spl38_144 | ~spl38_94 | ~spl38_143),
% 1.35/0.56 inference(avatar_split_clause,[],[f1540,f1537,f1063,f1542])).
% 1.35/0.56 tff(f1542,plain,(
% 1.35/0.56 spl38_144 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,var(X2),X1))) | foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_144])])).
% 1.35/0.56 tff(f1537,plain,(
% 1.35/0.56 spl38_143 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_143])])).
% 1.35/0.56 tff(f1540,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,var(X2),X1))) | foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0) ) | (~spl38_94 | ~spl38_143)),
% 1.35/0.56 inference(forward_demodulation,[],[f1538,f1064])).
% 1.35/0.56 tff(f1538,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) ) | ~spl38_143),
% 1.35/0.56 inference(avatar_component_clause,[],[f1537])).
% 1.35/0.56 tff(f1539,plain,(
% 1.35/0.56 spl38_143),
% 1.35/0.56 inference(avatar_split_clause,[],[f441,f1537])).
% 1.35/0.56 tff(f441,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f300])).
% 1.35/0.56 tff(f300,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : nat] : ((foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK23(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f224,f299])).
% 1.35/0.56 tff(f299,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : nat] : (? [X3 : list(dB)] : (foldl(dB,dB,app,var(X2),X3) = X0 & step1(dB,beta,X1,X3)) => (foldl(dB,dB,app,var(X2),sK23(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK23(X0,X1,X2))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f224,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : nat] : (? [X3 : list(dB)] : (foldl(dB,dB,app,var(X2),X3) = X0 & step1(dB,beta,X1,X3)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f159])).
% 1.35/0.56 tff(f159,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : nat] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) => ? [X3 : list(dB)] : (foldl(dB,dB,app,var(X2),X3) = X0 & step1(dB,beta,X1,X3)))),
% 1.35/0.56 inference(rectify,[],[f95])).
% 1.35/0.56 tff(f95,axiom,(
% 1.35/0.56 ! [X88 : dB,X39 : list(dB),X38 : nat] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X38),X39)),X88)) => ? [X89 : list(dB)] : (foldl(dB,dB,app,var(X38),X89) = X88 & step1(dB,beta,X39,X89)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_head__Var__reduction)).
% 1.35/0.56 tff(f1531,plain,(
% 1.35/0.56 spl38_142 | ~spl38_94 | ~spl38_141),
% 1.35/0.56 inference(avatar_split_clause,[],[f1526,f1521,f1063,f1528])).
% 1.35/0.56 tff(f1528,plain,(
% 1.35/0.56 spl38_142 <=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_142])])).
% 1.35/0.56 tff(f1521,plain,(
% 1.35/0.56 spl38_141 <=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_141])])).
% 1.35/0.56 tff(f1526,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))) | (~spl38_94 | ~spl38_141)),
% 1.35/0.56 inference(forward_demodulation,[],[f1525,f1064])).
% 1.35/0.56 tff(f1525,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))) | (~spl38_94 | ~spl38_141)),
% 1.35/0.56 inference(forward_demodulation,[],[f1523,f1064])).
% 1.35/0.56 tff(f1523,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat))))) | ~spl38_141),
% 1.35/0.56 inference(avatar_component_clause,[],[f1521])).
% 1.35/0.56 tff(f1524,plain,(
% 1.35/0.56 spl38_141),
% 1.35/0.56 inference(avatar_split_clause,[],[f368,f1521])).
% 1.35/0.56 tff(f368,plain,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))))),
% 1.35/0.56 inference(cnf_transformation,[],[f52])).
% 1.35/0.56 tff(f52,axiom,(
% 1.35/0.56 pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51__096IT_A_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_096)).
% 1.35/0.56 tff(f1519,plain,(
% 1.35/0.56 spl38_140 | ~spl38_21 | ~spl38_27),
% 1.35/0.56 inference(avatar_split_clause,[],[f701,f692,f655,f1517])).
% 1.35/0.56 tff(f1517,plain,(
% 1.35/0.56 spl38_140 <=> ! [X0 : dB] : (~sP0(X0) | sP1(sK11(X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_140])])).
% 1.35/0.56 tff(f701,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (~sP0(X0) | sP1(sK11(X0))) ) | (~spl38_21 | ~spl38_27)),
% 1.35/0.56 inference(resolution,[],[f693,f656])).
% 1.35/0.56 tff(f1505,plain,(
% 1.35/0.56 spl38_139 | ~spl38_94 | ~spl38_138),
% 1.35/0.56 inference(avatar_split_clause,[],[f1500,f1496,f1063,f1502])).
% 1.35/0.56 tff(f1502,plain,(
% 1.35/0.56 spl38_139 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,sK6,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_139])])).
% 1.35/0.56 tff(f1496,plain,(
% 1.35/0.56 spl38_138 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_138])])).
% 1.35/0.56 tff(f1500,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,sK6,t2))) | (~spl38_94 | ~spl38_138)),
% 1.35/0.56 inference(forward_demodulation,[],[f1498,f1064])).
% 1.35/0.56 tff(f1498,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t2))) | ~spl38_138),
% 1.35/0.56 inference(avatar_component_clause,[],[f1496])).
% 1.35/0.56 tff(f1499,plain,(
% 1.35/0.56 spl38_138),
% 1.35/0.56 inference(avatar_split_clause,[],[f522,f1496])).
% 1.35/0.56 tff(f522,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t2)))),
% 1.35/0.56 inference(definition_unfolding,[],[f372,f350])).
% 1.35/0.56 tff(f350,plain,(
% 1.35/0.56 n = i),
% 1.35/0.56 inference(cnf_transformation,[],[f3])).
% 1.35/0.56 tff(f3,axiom,(
% 1.35/0.56 n = i),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_True)).
% 1.35/0.56 tff(f372,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t2)))),
% 1.35/0.56 inference(cnf_transformation,[],[f269])).
% 1.35/0.56 tff(f269,plain,(
% 1.35/0.56 pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK6)) & pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t2)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f201,f268])).
% 1.35/0.56 tff(f268,plain,(
% 1.35/0.56 ? [X0 : list(type)] : (pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2)))) => (pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK6)) & pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t2))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f201,plain,(
% 1.35/0.56 ? [X0 : list(type)] : (pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2))))),
% 1.35/0.56 inference(ennf_transformation,[],[f115])).
% 1.35/0.56 tff(f115,plain,(
% 1.35/0.56 ~! [X0 : list(type)] : (pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2))) => ~pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)))),
% 1.35/0.56 inference(rectify,[],[f25])).
% 1.35/0.56 tff(f25,axiom,(
% 1.35/0.56 ~! [X25 : list(type)] : (pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X25,t2))) => ~pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X25)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)).
% 1.35/0.56 tff(f1488,plain,(
% 1.35/0.56 spl38_137 | ~spl38_94 | ~spl38_114 | ~spl38_136),
% 1.35/0.56 inference(avatar_split_clause,[],[f1483,f1478,f1193,f1063,f1485])).
% 1.35/0.56 tff(f1478,plain,(
% 1.35/0.56 spl38_136 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_136])])).
% 1.35/0.56 tff(f1483,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t2))) | (~spl38_94 | ~spl38_114 | ~spl38_136)),
% 1.35/0.56 inference(forward_demodulation,[],[f1482,f1238])).
% 1.35/0.56 tff(f1238,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,X0)),X3 : X1,X4 : list(X1),X5 : X0] : (foldr(X1,X0,X2,cons(X1,X3,X4),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3)) ) | (~spl38_94 | ~spl38_114)),
% 1.35/0.56 inference(superposition,[],[f1194,f1064])).
% 1.35/0.56 tff(f1482,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK5))) | (~spl38_94 | ~spl38_136)),
% 1.35/0.56 inference(forward_demodulation,[],[f1480,f1064])).
% 1.35/0.56 tff(f1480,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2)))) | ~spl38_136),
% 1.35/0.56 inference(avatar_component_clause,[],[f1478])).
% 1.35/0.56 tff(f1481,plain,(
% 1.35/0.56 spl38_136),
% 1.35/0.56 inference(avatar_split_clause,[],[f521,f1478])).
% 1.35/0.56 tff(f521,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.56 inference(definition_unfolding,[],[f370,f350])).
% 1.35/0.56 tff(f370,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.56 inference(cnf_transformation,[],[f267])).
% 1.35/0.56 tff(f267,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),a),sK5)) & pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f200,f266])).
% 1.35/0.56 tff(f266,plain,(
% 1.35/0.56 ? [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t1),a),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2))))) => (pp(aa(type,bool,typing(shift(type,e,i,t1),a),sK5)) & pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t2)))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f200,plain,(
% 1.35/0.56 ? [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t1),a),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2)))))),
% 1.35/0.56 inference(ennf_transformation,[],[f114])).
% 1.35/0.56 tff(f114,plain,(
% 1.35/0.56 ~! [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2)))) => ~pp(aa(type,bool,typing(shift(type,e,i,t1),a),X0)))),
% 1.35/0.56 inference(rectify,[],[f16])).
% 1.35/0.56 tff(f16,axiom,(
% 1.35/0.56 ~! [X17 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X17),foldr(type,type,fun1,ts,t2)))) => ~pp(aa(type,bool,typing(shift(type,e,i,t1),a),X17)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)).
% 1.35/0.56 tff(f1474,plain,(
% 1.35/0.56 spl38_135),
% 1.35/0.56 inference(avatar_split_clause,[],[f520,f1471])).
% 1.35/0.56 tff(f1471,plain,(
% 1.35/0.56 spl38_135 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_135])])).
% 1.35/0.56 tff(f520,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t2))),
% 1.35/0.56 inference(definition_unfolding,[],[f367,f350])).
% 1.35/0.56 tff(f367,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t2))),
% 1.35/0.56 inference(cnf_transformation,[],[f17])).
% 1.35/0.56 tff(f17,axiom,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t2))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096)).
% 1.35/0.56 tff(f1467,plain,(
% 1.35/0.56 spl38_134 | ~spl38_94 | ~spl38_132),
% 1.35/0.56 inference(avatar_split_clause,[],[f1457,f1453,f1063,f1464])).
% 1.35/0.56 tff(f1464,plain,(
% 1.35/0.56 spl38_134 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_134])])).
% 1.35/0.56 tff(f1453,plain,(
% 1.35/0.56 spl38_132 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_132])])).
% 1.35/0.56 tff(f1457,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,ts,t2))) | (~spl38_94 | ~spl38_132)),
% 1.35/0.56 inference(forward_demodulation,[],[f1455,f1064])).
% 1.35/0.56 tff(f1455,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2))) | ~spl38_132),
% 1.35/0.56 inference(avatar_component_clause,[],[f1453])).
% 1.35/0.56 tff(f1462,plain,(
% 1.35/0.56 spl38_133 | ~spl38_21 | ~spl38_26),
% 1.35/0.56 inference(avatar_split_clause,[],[f699,f687,f655,f1459])).
% 1.35/0.56 tff(f1459,plain,(
% 1.35/0.56 spl38_133 <=> sP1(subst(a,u,i))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_133])])).
% 1.35/0.56 tff(f699,plain,(
% 1.35/0.56 sP1(subst(a,u,i)) | (~spl38_21 | ~spl38_26)),
% 1.35/0.56 inference(resolution,[],[f689,f656])).
% 1.35/0.56 tff(f1456,plain,(
% 1.35/0.56 spl38_132),
% 1.35/0.56 inference(avatar_split_clause,[],[f519,f1453])).
% 1.35/0.56 tff(f519,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 inference(definition_unfolding,[],[f366,f350])).
% 1.35/0.56 tff(f366,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 inference(cnf_transformation,[],[f22])).
% 1.35/0.56 tff(f22,axiom,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t2)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_headT)).
% 1.35/0.56 tff(f1446,plain,(
% 1.35/0.56 spl38_131 | ~spl38_94 | ~spl38_130),
% 1.35/0.56 inference(avatar_split_clause,[],[f1442,f1439,f1063,f1444])).
% 1.35/0.56 tff(f1444,plain,(
% 1.35/0.56 spl38_131 <=> ! [X0 : dB,X3 : fun(nat,type),X2 : dB,X1 : type] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X2)) | pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(type,bool,typing(X3,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_131])])).
% 1.35/0.56 tff(f1439,plain,(
% 1.35/0.56 spl38_130 <=> ! [X0 : dB,X3 : fun(nat,type),X2 : dB,X1 : type] : (pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0)) | ~pp(aa(type,bool,typing(X3,X2),X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_130])])).
% 1.35/0.56 tff(f1442,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : dB,X1 : type] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X2)) | pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(type,bool,typing(X3,X2),X1))) ) | (~spl38_94 | ~spl38_130)),
% 1.35/0.56 inference(forward_demodulation,[],[f1440,f1064])).
% 1.35/0.56 tff(f1440,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : dB,X1 : type] : (pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0)) | ~pp(aa(type,bool,typing(X3,X2),X1))) ) | ~spl38_130),
% 1.35/0.56 inference(avatar_component_clause,[],[f1439])).
% 1.35/0.56 tff(f1441,plain,(
% 1.35/0.56 spl38_130),
% 1.35/0.56 inference(avatar_split_clause,[],[f453,f1439])).
% 1.35/0.56 tff(f453,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : dB,X1 : type] : (pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0)) | ~pp(aa(type,bool,typing(X3,X2),X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f228])).
% 1.35/0.56 tff(f228,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0)) | ~pp(aa(type,bool,typing(X3,X2),X1)))),
% 1.35/0.56 inference(flattening,[],[f227])).
% 1.35/0.56 tff(f227,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : dB,X3 : fun(nat,type)] : ((pp(aa(type,bool,typing(X3,X0),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))) | ~pp(aa(type,bool,typing(X3,X2),X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f165])).
% 1.35/0.56 tff(f165,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : type,X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,X2),X1)) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0)) => pp(aa(type,bool,typing(X3,X0),X1))))),
% 1.35/0.56 inference(rectify,[],[f86])).
% 1.35/0.56 tff(f86,axiom,(
% 1.35/0.56 ! [X81 : dB,X12 : type,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X13),X12)) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X13),X81)) => pp(aa(type,bool,typing(X14,X81),X12))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subject__reduction)).
% 1.35/0.56 tff(f1437,plain,(
% 1.35/0.56 spl38_129),
% 1.35/0.56 inference(avatar_split_clause,[],[f426,f1435])).
% 1.35/0.56 tff(f1435,plain,(
% 1.35/0.56 spl38_129 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK16(X0,X1,X2)),X1),sK17(X0,X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_129])])).
% 1.35/0.56 tff(f426,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK16(X0,X1,X2)),X1),sK17(X0,X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f289])).
% 1.35/0.56 tff(f289,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : ((pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK16(X0,X1,X2)),X1),sK17(X0,X1,X2))) & aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X0) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f214,f288])).
% 1.35/0.56 tff(f288,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (? [X3 : type,X4 : type] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4)) & aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0) => (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK16(X0,X1,X2)),X1),sK17(X0,X1,X2))) & aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f214,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (? [X3 : type,X4 : type] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4)) & aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f151])).
% 1.35/0.56 tff(f151,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,abs(X1)),X0)) => ~! [X3 : type,X4 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 => ~pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4))))),
% 1.35/0.56 inference(rectify,[],[f73])).
% 1.35/0.56 tff(f73,axiom,(
% 1.35/0.56 ! [X12 : type,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,abs(X13)),X12)) => ~! [X34 : type,X69 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X34),X69) = X12 => ~pp(aa(type,bool,typing(shift(type,X14,zero_zero(nat),X34),X13),X69))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_typing__elims_I3_J)).
% 1.35/0.56 tff(f1432,plain,(
% 1.35/0.56 spl38_128 | ~spl38_94 | ~spl38_127),
% 1.35/0.56 inference(avatar_split_clause,[],[f1428,f1425,f1063,f1430])).
% 1.35/0.56 tff(f1430,plain,(
% 1.35/0.56 spl38_128 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK17(X0,X1,X2)),sK16(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_128])])).
% 1.35/0.56 tff(f1425,plain,(
% 1.35/0.56 spl38_127 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_127])])).
% 1.35/0.56 tff(f1428,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK17(X0,X1,X2)),sK16(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) ) | (~spl38_94 | ~spl38_127)),
% 1.35/0.56 inference(forward_demodulation,[],[f1426,f1064])).
% 1.35/0.56 tff(f1426,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) ) | ~spl38_127),
% 1.35/0.56 inference(avatar_component_clause,[],[f1425])).
% 1.35/0.56 tff(f1427,plain,(
% 1.35/0.56 spl38_127),
% 1.35/0.56 inference(avatar_split_clause,[],[f425,f1425])).
% 1.35/0.56 tff(f425,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f289])).
% 1.35/0.56 tff(f1368,plain,(
% 1.35/0.56 spl38_126 | ~spl38_94 | ~spl38_125),
% 1.35/0.56 inference(avatar_split_clause,[],[f1364,f1361,f1063,f1366])).
% 1.35/0.56 tff(f1366,plain,(
% 1.35/0.56 spl38_126 <=> ! [X0 : $tType,X4 : fun(nat,X0),X3 : fun(type,fun(type,X0)),X2 : type,X1 : type] : aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_126])])).
% 1.35/0.56 tff(f1361,plain,(
% 1.35/0.56 spl38_125 <=> ! [X0 : $tType,X4 : fun(nat,X0),X3 : fun(type,fun(type,X0)),X2 : type,X1 : type] : type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_125])])).
% 1.35/0.56 tff(f1364,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : type,X3 : fun(type,fun(type,X0)),X1 : type,X4 : fun(nat,X0)] : (aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2))) ) | (~spl38_94 | ~spl38_125)),
% 1.35/0.56 inference(forward_demodulation,[],[f1362,f1064])).
% 1.35/0.56 tff(f1362,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : type,X3 : fun(type,fun(type,X0)),X1 : type,X4 : fun(nat,X0)] : (type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)) ) | ~spl38_125),
% 1.35/0.56 inference(avatar_component_clause,[],[f1361])).
% 1.35/0.56 tff(f1363,plain,(
% 1.35/0.56 spl38_125),
% 1.35/0.56 inference(avatar_split_clause,[],[f483,f1361])).
% 1.35/0.56 tff(f483,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : type,X3 : fun(type,fun(type,X0)),X1 : type,X4 : fun(nat,X0)] : (type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f180])).
% 1.35/0.56 tff(f180,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : type,X2 : type,X3 : fun(type,fun(type,X0)),X4 : fun(nat,X0)] : type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)),
% 1.35/0.56 inference(rectify,[],[f93])).
% 1.35/0.56 tff(f93,axiom,(
% 1.35/0.56 ! [X0 : $tType,X20 : type,X21 : type,X67 : fun(type,fun(type,X0)),X68 : fun(nat,X0)] : type_case(X0,X68,X67,aa(type,type,aa(type,fun(type,type),fun1,X21),X20)) = aa(type,X0,aa(type,fun(type,X0),X67,X21),X20)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_type_Osimps_I6_J)).
% 1.35/0.56 tff(f1359,plain,(
% 1.35/0.56 spl38_124),
% 1.35/0.56 inference(avatar_split_clause,[],[f462,f1357])).
% 1.35/0.56 tff(f1357,plain,(
% 1.35/0.56 spl38_124 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK29(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_124])])).
% 1.35/0.56 tff(f462,plain,(
% 1.35/0.56 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK29(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f315])).
% 1.35/0.56 tff(f1348,plain,(
% 1.35/0.56 spl38_123 | ~spl38_94 | ~spl38_122),
% 1.35/0.56 inference(avatar_split_clause,[],[f1344,f1341,f1063,f1346])).
% 1.35/0.56 tff(f1341,plain,(
% 1.35/0.56 spl38_122 <=> ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))) | ~step1(dB,beta,X2,X1))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_122])])).
% 1.35/0.56 tff(f1344,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,X1)),foldl(dB,dB,app,X0,X2))) | ~step1(dB,beta,X2,X1)) ) | (~spl38_94 | ~spl38_122)),
% 1.35/0.56 inference(forward_demodulation,[],[f1342,f1064])).
% 1.35/0.56 tff(f1342,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))) | ~step1(dB,beta,X2,X1)) ) | ~spl38_122),
% 1.35/0.56 inference(avatar_component_clause,[],[f1341])).
% 1.35/0.56 tff(f1343,plain,(
% 1.35/0.56 spl38_122),
% 1.35/0.56 inference(avatar_split_clause,[],[f421,f1341])).
% 1.35/0.56 tff(f421,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))) | ~step1(dB,beta,X2,X1)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f210])).
% 1.35/0.56 tff(f210,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : list(dB)] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))) | ~step1(dB,beta,X2,X1))),
% 1.35/0.56 inference(ennf_transformation,[],[f147])).
% 1.35/0.56 tff(f147,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : list(dB)] : (step1(dB,beta,X2,X1) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))))),
% 1.35/0.56 inference(rectify,[],[f94])).
% 1.35/0.56 tff(f94,axiom,(
% 1.35/0.56 ! [X44 : dB,X37 : list(dB),X39 : list(dB)] : (step1(dB,beta,X39,X37) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X44,X39)),foldl(dB,dB,app,X44,X37))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_apps__preserves__betas)).
% 1.35/0.56 tff(f1334,plain,(
% 1.35/0.56 spl38_121 | ~spl38_94 | ~spl38_120),
% 1.35/0.56 inference(avatar_split_clause,[],[f1330,f1326,f1063,f1332])).
% 1.35/0.56 tff(f1326,plain,(
% 1.35/0.56 spl38_120 <=> ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_120])])).
% 1.35/0.56 tff(f1330,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK13(X0,X1)),X1))) ) | (~spl38_94 | ~spl38_120)),
% 1.35/0.56 inference(forward_demodulation,[],[f1329,f1064])).
% 1.35/0.56 tff(f1329,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK13(X0,X1)),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | (~spl38_94 | ~spl38_120)),
% 1.35/0.56 inference(forward_demodulation,[],[f1327,f1064])).
% 1.35/0.56 tff(f1327,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | ~spl38_120),
% 1.35/0.56 inference(avatar_component_clause,[],[f1326])).
% 1.35/0.56 tff(f1328,plain,(
% 1.35/0.56 spl38_120),
% 1.35/0.56 inference(avatar_split_clause,[],[f408,f1326])).
% 1.35/0.56 tff(f408,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f283])).
% 1.35/0.56 tff(f283,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : ((pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1))) & abs(sK13(X0,X1)) = X0) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f209,f282])).
% 1.35/0.56 tff(f282,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : (? [X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2)) & abs(X2) = X0) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1))) & abs(sK13(X0,X1)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f209,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : (? [X2 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2)) & abs(X2) = X0) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f136])).
% 1.35/0.56 tff(f136,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) => ~! [X2 : dB] : (abs(X2) = X0 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2))))),
% 1.35/0.56 inference(rectify,[],[f88])).
% 1.35/0.56 tff(f88,axiom,(
% 1.35/0.56 ! [X42 : dB,X33 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X33)),X42)) => ~! [X82 : dB] : (abs(X82) = X42 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X33),X82))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_beta__cases_I2_J)).
% 1.35/0.56 tff(f1319,plain,(
% 1.35/0.56 spl38_119 | ~spl38_94 | ~spl38_118),
% 1.35/0.56 inference(avatar_split_clause,[],[f1315,f1311,f1063,f1317])).
% 1.35/0.56 tff(f1317,plain,(
% 1.35/0.56 spl38_119 <=> ! [X0 : dB,X1 : dB] : pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))),aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_119])])).
% 1.35/0.56 tff(f1311,plain,(
% 1.35/0.56 spl38_118 <=> ! [X0 : dB,X1 : dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat))))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_118])])).
% 1.35/0.56 tff(f1315,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))),aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1))))) ) | (~spl38_94 | ~spl38_118)),
% 1.35/0.56 inference(forward_demodulation,[],[f1314,f1064])).
% 1.35/0.56 tff(f1314,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)))) ) | (~spl38_94 | ~spl38_118)),
% 1.35/0.56 inference(forward_demodulation,[],[f1312,f1064])).
% 1.35/0.56 tff(f1312,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat))))) ) | ~spl38_118),
% 1.35/0.56 inference(avatar_component_clause,[],[f1311])).
% 1.35/0.56 tff(f1313,plain,(
% 1.35/0.56 spl38_118),
% 1.35/0.56 inference(avatar_split_clause,[],[f399,f1311])).
% 1.35/0.56 tff(f399,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat))))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f128])).
% 1.35/0.56 tff(f128,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat))))),
% 1.35/0.56 inference(rectify,[],[f80])).
% 1.35/0.56 tff(f80,axiom,(
% 1.35/0.56 ! [X28 : dB,X42 : dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X42)),X28)),subst(X42,X28,zero_zero(nat))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_beta)).
% 1.35/0.56 tff(f1211,plain,(
% 1.35/0.56 spl38_117 | ~spl38_15 | ~spl38_28),
% 1.35/0.56 inference(avatar_split_clause,[],[f704,f696,f626,f1209])).
% 1.35/0.56 tff(f1209,plain,(
% 1.35/0.56 spl38_117 <=> ! [X0 : nat] : sP1(abs(var(X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_117])])).
% 1.35/0.56 tff(f626,plain,(
% 1.35/0.56 spl38_15 <=> ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_15])])).
% 1.35/0.56 tff(f704,plain,(
% 1.35/0.56 ( ! [X0 : nat] : (sP1(abs(var(X0)))) ) | (~spl38_15 | ~spl38_28)),
% 1.35/0.56 inference(resolution,[],[f697,f627])).
% 1.35/0.56 tff(f627,plain,(
% 1.35/0.56 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) ) | ~spl38_15),
% 1.35/0.56 inference(avatar_component_clause,[],[f626])).
% 1.35/0.56 tff(f1203,plain,(
% 1.35/0.56 spl38_116),
% 1.35/0.56 inference(avatar_split_clause,[],[f500,f1201])).
% 1.35/0.56 tff(f500,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f192])).
% 1.35/0.56 tff(f192,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 1.35/0.56 inference(rectify,[],[f105])).
% 1.35/0.56 tff(f105,axiom,(
% 1.35/0.56 ! [X2 : $tType,X1 : $tType,X0 : $tType,X94 : X0,X95 : fun(X0,X1),X96 : fun(X0,fun(X1,X2))] : aa(X0,X2,combs(X0,X1,X2,X96,X95),X94) = aa(X1,X2,aa(X0,fun(X1,X2),X96,X94),aa(X0,X1,X95,X94))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 1.35/0.56 tff(f1199,plain,(
% 1.35/0.56 spl38_115),
% 1.35/0.56 inference(avatar_split_clause,[],[f499,f1197])).
% 1.35/0.56 tff(f1195,plain,(
% 1.35/0.56 spl38_114),
% 1.35/0.56 inference(avatar_split_clause,[],[f498,f1193])).
% 1.35/0.56 tff(f498,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f190])).
% 1.35/0.56 tff(f190,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))),
% 1.35/0.56 inference(rectify,[],[f47])).
% 1.35/0.56 tff(f47,axiom,(
% 1.35/0.56 ! [X1 : $tType,X0 : $tType,X57 : X0,X58 : list(X1),X22 : X1,X59 : fun(X1,fun(X0,X0))] : foldr(X1,X0,X59,cons(X1,X22,X58),X57) = aa(X0,X0,aa(X1,fun(X0,X0),X59,X22),foldr(X1,X0,X59,X58,X57))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_foldr_Osimps_I2_J)).
% 1.35/0.56 tff(f1191,plain,(
% 1.35/0.56 spl38_113),
% 1.35/0.56 inference(avatar_split_clause,[],[f478,f1189])).
% 1.35/0.56 tff(f1189,plain,(
% 1.35/0.56 spl38_113 <=> ! [X2 : dB,X0 : dB,X1 : dB,X3 : dB] : (X0 = X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_113])])).
% 1.35/0.56 tff(f478,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (X0 = X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f328])).
% 1.35/0.56 tff(f328,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : ((aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)))),
% 1.35/0.56 inference(flattening,[],[f327])).
% 1.35/0.56 tff(f327,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : ((aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)))),
% 1.35/0.56 inference(nnf_transformation,[],[f178])).
% 1.35/0.56 tff(f178,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) <=> (X0 = X2 & X1 = X3))),
% 1.35/0.56 inference(rectify,[],[f40])).
% 1.35/0.56 tff(f40,axiom,(
% 1.35/0.56 ! [X45 : dB,X46 : dB,X47 : dB,X48 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X48),X47) = aa(dB,dB,aa(dB,fun(dB,dB),app,X46),X45) <=> (X45 = X47 & X46 = X48))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_dB_Osimps_I2_J)).
% 1.35/0.56 tff(f1187,plain,(
% 1.35/0.56 spl38_112),
% 1.35/0.56 inference(avatar_split_clause,[],[f477,f1185])).
% 1.35/0.56 tff(f1185,plain,(
% 1.35/0.56 spl38_112 <=> ! [X0 : dB,X3 : dB,X2 : dB,X1 : dB] : (X1 = X3 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_112])])).
% 1.35/0.56 tff(f477,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (X1 = X3 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f328])).
% 1.35/0.56 tff(f1183,plain,(
% 1.35/0.56 spl38_111),
% 1.35/0.56 inference(avatar_split_clause,[],[f475,f1181])).
% 1.35/0.56 tff(f1181,plain,(
% 1.35/0.56 spl38_111 <=> ! [X2 : type,X0 : type,X1 : type,X3 : type] : (X0 = X2 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_111])])).
% 1.35/0.56 tff(f475,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (X0 = X2 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f326])).
% 1.35/0.56 tff(f326,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : type,X3 : type] : ((aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)))),
% 1.35/0.56 inference(flattening,[],[f325])).
% 1.35/0.56 tff(f325,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : type,X3 : type] : ((aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)))),
% 1.35/0.56 inference(nnf_transformation,[],[f177])).
% 1.35/0.56 tff(f177,plain,(
% 1.35/0.56 ! [X0 : type,X1 : type,X2 : type,X3 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) <=> (X0 = X2 & X1 = X3))),
% 1.35/0.56 inference(rectify,[],[f18])).
% 1.35/0.56 tff(f18,axiom,(
% 1.35/0.56 ! [X18 : type,X19 : type,X20 : type,X21 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X21),X20) = aa(type,type,aa(type,fun(type,type),fun1,X19),X18) <=> (X18 = X20 & X19 = X21))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type_Osimps_I2_J)).
% 1.35/0.56 tff(f1179,plain,(
% 1.35/0.56 spl38_110),
% 1.35/0.56 inference(avatar_split_clause,[],[f474,f1177])).
% 1.35/0.56 tff(f474,plain,(
% 1.35/0.56 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (X1 = X3 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f326])).
% 1.35/0.56 tff(f1175,plain,(
% 1.35/0.56 spl38_109),
% 1.35/0.56 inference(avatar_split_clause,[],[f459,f1173])).
% 1.35/0.56 tff(f1173,plain,(
% 1.35/0.56 spl38_109 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK28(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_109])])).
% 1.35/0.56 tff(f459,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK28(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f313])).
% 1.35/0.56 tff(f1171,plain,(
% 1.35/0.56 spl38_108),
% 1.35/0.56 inference(avatar_split_clause,[],[f457,f1169])).
% 1.35/0.56 tff(f1169,plain,(
% 1.35/0.56 spl38_108 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK27(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_108])])).
% 1.35/0.56 tff(f457,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK27(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f311])).
% 1.35/0.56 tff(f1166,plain,(
% 1.35/0.56 spl38_107 | ~spl38_94 | ~spl38_106),
% 1.35/0.56 inference(avatar_split_clause,[],[f1162,f1159,f1063,f1164])).
% 1.35/0.56 tff(f1159,plain,(
% 1.35/0.56 spl38_106 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK23(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_106])])).
% 1.35/0.56 tff(f1162,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,var(X2),X1))) | step1(dB,beta,X1,sK23(X0,X1,X2))) ) | (~spl38_94 | ~spl38_106)),
% 1.35/0.56 inference(forward_demodulation,[],[f1160,f1064])).
% 1.35/0.56 tff(f1160,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK23(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) ) | ~spl38_106),
% 1.35/0.56 inference(avatar_component_clause,[],[f1159])).
% 1.35/0.56 tff(f1161,plain,(
% 1.35/0.56 spl38_106),
% 1.35/0.56 inference(avatar_split_clause,[],[f440,f1159])).
% 1.35/0.56 tff(f440,plain,(
% 1.35/0.56 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK23(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f300])).
% 1.35/0.56 tff(f1157,plain,(
% 1.35/0.56 spl38_105),
% 1.35/0.56 inference(avatar_split_clause,[],[f424,f1155])).
% 1.35/0.56 tff(f1155,plain,(
% 1.35/0.56 spl38_105 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK14(X1,X2)),X1),sK15(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_105])])).
% 1.35/0.56 tff(f424,plain,(
% 1.35/0.56 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK14(X1,X2)),X1),sK15(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f287])).
% 1.35/0.56 tff(f287,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK14(X1,X2)),X1),sK15(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f213,f286])).
% 1.35/0.56 tff(f286,plain,(
% 1.35/0.56 ! [X1 : dB,X2 : fun(nat,type)] : (? [X3 : type,X4 : type] : pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4)) => pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK14(X1,X2)),X1),sK15(X1,X2))))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f213,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (? [X3 : type,X4 : type] : pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4)) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f150])).
% 1.35/0.56 tff(f150,plain,(
% 1.35/0.56 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,abs(X1)),X0)) => ~! [X3 : type,X4 : type] : ~pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),X3),X1),X4)))),
% 1.35/0.56 inference(rectify,[],[f76])).
% 1.35/0.56 tff(f76,axiom,(
% 1.35/0.56 ! [X12 : type,X13 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,abs(X13)),X12)) => ~! [X69 : type,X72 : type] : ~pp(aa(type,bool,typing(shift(type,X14,zero_zero(nat),X69),X13),X72)))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_abs__typeE)).
% 1.35/0.56 tff(f1150,plain,(
% 1.35/0.56 spl38_104 | ~spl38_94 | ~spl38_103),
% 1.35/0.56 inference(avatar_split_clause,[],[f1146,f1142,f1063,f1148])).
% 1.35/0.56 tff(f1142,plain,(
% 1.35/0.56 spl38_103 <=> ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_103])])).
% 1.35/0.56 tff(f1146,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,abs(X0)),abs(X1)))) ) | (~spl38_94 | ~spl38_103)),
% 1.35/0.56 inference(forward_demodulation,[],[f1145,f1064])).
% 1.35/0.56 tff(f1145,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,abs(X0)),abs(X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0))) ) | (~spl38_94 | ~spl38_103)),
% 1.35/0.56 inference(forward_demodulation,[],[f1143,f1064])).
% 1.35/0.56 tff(f1143,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0))) ) | ~spl38_103),
% 1.35/0.56 inference(avatar_component_clause,[],[f1142])).
% 1.35/0.56 tff(f1144,plain,(
% 1.35/0.56 spl38_103),
% 1.35/0.56 inference(avatar_split_clause,[],[f406,f1142])).
% 1.35/0.56 tff(f406,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f208])).
% 1.35/0.56 tff(f208,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)))),
% 1.35/0.56 inference(ennf_transformation,[],[f135])).
% 1.35/0.56 tff(f135,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))))),
% 1.35/0.56 inference(rectify,[],[f84])).
% 1.35/0.56 tff(f84,axiom,(
% 1.35/0.56 ! [X28 : dB,X42 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X42),X28)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X42)),abs(X28))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_abs)).
% 1.35/0.56 tff(f1140,plain,(
% 1.35/0.56 spl38_102),
% 1.35/0.56 inference(avatar_split_clause,[],[f435,f1138])).
% 1.35/0.56 tff(f1138,plain,(
% 1.35/0.56 spl38_102 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,subst(sK18(X0,X1,X2),sK19(X0,X1,X2),zero_zero(nat)),sK20(X0,X1,X2)) = X0 | ~sP2(X0,X1,X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_102])])).
% 1.35/0.56 tff(f435,plain,(
% 1.35/0.56 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,subst(sK18(X0,X1,X2),sK19(X0,X1,X2),zero_zero(nat)),sK20(X0,X1,X2)) = X0 | ~sP2(X0,X1,X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f294])).
% 1.35/0.56 tff(f294,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (((foldl(dB,dB,app,subst(sK18(X0,X1,X2),sK19(X0,X1,X2),zero_zero(nat)),sK20(X0,X1,X2)) = X0 & cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1) & abs(sK18(X0,X1,X2)) = X2) | ~sP2(X0,X1,X2))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f291,f293,f292])).
% 1.35/0.56 tff(f292,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X3 : dB] : (? [X4 : dB,X5 : list(dB)] : (foldl(dB,dB,app,subst(X3,X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) & abs(X3) = X2) => (? [X5 : list(dB),X4 : dB] : (foldl(dB,dB,app,subst(sK18(X0,X1,X2),X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) & abs(sK18(X0,X1,X2)) = X2))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f293,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X5 : list(dB),X4 : dB] : (foldl(dB,dB,app,subst(sK18(X0,X1,X2),X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) => (foldl(dB,dB,app,subst(sK18(X0,X1,X2),sK19(X0,X1,X2),zero_zero(nat)),sK20(X0,X1,X2)) = X0 & cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f291,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X3 : dB] : (? [X4 : dB,X5 : list(dB)] : (foldl(dB,dB,app,subst(X3,X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) & abs(X3) = X2) | ~sP2(X0,X1,X2))),
% 1.35/0.56 inference(rectify,[],[f290])).
% 1.35/0.56 tff(f290,plain,(
% 1.35/0.56 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X5 : dB] : (? [X6 : dB,X7 : list(dB)] : (foldl(dB,dB,app,subst(X5,X6,zero_zero(nat)),X7) = X0 & cons(dB,X6,X7) = X1) & abs(X5) = X2) | ~sP2(X0,X1,X2))),
% 1.35/0.56 inference(nnf_transformation,[],[f260])).
% 1.35/0.56 tff(f1125,plain,(
% 1.35/0.56 spl38_101),
% 1.35/0.56 inference(avatar_split_clause,[],[f465,f1123])).
% 1.35/0.56 tff(f1123,plain,(
% 1.35/0.56 spl38_101 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,X0),X2 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_101])])).
% 1.35/0.56 tff(f465,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f319])).
% 1.35/0.56 tff(f319,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f237,f318])).
% 1.35/0.56 tff(f318,plain,(
% 1.35/0.56 ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) => aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f237,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | ? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4))),
% 1.35/0.56 inference(ennf_transformation,[],[f173])).
% 1.35/0.56 tff(f173,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (! [X4 : X1] : aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) => X2 = X3)),
% 1.35/0.56 inference(rectify,[],[f75])).
% 1.35/0.56 tff(f75,axiom,(
% 1.35/0.56 ! [X1 : $tType,X0 : $tType,X70 : fun(X0,X1),X59 : fun(X0,X1)] : (! [X71 : X0] : aa(X0,X1,X59,X71) = aa(X0,X1,X70,X71) => X59 = X70)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext)).
% 1.35/0.56 tff(f1121,plain,(
% 1.35/0.56 spl38_100 | ~spl38_99),
% 1.35/0.56 inference(avatar_split_clause,[],[f1117,f1114,f1119])).
% 1.35/0.56 tff(f1119,plain,(
% 1.35/0.56 spl38_100 <=> ! [X0 : dB] : (foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0))) = X0 | ~sP0(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_100])])).
% 1.35/0.56 tff(f1114,plain,(
% 1.35/0.56 spl38_99 <=> ! [X0 : dB] : (foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 | ~sP0(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_99])])).
% 1.35/0.56 tff(f1117,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0))) = X0 | ~sP0(X0)) ) | ~spl38_99),
% 1.35/0.56 inference(forward_demodulation,[],[f1115,f499])).
% 1.35/0.56 tff(f1115,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 | ~sP0(X0)) ) | ~spl38_99),
% 1.35/0.56 inference(avatar_component_clause,[],[f1114])).
% 1.35/0.56 tff(f1116,plain,(
% 1.35/0.56 spl38_99),
% 1.35/0.56 inference(avatar_split_clause,[],[f389,f1114])).
% 1.35/0.56 tff(f389,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 | ~sP0(X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f280])).
% 1.35/0.56 tff(f1100,plain,(
% 1.35/0.56 spl38_98),
% 1.35/0.56 inference(avatar_split_clause,[],[f550,f1098])).
% 1.35/0.56 tff(f1098,plain,(
% 1.35/0.56 spl38_98 <=> ! [X3 : $tType,X4 : X3,X0 : list(X3),X5 : X3,X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | step1(X3,X2,X1,X0) | ~sP4(X3,X0,X1,X2,X4,X5))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_98])])).
% 1.35/0.56 tff(f550,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | step1(X3,X2,X1,X0) | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.56 inference(forward_demodulation,[],[f505,f496])).
% 1.35/0.56 tff(f505,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (step1(X3,X2,X1,X0) | pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5)) | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f341])).
% 1.35/0.56 tff(f341,plain,(
% 1.35/0.56 ! [X0 : list(X3),X1 : list(X3),X2 : fun(X3,fun(X3,bool)),X3 : $tType,X4 : X3,X5 : X3] : ((sP4(X3,X0,X1,X2,X4,X5) | ((~step1(X3,X2,X1,X0) | X4 != X5) & (X0 != X1 | ~pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))))) & ((step1(X3,X2,X1,X0) & X4 = X5) | (X0 = X1 & pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))) | ~sP4(X3,X0,X1,X2,X4,X5)))),
% 1.35/0.56 inference(rectify,[],[f340])).
% 1.35/0.56 tff(f340,plain,(
% 1.35/0.56 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : ((sP4(X0,X1,X3,X5,X4,X2) | ((~step1(X0,X5,X3,X1) | X2 != X4) & (X1 != X3 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2))))) & ((step1(X0,X5,X3,X1) & X2 = X4) | (X1 = X3 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2))) | ~sP4(X0,X1,X3,X5,X4,X2)))),
% 1.35/0.56 inference(flattening,[],[f339])).
% 1.35/0.56 tff(f339,plain,(
% 1.35/0.56 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : ((sP4(X0,X1,X3,X5,X4,X2) | ((~step1(X0,X5,X3,X1) | X2 != X4) & (X1 != X3 | ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2))))) & (((step1(X0,X5,X3,X1) & X2 = X4) | (X1 = X3 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2)))) | ~sP4(X0,X1,X3,X5,X4,X2)))),
% 1.35/0.56 inference(nnf_transformation,[],[f264])).
% 1.35/0.56 tff(f264,plain,(
% 1.35/0.56 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : (sP4(X0,X1,X3,X5,X4,X2) <=> ((step1(X0,X5,X3,X1) & X2 = X4) | (X1 = X3 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2)))))),
% 1.35/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])).
% 1.35/0.56 tff(f1096,plain,(
% 1.35/0.56 spl38_97),
% 1.35/0.56 inference(avatar_split_clause,[],[f497,f1094])).
% 1.35/0.56 tff(f497,plain,(
% 1.35/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : (list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f189])).
% 1.35/0.56 tff(f189,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 1.35/0.56 inference(rectify,[],[f71])).
% 1.35/0.56 tff(f71,axiom,(
% 1.35/0.56 ! [X0 : $tType,X1 : $tType,X56 : list(X1),X57 : X1,X67 : fun(X1,fun(list(X1),X0)),X68 : X0] : list_case(X0,X1,X68,X67,cons(X1,X57,X56)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X67,X57),X56)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_list_Osimps_I5_J)).
% 1.35/0.56 tff(f1088,plain,(
% 1.35/0.56 spl38_96 | ~spl38_94 | ~spl38_95),
% 1.35/0.56 inference(avatar_split_clause,[],[f1084,f1081,f1063,f1086])).
% 1.35/0.56 tff(f1081,plain,(
% 1.35/0.56 spl38_95 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_95])])).
% 1.35/0.56 tff(f1084,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1))) | ~pp(aa(dB,bool,it,X1))) ) | (~spl38_94 | ~spl38_95)),
% 1.35/0.56 inference(forward_demodulation,[],[f1082,f1064])).
% 1.35/0.56 tff(f1082,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1))) ) | ~spl38_95),
% 1.35/0.56 inference(avatar_component_clause,[],[f1081])).
% 1.35/0.56 tff(f1083,plain,(
% 1.35/0.56 spl38_95),
% 1.35/0.56 inference(avatar_split_clause,[],[f405,f1081])).
% 1.35/0.56 tff(f405,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f207])).
% 1.35/0.56 tff(f207,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f134])).
% 1.35/0.56 tff(f134,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,X1)) => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))))),
% 1.35/0.56 inference(rectify,[],[f27])).
% 1.35/0.56 tff(f27,axiom,(
% 1.35/0.56 ! [X27 : nat,X28 : dB] : (pp(aa(dB,bool,it,X28)) => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X28),var(X27)))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_app__Var__IT)).
% 1.35/0.56 tff(f1065,plain,(
% 1.35/0.56 spl38_94),
% 1.35/0.56 inference(avatar_split_clause,[],[f496,f1063])).
% 1.35/0.56 tff(f1058,plain,(
% 1.35/0.56 spl38_93 | ~spl38_92),
% 1.35/0.56 inference(avatar_split_clause,[],[f1054,f1051,f1056])).
% 1.35/0.56 tff(f1051,plain,(
% 1.35/0.56 spl38_92 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_92])])).
% 1.35/0.56 tff(f1054,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))) | ~pp(aa(dB,bool,it,X1))) ) | ~spl38_92),
% 1.35/0.56 inference(forward_demodulation,[],[f1052,f496])).
% 1.35/0.56 tff(f1052,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,it,X1))) ) | ~spl38_92),
% 1.35/0.56 inference(avatar_component_clause,[],[f1051])).
% 1.35/0.56 tff(f1053,plain,(
% 1.35/0.56 spl38_92),
% 1.35/0.56 inference(avatar_split_clause,[],[f404,f1051])).
% 1.35/0.56 tff(f404,plain,(
% 1.35/0.56 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,it,X1))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f206])).
% 1.35/0.56 tff(f206,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) | ~pp(aa(dB,bool,it,X1)))),
% 1.35/0.56 inference(ennf_transformation,[],[f133])).
% 1.35/0.56 tff(f133,plain,(
% 1.35/0.56 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,X1)) => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))))),
% 1.35/0.56 inference(rectify,[],[f54])).
% 1.35/0.56 tff(f54,axiom,(
% 1.35/0.56 ! [X27 : nat,X28 : dB] : (pp(aa(dB,bool,it,X28)) => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X28),X27))))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_lift__IT)).
% 1.35/0.56 tff(f1049,plain,(
% 1.35/0.56 spl38_91),
% 1.35/0.56 inference(avatar_split_clause,[],[f384,f1047])).
% 1.35/0.56 tff(f384,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f276])).
% 1.35/0.56 tff(f276,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) & ! [X2 : list(dB),X3 : nat] : (~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0))) & (sP0(X0) | (pp(aa(dB,bool,it,sK7(X0))) & abs(sK7(X0)) = X0) | (listsp(dB,it,sK8(X0)) & foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0) | ~sP1(X0)))),
% 1.35/0.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f273,f275,f274])).
% 1.35/0.56 tff(f274,plain,(
% 1.35/0.56 ! [X0 : dB] : (? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) => (pp(aa(dB,bool,it,sK7(X0))) & abs(sK7(X0)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f275,plain,(
% 1.35/0.56 ! [X0 : dB] : (? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) => (listsp(dB,it,sK8(X0)) & foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0))),
% 1.35/0.56 introduced(choice_axiom,[])).
% 1.35/0.56 tff(f273,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) & ! [X2 : list(dB),X3 : nat] : (~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0))) & (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) | ~sP1(X0)))),
% 1.35/0.56 inference(rectify,[],[f272])).
% 1.35/0.56 tff(f272,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X4 : dB] : (~pp(aa(dB,bool,it,X4)) | abs(X4) != X0) & ! [X5 : list(dB),X6 : nat] : (~listsp(dB,it,X5) | foldl(dB,dB,app,var(X6),X5) != X0))) & (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) | ~sP1(X0)))),
% 1.35/0.56 inference(flattening,[],[f271])).
% 1.35/0.56 tff(f271,plain,(
% 1.35/0.56 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X4 : dB] : (~pp(aa(dB,bool,it,X4)) | abs(X4) != X0) & ! [X5 : list(dB),X6 : nat] : (~listsp(dB,it,X5) | foldl(dB,dB,app,var(X6),X5) != X0))) & ((sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0)) | ~sP1(X0)))),
% 1.35/0.56 inference(nnf_transformation,[],[f258])).
% 1.35/0.56 tff(f258,plain,(
% 1.35/0.56 ! [X0 : dB] : (sP1(X0) <=> (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0)))),
% 1.35/0.56 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 1.35/0.56 tff(f1043,plain,(
% 1.35/0.56 spl38_90),
% 1.35/0.56 inference(avatar_split_clause,[],[f551,f1041])).
% 1.35/0.56 tff(f1041,plain,(
% 1.35/0.56 spl38_90 <=> ! [X3 : $tType,X4 : X3,X0 : list(X3),X5 : X3,X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | X4 = X5 | ~sP4(X3,X0,X1,X2,X4,X5))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_90])])).
% 1.35/0.56 tff(f551,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | X4 = X5 | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.56 inference(forward_demodulation,[],[f503,f496])).
% 1.35/0.56 tff(f503,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (X4 = X5 | pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5)) | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f341])).
% 1.35/0.56 tff(f1031,plain,(
% 1.35/0.56 spl38_89),
% 1.35/0.56 inference(avatar_split_clause,[],[f451,f1029])).
% 1.35/0.56 tff(f451,plain,(
% 1.35/0.56 ( ! [X2 : dB,X3 : dB,X0 : list(dB),X1 : nat] : (foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f163])).
% 1.35/0.56 tff(f163,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : nat,X2 : dB,X3 : dB] : foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2)),
% 1.35/0.56 inference(rectify,[],[f70])).
% 1.35/0.56 tff(f70,axiom,(
% 1.35/0.56 ! [X37 : list(dB),X38 : nat,X13 : dB,X24 : dB] : foldl(dB,dB,app,var(X38),X37) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X24)),X13)),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Abs__App__neq__Var__apps)).
% 1.35/0.56 tff(f1027,plain,(
% 1.35/0.56 spl38_88),
% 1.35/0.56 inference(avatar_split_clause,[],[f390,f1025])).
% 1.35/0.56 tff(f390,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f280])).
% 1.35/0.56 tff(f1023,plain,(
% 1.35/0.56 spl38_87),
% 1.35/0.56 inference(avatar_split_clause,[],[f382,f1021])).
% 1.35/0.56 tff(f1021,plain,(
% 1.35/0.56 spl38_87 <=> ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_87])])).
% 1.35/0.56 tff(f382,plain,(
% 1.35/0.56 ( ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f276])).
% 1.35/0.56 tff(f1017,plain,(
% 1.35/0.56 spl38_86),
% 1.35/0.56 inference(avatar_split_clause,[],[f472,f1015])).
% 1.35/0.56 tff(f1015,plain,(
% 1.35/0.56 spl38_86 <=> ! [X2 : list(dB),X0 : list(dB),X1 : nat,X3 : nat] : (X0 = X2 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_86])])).
% 1.35/0.56 tff(f472,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : nat] : (X0 = X2 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f324])).
% 1.35/0.56 tff(f324,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : ((foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)))),
% 1.35/0.56 inference(flattening,[],[f323])).
% 1.35/0.56 tff(f323,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : ((foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)))),
% 1.35/0.56 inference(nnf_transformation,[],[f176])).
% 1.35/0.56 tff(f176,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : (foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) <=> (X0 = X2 & X1 = X3))),
% 1.35/0.56 inference(rectify,[],[f35])).
% 1.35/0.56 tff(f35,axiom,(
% 1.35/0.56 ! [X37 : list(dB),X38 : nat,X39 : list(dB),X40 : nat] : (foldl(dB,dB,app,var(X40),X39) = foldl(dB,dB,app,var(X38),X37) <=> (X37 = X39 & X38 = X40))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Var__apps__eq__Var__apps__conv)).
% 1.35/0.56 tff(f1013,plain,(
% 1.35/0.56 spl38_85),
% 1.35/0.56 inference(avatar_split_clause,[],[f469,f1011])).
% 1.35/0.56 tff(f1011,plain,(
% 1.35/0.56 spl38_85 <=> ! [X2 : list(dB),X0 : list(dB),X1 : dB,X3 : dB] : (X0 = X2 | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_85])])).
% 1.35/0.56 tff(f469,plain,(
% 1.35/0.56 ( ! [X2 : list(dB),X3 : dB,X0 : list(dB),X1 : dB] : (X0 = X2 | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f322])).
% 1.35/0.56 tff(f322,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : dB] : ((foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2)))),
% 1.35/0.56 inference(flattening,[],[f321])).
% 1.35/0.56 tff(f321,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : dB] : ((foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2)))),
% 1.35/0.56 inference(nnf_transformation,[],[f175])).
% 1.35/0.56 tff(f175,plain,(
% 1.35/0.56 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : dB] : (foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) <=> (X0 = X2 & X1 = X3))),
% 1.35/0.56 inference(rectify,[],[f63])).
% 1.35/0.56 tff(f63,axiom,(
% 1.35/0.56 ! [X37 : list(dB),X24 : dB,X39 : list(dB),X44 : dB] : (foldl(dB,dB,app,abs(X44),X39) = foldl(dB,dB,app,abs(X24),X37) <=> (X37 = X39 & X24 = X44))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Abs__apps__eq__Abs__apps__conv)).
% 1.35/0.56 tff(f1008,plain,(
% 1.35/0.56 spl38_84 | ~spl38_83),
% 1.35/0.56 inference(avatar_split_clause,[],[f1004,f1001,f1006])).
% 1.35/0.56 tff(f1001,plain,(
% 1.35/0.56 spl38_83 <=> ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_83])])).
% 1.35/0.56 tff(f1004,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0) ) | ~spl38_83),
% 1.35/0.56 inference(forward_demodulation,[],[f1002,f496])).
% 1.35/0.56 tff(f1002,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | ~spl38_83),
% 1.35/0.56 inference(avatar_component_clause,[],[f1001])).
% 1.35/0.56 tff(f1003,plain,(
% 1.35/0.56 spl38_83),
% 1.35/0.56 inference(avatar_split_clause,[],[f407,f1001])).
% 1.35/0.56 tff(f407,plain,(
% 1.35/0.56 ( ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f283])).
% 1.35/0.56 tff(f989,plain,(
% 1.35/0.56 spl38_82 | ~spl38_8 | ~spl38_28),
% 1.35/0.56 inference(avatar_split_clause,[],[f708,f696,f588,f986])).
% 1.35/0.56 tff(f986,plain,(
% 1.35/0.56 spl38_82 <=> sP1(abs(ua))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_82])])).
% 1.35/0.56 tff(f708,plain,(
% 1.35/0.56 sP1(abs(ua)) | (~spl38_8 | ~spl38_28)),
% 1.35/0.56 inference(resolution,[],[f697,f590])).
% 1.35/0.56 tff(f983,plain,(
% 1.35/0.56 spl38_81),
% 1.35/0.56 inference(avatar_split_clause,[],[f549,f981])).
% 1.35/0.56 tff(f549,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X1 : list(X3),X4 : X3,X5 : X3] : (~pp(aa(X3,bool,combc(X3,X3,bool,X2,X5),X4)) | sP4(X3,X1,X1,X2,X4,X5)) )),
% 1.35/0.56 inference(forward_demodulation,[],[f544,f496])).
% 1.35/0.56 tff(f544,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X1 : list(X3),X4 : X3,X5 : X3] : (sP4(X3,X1,X1,X2,X4,X5) | ~pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))) )),
% 1.35/0.56 inference(equality_resolution,[],[f507])).
% 1.35/0.56 tff(f507,plain,(
% 1.35/0.56 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (sP4(X3,X0,X1,X2,X4,X5) | X0 != X1 | ~pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))) )),
% 1.35/0.56 inference(cnf_transformation,[],[f341])).
% 1.35/0.56 tff(f979,plain,(
% 1.35/0.56 spl38_80),
% 1.35/0.56 inference(avatar_split_clause,[],[f517,f976])).
% 1.35/0.56 tff(f976,plain,(
% 1.35/0.56 spl38_80 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t2))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_80])])).
% 1.35/0.56 tff(f517,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t2))),
% 1.35/0.56 inference(definition_unfolding,[],[f363,f350])).
% 1.35/0.56 tff(f363,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t2))),
% 1.35/0.56 inference(cnf_transformation,[],[f21])).
% 1.35/0.56 tff(f21,axiom,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t2))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_nT)).
% 1.35/0.56 tff(f974,plain,(
% 1.35/0.56 spl38_79),
% 1.35/0.56 inference(avatar_split_clause,[],[f516,f971])).
% 1.35/0.56 tff(f971,plain,(
% 1.35/0.56 spl38_79 <=> pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(i),rs)),t_a))),
% 1.35/0.56 introduced(avatar_definition,[new_symbols(naming,[spl38_79])])).
% 1.35/0.56 tff(f516,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(i),rs)),t_a))),
% 1.35/0.56 inference(definition_unfolding,[],[f362,f350])).
% 1.35/0.56 tff(f362,plain,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(n),rs)),t_a))),
% 1.35/0.56 inference(cnf_transformation,[],[f49])).
% 1.35/0.56 tff(f49,axiom,(
% 1.35/0.56 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(n),rs)),t_a))),
% 1.35/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Var_I2_J)).
% 1.35/0.56 tff(f969,plain,(
% 1.35/0.56 spl38_78),
% 1.35/0.56 inference(avatar_split_clause,[],[f510,f967])).
% 1.35/0.56 tff(f510,plain,(
% 1.35/0.56 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) | ~sP4(X0,X1,X3,X5,X4,X2)) )),
% 1.35/0.56 inference(cnf_transformation,[],[f342])).
% 1.35/0.56 tff(f342,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : ((step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) | ~sP4(X0,X1,X3,X5,X4,X2)) & (sP4(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1))))),
% 1.35/0.56 inference(nnf_transformation,[],[f265])).
% 1.35/0.56 tff(f265,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) <=> sP4(X0,X1,X3,X5,X4,X2))),
% 1.35/0.56 inference(definition_folding,[],[f195,f264])).
% 1.35/0.56 tff(f195,plain,(
% 1.35/0.56 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)) <=> ((step1(X0,X5,X3,X1) & X2 = X4) | (X1 = X3 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X5,X4),X2)))))),
% 1.35/0.57 inference(rectify,[],[f96])).
% 1.35/0.57 tff(f96,axiom,(
% 1.35/0.57 ! [X0 : $tType,X58 : list(X0),X22 : X0,X90 : list(X0),X91 : X0,X44 : fun(X0,fun(X0,bool))] : (step1(X0,X44,cons(X0,X91,X90),cons(X0,X22,X58)) <=> ((step1(X0,X44,X90,X58) & X22 = X91) | (X58 = X90 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X44,X91),X22)))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Cons__step1__Cons)).
% 1.35/0.57 tff(f965,plain,(
% 1.35/0.57 spl38_77),
% 1.35/0.57 inference(avatar_split_clause,[],[f509,f963])).
% 1.35/0.57 tff(f509,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (sP4(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f342])).
% 1.35/0.57 tff(f961,plain,(
% 1.35/0.57 spl38_76),
% 1.35/0.57 inference(avatar_split_clause,[],[f471,f959])).
% 1.35/0.57 tff(f959,plain,(
% 1.35/0.57 spl38_76 <=> ! [X0 : list(dB),X3 : nat,X2 : list(dB),X1 : nat] : (X1 = X3 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_76])])).
% 1.35/0.57 tff(f471,plain,(
% 1.35/0.57 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : nat] : (X1 = X3 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f324])).
% 1.35/0.57 tff(f957,plain,(
% 1.35/0.57 spl38_75),
% 1.35/0.57 inference(avatar_split_clause,[],[f468,f955])).
% 1.35/0.57 tff(f955,plain,(
% 1.35/0.57 spl38_75 <=> ! [X0 : list(dB),X3 : dB,X2 : list(dB),X1 : dB] : (X1 = X3 | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_75])])).
% 1.35/0.57 tff(f468,plain,(
% 1.35/0.57 ( ! [X2 : list(dB),X3 : dB,X0 : list(dB),X1 : dB] : (X1 = X3 | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f322])).
% 1.35/0.57 tff(f953,plain,(
% 1.35/0.57 spl38_74 | ~spl38_9 | ~spl38_28),
% 1.35/0.57 inference(avatar_split_clause,[],[f707,f696,f593,f950])).
% 1.35/0.57 tff(f950,plain,(
% 1.35/0.57 spl38_74 <=> sP1(abs(u))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_74])])).
% 1.35/0.57 tff(f707,plain,(
% 1.35/0.57 sP1(abs(u)) | (~spl38_9 | ~spl38_28)),
% 1.35/0.57 inference(resolution,[],[f697,f595])).
% 1.35/0.57 tff(f948,plain,(
% 1.35/0.57 spl38_73),
% 1.35/0.57 inference(avatar_split_clause,[],[f380,f946])).
% 1.35/0.57 tff(f946,plain,(
% 1.35/0.57 spl38_73 <=> ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_73])])).
% 1.35/0.57 tff(f380,plain,(
% 1.35/0.57 ( ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f203])).
% 1.35/0.57 tff(f203,plain,(
% 1.35/0.57 ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0))),
% 1.35/0.57 inference(ennf_transformation,[],[f121])).
% 1.35/0.57 tff(f121,plain,(
% 1.35/0.57 ! [X0 : list(dB)] : (listsp(dB,it,X0) => listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)))),
% 1.35/0.57 inference(rectify,[],[f99])).
% 1.35/0.57 tff(f99,axiom,(
% 1.35/0.57 ! [X30 : list(dB)] : (listsp(dB,it,X30) => listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X30)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_lifts__IT)).
% 1.35/0.57 tff(f944,plain,(
% 1.35/0.57 spl38_72),
% 1.35/0.57 inference(avatar_split_clause,[],[f361,f941])).
% 1.35/0.57 tff(f361,plain,(
% 1.35/0.57 t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))),
% 1.35/0.57 inference(cnf_transformation,[],[f23])).
% 1.35/0.57 tff(f23,axiom,(
% 1.35/0.57 t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_T)).
% 1.35/0.57 tff(f939,plain,(
% 1.35/0.57 spl38_71),
% 1.35/0.57 inference(avatar_split_clause,[],[f434,f937])).
% 1.35/0.57 tff(f937,plain,(
% 1.35/0.57 spl38_71 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1 | ~sP2(X0,X1,X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_71])])).
% 1.35/0.57 tff(f434,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1 | ~sP2(X0,X1,X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f294])).
% 1.35/0.57 tff(f932,plain,(
% 1.35/0.57 spl38_70 | ~spl38_69),
% 1.35/0.57 inference(avatar_split_clause,[],[f927,f923,f929])).
% 1.35/0.57 tff(f923,plain,(
% 1.35/0.57 spl38_69 <=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_69])])).
% 1.35/0.57 tff(f927,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | ~spl38_69),
% 1.35/0.57 inference(forward_demodulation,[],[f925,f496])).
% 1.35/0.57 tff(f925,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))) | ~spl38_69),
% 1.35/0.57 inference(avatar_component_clause,[],[f923])).
% 1.35/0.57 tff(f926,plain,(
% 1.35/0.57 spl38_69),
% 1.35/0.57 inference(avatar_split_clause,[],[f360,f923])).
% 1.35/0.57 tff(f360,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.35/0.57 inference(cnf_transformation,[],[f51])).
% 1.35/0.57 tff(f51,axiom,(
% 1.35/0.57 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50__096IT_A_Ilift_Au_A0_J_096)).
% 1.35/0.57 tff(f917,plain,(
% 1.35/0.57 spl38_68 | ~spl38_7 | ~spl38_28),
% 1.35/0.57 inference(avatar_split_clause,[],[f706,f696,f583,f914])).
% 1.35/0.57 tff(f914,plain,(
% 1.35/0.57 spl38_68 <=> sP1(abs(t3))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_68])])).
% 1.35/0.57 tff(f706,plain,(
% 1.35/0.57 sP1(abs(t3)) | (~spl38_7 | ~spl38_28)),
% 1.35/0.57 inference(resolution,[],[f697,f585])).
% 1.35/0.57 tff(f901,plain,(
% 1.35/0.57 spl38_67),
% 1.35/0.57 inference(avatar_split_clause,[],[f506,f899])).
% 1.35/0.57 tff(f899,plain,(
% 1.35/0.57 spl38_67 <=> ! [X3 : $tType,X5 : X3,X4 : X3,X0 : list(X3),X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (step1(X3,X2,X1,X0) | X0 = X1 | ~sP4(X3,X0,X1,X2,X4,X5))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_67])])).
% 1.35/0.57 tff(f506,plain,(
% 1.35/0.57 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (step1(X3,X2,X1,X0) | X0 = X1 | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f341])).
% 1.35/0.57 tff(f897,plain,(
% 1.35/0.57 spl38_66),
% 1.35/0.57 inference(avatar_split_clause,[],[f448,f895])).
% 1.35/0.57 tff(f895,plain,(
% 1.35/0.57 spl38_66 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_66])])).
% 1.35/0.57 tff(f448,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f309])).
% 1.35/0.57 tff(f309,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : list(dB),X2 : dB] : ((foldl(dB,dB,app,X0,X1) = foldl(dB,dB,app,X2,X1) | X0 != X2) & (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1)))),
% 1.35/0.57 inference(nnf_transformation,[],[f161])).
% 1.35/0.57 tff(f161,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : list(dB),X2 : dB] : (foldl(dB,dB,app,X0,X1) = foldl(dB,dB,app,X2,X1) <=> X0 = X2)),
% 1.35/0.57 inference(rectify,[],[f39])).
% 1.35/0.57 tff(f39,axiom,(
% 1.35/0.57 ! [X24 : dB,X30 : list(dB),X44 : dB] : (foldl(dB,dB,app,X44,X30) = foldl(dB,dB,app,X24,X30) <=> X24 = X44)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_apps__eq__tail__conv)).
% 1.35/0.57 tff(f893,plain,(
% 1.35/0.57 spl38_65),
% 1.35/0.57 inference(avatar_split_clause,[],[f427,f891])).
% 1.35/0.57 tff(f427,plain,(
% 1.35/0.57 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f215])).
% 1.35/0.57 tff(f215,plain,(
% 1.35/0.57 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.35/0.57 inference(ennf_transformation,[],[f152])).
% 1.35/0.57 tff(f152,plain,(
% 1.35/0.57 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) => aa(nat,type,X2,X1) = X0)),
% 1.35/0.57 inference(rectify,[],[f19])).
% 1.35/0.57 tff(f19,axiom,(
% 1.35/0.57 ! [X12 : type,X8 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,var(X8)),X12)) => aa(nat,type,X14,X8) = X12)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_typing__elims_I1_J)).
% 1.35/0.57 tff(f889,plain,(
% 1.35/0.57 spl38_64),
% 1.35/0.57 inference(avatar_split_clause,[],[f422,f887])).
% 1.35/0.57 tff(f422,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f211])).
% 1.35/0.57 tff(f211,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 1.35/0.57 inference(ennf_transformation,[],[f148])).
% 1.35/0.57 tff(f148,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,X2)) => pp(aa(dB,bool,it,subst(X2,var(X1),X0))))),
% 1.35/0.57 inference(rectify,[],[f31])).
% 1.35/0.57 tff(f31,axiom,(
% 1.35/0.57 ! [X32 : nat,X27 : nat,X33 : dB] : (pp(aa(dB,bool,it,X33)) => pp(aa(dB,bool,it,subst(X33,var(X27),X32))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_subst__Var__IT)).
% 1.35/0.57 tff(f885,plain,(
% 1.35/0.57 spl38_63 | ~spl38_62),
% 1.35/0.57 inference(avatar_split_clause,[],[f881,f878,f883])).
% 1.35/0.57 tff(f883,plain,(
% 1.35/0.57 spl38_63 <=> ! [X2 : dB,X0 : dB,X1 : nat] : subst(aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),X0,X1) = X2),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_63])])).
% 1.35/0.57 tff(f878,plain,(
% 1.35/0.57 spl38_62 <=> ! [X2 : dB,X0 : dB,X1 : nat] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_62])])).
% 1.35/0.57 tff(f881,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),X0,X1) = X2) ) | ~spl38_62),
% 1.35/0.57 inference(forward_demodulation,[],[f879,f496])).
% 1.35/0.57 tff(f879,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2) ) | ~spl38_62),
% 1.35/0.57 inference(avatar_component_clause,[],[f878])).
% 1.35/0.57 tff(f880,plain,(
% 1.35/0.57 spl38_62),
% 1.35/0.57 inference(avatar_split_clause,[],[f419,f878])).
% 1.35/0.57 tff(f419,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2) )),
% 1.35/0.57 inference(cnf_transformation,[],[f145])).
% 1.35/0.57 tff(f145,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : nat,X2 : dB] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2),
% 1.35/0.57 inference(rectify,[],[f56])).
% 1.35/0.57 tff(f56,axiom,(
% 1.35/0.57 ! [X42 : dB,X41 : nat,X28 : dB] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X28),X41),X42,X41) = X28),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_subst__lift)).
% 1.35/0.57 tff(f876,plain,(
% 1.35/0.57 spl38_61 | ~spl38_15 | ~spl38_21),
% 1.35/0.57 inference(avatar_split_clause,[],[f672,f655,f626,f874])).
% 1.35/0.57 tff(f874,plain,(
% 1.35/0.57 spl38_61 <=> ! [X0 : nat] : sP1(var(X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_61])])).
% 1.35/0.57 tff(f672,plain,(
% 1.35/0.57 ( ! [X0 : nat] : (sP1(var(X0))) ) | (~spl38_15 | ~spl38_21)),
% 1.35/0.57 inference(resolution,[],[f656,f627])).
% 1.35/0.57 tff(f872,plain,(
% 1.35/0.57 spl38_60),
% 1.35/0.57 inference(avatar_split_clause,[],[f403,f870])).
% 1.35/0.57 tff(f403,plain,(
% 1.35/0.57 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f205])).
% 1.35/0.57 tff(f205,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 1.35/0.57 inference(ennf_transformation,[],[f132])).
% 1.35/0.57 tff(f132,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : list(dB)] : (listsp(dB,it,X1) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))))),
% 1.35/0.57 inference(rectify,[],[f77])).
% 1.35/0.57 tff(f77,axiom,(
% 1.35/0.57 ! [X38 : nat,X39 : list(dB)] : (listsp(dB,it,X39) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X38),X39))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_IT_OVar)).
% 1.35/0.57 tff(f865,plain,(
% 1.35/0.57 spl38_59 | ~spl38_58),
% 1.35/0.57 inference(avatar_split_clause,[],[f861,f858,f863])).
% 1.35/0.57 tff(f858,plain,(
% 1.35/0.57 spl38_58 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_58])])).
% 1.35/0.57 tff(f861,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_58),
% 1.35/0.57 inference(forward_demodulation,[],[f859,f496])).
% 1.35/0.57 tff(f859,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_58),
% 1.35/0.57 inference(avatar_component_clause,[],[f858])).
% 1.35/0.57 tff(f860,plain,(
% 1.35/0.57 spl38_58),
% 1.35/0.57 inference(avatar_split_clause,[],[f400,f858])).
% 1.35/0.57 tff(f400,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f129])).
% 1.35/0.57 tff(f129,plain,(
% 1.35/0.57 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.35/0.57 inference(rectify,[],[f106])).
% 1.35/0.57 tff(f106,axiom,(
% 1.35/0.57 ! [X95 : bool,X96 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)) | ~pp(X95) | ~pp(X96))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 1.35/0.57 tff(f856,plain,(
% 1.35/0.57 spl38_57),
% 1.35/0.57 inference(avatar_split_clause,[],[f385,f854])).
% 1.35/0.57 tff(f385,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | listsp(dB,it,sK8(X0)) | ~sP1(X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f276])).
% 1.35/0.57 tff(f852,plain,(
% 1.35/0.57 spl38_56),
% 1.35/0.57 inference(avatar_split_clause,[],[f450,f850])).
% 1.35/0.57 tff(f850,plain,(
% 1.35/0.57 spl38_56 <=> ! [X2 : list(dB),X0 : list(dB),X1 : dB,X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_56])])).
% 1.35/0.57 tff(f450,plain,(
% 1.35/0.57 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f162])).
% 1.35/0.57 tff(f162,plain,(
% 1.35/0.57 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 1.35/0.57 inference(rectify,[],[f69])).
% 1.35/0.57 tff(f69,axiom,(
% 1.35/0.57 ! [X37 : list(dB),X44 : dB,X30 : list(dB),X38 : nat] : foldl(dB,dB,app,var(X38),X30) != foldl(dB,dB,app,abs(X44),X37)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Var__apps__neq__Abs__apps)).
% 1.35/0.57 tff(f844,plain,(
% 1.35/0.57 spl38_55),
% 1.35/0.57 inference(avatar_split_clause,[],[f504,f842])).
% 1.35/0.57 tff(f842,plain,(
% 1.35/0.57 spl38_55 <=> ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X4 : X3,X0 : list(X3),X5 : X3,X1 : list(X3)] : (X4 = X5 | X0 = X1 | ~sP4(X3,X0,X1,X2,X4,X5))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_55])])).
% 1.35/0.57 tff(f504,plain,(
% 1.35/0.57 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (X4 = X5 | X0 = X1 | ~sP4(X3,X0,X1,X2,X4,X5)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f341])).
% 1.35/0.57 tff(f840,plain,(
% 1.35/0.57 spl38_54),
% 1.35/0.57 inference(avatar_split_clause,[],[f494,f838])).
% 1.35/0.57 tff(f494,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f336])).
% 1.35/0.57 tff(f336,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((cons(X0,X2,X1) = cons(X0,X4,X3) | X1 != X3 | X2 != X4) & ((X1 = X3 & X2 = X4) | cons(X0,X2,X1) != cons(X0,X4,X3)))),
% 1.35/0.57 inference(flattening,[],[f335])).
% 1.35/0.57 tff(f335,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((cons(X0,X2,X1) = cons(X0,X4,X3) | (X1 != X3 | X2 != X4)) & ((X1 = X3 & X2 = X4) | cons(X0,X2,X1) != cons(X0,X4,X3)))),
% 1.35/0.57 inference(nnf_transformation,[],[f187])).
% 1.35/0.57 tff(f187,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : (cons(X0,X2,X1) = cons(X0,X4,X3) <=> (X1 = X3 & X2 = X4))),
% 1.35/0.57 inference(rectify,[],[f46])).
% 1.35/0.57 tff(f46,axiom,(
% 1.35/0.57 ! [X0 : $tType,X54 : list(X0),X55 : X0,X56 : list(X0),X57 : X0] : (cons(X0,X57,X56) = cons(X0,X55,X54) <=> (X54 = X56 & X55 = X57))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list_Oinject)).
% 1.35/0.57 tff(f836,plain,(
% 1.35/0.57 spl38_53),
% 1.35/0.57 inference(avatar_split_clause,[],[f442,f834])).
% 1.35/0.57 tff(f834,plain,(
% 1.35/0.57 spl38_53 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP3(X0,X1,X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_53])])).
% 1.35/0.57 tff(f442,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP3(X0,X1,X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f304])).
% 1.35/0.57 tff(f304,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB,X2 : dB] : ((abs(sK24(X0,X1,X2)) = X0 & subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1) | ~sP3(X0,X1,X2))),
% 1.35/0.57 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f302,f303])).
% 1.35/0.57 tff(f303,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (abs(X3) = X0 & subst(X3,X2,zero_zero(nat)) = X1) => (abs(sK24(X0,X1,X2)) = X0 & subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1))),
% 1.35/0.57 introduced(choice_axiom,[])).
% 1.35/0.57 tff(f302,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (abs(X3) = X0 & subst(X3,X2,zero_zero(nat)) = X1) | ~sP3(X0,X1,X2))),
% 1.35/0.57 inference(rectify,[],[f301])).
% 1.35/0.57 tff(f301,plain,(
% 1.35/0.57 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP3(X2,X0,X1))),
% 1.35/0.57 inference(nnf_transformation,[],[f262])).
% 1.35/0.57 tff(f832,plain,(
% 1.35/0.57 spl38_52),
% 1.35/0.57 inference(avatar_split_clause,[],[f417,f830])).
% 1.35/0.57 tff(f417,plain,(
% 1.35/0.57 ( ! [X2 : nat,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f143])).
% 1.35/0.57 tff(f143,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB,X2 : nat] : aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2)),
% 1.35/0.57 inference(rectify,[],[f43])).
% 1.35/0.57 tff(f43,axiom,(
% 1.35/0.57 ! [X52 : dB,X53 : dB,X51 : nat] : aa(dB,dB,aa(dB,fun(dB,dB),app,X53),X52) != var(X51)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dB_Osimps_I4_J)).
% 1.35/0.57 tff(f828,plain,(
% 1.35/0.57 spl38_51),
% 1.35/0.57 inference(avatar_split_clause,[],[f415,f826])).
% 1.35/0.57 tff(f415,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f141])).
% 1.35/0.57 tff(f141,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB,X2 : dB] : abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),
% 1.35/0.57 inference(rectify,[],[f64])).
% 1.35/0.57 tff(f64,axiom,(
% 1.35/0.57 ! [X64 : dB,X65 : dB,X66 : dB] : abs(X66) != aa(dB,dB,aa(dB,fun(dB,dB),app,X65),X64)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_dB_Osimps_I9_J)).
% 1.35/0.57 tff(f823,plain,(
% 1.35/0.57 spl38_50 | ~spl38_49),
% 1.35/0.57 inference(avatar_split_clause,[],[f819,f816,f821])).
% 1.35/0.57 tff(f821,plain,(
% 1.35/0.57 spl38_50 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_50])])).
% 1.35/0.57 tff(f816,plain,(
% 1.35/0.57 spl38_49 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_49])])).
% 1.35/0.57 tff(f819,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1)) ) | ~spl38_49),
% 1.35/0.57 inference(forward_demodulation,[],[f817,f496])).
% 1.35/0.57 tff(f817,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl38_49),
% 1.35/0.57 inference(avatar_component_clause,[],[f816])).
% 1.35/0.57 tff(f818,plain,(
% 1.35/0.57 spl38_49),
% 1.35/0.57 inference(avatar_split_clause,[],[f402,f816])).
% 1.35/0.57 tff(f402,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f131])).
% 1.35/0.57 tff(f131,plain,(
% 1.35/0.57 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.35/0.57 inference(rectify,[],[f107])).
% 1.35/0.57 tff(f107,axiom,(
% 1.35/0.57 ! [X95 : bool,X96 : bool] : (pp(X96) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 1.35/0.57 tff(f813,plain,(
% 1.35/0.57 spl38_48 | ~spl38_47),
% 1.35/0.57 inference(avatar_split_clause,[],[f809,f806,f811])).
% 1.35/0.57 tff(f806,plain,(
% 1.35/0.57 spl38_47 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_47])])).
% 1.35/0.57 tff(f809,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl38_47),
% 1.35/0.57 inference(forward_demodulation,[],[f807,f496])).
% 1.35/0.57 tff(f807,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl38_47),
% 1.35/0.57 inference(avatar_component_clause,[],[f806])).
% 1.35/0.57 tff(f808,plain,(
% 1.35/0.57 spl38_47),
% 1.35/0.57 inference(avatar_split_clause,[],[f401,f806])).
% 1.35/0.57 tff(f401,plain,(
% 1.35/0.57 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f130])).
% 1.35/0.57 tff(f130,plain,(
% 1.35/0.57 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.35/0.57 inference(rectify,[],[f108])).
% 1.35/0.57 tff(f108,axiom,(
% 1.35/0.57 ! [X95 : bool,X96 : bool] : (pp(X95) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 1.35/0.57 tff(f804,plain,(
% 1.35/0.57 spl38_46),
% 1.35/0.57 inference(avatar_split_clause,[],[f383,f802])).
% 1.35/0.57 tff(f802,plain,(
% 1.35/0.57 spl38_46 <=> ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | listsp(dB,it,sK8(X0)) | ~sP1(X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_46])])).
% 1.35/0.57 tff(f383,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | listsp(dB,it,sK8(X0)) | ~sP1(X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f276])).
% 1.35/0.57 tff(f790,plain,(
% 1.35/0.57 spl38_45),
% 1.35/0.57 inference(avatar_split_clause,[],[f547,f787])).
% 1.35/0.57 tff(f787,plain,(
% 1.35/0.57 spl38_45 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),t1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_45])])).
% 1.35/0.57 tff(f547,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),t1))),
% 1.35/0.57 inference(forward_demodulation,[],[f518,f361])).
% 1.35/0.57 tff(f518,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),var(i)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.57 inference(definition_unfolding,[],[f365,f350])).
% 1.35/0.57 tff(f365,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.57 inference(cnf_transformation,[],[f13])).
% 1.35/0.57 tff(f13,axiom,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_varT)).
% 1.35/0.57 tff(f785,plain,(
% 1.35/0.57 spl38_44),
% 1.35/0.57 inference(avatar_split_clause,[],[f530,f783])).
% 1.35/0.57 tff(f530,plain,(
% 1.35/0.57 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) )),
% 1.35/0.57 inference(equality_resolution,[],[f423])).
% 1.35/0.57 tff(f423,plain,(
% 1.35/0.57 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0) )),
% 1.35/0.57 inference(cnf_transformation,[],[f212])).
% 1.35/0.57 tff(f212,plain,(
% 1.35/0.57 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0)),
% 1.35/0.57 inference(ennf_transformation,[],[f149])).
% 1.35/0.57 tff(f149,plain,(
% 1.35/0.57 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 => pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.35/0.57 inference(rectify,[],[f20])).
% 1.35/0.57 tff(f20,axiom,(
% 1.35/0.57 ! [X12 : type,X22 : nat,X23 : fun(nat,type)] : (aa(nat,type,X23,X22) = X12 => pp(aa(type,bool,typing(X23,var(X22)),X12)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_typing_OVar)).
% 1.35/0.57 tff(f781,plain,(
% 1.35/0.57 spl38_43),
% 1.35/0.57 inference(avatar_split_clause,[],[f493,f779])).
% 1.35/0.57 tff(f493,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f336])).
% 1.35/0.57 tff(f776,plain,(
% 1.35/0.57 spl38_42 | ~spl38_41),
% 1.35/0.57 inference(avatar_split_clause,[],[f772,f769,f774])).
% 1.35/0.57 tff(f769,plain,(
% 1.35/0.57 spl38_41 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_41])])).
% 1.35/0.57 tff(f772,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl38_41),
% 1.35/0.57 inference(forward_demodulation,[],[f770,f496])).
% 1.35/0.57 tff(f770,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) ) | ~spl38_41),
% 1.35/0.57 inference(avatar_component_clause,[],[f769])).
% 1.35/0.57 tff(f771,plain,(
% 1.35/0.57 spl38_41),
% 1.35/0.57 inference(avatar_split_clause,[],[f398,f769])).
% 1.35/0.57 tff(f398,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f127])).
% 1.35/0.57 tff(f127,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 1.35/0.57 inference(rectify,[],[f83])).
% 1.35/0.57 tff(f83,axiom,(
% 1.35/0.57 ! [X28 : dB,X27 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X27)),X28))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_beta__cases_I1_J)).
% 1.35/0.57 tff(f767,plain,(
% 1.35/0.57 spl38_40),
% 1.35/0.57 inference(avatar_split_clause,[],[f381,f765])).
% 1.35/0.57 tff(f381,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f204])).
% 1.35/0.57 tff(f204,plain,(
% 1.35/0.57 ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0)))),
% 1.35/0.57 inference(ennf_transformation,[],[f122])).
% 1.35/0.57 tff(f122,plain,(
% 1.35/0.57 ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) => pp(aa(dB,bool,it,abs(X0))))),
% 1.35/0.57 inference(rectify,[],[f74])).
% 1.35/0.57 tff(f74,axiom,(
% 1.35/0.57 ! [X33 : dB] : (pp(aa(dB,bool,it,X33)) => pp(aa(dB,bool,it,abs(X33))))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Lambda)).
% 1.35/0.57 tff(f763,plain,(
% 1.35/0.57 spl38_39),
% 1.35/0.57 inference(avatar_split_clause,[],[f373,f760])).
% 1.35/0.57 tff(f760,plain,(
% 1.35/0.57 spl38_39 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK6))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_39])])).
% 1.35/0.57 tff(f373,plain,(
% 1.35/0.57 pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK6))),
% 1.35/0.57 inference(cnf_transformation,[],[f269])).
% 1.35/0.57 tff(f758,plain,(
% 1.35/0.57 spl38_38),
% 1.35/0.57 inference(avatar_split_clause,[],[f359,f755])).
% 1.35/0.57 tff(f755,plain,(
% 1.35/0.57 spl38_38 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_38])])).
% 1.35/0.57 tff(f359,plain,(
% 1.35/0.57 pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts))),
% 1.35/0.57 inference(cnf_transformation,[],[f10])).
% 1.35/0.57 tff(f10,axiom,(
% 1.35/0.57 pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_argsT)).
% 1.35/0.57 tff(f753,plain,(
% 1.35/0.57 spl38_37 | ~spl38_8 | ~spl38_21),
% 1.35/0.57 inference(avatar_split_clause,[],[f675,f655,f588,f750])).
% 1.35/0.57 tff(f750,plain,(
% 1.35/0.57 spl38_37 <=> sP1(ua)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_37])])).
% 1.35/0.57 tff(f675,plain,(
% 1.35/0.57 sP1(ua) | (~spl38_8 | ~spl38_21)),
% 1.35/0.57 inference(resolution,[],[f656,f590])).
% 1.35/0.57 tff(f746,plain,(
% 1.35/0.57 spl38_36),
% 1.35/0.57 inference(avatar_split_clause,[],[f543,f744])).
% 1.35/0.57 tff(f744,plain,(
% 1.35/0.57 spl38_36 <=> ! [X3 : $tType,X0 : list(X3),X5 : X3,X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (sP4(X3,X0,X1,X2,X5,X5) | ~step1(X3,X2,X1,X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_36])])).
% 1.35/0.57 tff(f543,plain,(
% 1.35/0.57 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X5 : X3] : (sP4(X3,X0,X1,X2,X5,X5) | ~step1(X3,X2,X1,X0)) )),
% 1.35/0.57 inference(equality_resolution,[],[f508])).
% 1.35/0.57 tff(f508,plain,(
% 1.35/0.57 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (sP4(X3,X0,X1,X2,X4,X5) | ~step1(X3,X2,X1,X0) | X4 != X5) )),
% 1.35/0.57 inference(cnf_transformation,[],[f341])).
% 1.35/0.57 tff(f742,plain,(
% 1.35/0.57 spl38_35),
% 1.35/0.57 inference(avatar_split_clause,[],[f526,f740])).
% 1.35/0.57 tff(f740,plain,(
% 1.35/0.57 spl38_35 <=> ! [X2 : list(dB),X3 : nat] : (sP1(foldl(dB,dB,app,var(X3),X2)) | ~listsp(dB,it,X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_35])])).
% 1.35/0.57 tff(f526,plain,(
% 1.35/0.57 ( ! [X2 : list(dB),X3 : nat] : (sP1(foldl(dB,dB,app,var(X3),X2)) | ~listsp(dB,it,X2)) )),
% 1.35/0.57 inference(equality_resolution,[],[f386])).
% 1.35/0.57 tff(f386,plain,(
% 1.35/0.57 ( ! [X2 : list(dB),X3 : nat,X0 : dB] : (sP1(X0) | ~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0) )),
% 1.35/0.57 inference(cnf_transformation,[],[f276])).
% 1.35/0.57 tff(f738,plain,(
% 1.35/0.57 spl38_34),
% 1.35/0.57 inference(avatar_split_clause,[],[f371,f735])).
% 1.35/0.57 tff(f371,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),a),sK5))),
% 1.35/0.57 inference(cnf_transformation,[],[f267])).
% 1.35/0.57 tff(f733,plain,(
% 1.35/0.57 spl38_33),
% 1.35/0.57 inference(avatar_split_clause,[],[f358,f730])).
% 1.35/0.57 tff(f358,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),a),t))),
% 1.35/0.57 inference(cnf_transformation,[],[f5])).
% 1.35/0.57 tff(f5,axiom,(
% 1.35/0.57 pp(aa(type,bool,typing(shift(type,e,i,t1),a),t))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_argT)).
% 1.35/0.57 tff(f727,plain,(
% 1.35/0.57 spl38_32 | ~spl38_9 | ~spl38_21),
% 1.35/0.57 inference(avatar_split_clause,[],[f674,f655,f593,f724])).
% 1.35/0.57 tff(f724,plain,(
% 1.35/0.57 spl38_32 <=> sP1(u)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_32])])).
% 1.35/0.57 tff(f674,plain,(
% 1.35/0.57 sP1(u) | (~spl38_9 | ~spl38_21)),
% 1.35/0.57 inference(resolution,[],[f656,f595])).
% 1.35/0.57 tff(f722,plain,(
% 1.35/0.57 spl38_31),
% 1.35/0.57 inference(avatar_split_clause,[],[f540,f720])).
% 1.35/0.57 tff(f540,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) )),
% 1.35/0.57 inference(equality_resolution,[],[f484])).
% 1.35/0.57 tff(f484,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4) )),
% 1.35/0.57 inference(cnf_transformation,[],[f238])).
% 1.35/0.57 tff(f238,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4)),
% 1.35/0.57 inference(ennf_transformation,[],[f181])).
% 1.35/0.57 tff(f181,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (X3 = X4 => aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1)),
% 1.35/0.57 inference(rectify,[],[f28])).
% 1.35/0.57 tff(f28,axiom,(
% 1.35/0.57 ! [X0 : $tType,X12 : X0,X14 : fun(nat,X0),X29 : nat,X8 : nat] : (X8 = X29 => aa(nat,X0,shift(X0,X14,X8,X12),X29) = X12)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_shift__eq)).
% 1.35/0.57 tff(f718,plain,(
% 1.35/0.57 spl38_30),
% 1.35/0.57 inference(avatar_split_clause,[],[f443,f716])).
% 1.35/0.57 tff(f716,plain,(
% 1.35/0.57 spl38_30 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK24(X0,X1,X2)) = X0 | ~sP3(X0,X1,X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_30])])).
% 1.35/0.57 tff(f443,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK24(X0,X1,X2)) = X0 | ~sP3(X0,X1,X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f304])).
% 1.35/0.57 tff(f714,plain,(
% 1.35/0.57 spl38_29),
% 1.35/0.57 inference(avatar_split_clause,[],[f433,f712])).
% 1.35/0.57 tff(f712,plain,(
% 1.35/0.57 spl38_29 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK18(X0,X1,X2)) = X2 | ~sP2(X0,X1,X2))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_29])])).
% 1.35/0.57 tff(f433,plain,(
% 1.35/0.57 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK18(X0,X1,X2)) = X2 | ~sP2(X0,X1,X2)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f294])).
% 1.35/0.57 tff(f698,plain,(
% 1.35/0.57 spl38_28),
% 1.35/0.57 inference(avatar_split_clause,[],[f525,f696])).
% 1.35/0.57 tff(f525,plain,(
% 1.35/0.57 ( ! [X1 : dB] : (sP1(abs(X1)) | ~pp(aa(dB,bool,it,X1))) )),
% 1.35/0.57 inference(equality_resolution,[],[f387])).
% 1.35/0.57 tff(f387,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) )),
% 1.35/0.57 inference(cnf_transformation,[],[f276])).
% 1.35/0.57 tff(f694,plain,(
% 1.35/0.57 spl38_27),
% 1.35/0.57 inference(avatar_split_clause,[],[f391,f692])).
% 1.35/0.57 tff(f391,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f280])).
% 1.35/0.57 tff(f690,plain,(
% 1.35/0.57 spl38_26),
% 1.35/0.57 inference(avatar_split_clause,[],[f357,f687])).
% 1.35/0.57 tff(f357,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.35/0.57 inference(cnf_transformation,[],[f6])).
% 1.35/0.57 tff(f6,axiom,(
% 1.35/0.57 pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096IT_A_Ia_091u_Pi_093_J_096)).
% 1.35/0.57 tff(f684,plain,(
% 1.35/0.57 spl38_25 | ~spl38_7 | ~spl38_21),
% 1.35/0.57 inference(avatar_split_clause,[],[f673,f655,f583,f681])).
% 1.35/0.57 tff(f681,plain,(
% 1.35/0.57 spl38_25 <=> sP1(t3)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_25])])).
% 1.35/0.57 tff(f673,plain,(
% 1.35/0.57 sP1(t3) | (~spl38_7 | ~spl38_21)),
% 1.35/0.57 inference(resolution,[],[f656,f585])).
% 1.35/0.57 tff(f669,plain,(
% 1.35/0.57 spl38_24),
% 1.35/0.57 inference(avatar_split_clause,[],[f411,f667])).
% 1.35/0.57 tff(f667,plain,(
% 1.35/0.57 spl38_24 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_24])])).
% 1.35/0.57 tff(f411,plain,(
% 1.35/0.57 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f285])).
% 1.35/0.57 tff(f285,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : nat] : ((var(X0) = var(X1) | X0 != X1) & (X0 = X1 | var(X0) != var(X1)))),
% 1.35/0.57 inference(nnf_transformation,[],[f138])).
% 1.35/0.57 tff(f138,plain,(
% 1.35/0.57 ! [X0 : nat,X1 : nat] : (var(X0) = var(X1) <=> X0 = X1)),
% 1.35/0.57 inference(rectify,[],[f41])).
% 1.35/0.57 tff(f41,axiom,(
% 1.35/0.57 ! [X49 : nat,X50 : nat] : (var(X50) = var(X49) <=> X49 = X50)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_dB_Osimps_I1_J)).
% 1.35/0.57 tff(f665,plain,(
% 1.35/0.57 spl38_23),
% 1.35/0.57 inference(avatar_split_clause,[],[f409,f663])).
% 1.35/0.57 tff(f663,plain,(
% 1.35/0.57 spl38_23 <=> ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_23])])).
% 1.35/0.57 tff(f409,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f284])).
% 1.35/0.57 tff(f284,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB] : ((abs(X0) = abs(X1) | X0 != X1) & (X0 = X1 | abs(X0) != abs(X1)))),
% 1.35/0.57 inference(nnf_transformation,[],[f137])).
% 1.35/0.57 tff(f137,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : dB] : (abs(X0) = abs(X1) <=> X0 = X1)),
% 1.35/0.57 inference(rectify,[],[f62])).
% 1.35/0.57 tff(f62,axiom,(
% 1.35/0.57 ! [X62 : dB,X63 : dB] : (abs(X63) = abs(X62) <=> X62 = X63)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dB_Osimps_I3_J)).
% 1.35/0.57 tff(f661,plain,(
% 1.35/0.57 spl38_22),
% 1.35/0.57 inference(avatar_split_clause,[],[f394,f659])).
% 1.35/0.57 tff(f394,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f281])).
% 1.35/0.57 tff(f281,plain,(
% 1.35/0.57 ! [X0 : dB] : ((pp(aa(dB,bool,it,X0)) | ~sP1(X0)) & (sP1(X0) | ~pp(aa(dB,bool,it,X0))))),
% 1.35/0.57 inference(nnf_transformation,[],[f259])).
% 1.35/0.57 tff(f259,plain,(
% 1.35/0.57 ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) <=> sP1(X0))),
% 1.35/0.57 inference(definition_folding,[],[f123,f258,f257])).
% 1.35/0.57 tff(f123,plain,(
% 1.35/0.57 ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) <=> (? [X1 : dB,X2 : dB,X3 : list(dB)] : (pp(aa(dB,bool,it,X2)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0)))),
% 1.35/0.57 inference(rectify,[],[f79])).
% 1.35/0.57 tff(f79,axiom,(
% 1.35/0.57 ! [X57 : dB] : (pp(aa(dB,bool,it,X57)) <=> (? [X78 : dB,X79 : dB,X80 : list(dB)] : (pp(aa(dB,bool,it,X79)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X78,X79,zero_zero(nat)),X80))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X78)),X79),X80) = X57) | ? [X78 : dB] : (pp(aa(dB,bool,it,X78)) & abs(X78) = X57) | ? [X76 : list(dB),X77 : nat] : (listsp(dB,it,X76) & foldl(dB,dB,app,var(X77),X76) = X57)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_IT_Osimps)).
% 1.35/0.57 tff(f657,plain,(
% 1.35/0.57 spl38_21),
% 1.35/0.57 inference(avatar_split_clause,[],[f393,f655])).
% 1.35/0.57 tff(f393,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f281])).
% 1.35/0.57 tff(f653,plain,(
% 1.35/0.57 spl38_20),
% 1.35/0.57 inference(avatar_split_clause,[],[f356,f650])).
% 1.35/0.57 tff(f356,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(e,u),t1))),
% 1.35/0.57 inference(cnf_transformation,[],[f1])).
% 1.35/0.57 tff(f1,axiom,(
% 1.35/0.57 pp(aa(type,bool,typing(e,u),t1))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uT)).
% 1.35/0.57 tff(f648,plain,(
% 1.35/0.57 ~spl38_19 | ~spl38_12 | ~spl38_17),
% 1.35/0.57 inference(avatar_split_clause,[],[f638,f634,f613,f645])).
% 1.35/0.57 tff(f645,plain,(
% 1.35/0.57 spl38_19 <=> as = rs),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_19])])).
% 1.35/0.57 tff(f634,plain,(
% 1.35/0.57 spl38_17 <=> ! [X0 : $tType,X2 : list(X0),X1 : X0] : cons(X0,X1,X2) != X2),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_17])])).
% 1.35/0.57 tff(f638,plain,(
% 1.35/0.57 as != rs | (~spl38_12 | ~spl38_17)),
% 1.35/0.57 inference(superposition,[],[f635,f615])).
% 1.35/0.57 tff(f635,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) ) | ~spl38_17),
% 1.35/0.57 inference(avatar_component_clause,[],[f634])).
% 1.35/0.57 tff(f643,plain,(
% 1.35/0.57 spl38_18),
% 1.35/0.57 inference(avatar_split_clause,[],[f355,f640])).
% 1.35/0.57 tff(f640,plain,(
% 1.35/0.57 spl38_18 <=> pp(aa(type,bool,typing(ea,ua),t1))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_18])])).
% 1.35/0.57 tff(f355,plain,(
% 1.35/0.57 pp(aa(type,bool,typing(ea,ua),t1))),
% 1.35/0.57 inference(cnf_transformation,[],[f50])).
% 1.35/0.57 tff(f50,axiom,(
% 1.35/0.57 pp(aa(type,bool,typing(ea,ua),t1))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Var_I4_J)).
% 1.35/0.57 tff(f636,plain,(
% 1.35/0.57 spl38_17),
% 1.35/0.57 inference(avatar_split_clause,[],[f413,f634])).
% 1.35/0.57 tff(f413,plain,(
% 1.35/0.57 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) )),
% 1.35/0.57 inference(cnf_transformation,[],[f139])).
% 1.35/0.57 tff(f139,plain,(
% 1.35/0.57 ! [X0 : $tType,X1 : X0,X2 : list(X0)] : cons(X0,X1,X2) != X2),
% 1.35/0.57 inference(rectify,[],[f57])).
% 1.35/0.57 tff(f57,axiom,(
% 1.35/0.57 ! [X0 : $tType,X60 : X0,X61 : list(X0)] : cons(X0,X60,X61) != X61),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__Cons__self)).
% 1.35/0.57 tff(f632,plain,(
% 1.35/0.57 spl38_16),
% 1.35/0.57 inference(avatar_split_clause,[],[f397,f630])).
% 1.35/0.57 tff(f630,plain,(
% 1.35/0.57 spl38_16 <=> ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_16])])).
% 1.35/0.57 tff(f397,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) )),
% 1.35/0.57 inference(cnf_transformation,[],[f126])).
% 1.35/0.57 tff(f126,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 1.35/0.57 inference(rectify,[],[f44])).
% 1.35/0.57 tff(f44,axiom,(
% 1.35/0.57 ! [X43 : dB,X41 : nat] : subst(var(X41),X43,X41) = X43),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_subst__eq)).
% 1.35/0.57 tff(f628,plain,(
% 1.35/0.57 spl38_15),
% 1.35/0.57 inference(avatar_split_clause,[],[f376,f626])).
% 1.35/0.57 tff(f376,plain,(
% 1.35/0.57 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f118])).
% 1.35/0.57 tff(f118,plain,(
% 1.35/0.57 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 1.35/0.57 inference(rectify,[],[f26])).
% 1.35/0.57 tff(f26,axiom,(
% 1.35/0.57 ! [X26 : nat] : pp(aa(dB,bool,it,var(X26)))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Var__IT)).
% 1.35/0.57 tff(f624,plain,(
% 1.35/0.57 spl38_14),
% 1.35/0.57 inference(avatar_split_clause,[],[f375,f622])).
% 1.35/0.57 tff(f622,plain,(
% 1.35/0.57 spl38_14 <=> ! [X0 : nat] : zero_zero(nat) = size_size(dB,var(X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_14])])).
% 1.35/0.57 tff(f375,plain,(
% 1.35/0.57 ( ! [X0 : nat] : (zero_zero(nat) = size_size(dB,var(X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f117])).
% 1.35/0.57 tff(f117,plain,(
% 1.35/0.57 ! [X0 : nat] : zero_zero(nat) = size_size(dB,var(X0))),
% 1.35/0.57 inference(rectify,[],[f91])).
% 1.35/0.57 tff(f91,axiom,(
% 1.35/0.57 ! [X51 : nat] : zero_zero(nat) = size_size(dB,var(X51))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_dB_Osize_I4_J)).
% 1.35/0.57 tff(f620,plain,(
% 1.35/0.57 spl38_13 | spl38_1 | ~spl38_11),
% 1.35/0.57 inference(avatar_split_clause,[],[f606,f602,f555,f618])).
% 1.35/0.57 tff(f555,plain,(
% 1.35/0.57 spl38_1 <=> pp(fFalse)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_1])])).
% 1.35/0.57 tff(f606,plain,(
% 1.35/0.57 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl38_1 | ~spl38_11)),
% 1.35/0.57 inference(superposition,[],[f557,f603])).
% 1.35/0.57 tff(f557,plain,(
% 1.35/0.57 ~pp(fFalse) | spl38_1),
% 1.35/0.57 inference(avatar_component_clause,[],[f555])).
% 1.35/0.57 tff(f616,plain,(
% 1.35/0.57 spl38_12),
% 1.35/0.57 inference(avatar_split_clause,[],[f354,f613])).
% 1.35/0.57 tff(f354,plain,(
% 1.35/0.57 rs = cons(dB,a,as)),
% 1.35/0.57 inference(cnf_transformation,[],[f12])).
% 1.35/0.57 tff(f12,axiom,(
% 1.35/0.57 rs = cons(dB,a,as)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Cons)).
% 1.35/0.57 tff(f604,plain,(
% 1.35/0.57 spl38_11),
% 1.35/0.57 inference(avatar_split_clause,[],[f377,f602])).
% 1.35/0.57 tff(f377,plain,(
% 1.35/0.57 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 1.35/0.57 inference(cnf_transformation,[],[f119])).
% 1.35/0.57 tff(f119,plain,(
% 1.35/0.57 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.35/0.57 inference(rectify,[],[f110])).
% 1.35/0.57 tff(f110,axiom,(
% 1.35/0.57 ! [X96 : bool] : (fFalse = X96 | fTrue = X96)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 1.35/0.57 tff(f600,plain,(
% 1.35/0.57 spl38_10),
% 1.35/0.57 inference(avatar_split_clause,[],[f374,f598])).
% 1.35/0.57 tff(f598,plain,(
% 1.35/0.57 spl38_10 <=> ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_10])])).
% 1.35/0.57 tff(f374,plain,(
% 1.35/0.57 ( ! [X0 : nat] : (zero_zero(nat) = dB_size(var(X0))) )),
% 1.35/0.57 inference(cnf_transformation,[],[f116])).
% 1.35/0.57 tff(f116,plain,(
% 1.35/0.57 ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 1.35/0.57 inference(rectify,[],[f60])).
% 1.35/0.57 tff(f60,axiom,(
% 1.35/0.57 ! [X51 : nat] : zero_zero(nat) = dB_size(var(X51))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dB_Osize_I1_J)).
% 1.35/0.57 tff(f596,plain,(
% 1.35/0.57 spl38_9),
% 1.35/0.57 inference(avatar_split_clause,[],[f353,f593])).
% 1.35/0.57 tff(f353,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,u))),
% 1.35/0.57 inference(cnf_transformation,[],[f4])).
% 1.35/0.57 tff(f4,axiom,(
% 1.35/0.57 pp(aa(dB,bool,it,u))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT)).
% 1.35/0.57 tff(f591,plain,(
% 1.35/0.57 spl38_8),
% 1.35/0.57 inference(avatar_split_clause,[],[f352,f588])).
% 1.35/0.57 tff(f352,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,ua))),
% 1.35/0.57 inference(cnf_transformation,[],[f8])).
% 1.35/0.57 tff(f8,axiom,(
% 1.35/0.57 pp(aa(dB,bool,it,ua))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Var_I3_J)).
% 1.35/0.57 tff(f586,plain,(
% 1.35/0.57 spl38_7),
% 1.35/0.57 inference(avatar_split_clause,[],[f351,f583])).
% 1.35/0.57 tff(f351,plain,(
% 1.35/0.57 pp(aa(dB,bool,it,t3))),
% 1.35/0.57 inference(cnf_transformation,[],[f2])).
% 1.35/0.57 tff(f2,axiom,(
% 1.35/0.57 pp(aa(dB,bool,it,t3))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096IT_At_096)).
% 1.35/0.57 tff(f581,plain,(
% 1.35/0.57 spl38_6),
% 1.35/0.57 inference(avatar_split_clause,[],[f395,f579])).
% 1.35/0.57 tff(f579,plain,(
% 1.35/0.57 spl38_6 <=> ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_6])])).
% 1.35/0.57 tff(f395,plain,(
% 1.35/0.57 ( ! [X0 : dB,X1 : nat] : (abs(X0) != var(X1)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f124])).
% 1.35/0.57 tff(f124,plain,(
% 1.35/0.57 ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 1.35/0.57 inference(rectify,[],[f67])).
% 1.35/0.57 tff(f67,axiom,(
% 1.35/0.57 ! [X66 : dB,X51 : nat] : var(X51) != abs(X66)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_dB_Osimps_I6_J)).
% 1.35/0.57 tff(f577,plain,(
% 1.35/0.57 spl38_5),
% 1.35/0.57 inference(avatar_split_clause,[],[f388,f575])).
% 1.35/0.57 tff(f575,plain,(
% 1.35/0.57 spl38_5 <=> ! [X0 : dB] : (sP1(X0) | ~sP0(X0))),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_5])])).
% 1.35/0.57 tff(f388,plain,(
% 1.35/0.57 ( ! [X0 : dB] : (sP1(X0) | ~sP0(X0)) )),
% 1.35/0.57 inference(cnf_transformation,[],[f276])).
% 1.35/0.57 tff(f573,plain,(
% 1.35/0.57 ~spl38_4),
% 1.35/0.57 inference(avatar_split_clause,[],[f345,f570])).
% 1.35/0.57 tff(f345,plain,(
% 1.35/0.57 ~pp(aa(type,bool,typing(e,subst(a,u,i)),t))),
% 1.35/0.57 inference(cnf_transformation,[],[f113])).
% 1.35/0.57 tff(f113,plain,(
% 1.35/0.57 ~pp(aa(type,bool,typing(e,subst(a,u,i)),t))),
% 1.35/0.57 inference(flattening,[],[f112])).
% 1.35/0.57 tff(f112,negated_conjecture,(
% 1.35/0.57 ~pp(aa(type,bool,typing(e,subst(a,u,i)),t))),
% 1.35/0.57 inference(negated_conjecture,[],[f111])).
% 1.35/0.57 tff(f111,conjecture,(
% 1.35/0.57 pp(aa(type,bool,typing(e,subst(a,u,i)),t))),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.35/0.57 tff(f568,plain,(
% 1.35/0.57 spl38_3),
% 1.35/0.57 inference(avatar_split_clause,[],[f349,f565])).
% 1.35/0.57 tff(f349,plain,(
% 1.35/0.57 pp(fTrue)),
% 1.35/0.57 inference(cnf_transformation,[],[f102])).
% 1.35/0.57 tff(f102,axiom,(
% 1.35/0.57 pp(fTrue)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 1.35/0.57 tff(f563,plain,(
% 1.35/0.57 spl38_2),
% 1.35/0.57 inference(avatar_split_clause,[],[f348,f560])).
% 1.35/0.57 tff(f560,plain,(
% 1.35/0.57 spl38_2 <=> zero(nat)),
% 1.35/0.57 introduced(avatar_definition,[new_symbols(naming,[spl38_2])])).
% 1.35/0.57 tff(f348,plain,(
% 1.35/0.57 zero(nat)),
% 1.35/0.57 inference(cnf_transformation,[],[f100])).
% 1.35/0.57 tff(f100,axiom,(
% 1.35/0.57 zero(nat)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 1.35/0.57 tff(f558,plain,(
% 1.35/0.57 ~spl38_1),
% 1.35/0.57 inference(avatar_split_clause,[],[f346,f555])).
% 1.35/0.57 tff(f346,plain,(
% 1.35/0.57 ~pp(fFalse)),
% 1.35/0.57 inference(cnf_transformation,[],[f101])).
% 1.35/0.57 tff(f101,axiom,(
% 1.35/0.57 ~pp(fFalse)),
% 1.35/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 1.35/0.57 % SZS output end Proof for theBenchmark
% 1.35/0.57 % (4034)------------------------------
% 1.35/0.57 % (4034)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.35/0.57 % (4034)Termination reason: Refutation
% 1.35/0.57
% 1.35/0.57 % (4034)Memory used [KB]: 2918
% 1.35/0.57 % (4034)Time elapsed: 0.162 s
% 1.35/0.57 % (4034)Instructions burned: 352 (million)
% 1.35/0.57 % (4034)------------------------------
% 1.35/0.57 % (4034)------------------------------
% 1.35/0.57 % (4025)Success in time 0.189 s
%------------------------------------------------------------------------------