TSTP Solution File: LCL798_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL798_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:34:24 EDT 2024
% Result : Theorem 1.94s 0.67s
% Output : Refutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL798_5 : TPTP v8.2.0. Released v6.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.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 May 20 02:28:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (26837)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (26840)WARNING: value z3 for option sas not known
% 0.15/0.39 % (26843)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (26842)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (26844)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (26841)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (26838)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (26839)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (26840)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.40 % (26844)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42 % (26847)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)
% 0.21/0.42 % (26846)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)
% 0.21/0.42 % (26845)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.43 % (26846)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % (26845)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (26848)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)
% 1.85/0.63 % (26842)First to succeed.
% 1.94/0.66 % (26842)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26837"
% 1.94/0.67 % (26842)Refutation found. Thanks to Tanya!
% 1.94/0.67 % SZS status Theorem for theBenchmark
% 1.94/0.67 % SZS output start Proof for theBenchmark
% 1.94/0.67 tff(type_def_5, type, bool: $tType).
% 1.94/0.67 tff(type_def_6, type, dB: $tType).
% 1.94/0.67 tff(type_def_7, type, list: $tType > $tType).
% 1.94/0.67 tff(type_def_8, type, nat: $tType).
% 1.94/0.67 tff(type_def_9, type, type: $tType).
% 1.94/0.67 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 1.94/0.67 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))))).
% 1.94/0.67 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * X1) > fun(X0,X2))).
% 1.94/0.67 tff(func_def_2, type, combi: !>[X0: $tType]:(fun(X0,X0))).
% 1.94/0.67 tff(func_def_3, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 1.94/0.67 tff(func_def_4, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.94/0.67 tff(func_def_5, type, it: fun(dB,bool)).
% 1.94/0.67 tff(func_def_6, type, beta: fun(dB,fun(dB,bool))).
% 1.94/0.67 tff(func_def_7, type, abs: dB > dB).
% 1.94/0.67 tff(func_def_8, type, app: fun(dB,fun(dB,dB))).
% 1.94/0.67 tff(func_def_9, type, var: nat > dB).
% 1.94/0.67 tff(func_def_10, type, dB_size: dB > nat).
% 1.94/0.67 tff(func_def_11, type, lift: fun(dB,fun(nat,dB))).
% 1.94/0.67 tff(func_def_12, type, subst: (dB * dB * nat) > dB).
% 1.94/0.67 tff(func_def_13, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 1.94/0.67 tff(func_def_14, type, foldr: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * list(X0) * X1) > X1)).
% 1.94/0.67 tff(func_def_15, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 1.94/0.67 tff(func_def_16, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 1.94/0.67 tff(func_def_17, type, map: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * list(X0)) > list(X1))).
% 1.94/0.67 tff(func_def_18, type, size_size: !>[X0: $tType]:((X0) > nat)).
% 1.94/0.67 tff(func_def_19, type, shift: !>[X0: $tType]:((fun(nat,X0) * nat * X0) > fun(nat,X0))).
% 1.94/0.67 tff(func_def_20, type, fun1: fun(type,fun(type,type))).
% 1.94/0.67 tff(func_def_21, type, type_case: !>[X0: $tType]:((fun(nat,X0) * fun(type,fun(type,X0)) * type) > X0)).
% 1.94/0.67 tff(func_def_22, type, typing: (fun(nat,type) * dB) > fun(type,bool)).
% 1.94/0.67 tff(func_def_23, type, typings: (fun(nat,type) * list(dB)) > fun(list(type),bool)).
% 1.94/0.67 tff(func_def_24, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 1.94/0.67 tff(func_def_25, type, fFalse: bool).
% 1.94/0.67 tff(func_def_26, type, fTrue: bool).
% 1.94/0.67 tff(func_def_27, type, fconj: fun(bool,fun(bool,bool))).
% 1.94/0.67 tff(func_def_28, type, t2: type).
% 1.94/0.67 tff(func_def_29, type, t1: type).
% 1.94/0.67 tff(func_def_30, type, t_a: type).
% 1.94/0.67 tff(func_def_31, type, t: type).
% 1.94/0.67 tff(func_def_32, type, ts: list(type)).
% 1.94/0.67 tff(func_def_33, type, a: dB).
% 1.94/0.67 tff(func_def_34, type, as: list(dB)).
% 1.94/0.67 tff(func_def_35, type, e: fun(nat,type)).
% 1.94/0.67 tff(func_def_36, type, ea: fun(nat,type)).
% 1.94/0.67 tff(func_def_37, type, i: nat).
% 1.94/0.67 tff(func_def_38, type, ia: nat).
% 1.94/0.67 tff(func_def_39, type, n: nat).
% 1.94/0.67 tff(func_def_40, type, rs: list(dB)).
% 1.94/0.67 tff(func_def_41, type, t3: dB).
% 1.94/0.67 tff(func_def_42, type, u: dB).
% 1.94/0.67 tff(func_def_43, type, ua: dB).
% 1.94/0.67 tff(func_def_44, type, sK5: type).
% 1.94/0.67 tff(func_def_45, type, sK6: list(type)).
% 1.94/0.67 tff(func_def_46, type, sK7: dB > dB).
% 1.94/0.67 tff(func_def_47, type, sK8: dB > list(dB)).
% 1.94/0.67 tff(func_def_48, type, sK9: dB > nat).
% 1.94/0.67 tff(func_def_49, type, sK10: dB > dB).
% 1.94/0.67 tff(func_def_50, type, sK11: dB > dB).
% 1.94/0.67 tff(func_def_51, type, sK12: dB > list(dB)).
% 1.94/0.67 tff(func_def_52, type, sK13: (dB * dB) > dB).
% 1.94/0.67 tff(func_def_53, type, sK14: (dB * fun(nat,type)) > type).
% 1.94/0.67 tff(func_def_54, type, sK15: (dB * fun(nat,type)) > type).
% 1.94/0.67 tff(func_def_55, type, sK16: (type * dB * fun(nat,type)) > type).
% 1.94/0.67 tff(func_def_56, type, sK17: (type * dB * fun(nat,type)) > type).
% 1.94/0.67 tff(func_def_57, type, sK18: (dB * list(dB) * dB) > dB).
% 1.94/0.67 tff(func_def_58, type, sK19: (dB * list(dB) * dB) > dB).
% 1.94/0.67 tff(func_def_59, type, sK20: (dB * list(dB) * dB) > list(dB)).
% 1.94/0.67 tff(func_def_60, type, sK21: (dB * list(dB) * dB) > list(dB)).
% 1.94/0.67 tff(func_def_61, type, sK22: (dB * list(dB) * dB) > dB).
% 1.94/0.67 tff(func_def_62, type, sK23: (dB * list(dB) * nat) > list(dB)).
% 1.94/0.67 tff(func_def_63, type, sK24: (dB * dB * dB) > dB).
% 1.94/0.67 tff(func_def_64, type, sK25: (dB * dB * dB) > dB).
% 1.94/0.67 tff(func_def_65, type, sK26: (dB * dB * dB) > dB).
% 1.94/0.67 tff(func_def_66, type, sK27: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 1.94/0.67 tff(func_def_67, type, sK28: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 1.94/0.67 tff(func_def_68, type, sK29: (type * list(dB) * nat * fun(nat,type)) > list(type)).
% 1.94/0.67 tff(func_def_69, type, sK30: (type * dB * dB * fun(nat,type)) > type).
% 1.94/0.67 tff(func_def_70, type, sK31: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 1.94/0.67 tff(func_def_71, type, sK32: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > list(X0))).
% 1.94/0.67 tff(func_def_72, type, sK33: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > X0)).
% 1.94/0.67 tff(func_def_73, type, sK34: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.94/0.67 tff(func_def_74, type, sK35: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.94/0.67 tff(func_def_75, type, sK36: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 1.94/0.67 tff(func_def_76, type, sK37: (type * type * list(dB) * fun(nat,type)) > list(type)).
% 1.94/0.67 tff(pred_def_1, type, zero: !>[X0: $tType]:($o)).
% 1.94/0.67 tff(pred_def_2, type, step1: !>[X0: $tType]:((fun(X0,fun(X0,bool)) * list(X0) * list(X0)) > $o)).
% 1.94/0.67 tff(pred_def_3, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.94/0.67 tff(pred_def_4, type, pp: bool > $o).
% 1.94/0.67 tff(pred_def_5, type, sP0: dB > $o).
% 1.94/0.67 tff(pred_def_6, type, sP1: dB > $o).
% 1.94/0.67 tff(pred_def_7, type, sP2: (dB * list(dB) * dB) > $o).
% 1.94/0.67 tff(pred_def_8, type, sP3: (dB * dB * dB) > $o).
% 1.94/0.67 tff(pred_def_9, type, sP4: !>[X0: $tType]:((list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0) > $o)).
% 1.94/0.67 tff(f3960,plain,(
% 1.94/0.67 $false),
% 1.94/0.67 inference(avatar_sat_refutation,[],[f562,f567,f572,f577,f581,f585,f590,f595,f600,f604,f608,f620,f624,f628,f632,f636,f640,f647,f652,f657,f661,f665,f669,f673,f677,f692,f699,f703,f707,f720,f724,f728,f734,f739,f743,f747,f753,f759,f764,f768,f772,f777,f782,f787,f791,f796,f810,f814,f819,f824,f829,f834,f839,f843,f847,f851,f855,f863,f867,f871,f876,f883,f887,f892,f896,f900,f904,f908,f928,f934,f941,f945,f950,f954,f958,f962,f966,f970,f975,f980,f984,f989,f1004,f1009,f1014,f1019,f1023,f1029,f1033,f1037,f1049,f1053,f1058,f1062,f1067,f1074,f1093,f1098,f1105,f1109,f1125,f1130,f1135,f1151,f1155,f1161,f1168,f1172,f1177,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1325,f1331,f1339,f1345,f1354,f1359,f1370,f1374,f1378,f1383,f1411,f1416,f1421,f1425,f1430,f1441,f1447,f1453,f1460,f1466,f1475,f1481,f1529,f1536,f1544,f1549,f1556,f1562,f1566,f1578,f1582,f1586,f1591,f1599,f1604,f1610,f1614,f1638,f1642,f1668,f1673,f1694,f1699,f1708,f1712,f1723,f1729,f1744,f1748,f1753,f1765,f1784,f1789,f1804,f1808,f1833,f1838,f1847,f1852,f1864,f1870,f1888,f1895,f1907,f1912,f1921,f1926,f1939,f1943,f1951,f1959,f1967,f1975,f1983,f1991,f1998,f2010,f2014,f2018,f2024,f2036,f2043,f2047,f2060,f2068,f2076,f2094,f2098,f2103,f2107,f2116,f2125,f2133,f2142,f2150,f2155,f2164,f2172,f2181,f2189,f2198,f2266,f2277,f2287,f2827,f2831,f2858,f2862,f2866,f2870,f2875,f2880,f2907,f3044,f3049,f3053,f3057,f3088,f3093,f3097,f3101,f3105,f3110,f3114,f3118,f3122,f3126,f3130,f3167,f3172,f3186,f3190,f3194,f3198,f3209,f3214,f3218,f3222,f3226,f3235,f3239,f3244,f3249,f3264,f3268,f3272,f3276,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3379,f3384,f3388,f3438,f3442,f3446,f3450,f3454,f3458,f3462,f3467,f3472,f3476,f3480,f3612,f3617,f3622,f3627,f3632,f3636,f3640,f3644,f3648,f3652,f3718,f3722,f3726,f3730,f3734,f3738,f3743,f3747,f3751,f3755,f3959])).
% 1.94/0.67 tff(f3959,plain,(
% 1.94/0.67 ~spl38_3 | spl38_4 | ~spl38_13 | ~spl38_20 | ~spl38_208 | ~spl38_308),
% 1.94/0.67 inference(avatar_split_clause,[],[f3956,f3749,f2100,f654,f622,f574,f569])).
% 1.94/0.67 tff(f569,plain,(
% 1.94/0.67 spl38_3 <=> pp(fTrue)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_3])])).
% 1.94/0.67 tff(f574,plain,(
% 1.94/0.67 spl38_4 <=> pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_4])])).
% 1.94/0.67 tff(f622,plain,(
% 1.94/0.67 spl38_13 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_13])])).
% 1.94/0.67 tff(f654,plain,(
% 1.94/0.67 spl38_20 <=> pp(aa(type,bool,typing(e,u),t))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_20])])).
% 1.94/0.67 tff(f2100,plain,(
% 1.94/0.67 spl38_208 <=> aa(dB,bool,it,u) = fTrue),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_208])])).
% 1.94/0.67 tff(f3749,plain,(
% 1.94/0.67 spl38_308 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | ~pp(aa(dB,bool,it,X0)) | pp(aa(dB,bool,it,subst(a,X0,i))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_308])])).
% 1.94/0.67 tff(f3956,plain,(
% 1.94/0.67 ~pp(fTrue) | (spl38_4 | ~spl38_13 | ~spl38_20 | ~spl38_208 | ~spl38_308)),
% 1.94/0.67 inference(duplicate_literal_removal,[],[f3955])).
% 1.94/0.67 tff(f3955,plain,(
% 1.94/0.67 ~pp(fTrue) | ~pp(fTrue) | (spl38_4 | ~spl38_13 | ~spl38_20 | ~spl38_208 | ~spl38_308)),
% 1.94/0.67 inference(forward_demodulation,[],[f3954,f1512])).
% 1.94/0.67 tff(f1512,plain,(
% 1.94/0.67 aa(type,bool,typing(e,u),t) = fTrue | (~spl38_13 | ~spl38_20)),
% 1.94/0.67 inference(resolution,[],[f623,f656])).
% 1.94/0.67 tff(f656,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(e,u),t)) | ~spl38_20),
% 1.94/0.67 inference(avatar_component_clause,[],[f654])).
% 1.94/0.67 tff(f623,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl38_13),
% 1.94/0.67 inference(avatar_component_clause,[],[f622])).
% 1.94/0.67 tff(f3954,plain,(
% 1.94/0.67 ~pp(fTrue) | ~pp(aa(type,bool,typing(e,u),t)) | (spl38_4 | ~spl38_208 | ~spl38_308)),
% 1.94/0.67 inference(forward_demodulation,[],[f3940,f2102])).
% 1.94/0.67 tff(f2102,plain,(
% 1.94/0.67 aa(dB,bool,it,u) = fTrue | ~spl38_208),
% 1.94/0.67 inference(avatar_component_clause,[],[f2100])).
% 1.94/0.67 tff(f3940,plain,(
% 1.94/0.67 ~pp(aa(dB,bool,it,u)) | ~pp(aa(type,bool,typing(e,u),t)) | (spl38_4 | ~spl38_308)),
% 1.94/0.67 inference(resolution,[],[f3750,f576])).
% 1.94/0.67 tff(f576,plain,(
% 1.94/0.67 ~pp(aa(dB,bool,it,subst(a,u,i))) | spl38_4),
% 1.94/0.67 inference(avatar_component_clause,[],[f574])).
% 1.94/0.67 tff(f3750,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,subst(a,X0,i))) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(e,X0),t))) ) | ~spl38_308),
% 1.94/0.67 inference(avatar_component_clause,[],[f3749])).
% 1.94/0.67 tff(f3755,plain,(
% 1.94/0.67 spl38_309 | ~spl38_89 | ~spl38_176),
% 1.94/0.67 inference(avatar_split_clause,[],[f1839,f1836,f1031,f3753])).
% 1.94/0.67 tff(f3753,plain,(
% 1.94/0.67 spl38_309 <=> ! [X0 : dB] : (~pp(aa(dB,bool,it,sK11(X0))) | sP0(foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0)))) | ~sP0(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_309])])).
% 1.94/0.67 tff(f1031,plain,(
% 1.94/0.67 spl38_89 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_89])])).
% 1.94/0.67 tff(f1836,plain,(
% 1.94/0.67 spl38_176 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_176])])).
% 1.94/0.67 tff(f1839,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,sK11(X0))) | sP0(foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0)))) | ~sP0(X0)) ) | (~spl38_89 | ~spl38_176)),
% 1.94/0.67 inference(resolution,[],[f1837,f1032])).
% 1.94/0.67 tff(f1032,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0)) ) | ~spl38_89),
% 1.94/0.67 inference(avatar_component_clause,[],[f1031])).
% 1.94/0.67 tff(f1837,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : list(dB),X1 : dB] : (~pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) | ~pp(aa(dB,bool,it,X2)) | sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3)))) ) | ~spl38_176),
% 1.94/0.67 inference(avatar_component_clause,[],[f1836])).
% 1.94/0.67 tff(f3751,plain,(
% 1.94/0.67 spl38_308 | ~spl38_33 | ~spl38_166),
% 1.94/0.67 inference(avatar_split_clause,[],[f1768,f1742,f731,f3749])).
% 1.94/0.67 tff(f731,plain,(
% 1.94/0.67 spl38_33 <=> pp(aa(type,bool,typing(shift(type,e,i,t),a),t2))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_33])])).
% 1.94/0.67 tff(f1742,plain,(
% 1.94/0.67 spl38_166 <=> ! [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),t)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_166])])).
% 1.94/0.67 tff(f1768,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | ~pp(aa(dB,bool,it,X0)) | pp(aa(dB,bool,it,subst(a,X0,i)))) ) | (~spl38_33 | ~spl38_166)),
% 1.94/0.67 inference(resolution,[],[f1743,f733])).
% 1.94/0.67 tff(f733,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,i,t),a),t2)) | ~spl38_33),
% 1.94/0.67 inference(avatar_component_clause,[],[f731])).
% 1.94/0.67 tff(f1743,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : nat,X0 : fun(nat,type),X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1)) | ~pp(aa(type,bool,typing(X0,X2),t)) | ~pp(aa(dB,bool,it,X2)) | pp(aa(dB,bool,it,subst(a,X2,X3)))) ) | ~spl38_166),
% 1.94/0.67 inference(avatar_component_clause,[],[f1742])).
% 1.94/0.67 tff(f3747,plain,(
% 1.94/0.67 spl38_307 | ~spl38_223 | ~spl38_295),
% 1.94/0.67 inference(avatar_split_clause,[],[f3706,f3634,f2285,f3745])).
% 1.94/0.67 tff(f3745,plain,(
% 1.94/0.67 spl38_307 <=> ! [X2 : bool,X0 : bool,X1 : bool] : (X0 != X1 | aa(bool,bool,combi(bool),X1) = X0 | X0 = X2 | fTrue = X2)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_307])])).
% 1.94/0.67 tff(f2285,plain,(
% 1.94/0.67 spl38_223 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_223])])).
% 1.94/0.67 tff(f3634,plain,(
% 1.94/0.67 spl38_295 <=> ! [X0 : bool] : (fTrue != X0 | fTrue = aa(bool,bool,combi(bool),X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_295])])).
% 1.94/0.67 tff(f3706,plain,(
% 1.94/0.67 ( ! [X2 : bool,X0 : bool,X1 : bool] : (X0 != X1 | aa(bool,bool,combi(bool),X1) = X0 | X0 = X2 | fTrue = X2) ) | (~spl38_223 | ~spl38_295)),
% 1.94/0.67 inference(superposition,[],[f3635,f2286])).
% 1.94/0.67 tff(f2286,plain,(
% 1.94/0.67 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl38_223),
% 1.94/0.67 inference(avatar_component_clause,[],[f2285])).
% 1.94/0.67 tff(f3635,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fTrue != X0 | fTrue = aa(bool,bool,combi(bool),X0)) ) | ~spl38_295),
% 1.94/0.67 inference(avatar_component_clause,[],[f3634])).
% 1.94/0.67 tff(f3743,plain,(
% 1.94/0.67 spl38_306 | ~spl38_21 | ~spl38_142),
% 1.94/0.67 inference(avatar_split_clause,[],[f1538,f1533,f659,f3740])).
% 1.94/0.67 tff(f3740,plain,(
% 1.94/0.67 spl38_306 <=> sP1(aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_306])])).
% 1.94/0.67 tff(f659,plain,(
% 1.94/0.67 spl38_21 <=> ! [X0 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_21])])).
% 1.94/0.67 tff(f1533,plain,(
% 1.94/0.67 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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_142])])).
% 1.94/0.67 tff(f1538,plain,(
% 1.94/0.67 sP1(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_21 | ~spl38_142)),
% 1.94/0.67 inference(resolution,[],[f1535,f660])).
% 1.94/0.67 tff(f660,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(X0)) ) | ~spl38_21),
% 1.94/0.67 inference(avatar_component_clause,[],[f659])).
% 1.94/0.67 tff(f1535,plain,(
% 1.94/0.67 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_142),
% 1.94/0.67 inference(avatar_component_clause,[],[f1533])).
% 1.94/0.67 tff(f3738,plain,(
% 1.94/0.67 spl38_305 | ~spl38_16 | ~spl38_120),
% 1.94/0.67 inference(avatar_split_clause,[],[f1333,f1329,f634,f3736])).
% 1.94/0.67 tff(f3736,plain,(
% 1.94/0.67 spl38_305 <=> ! [X0 : dB] : pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X0),abs(var(zero_zero(nat))))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_305])])).
% 1.94/0.67 tff(f634,plain,(
% 1.94/0.67 spl38_16 <=> ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_16])])).
% 1.94/0.67 tff(f1329,plain,(
% 1.94/0.67 spl38_120 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_120])])).
% 1.94/0.67 tff(f1333,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),aa(dB,dB,combc(dB,dB,dB,app,X0),abs(var(zero_zero(nat))))))) ) | (~spl38_16 | ~spl38_120)),
% 1.94/0.67 inference(superposition,[],[f1330,f635])).
% 1.94/0.67 tff(f635,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) ) | ~spl38_16),
% 1.94/0.67 inference(avatar_component_clause,[],[f634])).
% 1.94/0.67 tff(f1330,plain,(
% 1.94/0.67 ( ! [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_120),
% 1.94/0.67 inference(avatar_component_clause,[],[f1329])).
% 1.94/0.67 tff(f3734,plain,(
% 1.94/0.67 spl38_304 | ~spl38_23 | ~spl38_118),
% 1.94/0.67 inference(avatar_split_clause,[],[f1289,f1213,f667,f3732])).
% 1.94/0.67 tff(f3732,plain,(
% 1.94/0.67 spl38_304 <=> ! [X2 : $tType,X0 : $tType,X3 : fun(X0,fun(X0,X2)),X1 : X0] : aa(X0,X2,combs(X0,X0,X2,X3,combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_304])])).
% 1.94/0.67 tff(f667,plain,(
% 1.94/0.67 spl38_23 <=> ! [X0 : $tType,X1 : X0] : aa(X0,X0,combi(X0),X1) = X1),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_23])])).
% 1.94/0.67 tff(f1213,plain,(
% 1.94/0.67 spl38_118 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_118])])).
% 1.94/0.67 tff(f1289,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : $tType,X3 : fun(X0,fun(X0,X2)),X1 : X0] : (aa(X0,X2,combs(X0,X0,X2,X3,combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1)) ) | (~spl38_23 | ~spl38_118)),
% 1.94/0.67 inference(superposition,[],[f1214,f668])).
% 1.94/0.67 tff(f668,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X1 : X0] : (aa(X0,X0,combi(X0),X1) = X1) ) | ~spl38_23),
% 1.94/0.67 inference(avatar_component_clause,[],[f667])).
% 1.94/0.67 tff(f1214,plain,(
% 1.94/0.67 ( ! [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_118),
% 1.94/0.67 inference(avatar_component_clause,[],[f1213])).
% 1.94/0.67 tff(f3730,plain,(
% 1.94/0.67 spl38_303 | ~spl38_23 | ~spl38_103),
% 1.94/0.67 inference(avatar_split_clause,[],[f1142,f1133,f667,f3728])).
% 1.94/0.67 tff(f3728,plain,(
% 1.94/0.67 spl38_303 <=> ! [X0 : $tType,X1 : fun(X0,X0)] : (sK31(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK31(X0,X0,combi(X0),X1)) | combi(X0) = X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_303])])).
% 1.94/0.67 tff(f1133,plain,(
% 1.94/0.67 spl38_103 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_103])])).
% 1.94/0.67 tff(f1142,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X1 : fun(X0,X0)] : (sK31(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK31(X0,X0,combi(X0),X1)) | combi(X0) = X1) ) | (~spl38_23 | ~spl38_103)),
% 1.94/0.67 inference(superposition,[],[f1134,f668])).
% 1.94/0.67 tff(f1134,plain,(
% 1.94/0.67 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) | X2 = X3) ) | ~spl38_103),
% 1.94/0.67 inference(avatar_component_clause,[],[f1133])).
% 1.94/0.67 tff(f3726,plain,(
% 1.94/0.67 spl38_302 | ~spl38_11 | ~spl38_103),
% 1.94/0.67 inference(avatar_split_clause,[],[f1141,f1133,f606,f3724])).
% 1.94/0.67 tff(f3724,plain,(
% 1.94/0.67 spl38_302 <=> ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK31(X0,bool,X1,X2))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_302])])).
% 1.94/0.67 tff(f606,plain,(
% 1.94/0.67 spl38_11 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_11])])).
% 1.94/0.67 tff(f1141,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK31(X0,bool,X1,X2)) ) | (~spl38_11 | ~spl38_103)),
% 1.94/0.67 inference(superposition,[],[f1134,f607])).
% 1.94/0.67 tff(f607,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl38_11),
% 1.94/0.67 inference(avatar_component_clause,[],[f606])).
% 1.94/0.67 tff(f3722,plain,(
% 1.94/0.67 spl38_301 | ~spl38_23 | ~spl38_103),
% 1.94/0.67 inference(avatar_split_clause,[],[f1136,f1133,f667,f3720])).
% 1.94/0.67 tff(f3720,plain,(
% 1.94/0.67 spl38_301 <=> ! [X0 : $tType,X1 : fun(X0,X0)] : (sK31(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK31(X0,X0,X1,combi(X0))) | combi(X0) = X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_301])])).
% 1.94/0.67 tff(f1136,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X1 : fun(X0,X0)] : (sK31(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK31(X0,X0,X1,combi(X0))) | combi(X0) = X1) ) | (~spl38_23 | ~spl38_103)),
% 1.94/0.67 inference(superposition,[],[f1134,f668])).
% 1.94/0.67 tff(f3718,plain,(
% 1.94/0.67 spl38_300 | ~spl38_32 | ~spl38_99),
% 1.94/0.67 inference(avatar_split_clause,[],[f1112,f1103,f726,f3716])).
% 1.94/0.67 tff(f3716,plain,(
% 1.94/0.67 spl38_300 <=> ! [X0 : $tType,X3 : fun(list(nat),X0),X4 : X0,X5 : list(nat),X2 : nat,X1 : fun(nat,fun(list(nat),X0))] : list_case(X0,nat,X4,shift(fun(list(nat),X0),X1,X2,X3),cons(nat,X2,X5)) = aa(list(nat),X0,X3,X5)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_300])])).
% 1.94/0.67 tff(f726,plain,(
% 1.94/0.67 spl38_32 <=> ! [X0 : $tType,X2 : fun(nat,X0),X4 : nat,X1 : X0] : aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_32])])).
% 1.94/0.67 tff(f1103,plain,(
% 1.94/0.67 spl38_99 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_99])])).
% 1.94/0.67 tff(f1112,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : nat,X3 : fun(list(nat),X0),X1 : fun(nat,fun(list(nat),X0)),X4 : X0,X5 : list(nat)] : (list_case(X0,nat,X4,shift(fun(list(nat),X0),X1,X2,X3),cons(nat,X2,X5)) = aa(list(nat),X0,X3,X5)) ) | (~spl38_32 | ~spl38_99)),
% 1.94/0.67 inference(superposition,[],[f1104,f727])).
% 1.94/0.67 tff(f727,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) ) | ~spl38_32),
% 1.94/0.67 inference(avatar_component_clause,[],[f726])).
% 1.94/0.67 tff(f1104,plain,(
% 1.94/0.67 ( ! [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_99),
% 1.94/0.67 inference(avatar_component_clause,[],[f1103])).
% 1.94/0.67 tff(f3652,plain,(
% 1.94/0.67 spl38_299 | ~spl38_53 | ~spl38_205),
% 1.94/0.67 inference(avatar_split_clause,[],[f2084,f2074,f837,f3650])).
% 1.94/0.67 tff(f3650,plain,(
% 1.94/0.67 spl38_299 <=> ! [X2 : dB,X0 : nat,X1 : dB,X3 : dB] : abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_299])])).
% 1.94/0.67 tff(f837,plain,(
% 1.94/0.67 spl38_53 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_53])])).
% 1.94/0.67 tff(f2074,plain,(
% 1.94/0.67 spl38_205 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_205])])).
% 1.94/0.67 tff(f2084,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1))) ) | (~spl38_53 | ~spl38_205)),
% 1.94/0.67 inference(superposition,[],[f838,f2075])).
% 1.94/0.67 tff(f2075,plain,(
% 1.94/0.67 ( ! [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_205),
% 1.94/0.67 inference(avatar_component_clause,[],[f2074])).
% 1.94/0.67 tff(f838,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) ) | ~spl38_53),
% 1.94/0.67 inference(avatar_component_clause,[],[f837])).
% 1.94/0.67 tff(f3648,plain,(
% 1.94/0.67 spl38_298 | ~spl38_54 | ~spl38_205),
% 1.94/0.67 inference(avatar_split_clause,[],[f2083,f2074,f841,f3646])).
% 1.94/0.67 tff(f3646,plain,(
% 1.94/0.67 spl38_298 <=> ! [X2 : dB,X0 : nat,X1 : dB,X3 : nat] : var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_298])])).
% 1.94/0.67 tff(f841,plain,(
% 1.94/0.67 spl38_54 <=> ! [X2 : dB,X0 : nat,X1 : dB] : var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_54])])).
% 1.94/0.67 tff(f2083,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : nat,X0 : nat,X1 : dB] : (var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1))) ) | (~spl38_54 | ~spl38_205)),
% 1.94/0.67 inference(superposition,[],[f842,f2075])).
% 1.94/0.67 tff(f842,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : nat,X1 : dB] : (var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) ) | ~spl38_54),
% 1.94/0.67 inference(avatar_component_clause,[],[f841])).
% 1.94/0.67 tff(f3644,plain,(
% 1.94/0.67 spl38_297 | ~spl38_49 | ~spl38_171),
% 1.94/0.67 inference(avatar_split_clause,[],[f1792,f1787,f817,f3642])).
% 1.94/0.67 tff(f3642,plain,(
% 1.94/0.67 spl38_297 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK32(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_297])])).
% 1.94/0.67 tff(f817,plain,(
% 1.94/0.67 spl38_49 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_49])])).
% 1.94/0.67 tff(f1787,plain,(
% 1.94/0.67 spl38_171 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_171])])).
% 1.94/0.67 tff(f1792,plain,(
% 1.94/0.67 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK32(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0)) ) | (~spl38_49 | ~spl38_171)),
% 1.94/0.67 inference(resolution,[],[f1788,f818])).
% 1.94/0.67 tff(f818,plain,(
% 1.94/0.67 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl38_49),
% 1.94/0.67 inference(avatar_component_clause,[],[f817])).
% 1.94/0.67 tff(f1788,plain,(
% 1.94/0.67 ( ! [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_171),
% 1.94/0.67 inference(avatar_component_clause,[],[f1787])).
% 1.94/0.67 tff(f3640,plain,(
% 1.94/0.67 spl38_296 | ~spl38_81 | ~spl38_124),
% 1.94/0.67 inference(avatar_split_clause,[],[f1361,f1357,f982,f3638])).
% 1.94/0.67 tff(f3638,plain,(
% 1.94/0.67 spl38_296 <=> ! [X0 : list(dB),X3 : dB,X2 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | sP4(dB,X2,X2,beta,foldl(dB,dB,app,X3,X0),foldl(dB,dB,app,X3,X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_296])])).
% 1.94/0.67 tff(f982,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_81])])).
% 1.94/0.67 tff(f1357,plain,(
% 1.94/0.67 spl38_124 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_124])])).
% 1.94/0.67 tff(f1361,plain,(
% 1.94/0.67 ( ! [X2 : list(dB),X3 : dB,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | sP4(dB,X2,X2,beta,foldl(dB,dB,app,X3,X0),foldl(dB,dB,app,X3,X1))) ) | (~spl38_81 | ~spl38_124)),
% 1.94/0.67 inference(resolution,[],[f1358,f983])).
% 1.94/0.67 tff(f983,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f982])).
% 1.94/0.67 tff(f1358,plain,(
% 1.94/0.67 ( ! [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_124),
% 1.94/0.67 inference(avatar_component_clause,[],[f1357])).
% 1.94/0.67 tff(f3636,plain,(
% 1.94/0.67 spl38_295 | spl38_238 | ~spl38_284),
% 1.94/0.67 inference(avatar_split_clause,[],[f3545,f3456,f3090,f3634])).
% 1.94/0.67 tff(f3090,plain,(
% 1.94/0.67 spl38_238 <=> fTrue = aa(dB,bool,it,subst(a,u,i))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_238])])).
% 1.94/0.67 tff(f3456,plain,(
% 1.94/0.67 spl38_284 <=> ! [X0 : bool] : (aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = aa(bool,bool,combi(bool),X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_284])])).
% 1.94/0.67 tff(f3545,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fTrue != X0 | fTrue = aa(bool,bool,combi(bool),X0)) ) | (spl38_238 | ~spl38_284)),
% 1.94/0.67 inference(superposition,[],[f3092,f3457])).
% 1.94/0.67 tff(f3457,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = aa(bool,bool,combi(bool),X0)) ) | ~spl38_284),
% 1.94/0.67 inference(avatar_component_clause,[],[f3456])).
% 1.94/0.67 tff(f3092,plain,(
% 1.94/0.67 fTrue != aa(dB,bool,it,subst(a,u,i)) | spl38_238),
% 1.94/0.67 inference(avatar_component_clause,[],[f3090])).
% 1.94/0.67 tff(f3632,plain,(
% 1.94/0.67 spl38_294 | ~spl38_79 | ~spl38_111),
% 1.94/0.67 inference(avatar_split_clause,[],[f1222,f1185,f972,f3629])).
% 1.94/0.67 tff(f3629,plain,(
% 1.94/0.67 spl38_294 <=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK28(t_a,rs,var(i),shift(type,ea,ia,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_294])])).
% 1.94/0.67 tff(f972,plain,(
% 1.94/0.67 spl38_79 <=> pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(i),rs)),t_a))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_79])])).
% 1.94/0.67 tff(f1185,plain,(
% 1.94/0.67 spl38_111 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_111])])).
% 1.94/0.67 tff(f1222,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK28(t_a,rs,var(i),shift(type,ea,ia,t)))) | (~spl38_79 | ~spl38_111)),
% 1.94/0.67 inference(resolution,[],[f1186,f974])).
% 1.94/0.67 tff(f974,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(i),rs)),t_a)) | ~spl38_79),
% 1.94/0.67 inference(avatar_component_clause,[],[f972])).
% 1.94/0.67 tff(f1186,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) | pp(aa(list(type),bool,typings(X3,X1),sK28(X0,X1,X2,X3)))) ) | ~spl38_111),
% 1.94/0.67 inference(avatar_component_clause,[],[f1185])).
% 1.94/0.67 tff(f3627,plain,(
% 1.94/0.67 spl38_293 | ~spl38_80 | ~spl38_111),
% 1.94/0.67 inference(avatar_split_clause,[],[f1221,f1185,f977,f3624])).
% 1.94/0.67 tff(f3624,plain,(
% 1.94/0.67 spl38_293 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK28(t1,rs,var(i),shift(type,e,i,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_293])])).
% 1.94/0.67 tff(f977,plain,(
% 1.94/0.67 spl38_80 <=> pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(i),rs)),t1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_80])])).
% 1.94/0.67 tff(f1221,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK28(t1,rs,var(i),shift(type,e,i,t)))) | (~spl38_80 | ~spl38_111)),
% 1.94/0.67 inference(resolution,[],[f1186,f979])).
% 1.94/0.67 tff(f979,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(i),rs)),t1)) | ~spl38_80),
% 1.94/0.67 inference(avatar_component_clause,[],[f977])).
% 1.94/0.67 tff(f3622,plain,(
% 1.94/0.67 spl38_292 | ~spl38_79 | ~spl38_110),
% 1.94/0.67 inference(avatar_split_clause,[],[f1219,f1181,f972,f3619])).
% 1.94/0.67 tff(f3619,plain,(
% 1.94/0.67 spl38_292 <=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK27(t_a,rs,var(i),shift(type,ea,ia,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_292])])).
% 1.94/0.67 tff(f1181,plain,(
% 1.94/0.67 spl38_110 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_110])])).
% 1.94/0.67 tff(f1219,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK27(t_a,rs,var(i),shift(type,ea,ia,t)))) | (~spl38_79 | ~spl38_110)),
% 1.94/0.67 inference(resolution,[],[f1182,f974])).
% 1.94/0.67 tff(f1182,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) | pp(aa(list(type),bool,typings(X3,X1),sK27(X0,X1,X2,X3)))) ) | ~spl38_110),
% 1.94/0.67 inference(avatar_component_clause,[],[f1181])).
% 1.94/0.67 tff(f3617,plain,(
% 1.94/0.67 spl38_291 | ~spl38_80 | ~spl38_110),
% 1.94/0.67 inference(avatar_split_clause,[],[f1218,f1181,f977,f3614])).
% 1.94/0.67 tff(f3614,plain,(
% 1.94/0.67 spl38_291 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK27(t1,rs,var(i),shift(type,e,i,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_291])])).
% 1.94/0.67 tff(f1218,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK27(t1,rs,var(i),shift(type,e,i,t)))) | (~spl38_80 | ~spl38_110)),
% 1.94/0.67 inference(resolution,[],[f1182,f979])).
% 1.94/0.67 tff(f3612,plain,(
% 1.94/0.67 spl38_290 | ~spl38_32 | ~spl38_96),
% 1.94/0.67 inference(avatar_split_clause,[],[f1079,f1072,f726,f3610])).
% 1.94/0.67 tff(f3610,plain,(
% 1.94/0.67 spl38_290 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(nat,fun(X0,X1)),X3 : nat,X4 : fun(X0,X1),X5 : X0] : aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_290])])).
% 1.94/0.67 tff(f1072,plain,(
% 1.94/0.67 spl38_96 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_96])])).
% 1.94/0.67 tff(f1079,plain,(
% 1.94/0.67 ( ! [X1 : $tType,X0 : $tType,X2 : fun(nat,fun(X0,X1)),X3 : nat,X4 : fun(X0,X1),X5 : X0] : (aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5)) ) | (~spl38_32 | ~spl38_96)),
% 1.94/0.67 inference(superposition,[],[f1073,f727])).
% 1.94/0.67 tff(f1073,plain,(
% 1.94/0.67 ( ! [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_96),
% 1.94/0.67 inference(avatar_component_clause,[],[f1072])).
% 1.94/0.67 tff(f3480,plain,(
% 1.94/0.67 spl38_289 | ~spl38_79 | ~spl38_156),
% 1.94/0.67 inference(avatar_split_clause,[],[f1646,f1636,f972,f3478])).
% 1.94/0.67 tff(f3478,plain,(
% 1.94/0.67 spl38_289 <=> ! [X0 : type] : (~pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(i),rs)),X0)) | t_a = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_289])])).
% 1.94/0.67 tff(f1636,plain,(
% 1.94/0.67 spl38_156 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_156])])).
% 1.94/0.67 tff(f1646,plain,(
% 1.94/0.67 ( ! [X0 : type] : (~pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(i),rs)),X0)) | t_a = X0) ) | (~spl38_79 | ~spl38_156)),
% 1.94/0.67 inference(resolution,[],[f1637,f974])).
% 1.94/0.67 tff(f1637,plain,(
% 1.94/0.67 ( ! [X2 : list(dB),X3 : nat,X0 : type,X1 : type,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) ) | ~spl38_156),
% 1.94/0.67 inference(avatar_component_clause,[],[f1636])).
% 1.94/0.67 tff(f3476,plain,(
% 1.94/0.67 spl38_288 | ~spl38_80 | ~spl38_156),
% 1.94/0.67 inference(avatar_split_clause,[],[f1645,f1636,f977,f3474])).
% 1.94/0.67 tff(f3474,plain,(
% 1.94/0.67 spl38_288 <=> ! [X0 : type] : (~pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(i),rs)),X0)) | t1 = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_288])])).
% 1.94/0.67 tff(f1645,plain,(
% 1.94/0.67 ( ! [X0 : type] : (~pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(i),rs)),X0)) | t1 = X0) ) | (~spl38_80 | ~spl38_156)),
% 1.94/0.67 inference(resolution,[],[f1637,f979])).
% 1.94/0.67 tff(f3472,plain,(
% 1.94/0.67 spl38_287 | ~spl38_79 | ~spl38_125),
% 1.94/0.67 inference(avatar_split_clause,[],[f1406,f1368,f972,f3469])).
% 1.94/0.67 tff(f3469,plain,(
% 1.94/0.67 spl38_287 <=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK29(t_a,rs,i,shift(type,ea,ia,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_287])])).
% 1.94/0.67 tff(f1368,plain,(
% 1.94/0.67 spl38_125 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_125])])).
% 1.94/0.67 tff(f1406,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK29(t_a,rs,i,shift(type,ea,ia,t)))) | (~spl38_79 | ~spl38_125)),
% 1.94/0.67 inference(resolution,[],[f1369,f974])).
% 1.94/0.67 tff(f1369,plain,(
% 1.94/0.67 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)) | pp(aa(list(type),bool,typings(X3,X1),sK29(X0,X1,X2,X3)))) ) | ~spl38_125),
% 1.94/0.67 inference(avatar_component_clause,[],[f1368])).
% 1.94/0.67 tff(f3467,plain,(
% 1.94/0.67 spl38_286 | ~spl38_80 | ~spl38_125),
% 1.94/0.67 inference(avatar_split_clause,[],[f1405,f1368,f977,f3464])).
% 1.94/0.67 tff(f3464,plain,(
% 1.94/0.67 spl38_286 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK29(t1,rs,i,shift(type,e,i,t))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_286])])).
% 1.94/0.67 tff(f1405,plain,(
% 1.94/0.67 pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK29(t1,rs,i,shift(type,e,i,t)))) | (~spl38_80 | ~spl38_125)),
% 1.94/0.67 inference(resolution,[],[f1369,f979])).
% 1.94/0.67 tff(f3462,plain,(
% 1.94/0.67 spl38_285 | ~spl38_81 | ~spl38_122),
% 1.94/0.67 inference(avatar_split_clause,[],[f1349,f1343,f982,f3460])).
% 1.94/0.67 tff(f3460,plain,(
% 1.94/0.67 spl38_285 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | sP4(dB,X2,X2,beta,X1,sK13(X0,X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_285])])).
% 1.94/0.67 tff(f1343,plain,(
% 1.94/0.67 spl38_122 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_122])])).
% 1.94/0.67 tff(f1349,plain,(
% 1.94/0.67 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | sP4(dB,X2,X2,beta,X1,sK13(X0,X1))) ) | (~spl38_81 | ~spl38_122)),
% 1.94/0.67 inference(resolution,[],[f1344,f983])).
% 1.94/0.67 tff(f1344,plain,(
% 1.94/0.67 ( ! [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_122),
% 1.94/0.67 inference(avatar_component_clause,[],[f1343])).
% 1.94/0.67 tff(f3458,plain,(
% 1.94/0.67 spl38_284 | ~spl38_23 | ~spl38_227),
% 1.94/0.67 inference(avatar_split_clause,[],[f3004,f2860,f667,f3456])).
% 1.94/0.67 tff(f2860,plain,(
% 1.94/0.67 spl38_227 <=> ! [X0 : bool] : (aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_227])])).
% 1.94/0.67 tff(f3004,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = aa(bool,bool,combi(bool),X0)) ) | (~spl38_23 | ~spl38_227)),
% 1.94/0.67 inference(superposition,[],[f668,f2861])).
% 1.94/0.67 tff(f2861,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = X0) ) | ~spl38_227),
% 1.94/0.67 inference(avatar_component_clause,[],[f2860])).
% 1.94/0.67 tff(f3454,plain,(
% 1.94/0.67 spl38_283 | ~spl38_81 | ~spl38_120),
% 1.94/0.67 inference(avatar_split_clause,[],[f1332,f1329,f982,f3452])).
% 1.94/0.67 tff(f3452,plain,(
% 1.94/0.67 spl38_283 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : sP4(dB,X0,X0,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),subst(X2,X1,zero_zero(nat)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_283])])).
% 1.94/0.67 tff(f1332,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (sP4(dB,X0,X0,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),subst(X2,X1,zero_zero(nat)))) ) | (~spl38_81 | ~spl38_120)),
% 1.94/0.67 inference(resolution,[],[f1330,f983])).
% 1.94/0.67 tff(f3450,plain,(
% 1.94/0.67 spl38_282 | ~spl38_73 | ~spl38_117),
% 1.94/0.67 inference(avatar_split_clause,[],[f1270,f1209,f947,f3448])).
% 1.94/0.67 tff(f3448,plain,(
% 1.94/0.67 spl38_282 <=> ! [X0 : list(type)] : foldl(type,type,fun1,t2,cons(type,foldr(type,type,fun1,ts,t1),X0)) = foldl(type,type,fun1,t,X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_282])])).
% 1.94/0.67 tff(f947,plain,(
% 1.94/0.67 spl38_73 <=> t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_73])])).
% 1.94/0.67 tff(f1209,plain,(
% 1.94/0.67 spl38_117 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_117])])).
% 1.94/0.67 tff(f1270,plain,(
% 1.94/0.67 ( ! [X0 : list(type)] : (foldl(type,type,fun1,t2,cons(type,foldr(type,type,fun1,ts,t1),X0)) = foldl(type,type,fun1,t,X0)) ) | (~spl38_73 | ~spl38_117)),
% 1.94/0.67 inference(superposition,[],[f1210,f949])).
% 1.94/0.67 tff(f949,plain,(
% 1.94/0.67 t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)) | ~spl38_73),
% 1.94/0.67 inference(avatar_component_clause,[],[f947])).
% 1.94/0.67 tff(f1210,plain,(
% 1.94/0.67 ( ! [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_117),
% 1.94/0.67 inference(avatar_component_clause,[],[f1209])).
% 1.94/0.67 tff(f3446,plain,(
% 1.94/0.67 spl38_281 | ~spl38_73 | ~spl38_113),
% 1.94/0.67 inference(avatar_split_clause,[],[f1229,f1193,f947,f3444])).
% 1.94/0.67 tff(f3444,plain,(
% 1.94/0.67 spl38_281 <=> ! [X0 : type,X1 : type] : (t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | foldr(type,type,fun1,ts,t1) = X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_281])])).
% 1.94/0.67 tff(f1193,plain,(
% 1.94/0.67 spl38_113 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_113])])).
% 1.94/0.67 tff(f1229,plain,(
% 1.94/0.67 ( ! [X0 : type,X1 : type] : (t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | foldr(type,type,fun1,ts,t1) = X1) ) | (~spl38_73 | ~spl38_113)),
% 1.94/0.67 inference(superposition,[],[f1194,f949])).
% 1.94/0.67 tff(f1194,plain,(
% 1.94/0.67 ( ! [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) | X0 = X2) ) | ~spl38_113),
% 1.94/0.67 inference(avatar_component_clause,[],[f1193])).
% 1.94/0.67 tff(f3442,plain,(
% 1.94/0.67 spl38_280 | ~spl38_96 | ~spl38_99),
% 1.94/0.67 inference(avatar_split_clause,[],[f1117,f1103,f1072,f3440])).
% 1.94/0.67 tff(f3440,plain,(
% 1.94/0.67 spl38_280 <=> ! [X1 : $tType,X0 : $tType,X5 : X1,X4 : list(X0),X3 : X0,X2 : fun(X0,fun(list(X0),X1))] : list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_280])])).
% 1.94/0.67 tff(f1117,plain,(
% 1.94/0.67 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X0,X4 : list(X0),X5 : X1] : (list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3)) ) | (~spl38_96 | ~spl38_99)),
% 1.94/0.67 inference(superposition,[],[f1104,f1073])).
% 1.94/0.67 tff(f3438,plain,(
% 1.94/0.67 spl38_279 | ~spl38_64 | ~spl38_65),
% 1.94/0.67 inference(avatar_split_clause,[],[f918,f894,f890,f3436])).
% 1.94/0.67 tff(f3436,plain,(
% 1.94/0.67 spl38_279 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_279])])).
% 1.94/0.67 tff(f890,plain,(
% 1.94/0.67 spl38_64 <=> ! [X2 : dB,X0 : dB,X1 : nat] : subst(aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),X0,X1) = X2),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_64])])).
% 1.94/0.67 tff(f894,plain,(
% 1.94/0.67 spl38_65 <=> ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_65])])).
% 1.94/0.67 tff(f918,plain,(
% 1.94/0.67 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,X1)) | ~pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))) ) | (~spl38_64 | ~spl38_65)),
% 1.94/0.67 inference(superposition,[],[f895,f891])).
% 1.94/0.67 tff(f891,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),X0,X1) = X2) ) | ~spl38_64),
% 1.94/0.67 inference(avatar_component_clause,[],[f890])).
% 1.94/0.67 tff(f895,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2))) ) | ~spl38_65),
% 1.94/0.67 inference(avatar_component_clause,[],[f894])).
% 1.94/0.67 tff(f3388,plain,(
% 1.94/0.67 spl38_278 | ~spl38_49 | ~spl38_168),
% 1.94/0.67 inference(avatar_split_clause,[],[f1756,f1751,f817,f3386])).
% 1.94/0.67 tff(f3386,plain,(
% 1.94/0.67 spl38_278 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_278])])).
% 1.94/0.67 tff(f1751,plain,(
% 1.94/0.67 spl38_168 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_168])])).
% 1.94/0.67 tff(f1756,plain,(
% 1.94/0.67 ( ! [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_49 | ~spl38_168)),
% 1.94/0.67 inference(resolution,[],[f1752,f818])).
% 1.94/0.67 tff(f1752,plain,(
% 1.94/0.67 ( ! [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_168),
% 1.94/0.67 inference(avatar_component_clause,[],[f1751])).
% 1.94/0.67 tff(f3384,plain,(
% 1.94/0.67 spl38_277 | ~spl38_81 | ~spl38_106),
% 1.94/0.67 inference(avatar_split_clause,[],[f1163,f1159,f982,f3382])).
% 1.94/0.67 tff(f3382,plain,(
% 1.94/0.67 spl38_277 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_277])])).
% 1.94/0.67 tff(f1159,plain,(
% 1.94/0.67 spl38_106 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_106])])).
% 1.94/0.67 tff(f1163,plain,(
% 1.94/0.67 ( ! [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_106)),
% 1.94/0.67 inference(resolution,[],[f1160,f983])).
% 1.94/0.67 tff(f1160,plain,(
% 1.94/0.67 ( ! [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_106),
% 1.94/0.67 inference(avatar_component_clause,[],[f1159])).
% 1.94/0.67 tff(f3379,plain,(
% 1.94/0.67 spl38_276 | ~spl38_12 | ~spl38_99),
% 1.94/0.67 inference(avatar_split_clause,[],[f1110,f1103,f617,f3377])).
% 1.94/0.67 tff(f3377,plain,(
% 1.94/0.67 spl38_276 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_276])])).
% 1.94/0.67 tff(f617,plain,(
% 1.94/0.67 spl38_12 <=> rs = cons(dB,a,as)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_12])])).
% 1.94/0.67 tff(f1110,plain,(
% 1.94/0.67 ( ! [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_99)),
% 1.94/0.67 inference(superposition,[],[f1104,f619])).
% 1.94/0.67 tff(f619,plain,(
% 1.94/0.67 rs = cons(dB,a,as) | ~spl38_12),
% 1.94/0.67 inference(avatar_component_clause,[],[f617])).
% 1.94/0.67 tff(f3316,plain,(
% 1.94/0.67 spl38_275 | ~spl38_34 | ~spl38_157),
% 1.94/0.67 inference(avatar_split_clause,[],[f1659,f1640,f736,f3314])).
% 1.94/0.67 tff(f3314,plain,(
% 1.94/0.67 spl38_275 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),sK5)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_275])])).
% 1.94/0.67 tff(f736,plain,(
% 1.94/0.67 spl38_34 <=> pp(aa(type,bool,typing(shift(type,e,i,t),a),sK5))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_34])])).
% 1.94/0.67 tff(f1640,plain,(
% 1.94/0.67 spl38_157 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_157])])).
% 1.94/0.67 tff(f1659,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),sK5))) ) | (~spl38_34 | ~spl38_157)),
% 1.94/0.67 inference(resolution,[],[f1641,f738])).
% 1.94/0.67 tff(f738,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,i,t),a),sK5)) | ~spl38_34),
% 1.94/0.67 inference(avatar_component_clause,[],[f736])).
% 1.94/0.67 tff(f1641,plain,(
% 1.94/0.67 ( ! [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_157),
% 1.94/0.67 inference(avatar_component_clause,[],[f1640])).
% 1.94/0.67 tff(f3312,plain,(
% 1.94/0.67 spl38_274 | ~spl38_33 | ~spl38_157),
% 1.94/0.67 inference(avatar_split_clause,[],[f1656,f1640,f731,f3310])).
% 1.94/0.67 tff(f3310,plain,(
% 1.94/0.67 spl38_274 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),t2)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_274])])).
% 1.94/0.67 tff(f1656,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(a,X0,i)),t2))) ) | (~spl38_33 | ~spl38_157)),
% 1.94/0.67 inference(resolution,[],[f1641,f733])).
% 1.94/0.67 tff(f3308,plain,(
% 1.94/0.67 spl38_273 | ~spl38_109 | ~spl38_124),
% 1.94/0.67 inference(avatar_split_clause,[],[f1360,f1357,f1175,f3306])).
% 1.94/0.67 tff(f3306,plain,(
% 1.94/0.67 spl38_273 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_273])])).
% 1.94/0.67 tff(f1175,plain,(
% 1.94/0.67 spl38_109 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_109])])).
% 1.94/0.67 tff(f1360,plain,(
% 1.94/0.67 ( ! [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_109 | ~spl38_124)),
% 1.94/0.67 inference(resolution,[],[f1358,f1176])).
% 1.94/0.67 tff(f1176,plain,(
% 1.94/0.67 ( ! [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_109),
% 1.94/0.67 inference(avatar_component_clause,[],[f1175])).
% 1.94/0.67 tff(f3304,plain,(
% 1.94/0.67 spl38_272 | ~spl38_90 | ~spl38_118),
% 1.94/0.67 inference(avatar_split_clause,[],[f1310,f1213,f1035,f3302])).
% 1.94/0.67 tff(f3302,plain,(
% 1.94/0.67 spl38_272 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_272])])).
% 1.94/0.67 tff(f1035,plain,(
% 1.94/0.67 spl38_90 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_90])])).
% 1.94/0.67 tff(f1310,plain,(
% 1.94/0.67 ( ! [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_90 | ~spl38_118)),
% 1.94/0.67 inference(superposition,[],[f1036,f1214])).
% 1.94/0.67 tff(f1036,plain,(
% 1.94/0.67 ( ! [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_90),
% 1.94/0.67 inference(avatar_component_clause,[],[f1035])).
% 1.94/0.67 tff(f3300,plain,(
% 1.94/0.67 spl38_271 | ~spl38_84 | ~spl38_106),
% 1.94/0.67 inference(avatar_split_clause,[],[f1162,f1159,f1007,f3298])).
% 1.94/0.67 tff(f3298,plain,(
% 1.94/0.67 spl38_271 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | abs(X0) = abs(sK13(abs(X0),X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_271])])).
% 1.94/0.67 tff(f1007,plain,(
% 1.94/0.67 spl38_84 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_84])])).
% 1.94/0.67 tff(f1162,plain,(
% 1.94/0.67 ( ! [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_106)),
% 1.94/0.67 inference(resolution,[],[f1160,f1008])).
% 1.94/0.67 tff(f1008,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0) ) | ~spl38_84),
% 1.94/0.67 inference(avatar_component_clause,[],[f1007])).
% 1.94/0.67 tff(f3296,plain,(
% 1.94/0.67 spl38_270 | ~spl38_99),
% 1.94/0.67 inference(avatar_split_clause,[],[f1116,f1103,f3294])).
% 1.94/0.67 tff(f3294,plain,(
% 1.94/0.67 spl38_270 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_270])])).
% 1.94/0.67 tff(f1116,plain,(
% 1.94/0.67 ( ! [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_99),
% 1.94/0.67 inference(superposition,[],[f1104,f1104])).
% 1.94/0.67 tff(f3292,plain,(
% 1.94/0.67 spl38_269 | ~spl38_29 | ~spl38_98),
% 1.94/0.67 inference(avatar_split_clause,[],[f1099,f1096,f705,f3290])).
% 1.94/0.67 tff(f3290,plain,(
% 1.94/0.67 spl38_269 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_269])])).
% 1.94/0.67 tff(f705,plain,(
% 1.94/0.67 spl38_29 <=> ! [X1 : dB] : (sP1(abs(X1)) | ~pp(aa(dB,bool,it,X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_29])])).
% 1.94/0.67 tff(f1096,plain,(
% 1.94/0.67 spl38_98 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_98])])).
% 1.94/0.67 tff(f1099,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)))) ) | (~spl38_29 | ~spl38_98)),
% 1.94/0.67 inference(resolution,[],[f1097,f706])).
% 1.94/0.67 tff(f706,plain,(
% 1.94/0.67 ( ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | sP1(abs(X1))) ) | ~spl38_29),
% 1.94/0.67 inference(avatar_component_clause,[],[f705])).
% 1.94/0.67 tff(f1097,plain,(
% 1.94/0.67 ( ! [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_98),
% 1.94/0.67 inference(avatar_component_clause,[],[f1096])).
% 1.94/0.67 tff(f3288,plain,(
% 1.94/0.67 spl38_268 | ~spl38_90 | ~spl38_96),
% 1.94/0.67 inference(avatar_split_clause,[],[f1086,f1072,f1035,f3286])).
% 1.94/0.67 tff(f3286,plain,(
% 1.94/0.67 spl38_268 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_268])])).
% 1.94/0.67 tff(f1086,plain,(
% 1.94/0.67 ( ! [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_90 | ~spl38_96)),
% 1.94/0.67 inference(superposition,[],[f1036,f1073])).
% 1.94/0.67 tff(f3284,plain,(
% 1.94/0.67 spl38_267 | ~spl38_29 | ~spl38_93),
% 1.94/0.67 inference(avatar_split_clause,[],[f1075,f1056,f705,f3282])).
% 1.94/0.67 tff(f3282,plain,(
% 1.94/0.67 spl38_267 <=> ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(abs(sK7(X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_267])])).
% 1.94/0.67 tff(f1056,plain,(
% 1.94/0.67 spl38_93 <=> ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_93])])).
% 1.94/0.67 tff(f1075,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(abs(sK7(X0)))) ) | (~spl38_29 | ~spl38_93)),
% 1.94/0.67 inference(resolution,[],[f1057,f706])).
% 1.94/0.67 tff(f1057,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK7(X0))) | sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) ) | ~spl38_93),
% 1.94/0.67 inference(avatar_component_clause,[],[f1056])).
% 1.94/0.67 tff(f3276,plain,(
% 1.94/0.67 spl38_266 | ~spl38_90 | ~spl38_116),
% 1.94/0.67 inference(avatar_split_clause,[],[f1259,f1205,f1035,f3274])).
% 1.94/0.67 tff(f3274,plain,(
% 1.94/0.67 spl38_266 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_266])])).
% 1.94/0.67 tff(f1205,plain,(
% 1.94/0.67 spl38_116 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_116])])).
% 1.94/0.67 tff(f1259,plain,(
% 1.94/0.67 ( ! [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_90 | ~spl38_116)),
% 1.94/0.67 inference(superposition,[],[f1036,f1206])).
% 1.94/0.67 tff(f1206,plain,(
% 1.94/0.67 ( ! [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_116),
% 1.94/0.67 inference(avatar_component_clause,[],[f1205])).
% 1.94/0.67 tff(f3272,plain,(
% 1.94/0.67 spl38_265 | ~spl38_21 | ~spl38_98),
% 1.94/0.67 inference(avatar_split_clause,[],[f1100,f1096,f659,f3270])).
% 1.94/0.67 tff(f3270,plain,(
% 1.94/0.67 spl38_265 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_265])])).
% 1.94/0.67 tff(f1100,plain,(
% 1.94/0.67 ( ! [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_98)),
% 1.94/0.67 inference(resolution,[],[f1097,f660])).
% 1.94/0.67 tff(f3268,plain,(
% 1.94/0.67 spl38_264 | ~spl38_21 | ~spl38_93),
% 1.94/0.67 inference(avatar_split_clause,[],[f1076,f1056,f659,f3266])).
% 1.94/0.67 tff(f3266,plain,(
% 1.94/0.67 spl38_264 <=> ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(sK7(X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_264])])).
% 1.94/0.67 tff(f1076,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP0(X0) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0) | sP1(sK7(X0))) ) | (~spl38_21 | ~spl38_93)),
% 1.94/0.67 inference(resolution,[],[f1057,f660])).
% 1.94/0.67 tff(f3264,plain,(
% 1.94/0.67 spl38_263 | ~spl38_29 | ~spl38_95),
% 1.94/0.67 inference(avatar_split_clause,[],[f1068,f1065,f705,f3262])).
% 1.94/0.67 tff(f3262,plain,(
% 1.94/0.67 spl38_263 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_263])])).
% 1.94/0.67 tff(f1065,plain,(
% 1.94/0.67 spl38_95 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_95])])).
% 1.94/0.67 tff(f1068,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)))) ) | (~spl38_29 | ~spl38_95)),
% 1.94/0.67 inference(resolution,[],[f1066,f706])).
% 1.94/0.67 tff(f1066,plain,(
% 1.94/0.67 ( ! [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_95),
% 1.94/0.67 inference(avatar_component_clause,[],[f1065])).
% 1.94/0.67 tff(f3249,plain,(
% 1.94/0.67 spl38_262 | ~spl38_8 | ~spl38_224),
% 1.94/0.67 inference(avatar_split_clause,[],[f2844,f2825,f592,f3246])).
% 1.94/0.67 tff(f3246,plain,(
% 1.94/0.67 spl38_262 <=> sP1(abs(abs(ua)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_262])])).
% 1.94/0.67 tff(f592,plain,(
% 1.94/0.67 spl38_8 <=> pp(aa(dB,bool,it,ua))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_8])])).
% 1.94/0.67 tff(f2825,plain,(
% 1.94/0.67 spl38_224 <=> ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_224])])).
% 1.94/0.67 tff(f2844,plain,(
% 1.94/0.67 sP1(abs(abs(ua))) | (~spl38_8 | ~spl38_224)),
% 1.94/0.67 inference(resolution,[],[f2826,f594])).
% 1.94/0.67 tff(f594,plain,(
% 1.94/0.67 pp(aa(dB,bool,it,ua)) | ~spl38_8),
% 1.94/0.67 inference(avatar_component_clause,[],[f592])).
% 1.94/0.67 tff(f2826,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0)))) ) | ~spl38_224),
% 1.94/0.67 inference(avatar_component_clause,[],[f2825])).
% 1.94/0.67 tff(f3244,plain,(
% 1.94/0.67 spl38_261 | ~spl38_73 | ~spl38_96),
% 1.94/0.67 inference(avatar_split_clause,[],[f1082,f1072,f947,f3241])).
% 1.94/0.67 tff(f3241,plain,(
% 1.94/0.67 spl38_261 <=> t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),t2)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_261])])).
% 1.94/0.67 tff(f1082,plain,(
% 1.94/0.67 t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),t2) | (~spl38_73 | ~spl38_96)),
% 1.94/0.67 inference(superposition,[],[f1073,f949])).
% 1.94/0.67 tff(f3239,plain,(
% 1.94/0.67 spl38_260 | ~spl38_21 | ~spl38_95),
% 1.94/0.67 inference(avatar_split_clause,[],[f1069,f1065,f659,f3237])).
% 1.94/0.67 tff(f3237,plain,(
% 1.94/0.67 spl38_260 <=> ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_260])])).
% 1.94/0.67 tff(f1069,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) ) | (~spl38_21 | ~spl38_95)),
% 1.94/0.67 inference(resolution,[],[f1066,f660])).
% 1.94/0.67 tff(f3235,plain,(
% 1.94/0.67 spl38_259 | ~spl38_29 | ~spl38_89),
% 1.94/0.67 inference(avatar_split_clause,[],[f1042,f1031,f705,f3233])).
% 1.94/0.67 tff(f3233,plain,(
% 1.94/0.67 spl38_259 <=> ! [X0 : dB] : (~sP0(X0) | sP1(abs(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_259])])).
% 1.94/0.67 tff(f1042,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~sP0(X0) | sP1(abs(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0))))) ) | (~spl38_29 | ~spl38_89)),
% 1.94/0.67 inference(resolution,[],[f1032,f706])).
% 1.94/0.67 tff(f3226,plain,(
% 1.94/0.67 spl38_258 | ~spl38_53 | ~spl38_159),
% 1.94/0.67 inference(avatar_split_clause,[],[f1684,f1671,f837,f3224])).
% 1.94/0.67 tff(f3224,plain,(
% 1.94/0.67 spl38_258 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_258])])).
% 1.94/0.67 tff(f1671,plain,(
% 1.94/0.67 spl38_159 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_159])])).
% 1.94/0.67 tff(f1684,plain,(
% 1.94/0.67 ( ! [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_53 | ~spl38_159)),
% 1.94/0.67 inference(superposition,[],[f838,f1672])).
% 1.94/0.67 tff(f1672,plain,(
% 1.94/0.67 ( ! [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_159),
% 1.94/0.67 inference(avatar_component_clause,[],[f1671])).
% 1.94/0.67 tff(f3222,plain,(
% 1.94/0.67 spl38_257 | ~spl38_54 | ~spl38_159),
% 1.94/0.67 inference(avatar_split_clause,[],[f1683,f1671,f841,f3220])).
% 1.94/0.67 tff(f3220,plain,(
% 1.94/0.67 spl38_257 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_257])])).
% 1.94/0.67 tff(f1683,plain,(
% 1.94/0.67 ( ! [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_54 | ~spl38_159)),
% 1.94/0.67 inference(superposition,[],[f842,f1672])).
% 1.94/0.67 tff(f3218,plain,(
% 1.94/0.67 spl38_256 | ~spl38_73 | ~spl38_112),
% 1.94/0.67 inference(avatar_split_clause,[],[f1224,f1189,f947,f3216])).
% 1.94/0.67 tff(f3216,plain,(
% 1.94/0.67 spl38_256 <=> ! [X0 : type,X1 : type] : (t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | t2 = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_256])])).
% 1.94/0.67 tff(f1189,plain,(
% 1.94/0.67 spl38_112 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_112])])).
% 1.94/0.67 tff(f1224,plain,(
% 1.94/0.67 ( ! [X0 : type,X1 : type] : (t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) | t2 = X0) ) | (~spl38_73 | ~spl38_112)),
% 1.94/0.67 inference(superposition,[],[f1190,f949])).
% 1.94/0.67 tff(f1190,plain,(
% 1.94/0.67 ( ! [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_112),
% 1.94/0.67 inference(avatar_component_clause,[],[f1189])).
% 1.94/0.67 tff(f3214,plain,(
% 1.94/0.67 spl38_255 | ~spl38_9 | ~spl38_224),
% 1.94/0.67 inference(avatar_split_clause,[],[f2843,f2825,f597,f3211])).
% 1.94/0.67 tff(f3211,plain,(
% 1.94/0.67 spl38_255 <=> sP1(abs(abs(u)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_255])])).
% 1.94/0.67 tff(f597,plain,(
% 1.94/0.67 spl38_9 <=> pp(aa(dB,bool,it,u))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_9])])).
% 1.94/0.67 tff(f2843,plain,(
% 1.94/0.67 sP1(abs(abs(u))) | (~spl38_9 | ~spl38_224)),
% 1.94/0.67 inference(resolution,[],[f2826,f599])).
% 1.94/0.67 tff(f599,plain,(
% 1.94/0.67 pp(aa(dB,bool,it,u)) | ~spl38_9),
% 1.94/0.67 inference(avatar_component_clause,[],[f597])).
% 1.94/0.67 tff(f3209,plain,(
% 1.94/0.67 spl38_254 | ~spl38_21 | ~spl38_89),
% 1.94/0.67 inference(avatar_split_clause,[],[f1043,f1031,f659,f3207])).
% 1.94/0.67 tff(f3207,plain,(
% 1.94/0.67 spl38_254 <=> ! [X0 : dB] : (~sP0(X0) | sP1(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_254])])).
% 1.94/0.67 tff(f1043,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~sP0(X0) | sP1(foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) ) | (~spl38_21 | ~spl38_89)),
% 1.94/0.67 inference(resolution,[],[f1032,f660])).
% 1.94/0.67 tff(f3198,plain,(
% 1.94/0.67 spl38_253 | ~spl38_12 | ~spl38_78),
% 1.94/0.67 inference(avatar_split_clause,[],[f996,f968,f617,f3196])).
% 1.94/0.67 tff(f3196,plain,(
% 1.94/0.67 spl38_253 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_253])])).
% 1.94/0.67 tff(f968,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_78])])).
% 1.94/0.67 tff(f996,plain,(
% 1.94/0.67 ( ! [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)),
% 1.94/0.67 inference(superposition,[],[f969,f619])).
% 1.94/0.67 tff(f969,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f968])).
% 1.94/0.67 tff(f3194,plain,(
% 1.94/0.67 spl38_252 | ~spl38_12 | ~spl38_78),
% 1.94/0.67 inference(avatar_split_clause,[],[f995,f968,f617,f3192])).
% 1.94/0.67 tff(f3192,plain,(
% 1.94/0.67 spl38_252 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_252])])).
% 1.94/0.67 tff(f995,plain,(
% 1.94/0.67 ( ! [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)),
% 1.94/0.67 inference(superposition,[],[f969,f619])).
% 1.94/0.67 tff(f3190,plain,(
% 1.94/0.67 spl38_251 | ~spl38_12 | ~spl38_77),
% 1.94/0.67 inference(avatar_split_clause,[],[f993,f964,f617,f3188])).
% 1.94/0.67 tff(f3188,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_251])])).
% 1.94/0.67 tff(f964,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_77])])).
% 1.94/0.67 tff(f993,plain,(
% 1.94/0.67 ( ! [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)),
% 1.94/0.67 inference(superposition,[],[f965,f619])).
% 1.94/0.67 tff(f965,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f964])).
% 1.94/0.67 tff(f3186,plain,(
% 1.94/0.67 spl38_250 | ~spl38_12 | ~spl38_77),
% 1.94/0.67 inference(avatar_split_clause,[],[f992,f964,f617,f3184])).
% 1.94/0.67 tff(f3184,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_250])])).
% 1.94/0.67 tff(f992,plain,(
% 1.94/0.67 ( ! [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)),
% 1.94/0.67 inference(superposition,[],[f965,f619])).
% 1.94/0.67 tff(f3172,plain,(
% 1.94/0.67 spl38_249 | ~spl38_7 | ~spl38_224),
% 1.94/0.67 inference(avatar_split_clause,[],[f2842,f2825,f587,f3169])).
% 1.94/0.67 tff(f3169,plain,(
% 1.94/0.67 spl38_249 <=> sP1(abs(abs(t3)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_249])])).
% 1.94/0.67 tff(f587,plain,(
% 1.94/0.67 spl38_7 <=> pp(aa(dB,bool,it,t3))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_7])])).
% 1.94/0.67 tff(f2842,plain,(
% 1.94/0.67 sP1(abs(abs(t3))) | (~spl38_7 | ~spl38_224)),
% 1.94/0.67 inference(resolution,[],[f2826,f589])).
% 1.94/0.67 tff(f589,plain,(
% 1.94/0.67 pp(aa(dB,bool,it,t3)) | ~spl38_7),
% 1.94/0.67 inference(avatar_component_clause,[],[f587])).
% 1.94/0.67 tff(f3167,plain,(
% 1.94/0.67 spl38_248 | ~spl38_11 | ~spl38_32),
% 1.94/0.67 inference(avatar_split_clause,[],[f729,f726,f606,f3165])).
% 1.94/0.67 tff(f3165,plain,(
% 1.94/0.67 spl38_248 <=> ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_248])])).
% 1.94/0.67 tff(f729,plain,(
% 1.94/0.67 ( ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1)) ) | (~spl38_11 | ~spl38_32)),
% 1.94/0.67 inference(superposition,[],[f727,f607])).
% 1.94/0.67 tff(f3130,plain,(
% 1.94/0.67 spl38_247 | ~spl38_42 | ~spl38_122),
% 1.94/0.67 inference(avatar_split_clause,[],[f1346,f1343,f775,f3128])).
% 1.94/0.67 tff(f3128,plain,(
% 1.94/0.67 spl38_247 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_247])])).
% 1.94/0.67 tff(f775,plain,(
% 1.94/0.67 spl38_42 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_42])])).
% 1.94/0.67 tff(f1346,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))) ) | (~spl38_42 | ~spl38_122)),
% 1.94/0.67 inference(resolution,[],[f1344,f776])).
% 1.94/0.67 tff(f776,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl38_42),
% 1.94/0.67 inference(avatar_component_clause,[],[f775])).
% 1.94/0.67 tff(f3126,plain,(
% 1.94/0.67 spl38_246 | ~spl38_53 | ~spl38_118),
% 1.94/0.67 inference(avatar_split_clause,[],[f1309,f1213,f837,f3124])).
% 1.94/0.67 tff(f3124,plain,(
% 1.94/0.67 spl38_246 <=> ! [X2 : dB,X0 : dB,X1 : fun(dB,dB)] : abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_246])])).
% 1.94/0.67 tff(f1309,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : dB,X1 : fun(dB,dB)] : (abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)) ) | (~spl38_53 | ~spl38_118)),
% 1.94/0.67 inference(superposition,[],[f838,f1214])).
% 1.94/0.67 tff(f3122,plain,(
% 1.94/0.67 spl38_245 | ~spl38_54 | ~spl38_118),
% 1.94/0.67 inference(avatar_split_clause,[],[f1308,f1213,f841,f3120])).
% 1.94/0.67 tff(f3120,plain,(
% 1.94/0.67 spl38_245 <=> ! [X2 : nat,X0 : dB,X1 : fun(dB,dB)] : var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_245])])).
% 1.94/0.67 tff(f1308,plain,(
% 1.94/0.67 ( ! [X2 : nat,X0 : dB,X1 : fun(dB,dB)] : (var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0)) ) | (~spl38_54 | ~spl38_118)),
% 1.94/0.67 inference(superposition,[],[f842,f1214])).
% 1.94/0.67 tff(f3118,plain,(
% 1.94/0.67 spl38_244 | ~spl38_53 | ~spl38_96),
% 1.94/0.67 inference(avatar_split_clause,[],[f1085,f1072,f837,f3116])).
% 1.94/0.67 tff(f3116,plain,(
% 1.94/0.67 spl38_244 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_244])])).
% 1.94/0.67 tff(f1085,plain,(
% 1.94/0.67 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl38_53 | ~spl38_96)),
% 1.94/0.67 inference(superposition,[],[f838,f1073])).
% 1.94/0.67 tff(f3114,plain,(
% 1.94/0.67 spl38_243 | ~spl38_54 | ~spl38_96),
% 1.94/0.67 inference(avatar_split_clause,[],[f1084,f1072,f841,f3112])).
% 1.94/0.67 tff(f3112,plain,(
% 1.94/0.67 spl38_243 <=> ! [X2 : nat,X0 : dB,X1 : dB] : var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_243])])).
% 1.94/0.67 tff(f1084,plain,(
% 1.94/0.67 ( ! [X2 : nat,X0 : dB,X1 : dB] : (var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl38_54 | ~spl38_96)),
% 1.94/0.67 inference(superposition,[],[f842,f1073])).
% 1.94/0.67 tff(f3110,plain,(
% 1.94/0.67 spl38_242 | ~spl38_29 | ~spl38_70),
% 1.94/0.67 inference(avatar_split_clause,[],[f935,f931,f705,f3107])).
% 1.94/0.67 tff(f3107,plain,(
% 1.94/0.67 spl38_242 <=> sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_242])])).
% 1.94/0.67 tff(f931,plain,(
% 1.94/0.67 spl38_70 <=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_70])])).
% 1.94/0.67 tff(f935,plain,(
% 1.94/0.67 sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | (~spl38_29 | ~spl38_70)),
% 1.94/0.67 inference(resolution,[],[f933,f706])).
% 1.94/0.67 tff(f933,plain,(
% 1.94/0.67 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | ~spl38_70),
% 1.94/0.67 inference(avatar_component_clause,[],[f931])).
% 1.94/0.67 tff(f3105,plain,(
% 1.94/0.67 spl38_241 | ~spl38_29 | ~spl38_65),
% 1.94/0.67 inference(avatar_split_clause,[],[f915,f894,f705,f3103])).
% 1.94/0.67 tff(f3103,plain,(
% 1.94/0.67 spl38_241 <=> ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(subst(X0,var(X1),X2))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_241])])).
% 1.94/0.67 tff(f915,plain,(
% 1.94/0.67 ( ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(subst(X0,var(X1),X2)))) ) | (~spl38_29 | ~spl38_65)),
% 1.94/0.67 inference(resolution,[],[f895,f706])).
% 1.94/0.67 tff(f3101,plain,(
% 1.94/0.67 spl38_240 | ~spl38_29 | ~spl38_62),
% 1.94/0.67 inference(avatar_split_clause,[],[f912,f881,f705,f3099])).
% 1.94/0.67 tff(f3099,plain,(
% 1.94/0.67 spl38_240 <=> ! [X0 : list(dB),X1 : nat] : (~listsp(dB,it,X0) | sP1(abs(foldl(dB,dB,app,var(X1),X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_240])])).
% 1.94/0.67 tff(f881,plain,(
% 1.94/0.67 spl38_62 <=> ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_62])])).
% 1.94/0.67 tff(f912,plain,(
% 1.94/0.67 ( ! [X0 : list(dB),X1 : nat] : (~listsp(dB,it,X0) | sP1(abs(foldl(dB,dB,app,var(X1),X0)))) ) | (~spl38_29 | ~spl38_62)),
% 1.94/0.67 inference(resolution,[],[f882,f706])).
% 1.94/0.67 tff(f882,plain,(
% 1.94/0.67 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) ) | ~spl38_62),
% 1.94/0.67 inference(avatar_component_clause,[],[f881])).
% 1.94/0.67 tff(f3097,plain,(
% 1.94/0.67 spl38_239 | ~spl38_29 | ~spl38_59),
% 1.94/0.67 inference(avatar_split_clause,[],[f909,f865,f705,f3095])).
% 1.94/0.67 tff(f3095,plain,(
% 1.94/0.67 spl38_239 <=> ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(abs(sK7(X0))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_239])])).
% 1.94/0.67 tff(f865,plain,(
% 1.94/0.67 spl38_59 <=> ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | listsp(dB,it,sK8(X0)) | ~sP1(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_59])])).
% 1.94/0.67 tff(f909,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(abs(sK7(X0)))) ) | (~spl38_29 | ~spl38_59)),
% 1.94/0.67 inference(resolution,[],[f866,f706])).
% 1.94/0.67 tff(f866,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK7(X0))) | sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0)) ) | ~spl38_59),
% 1.94/0.67 inference(avatar_component_clause,[],[f865])).
% 1.94/0.67 tff(f3093,plain,(
% 1.94/0.67 spl38_172 | ~spl38_238 | ~spl38_227),
% 1.94/0.67 inference(avatar_split_clause,[],[f3025,f2860,f3090,f1798])).
% 1.94/0.67 tff(f1798,plain,(
% 1.94/0.67 spl38_172 <=> ! [X0 : bool] : fTrue = X0),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_172])])).
% 1.94/0.67 tff(f3025,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fTrue != aa(dB,bool,it,subst(a,u,i)) | fTrue = X0) ) | ~spl38_227),
% 1.94/0.67 inference(equality_factoring,[],[f2861])).
% 1.94/0.67 tff(f3088,plain,(
% 1.94/0.67 spl38_237 | ~spl38_32 | ~spl38_45),
% 1.94/0.67 inference(avatar_split_clause,[],[f805,f789,f726,f3086])).
% 1.94/0.67 tff(f3086,plain,(
% 1.94/0.67 spl38_237 <=> ! [X2 : type,X0 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_237])])).
% 1.94/0.67 tff(f789,plain,(
% 1.94/0.67 spl38_45 <=> ! [X2 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_45])])).
% 1.94/0.67 tff(f805,plain,(
% 1.94/0.67 ( ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))) ) | (~spl38_32 | ~spl38_45)),
% 1.94/0.67 inference(superposition,[],[f790,f727])).
% 1.94/0.67 tff(f790,plain,(
% 1.94/0.67 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) ) | ~spl38_45),
% 1.94/0.67 inference(avatar_component_clause,[],[f789])).
% 1.94/0.67 tff(f3057,plain,(
% 1.94/0.67 spl38_236 | ~spl38_53 | ~spl38_116),
% 1.94/0.67 inference(avatar_split_clause,[],[f1258,f1205,f837,f3055])).
% 1.94/0.67 tff(f3055,plain,(
% 1.94/0.67 spl38_236 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : dB] : abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_236])])).
% 1.94/0.67 tff(f1258,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : list(dB)] : (abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl38_53 | ~spl38_116)),
% 1.94/0.67 inference(superposition,[],[f838,f1206])).
% 1.94/0.67 tff(f3053,plain,(
% 1.94/0.67 spl38_235 | ~spl38_54 | ~spl38_116),
% 1.94/0.67 inference(avatar_split_clause,[],[f1257,f1205,f841,f3051])).
% 1.94/0.67 tff(f3051,plain,(
% 1.94/0.67 spl38_235 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : nat] : var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_235])])).
% 1.94/0.67 tff(f1257,plain,(
% 1.94/0.67 ( ! [X2 : dB,X3 : nat,X0 : dB,X1 : list(dB)] : (var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl38_54 | ~spl38_116)),
% 1.94/0.67 inference(superposition,[],[f842,f1206])).
% 1.94/0.67 tff(f3049,plain,(
% 1.94/0.67 spl38_234 | ~spl38_21 | ~spl38_70),
% 1.94/0.67 inference(avatar_split_clause,[],[f936,f931,f659,f3046])).
% 1.94/0.67 tff(f3046,plain,(
% 1.94/0.67 spl38_234 <=> sP1(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_234])])).
% 1.94/0.67 tff(f936,plain,(
% 1.94/0.67 sP1(aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)) | (~spl38_21 | ~spl38_70)),
% 1.94/0.67 inference(resolution,[],[f933,f660])).
% 1.94/0.67 tff(f3044,plain,(
% 1.94/0.67 spl38_233 | ~spl38_21 | ~spl38_65),
% 1.94/0.67 inference(avatar_split_clause,[],[f916,f894,f659,f3042])).
% 1.94/0.67 tff(f3042,plain,(
% 1.94/0.67 spl38_233 <=> ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(subst(X0,var(X1),X2)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_233])])).
% 1.94/0.67 tff(f916,plain,(
% 1.94/0.67 ( ! [X2 : nat,X0 : dB,X1 : nat] : (~pp(aa(dB,bool,it,X0)) | sP1(subst(X0,var(X1),X2))) ) | (~spl38_21 | ~spl38_65)),
% 1.94/0.67 inference(resolution,[],[f895,f660])).
% 1.94/0.67 tff(f2907,plain,(
% 1.94/0.67 spl38_232 | ~spl38_21 | ~spl38_59),
% 1.94/0.67 inference(avatar_split_clause,[],[f910,f865,f659,f2905])).
% 1.94/0.67 tff(f2905,plain,(
% 1.94/0.67 spl38_232 <=> ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(sK7(X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_232])])).
% 1.94/0.67 tff(f910,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP0(X0) | listsp(dB,it,sK8(X0)) | ~sP1(X0) | sP1(sK7(X0))) ) | (~spl38_21 | ~spl38_59)),
% 1.94/0.67 inference(resolution,[],[f866,f660])).
% 1.94/0.67 tff(f2880,plain,(
% 1.94/0.67 spl38_231 | ~spl38_32 | ~spl38_66 | ~spl38_138),
% 1.94/0.67 inference(avatar_split_clause,[],[f1469,f1463,f898,f726,f2877])).
% 1.94/0.67 tff(f2877,plain,(
% 1.94/0.67 spl38_231 <=> t = foldr(type,type,fun1,cons(type,sK5,ts),t1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_231])])).
% 1.94/0.67 tff(f898,plain,(
% 1.94/0.67 spl38_66 <=> ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_66])])).
% 1.94/0.67 tff(f1463,plain,(
% 1.94/0.67 spl38_138 <=> pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_138])])).
% 1.94/0.67 tff(f1469,plain,(
% 1.94/0.67 t = foldr(type,type,fun1,cons(type,sK5,ts),t1) | (~spl38_32 | ~spl38_66 | ~spl38_138)),
% 1.94/0.67 inference(forward_demodulation,[],[f1467,f727])).
% 1.94/0.67 tff(f1467,plain,(
% 1.94/0.67 foldr(type,type,fun1,cons(type,sK5,ts),t1) = aa(nat,type,shift(type,e,i,t),i) | (~spl38_66 | ~spl38_138)),
% 1.94/0.67 inference(resolution,[],[f1465,f899])).
% 1.94/0.67 tff(f899,plain,(
% 1.94/0.67 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (~pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) = X0) ) | ~spl38_66),
% 1.94/0.67 inference(avatar_component_clause,[],[f898])).
% 1.94/0.67 tff(f1465,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t1))) | ~spl38_138),
% 1.94/0.67 inference(avatar_component_clause,[],[f1463])).
% 1.94/0.67 tff(f2875,plain,(
% 1.94/0.67 spl38_230 | ~spl38_73 | ~spl38_116),
% 1.94/0.67 inference(avatar_split_clause,[],[f1247,f1205,f947,f2872])).
% 1.94/0.67 tff(f2872,plain,(
% 1.94/0.67 spl38_230 <=> t = foldr(type,type,fun1,cons(type,t2,ts),t1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_230])])).
% 1.94/0.67 tff(f1247,plain,(
% 1.94/0.67 t = foldr(type,type,fun1,cons(type,t2,ts),t1) | (~spl38_73 | ~spl38_116)),
% 1.94/0.67 inference(superposition,[],[f1206,f949])).
% 1.94/0.67 tff(f2870,plain,(
% 1.94/0.67 spl38_229 | ~spl38_61 | ~spl38_81),
% 1.94/0.67 inference(avatar_split_clause,[],[f999,f982,f874,f2868])).
% 1.94/0.67 tff(f2868,plain,(
% 1.94/0.67 spl38_229 <=> ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP4(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_229])])).
% 1.94/0.67 tff(f874,plain,(
% 1.94/0.67 spl38_61 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_61])])).
% 1.94/0.67 tff(f999,plain,(
% 1.94/0.67 ( ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP4(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1)) ) | (~spl38_61 | ~spl38_81)),
% 1.94/0.67 inference(resolution,[],[f983,f875])).
% 1.94/0.67 tff(f875,plain,(
% 1.94/0.67 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_61),
% 1.94/0.67 inference(avatar_component_clause,[],[f874])).
% 1.94/0.67 tff(f2866,plain,(
% 1.94/0.67 spl38_228 | ~spl38_12 | ~spl38_56),
% 1.94/0.67 inference(avatar_split_clause,[],[f856,f849,f617,f2864])).
% 1.94/0.67 tff(f2864,plain,(
% 1.94/0.67 spl38_228 <=> ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | as = X1)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_228])])).
% 1.94/0.67 tff(f849,plain,(
% 1.94/0.67 spl38_56 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : list(X0),X1 : list(X0)] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_56])])).
% 1.94/0.67 tff(f856,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | as = X1) ) | (~spl38_12 | ~spl38_56)),
% 1.94/0.67 inference(superposition,[],[f850,f619])).
% 1.94/0.67 tff(f850,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X1 = X3) ) | ~spl38_56),
% 1.94/0.67 inference(avatar_component_clause,[],[f849])).
% 1.94/0.67 tff(f2862,plain,(
% 1.94/0.67 spl38_227 | ~spl38_3 | spl38_4 | ~spl38_223),
% 1.94/0.67 inference(avatar_split_clause,[],[f2542,f2285,f574,f569,f2860])).
% 1.94/0.67 tff(f2542,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (~pp(fTrue) | aa(dB,bool,it,subst(a,u,i)) = X0 | fTrue = X0) ) | (spl38_4 | ~spl38_223)),
% 1.94/0.67 inference(superposition,[],[f576,f2286])).
% 1.94/0.67 tff(f2858,plain,(
% 1.94/0.67 spl38_226 | ~spl38_11 | ~spl38_23),
% 1.94/0.67 inference(avatar_split_clause,[],[f693,f667,f606,f2856])).
% 1.94/0.67 tff(f2856,plain,(
% 1.94/0.67 spl38_226 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = aa(bool,bool,combi(bool),X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_226])])).
% 1.94/0.67 tff(f693,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fFalse = X0 | fTrue = aa(bool,bool,combi(bool),X0)) ) | (~spl38_11 | ~spl38_23)),
% 1.94/0.67 inference(superposition,[],[f668,f607])).
% 1.94/0.67 tff(f2831,plain,(
% 1.94/0.67 spl38_225 | ~spl38_12 | ~spl38_43),
% 1.94/0.67 inference(avatar_split_clause,[],[f802,f780,f617,f2829])).
% 1.94/0.67 tff(f2829,plain,(
% 1.94/0.67 spl38_225 <=> ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | a = X0)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_225])])).
% 1.94/0.67 tff(f780,plain,(
% 1.94/0.67 spl38_43 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_43])])).
% 1.94/0.67 tff(f802,plain,(
% 1.94/0.67 ( ! [X0 : dB,X1 : list(dB)] : (rs != cons(dB,X0,X1) | a = X0) ) | (~spl38_12 | ~spl38_43)),
% 1.94/0.67 inference(superposition,[],[f781,f619])).
% 1.94/0.67 tff(f781,plain,(
% 1.94/0.67 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X2 = X4) ) | ~spl38_43),
% 1.94/0.67 inference(avatar_component_clause,[],[f780])).
% 1.94/0.67 tff(f2827,plain,(
% 1.94/0.67 spl38_224 | ~spl38_29 | ~spl38_40),
% 1.94/0.67 inference(avatar_split_clause,[],[f799,f766,f705,f2825])).
% 1.94/0.67 tff(f766,plain,(
% 1.94/0.67 spl38_40 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_40])])).
% 1.94/0.67 tff(f799,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (~pp(aa(dB,bool,it,X0)) | sP1(abs(abs(X0)))) ) | (~spl38_29 | ~spl38_40)),
% 1.94/0.67 inference(resolution,[],[f767,f706])).
% 1.94/0.67 tff(f767,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0))) ) | ~spl38_40),
% 1.94/0.67 inference(avatar_component_clause,[],[f766])).
% 1.94/0.67 tff(f2287,plain,(
% 1.94/0.67 spl38_223 | ~spl38_11),
% 1.94/0.67 inference(avatar_split_clause,[],[f609,f606,f2285])).
% 1.94/0.67 tff(f609,plain,(
% 1.94/0.67 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl38_11),
% 1.94/0.67 inference(superposition,[],[f607,f607])).
% 1.94/0.67 tff(f2277,plain,(
% 1.94/0.67 spl38_222),
% 1.94/0.67 inference(avatar_split_clause,[],[f471,f2275])).
% 1.94/0.67 tff(f2275,plain,(
% 1.94/0.67 spl38_222 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_222])])).
% 1.94/0.67 tff(f471,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f323])).
% 1.94/0.67 tff(f323,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(nnf_transformation,[],[f177])).
% 1.94/0.67 tff(f177,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f85])).
% 1.94/0.67 tff(f85,axiom,(
% 1.94/0.67 ! [X55 : list(type),X54 : list(dB),X15 : dB,X14 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X14,cons(dB,X15,X54)),X55)) <=> 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,X15))),typings(X14,X54)),X55)))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_typings_Osimps_I2_J)).
% 1.94/0.67 tff(f2266,plain,(
% 1.94/0.67 spl38_221),
% 1.94/0.67 inference(avatar_split_clause,[],[f470,f2264])).
% 1.94/0.67 tff(f2264,plain,(
% 1.94/0.67 spl38_221 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_221])])).
% 1.94/0.67 tff(f470,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f323])).
% 1.94/0.67 tff(f2198,plain,(
% 1.94/0.67 spl38_220),
% 1.94/0.67 inference(avatar_split_clause,[],[f552,f2196])).
% 1.94/0.67 tff(f2196,plain,(
% 1.94/0.67 spl38_220 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_220])])).
% 1.94/0.67 tff(f552,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(forward_demodulation,[],[f506,f503])).
% 1.94/0.67 tff(f503,plain,(
% 1.94/0.67 ( ! [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)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f194])).
% 1.94/0.67 tff(f194,plain,(
% 1.94/0.67 ! [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)),
% 1.94/0.67 inference(rectify,[],[f67])).
% 1.94/0.67 tff(f67,axiom,(
% 1.94/0.67 ! [X0 : $tType,X1 : $tType,X67 : list(X1),X37 : X1,X64 : X0,X68 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X68,X64,cons(X1,X37,X67)) = foldl(X0,X1,X68,aa(X1,X0,aa(X0,fun(X1,X0),X68,X64),X37),X67)),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_foldl__Cons)).
% 1.94/0.67 tff(f506,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f341])).
% 1.94/0.67 tff(f341,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f251,f340])).
% 1.94/0.67 tff(f340,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f251,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(ennf_transformation,[],[f197])).
% 1.94/0.67 tff(f197,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(rectify,[],[f97])).
% 1.94/0.67 tff(f97,axiom,(
% 1.94/0.67 ! [X1 : $tType,X0 : $tType,X37 : X0,X67 : list(X0),X39 : X1,X68 : fun(X1,fun(X0,X1))] : (! [X75 : X0,X92 : X0,X83 : X1] : aa(X0,X1,aa(X1,fun(X0,X1),X68,aa(X0,X1,aa(X1,fun(X0,X1),X68,X83),X75)),X92) = aa(X0,X1,aa(X1,fun(X0,X1),X68,aa(X0,X1,aa(X1,fun(X0,X1),X68,X83),X92)),X75) => aa(X0,X1,aa(X1,fun(X0,X1),X68,foldl(X1,X0,X68,X39,X67)),X37) = foldl(X1,X0,X68,aa(X0,X1,aa(X1,fun(X0,X1),X68,X39),X37),X67))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_foldl__fun__comm)).
% 1.94/0.67 tff(f2189,plain,(
% 1.94/0.67 spl38_219 | ~spl38_96 | ~spl38_218),
% 1.94/0.67 inference(avatar_split_clause,[],[f2185,f2179,f1072,f2187])).
% 1.94/0.67 tff(f2187,plain,(
% 1.94/0.67 spl38_219 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_219])])).
% 1.94/0.67 tff(f2179,plain,(
% 1.94/0.67 spl38_218 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_218])])).
% 1.94/0.67 tff(f2185,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_218)),
% 1.94/0.67 inference(forward_demodulation,[],[f2184,f1073])).
% 1.94/0.67 tff(f2184,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_218)),
% 1.94/0.67 inference(forward_demodulation,[],[f2183,f1073])).
% 1.94/0.67 tff(f2183,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_218)),
% 1.94/0.67 inference(forward_demodulation,[],[f2182,f1073])).
% 1.94/0.67 tff(f2182,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_218)),
% 1.94/0.67 inference(forward_demodulation,[],[f2180,f1073])).
% 1.94/0.67 tff(f2180,plain,(
% 1.94/0.67 ( ! [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_218),
% 1.94/0.67 inference(avatar_component_clause,[],[f2179])).
% 1.94/0.67 tff(f2181,plain,(
% 1.94/0.67 spl38_218),
% 1.94/0.67 inference(avatar_split_clause,[],[f448,f2179])).
% 1.94/0.67 tff(f448,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f311])).
% 1.94/0.67 tff(f311,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f308,f310,f309])).
% 1.94/0.67 tff(f309,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f310,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f308,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f266])).
% 1.94/0.67 tff(f266,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(definition_folding,[],[f229,f265])).
% 1.94/0.67 tff(f265,plain,(
% 1.94/0.67 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP3(X2,X0,X1))),
% 1.94/0.67 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])).
% 1.94/0.67 tff(f229,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f228])).
% 1.94/0.67 tff(f228,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f163])).
% 1.94/0.67 tff(f163,plain,(
% 1.94/0.67 ! [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))))))),
% 1.94/0.67 inference(rectify,[],[f89])).
% 1.94/0.67 tff(f89,axiom,(
% 1.94/0.67 ! [X36 : dB,X18 : dB,X22 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X18)),X36)) => (! [X83 : dB] : (subst(X83,X18,zero_zero(nat)) = X36 => abs(X83) != X22) => (! [X80 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X80),X18) = X36 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X22),X80))) => ~! [X80 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X80) = X36 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X18),X80))))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_beta__cases_I3_J)).
% 1.94/0.67 tff(f2172,plain,(
% 1.94/0.67 spl38_217 | ~spl38_96 | ~spl38_216),
% 1.94/0.67 inference(avatar_split_clause,[],[f2168,f2162,f1072,f2170])).
% 1.94/0.67 tff(f2170,plain,(
% 1.94/0.67 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 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_217])])).
% 1.94/0.67 tff(f2162,plain,(
% 1.94/0.67 spl38_216 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_216])])).
% 1.94/0.67 tff(f2168,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_216)),
% 1.94/0.67 inference(forward_demodulation,[],[f2167,f1073])).
% 1.94/0.67 tff(f2167,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_216)),
% 1.94/0.67 inference(forward_demodulation,[],[f2166,f1073])).
% 1.94/0.67 tff(f2166,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_216)),
% 1.94/0.67 inference(forward_demodulation,[],[f2165,f1073])).
% 1.94/0.67 tff(f2165,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_216)),
% 1.94/0.67 inference(forward_demodulation,[],[f2163,f1073])).
% 1.94/0.67 tff(f2163,plain,(
% 1.94/0.67 ( ! [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_216),
% 1.94/0.67 inference(avatar_component_clause,[],[f2162])).
% 1.94/0.67 tff(f2164,plain,(
% 1.94/0.67 spl38_216),
% 1.94/0.67 inference(avatar_split_clause,[],[f450,f2162])).
% 1.94/0.67 tff(f450,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f311])).
% 1.94/0.67 tff(f2155,plain,(
% 1.94/0.67 spl38_215 | ~spl38_8 | ~spl38_13),
% 1.94/0.67 inference(avatar_split_clause,[],[f1495,f622,f592,f2152])).
% 1.94/0.67 tff(f2152,plain,(
% 1.94/0.67 spl38_215 <=> aa(dB,bool,it,ua) = fTrue),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_215])])).
% 1.94/0.67 tff(f1495,plain,(
% 1.94/0.67 aa(dB,bool,it,ua) = fTrue | (~spl38_8 | ~spl38_13)),
% 1.94/0.67 inference(resolution,[],[f623,f594])).
% 1.94/0.67 tff(f2150,plain,(
% 1.94/0.67 spl38_214 | ~spl38_96 | ~spl38_213),
% 1.94/0.67 inference(avatar_split_clause,[],[f2146,f2140,f1072,f2148])).
% 1.94/0.67 tff(f2148,plain,(
% 1.94/0.67 spl38_214 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_214])])).
% 1.94/0.67 tff(f2140,plain,(
% 1.94/0.67 spl38_213 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_213])])).
% 1.94/0.67 tff(f2146,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_213)),
% 1.94/0.67 inference(forward_demodulation,[],[f2145,f1073])).
% 1.94/0.67 tff(f2145,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_213)),
% 1.94/0.67 inference(forward_demodulation,[],[f2144,f1073])).
% 1.94/0.67 tff(f2144,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_213)),
% 1.94/0.67 inference(forward_demodulation,[],[f2143,f1073])).
% 1.94/0.67 tff(f2143,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_213)),
% 1.94/0.67 inference(forward_demodulation,[],[f2141,f1073])).
% 1.94/0.67 tff(f2141,plain,(
% 1.94/0.67 ( ! [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_213),
% 1.94/0.67 inference(avatar_component_clause,[],[f2140])).
% 1.94/0.67 tff(f2142,plain,(
% 1.94/0.67 spl38_213),
% 1.94/0.67 inference(avatar_split_clause,[],[f449,f2140])).
% 1.94/0.67 tff(f449,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f311])).
% 1.94/0.67 tff(f2133,plain,(
% 1.94/0.67 spl38_212 | ~spl38_96 | ~spl38_211),
% 1.94/0.67 inference(avatar_split_clause,[],[f2129,f2123,f1072,f2131])).
% 1.94/0.67 tff(f2131,plain,(
% 1.94/0.67 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)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK25(X0,X1,X2)),X1)) | sP3(X2,X0,X1))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_212])])).
% 1.94/0.67 tff(f2123,plain,(
% 1.94/0.67 spl38_211 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_211])])).
% 1.94/0.67 tff(f2129,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_211)),
% 1.94/0.67 inference(forward_demodulation,[],[f2128,f1073])).
% 1.94/0.67 tff(f2128,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_211)),
% 1.94/0.67 inference(forward_demodulation,[],[f2127,f1073])).
% 1.94/0.67 tff(f2127,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_211)),
% 1.94/0.67 inference(forward_demodulation,[],[f2126,f1073])).
% 1.94/0.67 tff(f2126,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_211)),
% 1.94/0.67 inference(forward_demodulation,[],[f2124,f1073])).
% 1.94/0.67 tff(f2124,plain,(
% 1.94/0.67 ( ! [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_211),
% 1.94/0.67 inference(avatar_component_clause,[],[f2123])).
% 1.94/0.67 tff(f2125,plain,(
% 1.94/0.67 spl38_211),
% 1.94/0.67 inference(avatar_split_clause,[],[f451,f2123])).
% 1.94/0.67 tff(f451,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f311])).
% 1.94/0.67 tff(f2116,plain,(
% 1.94/0.67 spl38_210),
% 1.94/0.67 inference(avatar_split_clause,[],[f519,f2114])).
% 1.94/0.67 tff(f2114,plain,(
% 1.94/0.67 spl38_210 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_210])])).
% 1.94/0.67 tff(f519,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f347])).
% 1.94/0.67 tff(f347,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f259,f346])).
% 1.94/0.67 tff(f346,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f259,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f258])).
% 1.94/0.67 tff(f258,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f202])).
% 1.94/0.67 tff(f202,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f55])).
% 1.94/0.67 tff(f55,axiom,(
% 1.94/0.67 ! [X20 : type,X55 : list(type),X12 : type,X56 : list(dB),X54 : list(dB),X13 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,foldl(dB,dB,app,var(X13),X54),X56)),X12)) => (pp(aa(list(type),bool,typings(X14,X54),X55)) => (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X13),X54)),X20)) => ? [X57 : list(type)] : (pp(aa(list(type),bool,typings(X14,X56),X57)) & foldr(type,type,fun1,X57,X12) = X20))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_var__app__types)).
% 1.94/0.67 tff(f2107,plain,(
% 1.94/0.67 spl38_209),
% 1.94/0.67 inference(avatar_split_clause,[],[f518,f2105])).
% 1.94/0.67 tff(f2105,plain,(
% 1.94/0.67 spl38_209 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_209])])).
% 1.94/0.67 tff(f518,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f347])).
% 1.94/0.67 tff(f2103,plain,(
% 1.94/0.67 spl38_208 | ~spl38_9 | ~spl38_13),
% 1.94/0.67 inference(avatar_split_clause,[],[f1494,f622,f597,f2100])).
% 1.94/0.67 tff(f1494,plain,(
% 1.94/0.67 aa(dB,bool,it,u) = fTrue | (~spl38_9 | ~spl38_13)),
% 1.94/0.67 inference(resolution,[],[f623,f599])).
% 1.94/0.67 tff(f2098,plain,(
% 1.94/0.67 spl38_207),
% 1.94/0.67 inference(avatar_split_clause,[],[f557,f2096])).
% 1.94/0.67 tff(f2096,plain,(
% 1.94/0.67 spl38_207 <=> ! [X5 : type,X3 : fun(nat,type),X4 : dB,X0 : dB,X6 : type,X2 : nat,X1 : type] : (t != 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_207])])).
% 1.94/0.67 tff(f557,plain,(
% 1.94/0.67 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (t != 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))) )),
% 1.94/0.67 inference(forward_demodulation,[],[f517,f500])).
% 1.94/0.67 tff(f500,plain,(
% 1.94/0.67 ( ! [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)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f191])).
% 1.94/0.67 tff(f191,plain,(
% 1.94/0.67 ! [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)),
% 1.94/0.67 inference(rectify,[],[f104])).
% 1.94/0.67 tff(f104,axiom,(
% 1.94/0.67 ! [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)),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 1.94/0.67 tff(f517,plain,(
% 1.94/0.67 ( ! [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)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f257])).
% 1.94/0.67 tff(f257,plain,(
% 1.94/0.67 ! [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)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.94/0.67 inference(flattening,[],[f256])).
% 1.94/0.67 tff(f256,plain,(
% 1.94/0.67 ! [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))) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.94/0.67 inference(ennf_transformation,[],[f201])).
% 1.94/0.67 tff(f201,plain,(
% 1.94/0.67 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (t = 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))))))))),
% 1.94/0.67 inference(rectify,[],[f11])).
% 1.94/0.67 tff(f11,axiom,(
% 1.94/0.67 ! [X11 : dB,X12 : type,X13 : nat,X14 : fun(nat,type),X15 : dB,X16 : type,X17 : type] : (t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) => (pp(aa(dB,bool,it,X15)) => (pp(aa(type,bool,typing(shift(type,X14,X13,X16),X15),X12)) => (pp(aa(dB,bool,it,X11)) => (pp(aa(type,bool,typing(X14,X11),X16)) => pp(aa(dB,bool,it,subst(X15,X11,X13))))))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_MI2)).
% 1.94/0.67 tff(f2094,plain,(
% 1.94/0.67 spl38_206),
% 1.94/0.67 inference(avatar_split_clause,[],[f556,f2092])).
% 1.94/0.67 tff(f2092,plain,(
% 1.94/0.67 spl38_206 <=> ! [X5 : type,X3 : fun(nat,type),X4 : dB,X0 : dB,X6 : type,X2 : nat,X1 : type] : (t != 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_206])])).
% 1.94/0.67 tff(f556,plain,(
% 1.94/0.67 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (t != 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))) )),
% 1.94/0.67 inference(forward_demodulation,[],[f516,f500])).
% 1.94/0.67 tff(f516,plain,(
% 1.94/0.67 ( ! [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)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f255])).
% 1.94/0.67 tff(f255,plain,(
% 1.94/0.67 ! [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)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.94/0.67 inference(flattening,[],[f254])).
% 1.94/0.67 tff(f254,plain,(
% 1.94/0.67 ! [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))) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 1.94/0.67 inference(ennf_transformation,[],[f200])).
% 1.94/0.67 tff(f200,plain,(
% 1.94/0.67 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (t = 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))))))))),
% 1.94/0.67 inference(rectify,[],[f10])).
% 1.94/0.67 tff(f10,axiom,(
% 1.94/0.67 ! [X11 : dB,X12 : type,X13 : nat,X14 : fun(nat,type),X15 : dB,X16 : type,X17 : type] : (t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) => (pp(aa(dB,bool,it,X15)) => (pp(aa(type,bool,typing(shift(type,X14,X13,X17),X15),X12)) => (pp(aa(dB,bool,it,X11)) => (pp(aa(type,bool,typing(X14,X11),X17)) => pp(aa(dB,bool,it,subst(X15,X11,X13))))))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_MI1)).
% 1.94/0.67 tff(f2076,plain,(
% 1.94/0.67 spl38_205 | ~spl38_96 | ~spl38_204),
% 1.94/0.67 inference(avatar_split_clause,[],[f2072,f2066,f1072,f2074])).
% 1.94/0.67 tff(f2066,plain,(
% 1.94/0.67 spl38_204 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_204])])).
% 1.94/0.67 tff(f2072,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_204)),
% 1.94/0.67 inference(forward_demodulation,[],[f2071,f1073])).
% 1.94/0.67 tff(f2071,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_204)),
% 1.94/0.67 inference(forward_demodulation,[],[f2070,f1073])).
% 1.94/0.67 tff(f2070,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_204)),
% 1.94/0.67 inference(forward_demodulation,[],[f2069,f1073])).
% 1.94/0.67 tff(f2069,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_204)),
% 1.94/0.67 inference(forward_demodulation,[],[f2067,f1073])).
% 1.94/0.67 tff(f2067,plain,(
% 1.94/0.67 ( ! [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_204),
% 1.94/0.67 inference(avatar_component_clause,[],[f2066])).
% 1.94/0.67 tff(f2068,plain,(
% 1.94/0.67 spl38_204),
% 1.94/0.67 inference(avatar_split_clause,[],[f424,f2066])).
% 1.94/0.67 tff(f424,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f149])).
% 1.94/0.67 tff(f149,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(rectify,[],[f27])).
% 1.94/0.67 tff(f27,axiom,(
% 1.94/0.67 ! [X23 : nat,X18 : dB,X22 : dB] : aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X18)),X23) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X22),X23)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X18),X23))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_lift_Osimps_I2_J)).
% 1.94/0.67 tff(f2060,plain,(
% 1.94/0.67 spl38_203),
% 1.94/0.67 inference(avatar_split_clause,[],[f486,f2058])).
% 1.94/0.67 tff(f2058,plain,(
% 1.94/0.67 spl38_203 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_203])])).
% 1.94/0.67 tff(f486,plain,(
% 1.94/0.67 ( ! [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)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f333])).
% 1.94/0.67 tff(f333,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f332])).
% 1.94/0.67 tff(f332,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(nnf_transformation,[],[f182])).
% 1.94/0.67 tff(f182,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f77])).
% 1.94/0.67 tff(f77,axiom,(
% 1.94/0.67 ! [X0 : $tType,X76 : fun(X0,bool),X77 : fun(X0,bool),X78 : 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),X77),X76),X78) <=> (listsp(X0,X76,X78) & listsp(X0,X77,X78)))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_listsp__conj__eq)).
% 1.94/0.67 tff(f2047,plain,(
% 1.94/0.67 spl38_202 | ~spl38_96 | ~spl38_200),
% 1.94/0.67 inference(avatar_split_clause,[],[f2038,f2034,f1072,f2045])).
% 1.94/0.67 tff(f2045,plain,(
% 1.94/0.67 spl38_202 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_202])])).
% 1.94/0.67 tff(f2034,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_200])])).
% 1.94/0.67 tff(f2038,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_200)),
% 1.94/0.67 inference(forward_demodulation,[],[f2037,f1073])).
% 1.94/0.67 tff(f2037,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_200)),
% 1.94/0.67 inference(forward_demodulation,[],[f2035,f1073])).
% 1.94/0.67 tff(f2035,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f2034])).
% 1.94/0.67 tff(f2043,plain,(
% 1.94/0.67 spl38_201 | ~spl38_7 | ~spl38_13),
% 1.94/0.67 inference(avatar_split_clause,[],[f1493,f622,f587,f2040])).
% 1.94/0.67 tff(f2040,plain,(
% 1.94/0.67 spl38_201 <=> aa(dB,bool,it,t3) = fTrue),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_201])])).
% 1.94/0.67 tff(f1493,plain,(
% 1.94/0.67 aa(dB,bool,it,t3) = fTrue | (~spl38_7 | ~spl38_13)),
% 1.94/0.67 inference(resolution,[],[f623,f589])).
% 1.94/0.67 tff(f2036,plain,(
% 1.94/0.67 spl38_200),
% 1.94/0.67 inference(avatar_split_clause,[],[f442,f2034])).
% 1.94/0.67 tff(f442,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f301])).
% 1.94/0.67 tff(f301,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f298,f300,f299])).
% 1.94/0.67 tff(f299,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f300,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f298,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f264])).
% 1.94/0.67 tff(f264,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(definition_folding,[],[f226,f263])).
% 1.94/0.67 tff(f263,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 1.94/0.67 tff(f226,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f225])).
% 1.94/0.67 tff(f225,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f161])).
% 1.94/0.67 tff(f161,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 inference(rectify,[],[f91])).
% 1.94/0.67 tff(f91,axiom,(
% 1.94/0.67 ! [X39 : dB,X58 : list(dB),X52 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X52,X58)),X39)) => (! [X84 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X52),X84)) => foldl(dB,dB,app,X84,X58) != X39) => (! [X85 : list(dB)] : (step1(dB,beta,X58,X85) => foldl(dB,dB,app,X52,X85) != X39) => ~! [X80 : dB] : (abs(X80) = X52 => ! [X86 : dB,X87 : list(dB)] : (cons(dB,X86,X87) = X58 => foldl(dB,dB,app,subst(X80,X86,zero_zero(nat)),X87) != X39)))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_apps__betasE)).
% 1.94/0.67 tff(f2024,plain,(
% 1.94/0.67 spl38_199 | ~spl38_96 | ~spl38_198),
% 1.94/0.67 inference(avatar_split_clause,[],[f2020,f2016,f1072,f2022])).
% 1.94/0.67 tff(f2022,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_199])])).
% 1.94/0.67 tff(f2016,plain,(
% 1.94/0.67 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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_198])])).
% 1.94/0.67 tff(f2020,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_198)),
% 1.94/0.67 inference(forward_demodulation,[],[f2019,f1073])).
% 1.94/0.67 tff(f2019,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_198)),
% 1.94/0.67 inference(forward_demodulation,[],[f2017,f1073])).
% 1.94/0.67 tff(f2017,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f2016])).
% 1.94/0.67 tff(f2018,plain,(
% 1.94/0.67 spl38_198),
% 1.94/0.67 inference(avatar_split_clause,[],[f496,f2016])).
% 1.94/0.67 tff(f496,plain,(
% 1.94/0.67 ( ! [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)))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f250])).
% 1.94/0.67 tff(f250,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(flattening,[],[f249])).
% 1.94/0.67 tff(f249,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(ennf_transformation,[],[f189])).
% 1.94/0.67 tff(f189,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f28])).
% 1.94/0.67 tff(f28,axiom,(
% 1.94/0.67 ! [X15 : dB,X20 : type,X12 : type,X39 : dB,X38 : fun(nat,type)] : (pp(aa(type,bool,typing(X38,X39),aa(type,type,aa(type,fun(type,type),fun1,X12),X20))) => (pp(aa(type,bool,typing(X38,X15),X12)) => pp(aa(type,bool,typing(X38,aa(dB,dB,aa(dB,fun(dB,dB),app,X39),X15)),X20))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_App)).
% 1.94/0.67 tff(f2014,plain,(
% 1.94/0.67 spl38_197),
% 1.94/0.67 inference(avatar_split_clause,[],[f485,f2012])).
% 1.94/0.67 tff(f2012,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_197])])).
% 1.94/0.67 tff(f485,plain,(
% 1.94/0.67 ( ! [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)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f333])).
% 1.94/0.67 tff(f2010,plain,(
% 1.94/0.67 spl38_196),
% 1.94/0.67 inference(avatar_split_clause,[],[f484,f2008])).
% 1.94/0.67 tff(f2008,plain,(
% 1.94/0.67 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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_196])])).
% 1.94/0.67 tff(f484,plain,(
% 1.94/0.67 ( ! [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)) )),
% 1.94/0.67 inference(cnf_transformation,[],[f333])).
% 1.94/0.67 tff(f1998,plain,(
% 1.94/0.67 spl38_195 | ~spl38_96 | ~spl38_194),
% 1.94/0.67 inference(avatar_split_clause,[],[f1993,f1989,f1072,f1996])).
% 1.94/0.67 tff(f1996,plain,(
% 1.94/0.67 spl38_195 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_195])])).
% 1.94/0.67 tff(f1989,plain,(
% 1.94/0.67 spl38_194 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_194])])).
% 1.94/0.67 tff(f1993,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_194)),
% 1.94/0.67 inference(forward_demodulation,[],[f1992,f1073])).
% 1.94/0.67 tff(f1992,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_194)),
% 1.94/0.67 inference(forward_demodulation,[],[f1990,f1073])).
% 1.94/0.67 tff(f1990,plain,(
% 1.94/0.67 ( ! [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_194),
% 1.94/0.67 inference(avatar_component_clause,[],[f1989])).
% 1.94/0.67 tff(f1991,plain,(
% 1.94/0.67 spl38_194),
% 1.94/0.67 inference(avatar_split_clause,[],[f440,f1989])).
% 1.94/0.67 tff(f440,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f301])).
% 1.94/0.67 tff(f1983,plain,(
% 1.94/0.67 spl38_193 | ~spl38_96 | ~spl38_192),
% 1.94/0.67 inference(avatar_split_clause,[],[f1979,f1973,f1072,f1981])).
% 1.94/0.67 tff(f1981,plain,(
% 1.94/0.67 spl38_193 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_193])])).
% 1.94/0.67 tff(f1973,plain,(
% 1.94/0.67 spl38_192 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_192])])).
% 1.94/0.67 tff(f1979,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_192)),
% 1.94/0.67 inference(forward_demodulation,[],[f1978,f1073])).
% 1.94/0.67 tff(f1978,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_192)),
% 1.94/0.67 inference(forward_demodulation,[],[f1977,f1073])).
% 1.94/0.67 tff(f1977,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_192)),
% 1.94/0.67 inference(forward_demodulation,[],[f1976,f1073])).
% 1.94/0.67 tff(f1976,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_192)),
% 1.94/0.67 inference(forward_demodulation,[],[f1974,f1073])).
% 1.94/0.67 tff(f1974,plain,(
% 1.94/0.67 ( ! [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_192),
% 1.94/0.67 inference(avatar_component_clause,[],[f1973])).
% 1.94/0.67 tff(f1975,plain,(
% 1.94/0.67 spl38_192),
% 1.94/0.67 inference(avatar_split_clause,[],[f435,f1973])).
% 1.94/0.67 tff(f435,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f222])).
% 1.94/0.67 tff(f222,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f159])).
% 1.94/0.67 tff(f159,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f78])).
% 1.94/0.67 tff(f78,axiom,(
% 1.94/0.67 ! [X36 : dB,X18 : dB,X22 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X22),X18)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X36)),aa(dB,dB,aa(dB,fun(dB,dB),app,X18),X36))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_appL)).
% 1.94/0.67 tff(f1967,plain,(
% 1.94/0.67 spl38_191 | ~spl38_96 | ~spl38_190),
% 1.94/0.67 inference(avatar_split_clause,[],[f1963,f1957,f1072,f1965])).
% 1.94/0.67 tff(f1965,plain,(
% 1.94/0.67 spl38_191 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_191])])).
% 1.94/0.67 tff(f1957,plain,(
% 1.94/0.67 spl38_190 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_190])])).
% 1.94/0.67 tff(f1963,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_190)),
% 1.94/0.67 inference(forward_demodulation,[],[f1962,f1073])).
% 1.94/0.67 tff(f1962,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_190)),
% 1.94/0.67 inference(forward_demodulation,[],[f1961,f1073])).
% 1.94/0.67 tff(f1961,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_190)),
% 1.94/0.67 inference(forward_demodulation,[],[f1960,f1073])).
% 1.94/0.67 tff(f1960,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_190)),
% 1.94/0.67 inference(forward_demodulation,[],[f1958,f1073])).
% 1.94/0.67 tff(f1958,plain,(
% 1.94/0.67 ( ! [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_190),
% 1.94/0.67 inference(avatar_component_clause,[],[f1957])).
% 1.94/0.67 tff(f1959,plain,(
% 1.94/0.67 spl38_190),
% 1.94/0.67 inference(avatar_split_clause,[],[f434,f1957])).
% 1.94/0.67 tff(f434,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f221])).
% 1.94/0.67 tff(f221,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f158])).
% 1.94/0.67 tff(f158,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f79])).
% 1.94/0.67 tff(f79,axiom,(
% 1.94/0.67 ! [X36 : dB,X18 : dB,X22 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X22),X18)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X22)),aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X18))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_appR)).
% 1.94/0.67 tff(f1951,plain,(
% 1.94/0.67 spl38_189 | ~spl38_96 | ~spl38_188),
% 1.94/0.67 inference(avatar_split_clause,[],[f1947,f1941,f1072,f1949])).
% 1.94/0.67 tff(f1949,plain,(
% 1.94/0.67 spl38_189 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_189])])).
% 1.94/0.67 tff(f1941,plain,(
% 1.94/0.67 spl38_188 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_188])])).
% 1.94/0.67 tff(f1947,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_188)),
% 1.94/0.67 inference(forward_demodulation,[],[f1946,f1073])).
% 1.94/0.67 tff(f1946,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_188)),
% 1.94/0.67 inference(forward_demodulation,[],[f1945,f1073])).
% 1.94/0.67 tff(f1945,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_188)),
% 1.94/0.67 inference(forward_demodulation,[],[f1944,f1073])).
% 1.94/0.67 tff(f1944,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_188)),
% 1.94/0.67 inference(forward_demodulation,[],[f1942,f1073])).
% 1.94/0.67 tff(f1942,plain,(
% 1.94/0.67 ( ! [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_188),
% 1.94/0.67 inference(avatar_component_clause,[],[f1941])).
% 1.94/0.67 tff(f1943,plain,(
% 1.94/0.67 spl38_188),
% 1.94/0.67 inference(avatar_split_clause,[],[f433,f1941])).
% 1.94/0.67 tff(f433,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f220])).
% 1.94/0.67 tff(f220,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f157])).
% 1.94/0.67 tff(f157,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f82])).
% 1.94/0.67 tff(f82,axiom,(
% 1.94/0.67 ! [X9 : nat,X22 : dB,X10 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X10),X22)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X9)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X22),X9))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_lift__preserves__beta)).
% 1.94/0.67 tff(f1939,plain,(
% 1.94/0.67 spl38_187 | ~spl38_27 | ~spl38_29),
% 1.94/0.67 inference(avatar_split_clause,[],[f715,f705,f697,f1937])).
% 1.94/0.67 tff(f1937,plain,(
% 1.94/0.67 spl38_187 <=> ! [X0 : dB] : (sP1(abs(sK11(X0))) | ~sP0(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_187])])).
% 1.94/0.67 tff(f697,plain,(
% 1.94/0.67 spl38_27 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_27])])).
% 1.94/0.67 tff(f715,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP1(abs(sK11(X0))) | ~sP0(X0)) ) | (~spl38_27 | ~spl38_29)),
% 1.94/0.67 inference(resolution,[],[f706,f698])).
% 1.94/0.67 tff(f698,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0)) ) | ~spl38_27),
% 1.94/0.67 inference(avatar_component_clause,[],[f697])).
% 1.94/0.67 tff(f1926,plain,(
% 1.94/0.67 spl38_186 | ~spl38_96 | ~spl38_185),
% 1.94/0.67 inference(avatar_split_clause,[],[f1922,f1919,f1072,f1924])).
% 1.94/0.67 tff(f1924,plain,(
% 1.94/0.67 spl38_186 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_186])])).
% 1.94/0.67 tff(f1919,plain,(
% 1.94/0.67 spl38_185 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_185])])).
% 1.94/0.67 tff(f1922,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_185)),
% 1.94/0.67 inference(forward_demodulation,[],[f1920,f1073])).
% 1.94/0.67 tff(f1920,plain,(
% 1.94/0.67 ( ! [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_185),
% 1.94/0.67 inference(avatar_component_clause,[],[f1919])).
% 1.94/0.67 tff(f1921,plain,(
% 1.94/0.67 spl38_185),
% 1.94/0.67 inference(avatar_split_clause,[],[f443,f1919])).
% 1.94/0.67 tff(f443,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f301])).
% 1.94/0.67 tff(f1912,plain,(
% 1.94/0.67 spl38_184 | ~spl38_117 | ~spl38_183),
% 1.94/0.67 inference(avatar_split_clause,[],[f1908,f1905,f1209,f1910])).
% 1.94/0.67 tff(f1910,plain,(
% 1.94/0.67 spl38_184 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_184])])).
% 1.94/0.67 tff(f1905,plain,(
% 1.94/0.67 spl38_183 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_183])])).
% 1.94/0.67 tff(f1908,plain,(
% 1.94/0.67 ( ! [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_117 | ~spl38_183)),
% 1.94/0.67 inference(forward_demodulation,[],[f1906,f1210])).
% 1.94/0.67 tff(f1906,plain,(
% 1.94/0.67 ( ! [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_183),
% 1.94/0.67 inference(avatar_component_clause,[],[f1905])).
% 1.94/0.67 tff(f1907,plain,(
% 1.94/0.67 spl38_183),
% 1.94/0.67 inference(avatar_split_clause,[],[f436,f1905])).
% 1.94/0.67 tff(f436,plain,(
% 1.94/0.67 ( ! [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)))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f224])).
% 1.94/0.67 tff(f224,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(flattening,[],[f223])).
% 1.94/0.67 tff(f223,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(ennf_transformation,[],[f160])).
% 1.94/0.67 tff(f160,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 inference(rectify,[],[f51])).
% 1.94/0.67 tff(f51,axiom,(
% 1.94/0.67 ! [X51 : list(dB),X39 : dB,X52 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X52,X39,zero_zero(nat)),X51))) => (pp(aa(dB,bool,it,X39)) => pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X52)),X39),X51)))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Beta)).
% 1.94/0.67 tff(f1895,plain,(
% 1.94/0.67 spl38_182 | ~spl38_96 | ~spl38_181),
% 1.94/0.67 inference(avatar_split_clause,[],[f1890,f1885,f1072,f1892])).
% 1.94/0.67 tff(f1892,plain,(
% 1.94/0.67 spl38_182 <=> pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_182])])).
% 1.94/0.67 tff(f1885,plain,(
% 1.94/0.67 spl38_181 <=> pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_181])])).
% 1.94/0.67 tff(f1890,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1))) | (~spl38_96 | ~spl38_181)),
% 1.94/0.67 inference(forward_demodulation,[],[f1889,f1073])).
% 1.94/0.67 tff(f1889,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1))) | (~spl38_96 | ~spl38_181)),
% 1.94/0.67 inference(forward_demodulation,[],[f1887,f1073])).
% 1.94/0.67 tff(f1887,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1))) | ~spl38_181),
% 1.94/0.67 inference(avatar_component_clause,[],[f1885])).
% 1.94/0.67 tff(f1888,plain,(
% 1.94/0.67 spl38_181),
% 1.94/0.67 inference(avatar_split_clause,[],[f371,f1885])).
% 1.94/0.67 tff(f371,plain,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1)))),
% 1.94/0.67 inference(cnf_transformation,[],[f46])).
% 1.94/0.67 tff(f46,axiom,(
% 1.94/0.67 pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t2),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,t1)))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45__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)).
% 1.94/0.67 tff(f1870,plain,(
% 1.94/0.67 spl38_180 | ~spl38_96 | ~spl38_179),
% 1.94/0.67 inference(avatar_split_clause,[],[f1866,f1862,f1072,f1868])).
% 1.94/0.67 tff(f1868,plain,(
% 1.94/0.67 spl38_180 <=> ! [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)))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_180])])).
% 1.94/0.67 tff(f1862,plain,(
% 1.94/0.67 spl38_179 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_179])])).
% 1.94/0.67 tff(f1866,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_179)),
% 1.94/0.67 inference(forward_demodulation,[],[f1865,f1073])).
% 1.94/0.67 tff(f1865,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_179)),
% 1.94/0.67 inference(forward_demodulation,[],[f1863,f1073])).
% 1.94/0.67 tff(f1863,plain,(
% 1.94/0.67 ( ! [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_179),
% 1.94/0.67 inference(avatar_component_clause,[],[f1862])).
% 1.94/0.67 tff(f1864,plain,(
% 1.94/0.67 spl38_179),
% 1.94/0.67 inference(avatar_split_clause,[],[f467,f1862])).
% 1.94/0.67 tff(f467,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f320])).
% 1.94/0.67 tff(f320,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f239,f319])).
% 1.94/0.67 tff(f319,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f239,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f175])).
% 1.94/0.67 tff(f175,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f43])).
% 1.94/0.67 tff(f43,axiom,(
% 1.94/0.67 ! [X12 : type,X11 : dB,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X11)),X12)) => ~! [X47 : type] : (pp(aa(type,bool,typing(X14,X15),aa(type,type,aa(type,fun(type,type),fun1,X47),X12))) => ~pp(aa(type,bool,typing(X14,X11),X47))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_typing__elims_I2_J)).
% 1.94/0.67 tff(f1852,plain,(
% 1.94/0.67 spl38_178 | ~spl38_96 | ~spl38_177),
% 1.94/0.67 inference(avatar_split_clause,[],[f1848,f1845,f1072,f1850])).
% 1.94/0.67 tff(f1850,plain,(
% 1.94/0.67 spl38_178 <=> ! [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)),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_178])])).
% 1.94/0.67 tff(f1845,plain,(
% 1.94/0.67 spl38_177 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_177])])).
% 1.94/0.67 tff(f1848,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_177)),
% 1.94/0.67 inference(forward_demodulation,[],[f1846,f1073])).
% 1.94/0.67 tff(f1846,plain,(
% 1.94/0.67 ( ! [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_177),
% 1.94/0.67 inference(avatar_component_clause,[],[f1845])).
% 1.94/0.67 tff(f1847,plain,(
% 1.94/0.67 spl38_177),
% 1.94/0.67 inference(avatar_split_clause,[],[f441,f1845])).
% 1.94/0.67 tff(f441,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f301])).
% 1.94/0.67 tff(f1838,plain,(
% 1.94/0.67 spl38_176 | ~spl38_117 | ~spl38_175),
% 1.94/0.67 inference(avatar_split_clause,[],[f1834,f1831,f1209,f1836])).
% 1.94/0.67 tff(f1831,plain,(
% 1.94/0.67 spl38_175 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_175])])).
% 1.94/0.67 tff(f1834,plain,(
% 1.94/0.67 ( ! [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_117 | ~spl38_175)),
% 1.94/0.67 inference(forward_demodulation,[],[f1832,f1210])).
% 1.94/0.67 tff(f1832,plain,(
% 1.94/0.67 ( ! [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_175),
% 1.94/0.67 inference(avatar_component_clause,[],[f1831])).
% 1.94/0.67 tff(f1833,plain,(
% 1.94/0.67 spl38_175),
% 1.94/0.67 inference(avatar_split_clause,[],[f531,f1831])).
% 1.94/0.67 tff(f531,plain,(
% 1.94/0.67 ( ! [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)))) )),
% 1.94/0.67 inference(equality_resolution,[],[f394])).
% 1.94/0.67 tff(f394,plain,(
% 1.94/0.67 ( ! [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) )),
% 1.94/0.67 inference(cnf_transformation,[],[f283])).
% 1.94/0.67 tff(f283,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f281,f282])).
% 1.94/0.67 tff(f282,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f281,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f280])).
% 1.94/0.67 tff(f280,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(nnf_transformation,[],[f260])).
% 1.94/0.67 tff(f260,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 1.94/0.67 tff(f1808,plain,(
% 1.94/0.67 spl38_174),
% 1.94/0.67 inference(avatar_split_clause,[],[f505,f1806])).
% 1.94/0.67 tff(f1806,plain,(
% 1.94/0.67 spl38_174 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_174])])).
% 1.94/0.67 tff(f505,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f196])).
% 1.94/0.67 tff(f196,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(rectify,[],[f103])).
% 1.94/0.67 tff(f103,axiom,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 1.94/0.67 tff(f1804,plain,(
% 1.94/0.67 spl38_172 | ~spl38_173 | ~spl38_11),
% 1.94/0.67 inference(avatar_split_clause,[],[f615,f606,f1801,f1798])).
% 1.94/0.67 tff(f1801,plain,(
% 1.94/0.67 spl38_173 <=> fFalse = fTrue),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_173])])).
% 1.94/0.67 tff(f615,plain,(
% 1.94/0.67 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl38_11),
% 1.94/0.67 inference(equality_factoring,[],[f607])).
% 1.94/0.67 tff(f1789,plain,(
% 1.94/0.67 spl38_171 | ~spl38_96 | ~spl38_170),
% 1.94/0.67 inference(avatar_split_clause,[],[f1785,f1782,f1072,f1787])).
% 1.94/0.67 tff(f1782,plain,(
% 1.94/0.67 spl38_170 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_170])])).
% 1.94/0.67 tff(f1785,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_170)),
% 1.94/0.67 inference(forward_demodulation,[],[f1783,f1073])).
% 1.94/0.67 tff(f1783,plain,(
% 1.94/0.67 ( ! [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_170),
% 1.94/0.67 inference(avatar_component_clause,[],[f1782])).
% 1.94/0.67 tff(f1784,plain,(
% 1.94/0.67 spl38_170),
% 1.94/0.67 inference(avatar_split_clause,[],[f491,f1782])).
% 1.94/0.67 tff(f491,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f337])).
% 1.94/0.67 tff(f337,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f334,f336,f335])).
% 1.94/0.67 tff(f335,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f336,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f334,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f244])).
% 1.94/0.67 tff(f244,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f243])).
% 1.94/0.67 tff(f243,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f186])).
% 1.94/0.67 tff(f186,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f95])).
% 1.94/0.67 tff(f95,axiom,(
% 1.94/0.67 ! [X0 : $tType,X67 : list(X0),X37 : X0,X90 : list(X0),X52 : fun(X0,fun(X0,bool))] : (step1(X0,X52,X90,cons(X0,X37,X67)) => (! [X92 : X0] : (cons(X0,X92,X67) = X90 => ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X52,X92),X37))) => ~! [X93 : list(X0)] : (cons(X0,X37,X93) = X90 => ~step1(X0,X52,X93,X67))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Cons__step1E)).
% 1.94/0.67 tff(f1765,plain,(
% 1.94/0.67 spl38_169),
% 1.94/0.67 inference(avatar_split_clause,[],[f494,f1763])).
% 1.94/0.67 tff(f1763,plain,(
% 1.94/0.67 spl38_169 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_169])])).
% 1.94/0.67 tff(f494,plain,(
% 1.94/0.67 ( ! [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)))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f246])).
% 1.94/0.67 tff(f246,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(flattening,[],[f245])).
% 1.94/0.67 tff(f245,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(ennf_transformation,[],[f187])).
% 1.94/0.67 tff(f187,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f53])).
% 1.94/0.67 tff(f53,axiom,(
% 1.94/0.67 ! [X54 : list(dB),X12 : type,X55 : list(type),X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X15),foldr(type,type,fun1,X55,X12))) => (pp(aa(list(type),bool,typings(X14,X54),X55)) => pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X15,X54)),X12))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_list__app__typeI)).
% 1.94/0.67 tff(f1753,plain,(
% 1.94/0.67 spl38_168 | ~spl38_96 | ~spl38_167),
% 1.94/0.67 inference(avatar_split_clause,[],[f1749,f1746,f1072,f1751])).
% 1.94/0.67 tff(f1746,plain,(
% 1.94/0.67 spl38_167 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_167])])).
% 1.94/0.67 tff(f1749,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_167)),
% 1.94/0.67 inference(forward_demodulation,[],[f1747,f1073])).
% 1.94/0.67 tff(f1747,plain,(
% 1.94/0.67 ( ! [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_167),
% 1.94/0.67 inference(avatar_component_clause,[],[f1746])).
% 1.94/0.67 tff(f1748,plain,(
% 1.94/0.67 spl38_167),
% 1.94/0.67 inference(avatar_split_clause,[],[f493,f1746])).
% 1.94/0.67 tff(f493,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f337])).
% 1.94/0.67 tff(f1744,plain,(
% 1.94/0.67 spl38_166),
% 1.94/0.67 inference(avatar_split_clause,[],[f459,f1742])).
% 1.94/0.67 tff(f459,plain,(
% 1.94/0.67 ( ! [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),t)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f234])).
% 1.94/0.67 tff(f234,plain,(
% 1.94/0.67 ! [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),t)) | ~pp(aa(dB,bool,it,X2)) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1)))),
% 1.94/0.67 inference(flattening,[],[f233])).
% 1.94/0.67 tff(f233,plain,(
% 1.94/0.67 ! [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),t))) | ~pp(aa(dB,bool,it,X2))) | ~pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1)))),
% 1.94/0.67 inference(ennf_transformation,[],[f170])).
% 1.94/0.67 tff(f170,plain,(
% 1.94/0.67 ! [X0 : fun(nat,type),X1 : type,X2 : dB,X3 : nat] : (pp(aa(type,bool,typing(shift(type,X0,X3,t),a),X1)) => (pp(aa(dB,bool,it,X2)) => (pp(aa(type,bool,typing(X0,X2),t)) => pp(aa(dB,bool,it,subst(a,X2,X3))))))),
% 1.94/0.67 inference(rectify,[],[f5])).
% 1.94/0.67 tff(f5,axiom,(
% 1.94/0.67 ! [X4 : fun(nat,type),X5 : type,X6 : dB,X7 : nat] : (pp(aa(type,bool,typing(shift(type,X4,X7,t),a),X5)) => (pp(aa(dB,bool,it,X6)) => (pp(aa(type,bool,typing(X4,X6),t)) => pp(aa(dB,bool,it,subst(a,X6,X7))))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__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)).
% 1.94/0.67 tff(f1729,plain,(
% 1.94/0.67 spl38_165 | ~spl38_96 | ~spl38_164),
% 1.94/0.67 inference(avatar_split_clause,[],[f1725,f1721,f1072,f1727])).
% 1.94/0.67 tff(f1727,plain,(
% 1.94/0.67 spl38_165 <=> ! [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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_165])])).
% 1.94/0.67 tff(f1721,plain,(
% 1.94/0.67 spl38_164 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_164])])).
% 1.94/0.67 tff(f1725,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_164)),
% 1.94/0.67 inference(forward_demodulation,[],[f1724,f1073])).
% 1.94/0.67 tff(f1724,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_164)),
% 1.94/0.67 inference(forward_demodulation,[],[f1722,f1073])).
% 1.94/0.67 tff(f1722,plain,(
% 1.94/0.67 ( ! [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_164),
% 1.94/0.67 inference(avatar_component_clause,[],[f1721])).
% 1.94/0.67 tff(f1723,plain,(
% 1.94/0.67 spl38_164),
% 1.94/0.67 inference(avatar_split_clause,[],[f432,f1721])).
% 1.94/0.67 tff(f432,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f219])).
% 1.94/0.67 tff(f219,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f156])).
% 1.94/0.67 tff(f156,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f88])).
% 1.94/0.67 tff(f88,axiom,(
% 1.94/0.67 ! [X51 : list(dB),X39 : dB,X52 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X52),X39)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X52,X51)),foldl(dB,dB,app,X39,X51))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_apps__preserves__beta)).
% 1.94/0.67 tff(f1712,plain,(
% 1.94/0.67 spl38_163),
% 1.94/0.67 inference(avatar_split_clause,[],[f490,f1710])).
% 1.94/0.67 tff(f1710,plain,(
% 1.94/0.67 spl38_163 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_163])])).
% 1.94/0.67 tff(f490,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f337])).
% 1.94/0.67 tff(f1708,plain,(
% 1.94/0.67 spl38_162),
% 1.94/0.67 inference(avatar_split_clause,[],[f465,f1706])).
% 1.94/0.67 tff(f1706,plain,(
% 1.94/0.67 spl38_162 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_162])])).
% 1.94/0.67 tff(f465,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f318])).
% 1.94/0.67 tff(f318,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f238,f317])).
% 1.94/0.67 tff(f317,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 introduced(choice_axiom,[])).
% 1.94/0.67 tff(f238,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f174])).
% 1.94/0.67 tff(f174,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f56])).
% 1.94/0.67 tff(f56,axiom,(
% 1.94/0.67 ! [X12 : type,X54 : list(dB),X13 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X13),X54)),X12)) => ~! [X50 : list(type)] : (pp(aa(type,bool,typing(X14,var(X13)),foldr(type,type,fun1,X50,X12))) => ~pp(aa(list(type),bool,typings(X14,X54),X50))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_var__app__typesE)).
% 1.94/0.67 tff(f1699,plain,(
% 1.94/0.67 spl38_161 | ~spl38_96 | ~spl38_160),
% 1.94/0.67 inference(avatar_split_clause,[],[f1695,f1692,f1072,f1697])).
% 1.94/0.67 tff(f1697,plain,(
% 1.94/0.67 spl38_161 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_161])])).
% 1.94/0.67 tff(f1692,plain,(
% 1.94/0.67 spl38_160 <=> ! [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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_160])])).
% 1.94/0.67 tff(f1695,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_160)),
% 1.94/0.67 inference(forward_demodulation,[],[f1693,f1073])).
% 1.94/0.67 tff(f1693,plain,(
% 1.94/0.67 ( ! [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_160),
% 1.94/0.67 inference(avatar_component_clause,[],[f1692])).
% 1.94/0.67 tff(f1694,plain,(
% 1.94/0.67 spl38_160),
% 1.94/0.67 inference(avatar_split_clause,[],[f464,f1692])).
% 1.94/0.67 tff(f464,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f237])).
% 1.94/0.67 tff(f237,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f173])).
% 1.94/0.67 tff(f173,plain,(
% 1.94/0.67 ! [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))))),
% 1.94/0.67 inference(rectify,[],[f30])).
% 1.94/0.67 tff(f30,axiom,(
% 1.94/0.67 ! [X20 : type,X15 : dB,X12 : type,X38 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X38,zero_zero(nat),X12),X15),X20)) => pp(aa(type,bool,typing(X38,abs(X15)),aa(type,type,aa(type,fun(type,type),fun1,X12),X20))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Abs)).
% 1.94/0.67 tff(f1673,plain,(
% 1.94/0.67 spl38_159 | ~spl38_96 | ~spl38_158),
% 1.94/0.67 inference(avatar_split_clause,[],[f1669,f1666,f1072,f1671])).
% 1.94/0.67 tff(f1666,plain,(
% 1.94/0.67 spl38_158 <=> ! [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))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_158])])).
% 1.94/0.67 tff(f1669,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_158)),
% 1.94/0.67 inference(forward_demodulation,[],[f1667,f1073])).
% 1.94/0.67 tff(f1667,plain,(
% 1.94/0.67 ( ! [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_158),
% 1.94/0.67 inference(avatar_component_clause,[],[f1666])).
% 1.94/0.67 tff(f1668,plain,(
% 1.94/0.67 spl38_158),
% 1.94/0.67 inference(avatar_split_clause,[],[f456,f1666])).
% 1.94/0.67 tff(f456,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f167])).
% 1.94/0.67 tff(f167,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(rectify,[],[f24])).
% 1.94/0.67 tff(f24,axiom,(
% 1.94/0.67 ! [X23 : nat,X22 : dB,X36 : dB,X18 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X18),X36),X22,X23) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X18,X22,X23)),subst(X36,X22,X23))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_subst__App)).
% 1.94/0.67 tff(f1642,plain,(
% 1.94/0.67 spl38_157),
% 1.94/0.67 inference(avatar_split_clause,[],[f549,f1640])).
% 1.94/0.67 tff(f549,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(equality_resolution,[],[f515])).
% 1.94/0.67 tff(f515,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f253])).
% 1.94/0.67 tff(f253,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f252])).
% 1.94/0.67 tff(f252,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f199])).
% 1.94/0.67 tff(f199,plain,(
% 1.94/0.67 ! [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)))))),
% 1.94/0.67 inference(rectify,[],[f15])).
% 1.94/0.67 tff(f15,axiom,(
% 1.94/0.67 ! [X13 : nat,X20 : type,X11 : dB,X21 : fun(nat,type),X12 : type,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X15),X12)) => (pp(aa(type,bool,typing(X21,X11),X20)) => (shift(type,X21,X13,X20) = X14 => pp(aa(type,bool,typing(X21,subst(X15,X11,X13)),X12)))))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__lemma)).
% 1.94/0.67 tff(f1638,plain,(
% 1.94/0.67 spl38_156),
% 1.94/0.67 inference(avatar_split_clause,[],[f495,f1636])).
% 1.94/0.67 tff(f495,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f248])).
% 1.94/0.67 tff(f248,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(flattening,[],[f247])).
% 1.94/0.67 tff(f247,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f188])).
% 1.94/0.67 tff(f188,plain,(
% 1.94/0.67 ! [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))),
% 1.94/0.67 inference(rectify,[],[f54])).
% 1.94/0.67 tff(f54,axiom,(
% 1.94/0.67 ! [X20 : type,X12 : type,X54 : list(dB),X13 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X13),X54)),X12)) => (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,var(X13),X54)),X20)) => X12 = X20))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_var__app__type__eq)).
% 1.94/0.67 tff(f1614,plain,(
% 1.94/0.67 spl38_155 | ~spl38_22 | ~spl38_29),
% 1.94/0.67 inference(avatar_split_clause,[],[f710,f705,f663,f1612])).
% 1.94/0.67 tff(f1612,plain,(
% 1.94/0.67 spl38_155 <=> ! [X0 : dB] : (sP1(abs(X0)) | ~sP1(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_155])])).
% 1.94/0.67 tff(f663,plain,(
% 1.94/0.67 spl38_22 <=> ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_22])])).
% 1.94/0.67 tff(f710,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (sP1(abs(X0)) | ~sP1(X0)) ) | (~spl38_22 | ~spl38_29)),
% 1.94/0.67 inference(resolution,[],[f706,f664])).
% 1.94/0.67 tff(f664,plain,(
% 1.94/0.67 ( ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0)) ) | ~spl38_22),
% 1.94/0.67 inference(avatar_component_clause,[],[f663])).
% 1.94/0.67 tff(f1610,plain,(
% 1.94/0.67 spl38_154),
% 1.94/0.67 inference(avatar_split_clause,[],[f492,f1608])).
% 1.94/0.67 tff(f1608,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_154])])).
% 1.94/0.67 tff(f492,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f337])).
% 1.94/0.67 tff(f1604,plain,(
% 1.94/0.67 spl38_153 | ~spl38_96 | ~spl38_152),
% 1.94/0.67 inference(avatar_split_clause,[],[f1600,f1597,f1072,f1602])).
% 1.94/0.67 tff(f1602,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_153])])).
% 1.94/0.67 tff(f1597,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_152])])).
% 1.94/0.67 tff(f1600,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_152)),
% 1.94/0.67 inference(forward_demodulation,[],[f1598,f1073])).
% 1.94/0.67 tff(f1598,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f1597])).
% 1.94/0.67 tff(f1599,plain,(
% 1.94/0.67 spl38_152),
% 1.94/0.67 inference(avatar_split_clause,[],[f489,f1597])).
% 1.94/0.67 tff(f489,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f242])).
% 1.94/0.67 tff(f242,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(ennf_transformation,[],[f185])).
% 1.94/0.67 tff(f185,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(rectify,[],[f29])).
% 1.94/0.67 tff(f29,axiom,(
% 1.94/0.67 ! [X20 : type,X13 : nat,X12 : type,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X15),X12)) => pp(aa(type,bool,typing(shift(type,X14,X13,X20),aa(nat,dB,aa(dB,fun(nat,dB),lift,X15),X13)),X12)))),
% 1.94/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_lift__type)).
% 1.94/0.67 tff(f1591,plain,(
% 1.94/0.67 spl38_151 | ~spl38_96 | ~spl38_150),
% 1.94/0.67 inference(avatar_split_clause,[],[f1587,f1584,f1072,f1589])).
% 1.94/0.67 tff(f1589,plain,(
% 1.94/0.67 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))))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_151])])).
% 1.94/0.67 tff(f1584,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_150])])).
% 1.94/0.67 tff(f1587,plain,(
% 1.94/0.67 ( ! [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_96 | ~spl38_150)),
% 1.94/0.67 inference(forward_demodulation,[],[f1585,f1073])).
% 1.94/0.67 tff(f1585,plain,(
% 1.94/0.67 ( ! [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),
% 1.94/0.67 inference(avatar_component_clause,[],[f1584])).
% 1.94/0.67 tff(f1586,plain,(
% 1.94/0.67 spl38_150),
% 1.94/0.67 inference(avatar_split_clause,[],[f468,f1584])).
% 1.94/0.67 tff(f468,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f320])).
% 1.94/0.67 tff(f1582,plain,(
% 1.94/0.67 spl38_149),
% 1.94/0.67 inference(avatar_split_clause,[],[f462,f1580])).
% 1.94/0.67 tff(f1580,plain,(
% 1.94/0.67 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)))),
% 1.94/0.67 introduced(avatar_definition,[new_symbols(naming,[spl38_149])])).
% 1.94/0.67 tff(f462,plain,(
% 1.94/0.67 ( ! [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))) )),
% 1.94/0.67 inference(cnf_transformation,[],[f316])).
% 1.94/0.67 tff(f316,plain,(
% 1.94/0.67 ! [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)))),
% 1.94/0.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f236,f315])).
% 1.94/0.68 tff(f315,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f236,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f172])).
% 1.94/0.68 tff(f172,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 inference(rectify,[],[f62])).
% 1.94/0.68 tff(f62,axiom,(
% 1.94/0.68 ! [X12 : type,X54 : list(dB),X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X15,X54)),X12)) => ? [X50 : list(type)] : (pp(aa(list(type),bool,typings(X14,X54),X50)) & pp(aa(type,bool,typing(X14,X15),foldr(type,type,fun1,X50,X12)))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_list__app__typeD)).
% 1.94/0.68 tff(f1578,plain,(
% 1.94/0.68 spl38_148),
% 1.94/0.68 inference(avatar_split_clause,[],[f460,f1576])).
% 1.94/0.68 tff(f1576,plain,(
% 1.94/0.68 spl38_148 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_148])])).
% 1.94/0.68 tff(f460,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f314])).
% 1.94/0.68 tff(f314,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f235,f313])).
% 1.94/0.68 tff(f313,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f235,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f171])).
% 1.94/0.68 tff(f171,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f63])).
% 1.94/0.68 tff(f63,axiom,(
% 1.94/0.68 ! [X12 : type,X54 : list(dB),X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,foldl(dB,dB,app,X15,X54)),X12)) => ~! [X50 : list(type)] : (pp(aa(type,bool,typing(X14,X15),foldr(type,type,fun1,X50,X12))) => ~pp(aa(list(type),bool,typings(X14,X54),X50))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_list__app__typeE)).
% 1.94/0.68 tff(f1566,plain,(
% 1.94/0.68 spl38_147 | ~spl38_21 | ~spl38_27),
% 1.94/0.68 inference(avatar_split_clause,[],[f708,f697,f659,f1564])).
% 1.94/0.68 tff(f1564,plain,(
% 1.94/0.68 spl38_147 <=> ! [X0 : dB] : (~sP0(X0) | sP1(sK11(X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_147])])).
% 1.94/0.68 tff(f708,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (~sP0(X0) | sP1(sK11(X0))) ) | (~spl38_21 | ~spl38_27)),
% 1.94/0.68 inference(resolution,[],[f698,f660])).
% 1.94/0.68 tff(f1562,plain,(
% 1.94/0.68 spl38_146 | ~spl38_96 | ~spl38_145),
% 1.94/0.68 inference(avatar_split_clause,[],[f1558,f1554,f1072,f1560])).
% 1.94/0.68 tff(f1560,plain,(
% 1.94/0.68 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))))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_146])])).
% 1.94/0.68 tff(f1554,plain,(
% 1.94/0.68 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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_145])])).
% 1.94/0.68 tff(f1558,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_145)),
% 1.94/0.68 inference(forward_demodulation,[],[f1557,f1073])).
% 1.94/0.68 tff(f1557,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_145)),
% 1.94/0.68 inference(forward_demodulation,[],[f1555,f1073])).
% 1.94/0.68 tff(f1555,plain,(
% 1.94/0.68 ( ! [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),
% 1.94/0.68 inference(avatar_component_clause,[],[f1554])).
% 1.94/0.68 tff(f1556,plain,(
% 1.94/0.68 spl38_145),
% 1.94/0.68 inference(avatar_split_clause,[],[f458,f1554])).
% 1.94/0.68 tff(f458,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f232])).
% 1.94/0.68 tff(f232,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f169])).
% 1.94/0.68 tff(f169,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f83])).
% 1.94/0.68 tff(f83,axiom,(
% 1.94/0.68 ! [X9 : nat,X18 : dB,X22 : dB,X10 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X10),X22)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X10,X18,X9)),subst(X22,X18,X9))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_subst__preserves__beta)).
% 1.94/0.68 tff(f1549,plain,(
% 1.94/0.68 spl38_144 | ~spl38_96 | ~spl38_143),
% 1.94/0.68 inference(avatar_split_clause,[],[f1545,f1542,f1072,f1547])).
% 1.94/0.68 tff(f1547,plain,(
% 1.94/0.68 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)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_144])])).
% 1.94/0.68 tff(f1542,plain,(
% 1.94/0.68 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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_143])])).
% 1.94/0.68 tff(f1545,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_143)),
% 1.94/0.68 inference(forward_demodulation,[],[f1543,f1073])).
% 1.94/0.68 tff(f1543,plain,(
% 1.94/0.68 ( ! [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),
% 1.94/0.68 inference(avatar_component_clause,[],[f1542])).
% 1.94/0.68 tff(f1544,plain,(
% 1.94/0.68 spl38_143),
% 1.94/0.68 inference(avatar_split_clause,[],[f445,f1542])).
% 1.94/0.68 tff(f445,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f303])).
% 1.94/0.68 tff(f303,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f227,f302])).
% 1.94/0.68 tff(f302,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f227,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f162])).
% 1.94/0.68 tff(f162,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(rectify,[],[f93])).
% 1.94/0.68 tff(f93,axiom,(
% 1.94/0.68 ! [X88 : dB,X58 : list(dB),X59 : nat] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X59),X58)),X88)) => ? [X89 : list(dB)] : (foldl(dB,dB,app,var(X59),X89) = X88 & step1(dB,beta,X58,X89)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_head__Var__reduction)).
% 1.94/0.68 tff(f1536,plain,(
% 1.94/0.68 spl38_142 | ~spl38_96 | ~spl38_141),
% 1.94/0.68 inference(avatar_split_clause,[],[f1531,f1526,f1072,f1533])).
% 1.94/0.68 tff(f1526,plain,(
% 1.94/0.68 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)))))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_141])])).
% 1.94/0.68 tff(f1531,plain,(
% 1.94/0.68 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_96 | ~spl38_141)),
% 1.94/0.68 inference(forward_demodulation,[],[f1530,f1073])).
% 1.94/0.68 tff(f1530,plain,(
% 1.94/0.68 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_96 | ~spl38_141)),
% 1.94/0.68 inference(forward_demodulation,[],[f1528,f1073])).
% 1.94/0.68 tff(f1528,plain,(
% 1.94/0.68 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),
% 1.94/0.68 inference(avatar_component_clause,[],[f1526])).
% 1.94/0.68 tff(f1529,plain,(
% 1.94/0.68 spl38_141),
% 1.94/0.68 inference(avatar_split_clause,[],[f370,f1526])).
% 1.94/0.68 tff(f370,plain,(
% 1.94/0.68 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)))))),
% 1.94/0.68 inference(cnf_transformation,[],[f17])).
% 1.94/0.68 tff(f17,axiom,(
% 1.94/0.68 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)))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096IT_A_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_096)).
% 1.94/0.68 tff(f1481,plain,(
% 1.94/0.68 spl38_140 | ~spl38_96 | ~spl38_139),
% 1.94/0.68 inference(avatar_split_clause,[],[f1476,f1472,f1072,f1478])).
% 1.94/0.68 tff(f1478,plain,(
% 1.94/0.68 spl38_140 <=> pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,sK6,t1)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_140])])).
% 1.94/0.68 tff(f1472,plain,(
% 1.94/0.68 spl38_139 <=> pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t1)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_139])])).
% 1.94/0.68 tff(f1476,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,sK6,t1))) | (~spl38_96 | ~spl38_139)),
% 1.94/0.68 inference(forward_demodulation,[],[f1474,f1073])).
% 1.94/0.68 tff(f1474,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t1))) | ~spl38_139),
% 1.94/0.68 inference(avatar_component_clause,[],[f1472])).
% 1.94/0.68 tff(f1475,plain,(
% 1.94/0.68 spl38_139),
% 1.94/0.68 inference(avatar_split_clause,[],[f526,f1472])).
% 1.94/0.68 tff(f526,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK6,t1)))),
% 1.94/0.68 inference(definition_unfolding,[],[f374,f353])).
% 1.94/0.68 tff(f353,plain,(
% 1.94/0.68 n = i),
% 1.94/0.68 inference(cnf_transformation,[],[f6])).
% 1.94/0.68 tff(f6,axiom,(
% 1.94/0.68 n = i),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_True)).
% 1.94/0.68 tff(f374,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t1)))),
% 1.94/0.68 inference(cnf_transformation,[],[f272])).
% 1.94/0.68 tff(f272,plain,(
% 1.94/0.68 pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK6)) & pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t1)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f204,f271])).
% 1.94/0.68 tff(f271,plain,(
% 1.94/0.68 ? [X0 : list(type)] : (pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1)))) => (pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK6)) & pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK6,t1))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f204,plain,(
% 1.94/0.68 ? [X0 : list(type)] : (pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))))),
% 1.94/0.68 inference(ennf_transformation,[],[f116])).
% 1.94/0.68 tff(f116,plain,(
% 1.94/0.68 ~! [X0 : list(type)] : (pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) => ~pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)))),
% 1.94/0.68 inference(rectify,[],[f47])).
% 1.94/0.68 tff(f47,axiom,(
% 1.94/0.68 ~! [X50 : list(type)] : (pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X50,t1))) => ~pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X50)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46__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)).
% 1.94/0.68 tff(f1466,plain,(
% 1.94/0.68 spl38_138 | ~spl38_116 | ~spl38_137),
% 1.94/0.68 inference(avatar_split_clause,[],[f1461,f1457,f1205,f1463])).
% 1.94/0.68 tff(f1457,plain,(
% 1.94/0.68 spl38_137 <=> pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_137])])).
% 1.94/0.68 tff(f1461,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),foldr(type,type,fun1,cons(type,sK5,ts),t1))) | (~spl38_116 | ~spl38_137)),
% 1.94/0.68 inference(forward_demodulation,[],[f1459,f1206])).
% 1.94/0.68 tff(f1459,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1)))) | ~spl38_137),
% 1.94/0.68 inference(avatar_component_clause,[],[f1457])).
% 1.94/0.68 tff(f1460,plain,(
% 1.94/0.68 spl38_137),
% 1.94/0.68 inference(avatar_split_clause,[],[f525,f1457])).
% 1.94/0.68 tff(f525,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 inference(definition_unfolding,[],[f372,f353])).
% 1.94/0.68 tff(f372,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 inference(cnf_transformation,[],[f270])).
% 1.94/0.68 tff(f270,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),a),sK5)) & pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f203,f269])).
% 1.94/0.68 tff(f269,plain,(
% 1.94/0.68 ? [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t),a),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1))))) => (pp(aa(type,bool,typing(shift(type,e,i,t),a),sK5)) & pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK5),foldr(type,type,fun1,ts,t1)))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f203,plain,(
% 1.94/0.68 ? [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t),a),X0)) & pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))))),
% 1.94/0.68 inference(ennf_transformation,[],[f115])).
% 1.94/0.68 tff(f115,plain,(
% 1.94/0.68 ~! [X0 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) => ~pp(aa(type,bool,typing(shift(type,e,i,t),a),X0)))),
% 1.94/0.68 inference(rectify,[],[f52])).
% 1.94/0.68 tff(f52,axiom,(
% 1.94/0.68 ~! [X53 : type] : (pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X53),foldr(type,type,fun1,ts,t1)))) => ~pp(aa(type,bool,typing(shift(type,e,i,t),a),X53)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51__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)).
% 1.94/0.68 tff(f1453,plain,(
% 1.94/0.68 spl38_136),
% 1.94/0.68 inference(avatar_split_clause,[],[f524,f1450])).
% 1.94/0.68 tff(f1450,plain,(
% 1.94/0.68 spl38_136 <=> pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_136])])).
% 1.94/0.68 tff(f524,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1))),
% 1.94/0.68 inference(definition_unfolding,[],[f369,f353])).
% 1.94/0.68 tff(f369,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1))),
% 1.94/0.68 inference(cnf_transformation,[],[f50])).
% 1.94/0.68 tff(f50,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49__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)).
% 1.94/0.68 tff(f1447,plain,(
% 1.94/0.68 spl38_135 | ~spl38_96 | ~spl38_134),
% 1.94/0.68 inference(avatar_split_clause,[],[f1442,f1438,f1072,f1444])).
% 1.94/0.68 tff(f1444,plain,(
% 1.94/0.68 spl38_135 <=> pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,ts,t1)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_135])])).
% 1.94/0.68 tff(f1438,plain,(
% 1.94/0.68 spl38_134 <=> pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_134])])).
% 1.94/0.68 tff(f1442,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),foldr(type,type,fun1,ts,t1))) | (~spl38_96 | ~spl38_134)),
% 1.94/0.68 inference(forward_demodulation,[],[f1440,f1073])).
% 1.94/0.68 tff(f1440,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))) | ~spl38_134),
% 1.94/0.68 inference(avatar_component_clause,[],[f1438])).
% 1.94/0.68 tff(f1441,plain,(
% 1.94/0.68 spl38_134),
% 1.94/0.68 inference(avatar_split_clause,[],[f523,f1438])).
% 1.94/0.68 tff(f523,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1)))),
% 1.94/0.68 inference(definition_unfolding,[],[f368,f353])).
% 1.94/0.68 tff(f368,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1)))),
% 1.94/0.68 inference(cnf_transformation,[],[f41])).
% 1.94/0.68 tff(f41,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_headT)).
% 1.94/0.68 tff(f1430,plain,(
% 1.94/0.68 spl38_133 | ~spl38_96 | ~spl38_132),
% 1.94/0.68 inference(avatar_split_clause,[],[f1426,f1423,f1072,f1428])).
% 1.94/0.68 tff(f1428,plain,(
% 1.94/0.68 spl38_133 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_133])])).
% 1.94/0.68 tff(f1423,plain,(
% 1.94/0.68 spl38_132 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_132])])).
% 1.94/0.68 tff(f1426,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_132)),
% 1.94/0.68 inference(forward_demodulation,[],[f1424,f1073])).
% 1.94/0.68 tff(f1424,plain,(
% 1.94/0.68 ( ! [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_132),
% 1.94/0.68 inference(avatar_component_clause,[],[f1423])).
% 1.94/0.68 tff(f1425,plain,(
% 1.94/0.68 spl38_132),
% 1.94/0.68 inference(avatar_split_clause,[],[f457,f1423])).
% 1.94/0.68 tff(f457,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f231])).
% 1.94/0.68 tff(f231,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f230])).
% 1.94/0.68 tff(f230,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f168])).
% 1.94/0.68 tff(f168,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f84])).
% 1.94/0.68 tff(f84,axiom,(
% 1.94/0.68 ! [X79 : dB,X12 : type,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,X15),X12)) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X15),X79)) => pp(aa(type,bool,typing(X14,X79),X12))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subject__reduction)).
% 1.94/0.68 tff(f1421,plain,(
% 1.94/0.68 spl38_131),
% 1.94/0.68 inference(avatar_split_clause,[],[f430,f1419])).
% 1.94/0.68 tff(f1419,plain,(
% 1.94/0.68 spl38_131 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_131])])).
% 1.94/0.68 tff(f430,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f292])).
% 1.94/0.68 tff(f292,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f217,f291])).
% 1.94/0.68 tff(f291,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f217,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f154])).
% 1.94/0.68 tff(f154,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f40])).
% 1.94/0.68 tff(f40,axiom,(
% 1.94/0.68 ! [X12 : type,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,abs(X15)),X12)) => ~! [X47 : type,X48 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X47),X48) = X12 => ~pp(aa(type,bool,typing(shift(type,X14,zero_zero(nat),X47),X15),X48))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_typing__elims_I3_J)).
% 1.94/0.68 tff(f1416,plain,(
% 1.94/0.68 spl38_130 | ~spl38_96 | ~spl38_129),
% 1.94/0.68 inference(avatar_split_clause,[],[f1412,f1409,f1072,f1414])).
% 1.94/0.68 tff(f1414,plain,(
% 1.94/0.68 spl38_130 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_130])])).
% 1.94/0.68 tff(f1409,plain,(
% 1.94/0.68 spl38_129 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_129])])).
% 1.94/0.68 tff(f1412,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_129)),
% 1.94/0.68 inference(forward_demodulation,[],[f1410,f1073])).
% 1.94/0.68 tff(f1410,plain,(
% 1.94/0.68 ( ! [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_129),
% 1.94/0.68 inference(avatar_component_clause,[],[f1409])).
% 1.94/0.68 tff(f1411,plain,(
% 1.94/0.68 spl38_129),
% 1.94/0.68 inference(avatar_split_clause,[],[f429,f1409])).
% 1.94/0.68 tff(f429,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f292])).
% 1.94/0.68 tff(f1383,plain,(
% 1.94/0.68 spl38_128 | ~spl38_96 | ~spl38_127),
% 1.94/0.68 inference(avatar_split_clause,[],[f1379,f1376,f1072,f1381])).
% 1.94/0.68 tff(f1381,plain,(
% 1.94/0.68 spl38_128 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_128])])).
% 1.94/0.68 tff(f1376,plain,(
% 1.94/0.68 spl38_127 <=> ! [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)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_127])])).
% 1.94/0.68 tff(f1379,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_127)),
% 1.94/0.68 inference(forward_demodulation,[],[f1377,f1073])).
% 1.94/0.68 tff(f1377,plain,(
% 1.94/0.68 ( ! [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_127),
% 1.94/0.68 inference(avatar_component_clause,[],[f1376])).
% 1.94/0.68 tff(f1378,plain,(
% 1.94/0.68 spl38_127),
% 1.94/0.68 inference(avatar_split_clause,[],[f487,f1376])).
% 1.94/0.68 tff(f487,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f183])).
% 1.94/0.68 tff(f183,plain,(
% 1.94/0.68 ! [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)),
% 1.94/0.68 inference(rectify,[],[f96])).
% 1.94/0.68 tff(f96,axiom,(
% 1.94/0.68 ! [X0 : $tType,X34 : type,X35 : type,X81 : fun(type,fun(type,X0)),X82 : fun(nat,X0)] : type_case(X0,X82,X81,aa(type,type,aa(type,fun(type,type),fun1,X35),X34)) = aa(type,X0,aa(type,fun(type,X0),X81,X35),X34)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_type_Osimps_I6_J)).
% 1.94/0.68 tff(f1374,plain,(
% 1.94/0.68 spl38_126 | ~spl38_15 | ~spl38_29),
% 1.94/0.68 inference(avatar_split_clause,[],[f711,f705,f630,f1372])).
% 1.94/0.68 tff(f1372,plain,(
% 1.94/0.68 spl38_126 <=> ! [X0 : nat] : sP1(abs(var(X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_126])])).
% 1.94/0.68 tff(f630,plain,(
% 1.94/0.68 spl38_15 <=> ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_15])])).
% 1.94/0.68 tff(f711,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (sP1(abs(var(X0)))) ) | (~spl38_15 | ~spl38_29)),
% 1.94/0.68 inference(resolution,[],[f706,f631])).
% 1.94/0.68 tff(f631,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) ) | ~spl38_15),
% 1.94/0.68 inference(avatar_component_clause,[],[f630])).
% 1.94/0.68 tff(f1370,plain,(
% 1.94/0.68 spl38_125),
% 1.94/0.68 inference(avatar_split_clause,[],[f466,f1368])).
% 1.94/0.68 tff(f466,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f318])).
% 1.94/0.68 tff(f1359,plain,(
% 1.94/0.68 spl38_124 | ~spl38_96 | ~spl38_123),
% 1.94/0.68 inference(avatar_split_clause,[],[f1355,f1352,f1072,f1357])).
% 1.94/0.68 tff(f1352,plain,(
% 1.94/0.68 spl38_123 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_123])])).
% 1.94/0.68 tff(f1355,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_123)),
% 1.94/0.68 inference(forward_demodulation,[],[f1353,f1073])).
% 1.94/0.68 tff(f1353,plain,(
% 1.94/0.68 ( ! [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_123),
% 1.94/0.68 inference(avatar_component_clause,[],[f1352])).
% 1.94/0.68 tff(f1354,plain,(
% 1.94/0.68 spl38_123),
% 1.94/0.68 inference(avatar_split_clause,[],[f425,f1352])).
% 1.94/0.68 tff(f425,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f213])).
% 1.94/0.68 tff(f213,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(ennf_transformation,[],[f150])).
% 1.94/0.68 tff(f150,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f92])).
% 1.94/0.68 tff(f92,axiom,(
% 1.94/0.68 ! [X52 : dB,X51 : list(dB),X58 : list(dB)] : (step1(dB,beta,X58,X51) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X52,X58)),foldl(dB,dB,app,X52,X51))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_apps__preserves__betas)).
% 1.94/0.68 tff(f1345,plain,(
% 1.94/0.68 spl38_122 | ~spl38_96 | ~spl38_121),
% 1.94/0.68 inference(avatar_split_clause,[],[f1341,f1337,f1072,f1343])).
% 1.94/0.68 tff(f1337,plain,(
% 1.94/0.68 spl38_121 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_121])])).
% 1.94/0.68 tff(f1341,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_121)),
% 1.94/0.68 inference(forward_demodulation,[],[f1340,f1073])).
% 1.94/0.68 tff(f1340,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_121)),
% 1.94/0.68 inference(forward_demodulation,[],[f1338,f1073])).
% 1.94/0.68 tff(f1338,plain,(
% 1.94/0.68 ( ! [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_121),
% 1.94/0.68 inference(avatar_component_clause,[],[f1337])).
% 1.94/0.68 tff(f1339,plain,(
% 1.94/0.68 spl38_121),
% 1.94/0.68 inference(avatar_split_clause,[],[f412,f1337])).
% 1.94/0.68 tff(f412,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f286])).
% 1.94/0.68 tff(f286,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f212,f285])).
% 1.94/0.68 tff(f285,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f212,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f139])).
% 1.94/0.68 tff(f139,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f86])).
% 1.94/0.68 tff(f86,axiom,(
% 1.94/0.68 ! [X22 : dB,X10 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X10)),X22)) => ~! [X80 : dB] : (abs(X80) = X22 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X10),X80))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_beta__cases_I2_J)).
% 1.94/0.68 tff(f1331,plain,(
% 1.94/0.68 spl38_120 | ~spl38_96 | ~spl38_119),
% 1.94/0.68 inference(avatar_split_clause,[],[f1327,f1323,f1072,f1329])).
% 1.94/0.68 tff(f1323,plain,(
% 1.94/0.68 spl38_119 <=> ! [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))))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_119])])).
% 1.94/0.68 tff(f1327,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_119)),
% 1.94/0.68 inference(forward_demodulation,[],[f1326,f1073])).
% 1.94/0.68 tff(f1326,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_119)),
% 1.94/0.68 inference(forward_demodulation,[],[f1324,f1073])).
% 1.94/0.68 tff(f1324,plain,(
% 1.94/0.68 ( ! [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_119),
% 1.94/0.68 inference(avatar_component_clause,[],[f1323])).
% 1.94/0.68 tff(f1325,plain,(
% 1.94/0.68 spl38_119),
% 1.94/0.68 inference(avatar_split_clause,[],[f403,f1323])).
% 1.94/0.68 tff(f403,plain,(
% 1.94/0.68 ( ! [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))))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f131])).
% 1.94/0.68 tff(f131,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f74])).
% 1.94/0.68 tff(f74,axiom,(
% 1.94/0.68 ! [X18 : dB,X22 : dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X22)),X18)),subst(X22,X18,zero_zero(nat))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_beta)).
% 1.94/0.68 tff(f1215,plain,(
% 1.94/0.68 spl38_118),
% 1.94/0.68 inference(avatar_split_clause,[],[f504,f1213])).
% 1.94/0.68 tff(f504,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f195])).
% 1.94/0.68 tff(f195,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f106])).
% 1.94/0.68 tff(f106,axiom,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 1.94/0.68 tff(f1211,plain,(
% 1.94/0.68 spl38_117),
% 1.94/0.68 inference(avatar_split_clause,[],[f503,f1209])).
% 1.94/0.68 tff(f1207,plain,(
% 1.94/0.68 spl38_116),
% 1.94/0.68 inference(avatar_split_clause,[],[f502,f1205])).
% 1.94/0.68 tff(f502,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f193])).
% 1.94/0.68 tff(f193,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f68])).
% 1.94/0.68 tff(f68,axiom,(
% 1.94/0.68 ! [X1 : $tType,X0 : $tType,X64 : X0,X67 : list(X1),X37 : X1,X68 : fun(X1,fun(X0,X0))] : foldr(X1,X0,X68,cons(X1,X37,X67),X64) = aa(X0,X0,aa(X1,fun(X0,X0),X68,X37),foldr(X1,X0,X68,X67,X64))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_foldr_Osimps_I2_J)).
% 1.94/0.68 tff(f1203,plain,(
% 1.94/0.68 spl38_115),
% 1.94/0.68 inference(avatar_split_clause,[],[f482,f1201])).
% 1.94/0.68 tff(f1201,plain,(
% 1.94/0.68 spl38_115 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_115])])).
% 1.94/0.68 tff(f482,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f331])).
% 1.94/0.68 tff(f331,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f330])).
% 1.94/0.68 tff(f330,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f181])).
% 1.94/0.68 tff(f181,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f20])).
% 1.94/0.68 tff(f20,axiom,(
% 1.94/0.68 ! [X24 : dB,X25 : dB,X26 : dB,X27 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X27),X26) = aa(dB,dB,aa(dB,fun(dB,dB),app,X25),X24) <=> (X24 = X26 & X25 = X27))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dB_Osimps_I2_J)).
% 1.94/0.68 tff(f1199,plain,(
% 1.94/0.68 spl38_114),
% 1.94/0.68 inference(avatar_split_clause,[],[f481,f1197])).
% 1.94/0.68 tff(f1197,plain,(
% 1.94/0.68 spl38_114 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_114])])).
% 1.94/0.68 tff(f481,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f331])).
% 1.94/0.68 tff(f1195,plain,(
% 1.94/0.68 spl38_113),
% 1.94/0.68 inference(avatar_split_clause,[],[f479,f1193])).
% 1.94/0.68 tff(f479,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f329])).
% 1.94/0.68 tff(f329,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f328])).
% 1.94/0.68 tff(f328,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f180])).
% 1.94/0.68 tff(f180,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f23])).
% 1.94/0.68 tff(f23,axiom,(
% 1.94/0.68 ! [X32 : type,X33 : type,X34 : type,X35 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X35),X34) = aa(type,type,aa(type,fun(type,type),fun1,X33),X32) <=> (X32 = X34 & X33 = X35))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_type_Osimps_I2_J)).
% 1.94/0.68 tff(f1191,plain,(
% 1.94/0.68 spl38_112),
% 1.94/0.68 inference(avatar_split_clause,[],[f478,f1189])).
% 1.94/0.68 tff(f478,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f329])).
% 1.94/0.68 tff(f1187,plain,(
% 1.94/0.68 spl38_111),
% 1.94/0.68 inference(avatar_split_clause,[],[f463,f1185])).
% 1.94/0.68 tff(f463,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f316])).
% 1.94/0.68 tff(f1183,plain,(
% 1.94/0.68 spl38_110),
% 1.94/0.68 inference(avatar_split_clause,[],[f461,f1181])).
% 1.94/0.68 tff(f461,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f314])).
% 1.94/0.68 tff(f1177,plain,(
% 1.94/0.68 spl38_109 | ~spl38_96 | ~spl38_108),
% 1.94/0.68 inference(avatar_split_clause,[],[f1173,f1170,f1072,f1175])).
% 1.94/0.68 tff(f1170,plain,(
% 1.94/0.68 spl38_108 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_108])])).
% 1.94/0.68 tff(f1173,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_108)),
% 1.94/0.68 inference(forward_demodulation,[],[f1171,f1073])).
% 1.94/0.68 tff(f1171,plain,(
% 1.94/0.68 ( ! [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_108),
% 1.94/0.68 inference(avatar_component_clause,[],[f1170])).
% 1.94/0.68 tff(f1172,plain,(
% 1.94/0.68 spl38_108),
% 1.94/0.68 inference(avatar_split_clause,[],[f444,f1170])).
% 1.94/0.68 tff(f444,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f303])).
% 1.94/0.68 tff(f1168,plain,(
% 1.94/0.68 spl38_107),
% 1.94/0.68 inference(avatar_split_clause,[],[f428,f1166])).
% 1.94/0.68 tff(f1166,plain,(
% 1.94/0.68 spl38_107 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_107])])).
% 1.94/0.68 tff(f428,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f290])).
% 1.94/0.68 tff(f290,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f216,f289])).
% 1.94/0.68 tff(f289,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f216,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f153])).
% 1.94/0.68 tff(f153,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(rectify,[],[f45])).
% 1.94/0.68 tff(f45,axiom,(
% 1.94/0.68 ! [X12 : type,X15 : dB,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,abs(X15)),X12)) => ~! [X48 : type,X49 : type] : ~pp(aa(type,bool,typing(shift(type,X14,zero_zero(nat),X48),X15),X49)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_abs__typeE)).
% 1.94/0.68 tff(f1161,plain,(
% 1.94/0.68 spl38_106 | ~spl38_96 | ~spl38_105),
% 1.94/0.68 inference(avatar_split_clause,[],[f1157,f1153,f1072,f1159])).
% 1.94/0.68 tff(f1153,plain,(
% 1.94/0.68 spl38_105 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_105])])).
% 1.94/0.68 tff(f1157,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_105)),
% 1.94/0.68 inference(forward_demodulation,[],[f1156,f1073])).
% 1.94/0.68 tff(f1156,plain,(
% 1.94/0.68 ( ! [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_96 | ~spl38_105)),
% 1.94/0.68 inference(forward_demodulation,[],[f1154,f1073])).
% 1.94/0.68 tff(f1154,plain,(
% 1.94/0.68 ( ! [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_105),
% 1.94/0.68 inference(avatar_component_clause,[],[f1153])).
% 1.94/0.68 tff(f1155,plain,(
% 1.94/0.68 spl38_105),
% 1.94/0.68 inference(avatar_split_clause,[],[f410,f1153])).
% 1.94/0.68 tff(f410,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f211])).
% 1.94/0.68 tff(f211,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f138])).
% 1.94/0.68 tff(f138,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f81])).
% 1.94/0.68 tff(f81,axiom,(
% 1.94/0.68 ! [X18 : dB,X22 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X22),X18)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X22)),abs(X18))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_abs)).
% 1.94/0.68 tff(f1151,plain,(
% 1.94/0.68 spl38_104),
% 1.94/0.68 inference(avatar_split_clause,[],[f439,f1149])).
% 1.94/0.68 tff(f1149,plain,(
% 1.94/0.68 spl38_104 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_104])])).
% 1.94/0.68 tff(f439,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f297])).
% 1.94/0.68 tff(f297,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f294,f296,f295])).
% 1.94/0.68 tff(f295,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f296,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f294,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f293])).
% 1.94/0.68 tff(f293,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(nnf_transformation,[],[f263])).
% 1.94/0.68 tff(f1135,plain,(
% 1.94/0.68 spl38_103),
% 1.94/0.68 inference(avatar_split_clause,[],[f469,f1133])).
% 1.94/0.68 tff(f469,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f322])).
% 1.94/0.68 tff(f322,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f240,f321])).
% 1.94/0.68 tff(f321,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f240,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(ennf_transformation,[],[f176])).
% 1.94/0.68 tff(f176,plain,(
% 1.94/0.68 ! [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)),
% 1.94/0.68 inference(rectify,[],[f75])).
% 1.94/0.68 tff(f75,axiom,(
% 1.94/0.68 ! [X1 : $tType,X0 : $tType,X74 : fun(X0,X1),X68 : fun(X0,X1)] : (! [X75 : X0] : aa(X0,X1,X68,X75) = aa(X0,X1,X74,X75) => X68 = X74)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext)).
% 1.94/0.68 tff(f1130,plain,(
% 1.94/0.68 spl38_102 | ~spl38_101),
% 1.94/0.68 inference(avatar_split_clause,[],[f1126,f1123,f1128])).
% 1.94/0.68 tff(f1128,plain,(
% 1.94/0.68 spl38_102 <=> ! [X0 : dB] : (foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0))) = X0 | ~sP0(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_102])])).
% 1.94/0.68 tff(f1123,plain,(
% 1.94/0.68 spl38_101 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_101])])).
% 1.94/0.68 tff(f1126,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (foldl(dB,dB,app,abs(sK10(X0)),cons(dB,sK11(X0),sK12(X0))) = X0 | ~sP0(X0)) ) | ~spl38_101),
% 1.94/0.68 inference(forward_demodulation,[],[f1124,f503])).
% 1.94/0.68 tff(f1124,plain,(
% 1.94/0.68 ( ! [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_101),
% 1.94/0.68 inference(avatar_component_clause,[],[f1123])).
% 1.94/0.68 tff(f1125,plain,(
% 1.94/0.68 spl38_101),
% 1.94/0.68 inference(avatar_split_clause,[],[f391,f1123])).
% 1.94/0.68 tff(f391,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f283])).
% 1.94/0.68 tff(f1109,plain,(
% 1.94/0.68 spl38_100),
% 1.94/0.68 inference(avatar_split_clause,[],[f554,f1107])).
% 1.94/0.68 tff(f1107,plain,(
% 1.94/0.68 spl38_100 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_100])])).
% 1.94/0.68 tff(f554,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(forward_demodulation,[],[f509,f500])).
% 1.94/0.68 tff(f509,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f344,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(rectify,[],[f343])).
% 1.94/0.68 tff(f343,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f342])).
% 1.94/0.68 tff(f342,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f267])).
% 1.94/0.68 tff(f267,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])).
% 1.94/0.68 tff(f1105,plain,(
% 1.94/0.68 spl38_99),
% 1.94/0.68 inference(avatar_split_clause,[],[f501,f1103])).
% 1.94/0.68 tff(f501,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f192])).
% 1.94/0.68 tff(f192,plain,(
% 1.94/0.68 ! [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)),
% 1.94/0.68 inference(rectify,[],[f87])).
% 1.94/0.68 tff(f87,axiom,(
% 1.94/0.68 ! [X0 : $tType,X1 : $tType,X63 : list(X1),X64 : X1,X81 : fun(X1,fun(list(X1),X0)),X82 : X0] : list_case(X0,X1,X82,X81,cons(X1,X64,X63)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X81,X64),X63)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list_Osimps_I5_J)).
% 1.94/0.68 tff(f1098,plain,(
% 1.94/0.68 spl38_98 | ~spl38_96 | ~spl38_97),
% 1.94/0.68 inference(avatar_split_clause,[],[f1094,f1091,f1072,f1096])).
% 1.94/0.68 tff(f1091,plain,(
% 1.94/0.68 spl38_97 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_97])])).
% 1.94/0.68 tff(f1094,plain,(
% 1.94/0.68 ( ! [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 | ~spl38_97)),
% 1.94/0.68 inference(forward_demodulation,[],[f1092,f1073])).
% 1.94/0.68 tff(f1092,plain,(
% 1.94/0.68 ( ! [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_97),
% 1.94/0.68 inference(avatar_component_clause,[],[f1091])).
% 1.94/0.68 tff(f1093,plain,(
% 1.94/0.68 spl38_97),
% 1.94/0.68 inference(avatar_split_clause,[],[f409,f1091])).
% 1.94/0.68 tff(f409,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f210])).
% 1.94/0.68 tff(f210,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f137])).
% 1.94/0.68 tff(f137,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 inference(rectify,[],[f38])).
% 1.94/0.68 tff(f38,axiom,(
% 1.94/0.68 ! [X9 : nat,X18 : dB] : (pp(aa(dB,bool,it,X18)) => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X18),var(X9)))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_app__Var__IT)).
% 1.94/0.68 tff(f1074,plain,(
% 1.94/0.68 spl38_96),
% 1.94/0.68 inference(avatar_split_clause,[],[f500,f1072])).
% 1.94/0.68 tff(f1067,plain,(
% 1.94/0.68 spl38_95 | ~spl38_94),
% 1.94/0.68 inference(avatar_split_clause,[],[f1063,f1060,f1065])).
% 1.94/0.68 tff(f1060,plain,(
% 1.94/0.68 spl38_94 <=> ! [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)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_94])])).
% 1.94/0.68 tff(f1063,plain,(
% 1.94/0.68 ( ! [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_94),
% 1.94/0.68 inference(forward_demodulation,[],[f1061,f500])).
% 1.94/0.68 tff(f1061,plain,(
% 1.94/0.68 ( ! [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_94),
% 1.94/0.68 inference(avatar_component_clause,[],[f1060])).
% 1.94/0.68 tff(f1062,plain,(
% 1.94/0.68 spl38_94),
% 1.94/0.68 inference(avatar_split_clause,[],[f408,f1060])).
% 1.94/0.68 tff(f408,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f209])).
% 1.94/0.68 tff(f209,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(ennf_transformation,[],[f136])).
% 1.94/0.68 tff(f136,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(rectify,[],[f13])).
% 1.94/0.68 tff(f13,axiom,(
% 1.94/0.68 ! [X9 : nat,X18 : dB] : (pp(aa(dB,bool,it,X18)) => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X18),X9))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_lift__IT)).
% 1.94/0.68 tff(f1058,plain,(
% 1.94/0.68 spl38_93),
% 1.94/0.68 inference(avatar_split_clause,[],[f386,f1056])).
% 1.94/0.68 tff(f386,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f279,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f276,f278,f277])).
% 1.94/0.68 tff(f277,plain,(
% 1.94/0.68 ! [X0 : dB] : (? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) => (pp(aa(dB,bool,it,sK7(X0))) & abs(sK7(X0)) = X0))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f278,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f276,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(rectify,[],[f275])).
% 1.94/0.68 tff(f275,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f274])).
% 1.94/0.68 tff(f274,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f261])).
% 1.94/0.68 tff(f261,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 1.94/0.68 tff(f1053,plain,(
% 1.94/0.68 spl38_92),
% 1.94/0.68 inference(avatar_split_clause,[],[f555,f1051])).
% 1.94/0.68 tff(f1051,plain,(
% 1.94/0.68 spl38_92 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_92])])).
% 1.94/0.68 tff(f555,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(forward_demodulation,[],[f507,f500])).
% 1.94/0.68 tff(f507,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f1049,plain,(
% 1.94/0.68 spl38_91 | ~spl38_8 | ~spl38_29),
% 1.94/0.68 inference(avatar_split_clause,[],[f714,f705,f592,f1046])).
% 1.94/0.68 tff(f1046,plain,(
% 1.94/0.68 spl38_91 <=> sP1(abs(ua))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_91])])).
% 1.94/0.68 tff(f714,plain,(
% 1.94/0.68 sP1(abs(ua)) | (~spl38_8 | ~spl38_29)),
% 1.94/0.68 inference(resolution,[],[f706,f594])).
% 1.94/0.68 tff(f1037,plain,(
% 1.94/0.68 spl38_90),
% 1.94/0.68 inference(avatar_split_clause,[],[f455,f1035])).
% 1.94/0.68 tff(f455,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f166])).
% 1.94/0.68 tff(f166,plain,(
% 1.94/0.68 ! [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)),
% 1.94/0.68 inference(rectify,[],[f60])).
% 1.94/0.68 tff(f60,axiom,(
% 1.94/0.68 ! [X51 : list(dB),X59 : nat,X15 : dB,X39 : dB] : foldl(dB,dB,app,var(X59),X51) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X39)),X15)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Abs__App__neq__Var__apps)).
% 1.94/0.68 tff(f1033,plain,(
% 1.94/0.68 spl38_89),
% 1.94/0.68 inference(avatar_split_clause,[],[f392,f1031])).
% 1.94/0.68 tff(f392,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK10(X0),sK11(X0),zero_zero(nat)),sK12(X0)))) | ~sP0(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f283])).
% 1.94/0.68 tff(f1029,plain,(
% 1.94/0.68 spl38_88),
% 1.94/0.68 inference(avatar_split_clause,[],[f384,f1027])).
% 1.94/0.68 tff(f1027,plain,(
% 1.94/0.68 spl38_88 <=> ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_88])])).
% 1.94/0.68 tff(f384,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 | ~sP1(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f1023,plain,(
% 1.94/0.68 spl38_87),
% 1.94/0.68 inference(avatar_split_clause,[],[f476,f1021])).
% 1.94/0.68 tff(f1021,plain,(
% 1.94/0.68 spl38_87 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_87])])).
% 1.94/0.68 tff(f476,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f327])).
% 1.94/0.68 tff(f327,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f326])).
% 1.94/0.68 tff(f326,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f179])).
% 1.94/0.68 tff(f179,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f58])).
% 1.94/0.68 tff(f58,axiom,(
% 1.94/0.68 ! [X51 : list(dB),X59 : nat,X58 : list(dB),X60 : nat] : (foldl(dB,dB,app,var(X60),X58) = foldl(dB,dB,app,var(X59),X51) <=> (X51 = X58 & X59 = X60))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Var__apps__eq__Var__apps__conv)).
% 1.94/0.68 tff(f1019,plain,(
% 1.94/0.68 spl38_86),
% 1.94/0.68 inference(avatar_split_clause,[],[f473,f1017])).
% 1.94/0.68 tff(f1017,plain,(
% 1.94/0.68 spl38_86 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_86])])).
% 1.94/0.68 tff(f473,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f325])).
% 1.94/0.68 tff(f325,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f324])).
% 1.94/0.68 tff(f324,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f178])).
% 1.94/0.68 tff(f178,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(rectify,[],[f57])).
% 1.94/0.68 tff(f57,axiom,(
% 1.94/0.68 ! [X51 : list(dB),X39 : dB,X58 : list(dB),X52 : dB] : (foldl(dB,dB,app,abs(X52),X58) = foldl(dB,dB,app,abs(X39),X51) <=> (X51 = X58 & X39 = X52))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Abs__apps__eq__Abs__apps__conv)).
% 1.94/0.68 tff(f1014,plain,(
% 1.94/0.68 spl38_85 | ~spl38_9 | ~spl38_29),
% 1.94/0.68 inference(avatar_split_clause,[],[f713,f705,f597,f1011])).
% 1.94/0.68 tff(f1011,plain,(
% 1.94/0.68 spl38_85 <=> sP1(abs(u))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_85])])).
% 1.94/0.68 tff(f713,plain,(
% 1.94/0.68 sP1(abs(u)) | (~spl38_9 | ~spl38_29)),
% 1.94/0.68 inference(resolution,[],[f706,f599])).
% 1.94/0.68 tff(f1009,plain,(
% 1.94/0.68 spl38_84 | ~spl38_83),
% 1.94/0.68 inference(avatar_split_clause,[],[f1005,f1002,f1007])).
% 1.94/0.68 tff(f1002,plain,(
% 1.94/0.68 spl38_83 <=> ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_83])])).
% 1.94/0.68 tff(f1005,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK13(X0,X1)) = X0) ) | ~spl38_83),
% 1.94/0.68 inference(forward_demodulation,[],[f1003,f500])).
% 1.94/0.68 tff(f1003,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | ~spl38_83),
% 1.94/0.68 inference(avatar_component_clause,[],[f1002])).
% 1.94/0.68 tff(f1004,plain,(
% 1.94/0.68 spl38_83),
% 1.94/0.68 inference(avatar_split_clause,[],[f411,f1002])).
% 1.94/0.68 tff(f411,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : dB] : (abs(sK13(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f286])).
% 1.94/0.68 tff(f989,plain,(
% 1.94/0.68 spl38_82 | ~spl38_7 | ~spl38_29),
% 1.94/0.68 inference(avatar_split_clause,[],[f712,f705,f587,f986])).
% 1.94/0.68 tff(f986,plain,(
% 1.94/0.68 spl38_82 <=> sP1(abs(t3))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_82])])).
% 1.94/0.68 tff(f712,plain,(
% 1.94/0.68 sP1(abs(t3)) | (~spl38_7 | ~spl38_29)),
% 1.94/0.68 inference(resolution,[],[f706,f589])).
% 1.94/0.68 tff(f984,plain,(
% 1.94/0.68 spl38_81),
% 1.94/0.68 inference(avatar_split_clause,[],[f553,f982])).
% 1.94/0.68 tff(f553,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(forward_demodulation,[],[f548,f500])).
% 1.94/0.68 tff(f548,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(equality_resolution,[],[f511])).
% 1.94/0.68 tff(f511,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f980,plain,(
% 1.94/0.68 spl38_80),
% 1.94/0.68 inference(avatar_split_clause,[],[f521,f977])).
% 1.94/0.68 tff(f521,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(i),rs)),t1))),
% 1.94/0.68 inference(definition_unfolding,[],[f365,f353])).
% 1.94/0.68 tff(f365,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(n),rs)),t1))),
% 1.94/0.68 inference(cnf_transformation,[],[f44])).
% 1.94/0.68 tff(f44,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,var(n),rs)),t1))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_nT)).
% 1.94/0.68 tff(f975,plain,(
% 1.94/0.68 spl38_79),
% 1.94/0.68 inference(avatar_split_clause,[],[f520,f972])).
% 1.94/0.68 tff(f520,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(i),rs)),t_a))),
% 1.94/0.68 inference(definition_unfolding,[],[f364,f353])).
% 1.94/0.68 tff(f364,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(n),rs)),t_a))),
% 1.94/0.68 inference(cnf_transformation,[],[f73])).
% 1.94/0.68 tff(f73,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,var(n),rs)),t_a))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Var_I2_J)).
% 1.94/0.68 tff(f970,plain,(
% 1.94/0.68 spl38_78),
% 1.94/0.68 inference(avatar_split_clause,[],[f514,f968])).
% 1.94/0.68 tff(f514,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f345])).
% 1.94/0.68 tff(f345,plain,(
% 1.94/0.68 ! [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))))),
% 1.94/0.68 inference(nnf_transformation,[],[f268])).
% 1.94/0.68 tff(f268,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(definition_folding,[],[f198,f267])).
% 1.94/0.68 tff(f198,plain,(
% 1.94/0.68 ! [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)))))),
% 1.94/0.68 inference(rectify,[],[f94])).
% 1.94/0.68 tff(f94,axiom,(
% 1.94/0.68 ! [X0 : $tType,X67 : list(X0),X37 : X0,X90 : list(X0),X91 : X0,X52 : fun(X0,fun(X0,bool))] : (step1(X0,X52,cons(X0,X91,X90),cons(X0,X37,X67)) <=> ((step1(X0,X52,X90,X67) & X37 = X91) | (X67 = X90 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X52,X91),X37)))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Cons__step1__Cons)).
% 1.94/0.68 tff(f966,plain,(
% 1.94/0.68 spl38_77),
% 1.94/0.68 inference(avatar_split_clause,[],[f513,f964])).
% 1.94/0.68 tff(f513,plain,(
% 1.94/0.68 ( ! [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))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f345])).
% 1.94/0.68 tff(f962,plain,(
% 1.94/0.68 spl38_76),
% 1.94/0.68 inference(avatar_split_clause,[],[f475,f960])).
% 1.94/0.68 tff(f960,plain,(
% 1.94/0.68 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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_76])])).
% 1.94/0.68 tff(f475,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f327])).
% 1.94/0.68 tff(f958,plain,(
% 1.94/0.68 spl38_75),
% 1.94/0.68 inference(avatar_split_clause,[],[f472,f956])).
% 1.94/0.68 tff(f956,plain,(
% 1.94/0.68 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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_75])])).
% 1.94/0.68 tff(f472,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f325])).
% 1.94/0.68 tff(f954,plain,(
% 1.94/0.68 spl38_74),
% 1.94/0.68 inference(avatar_split_clause,[],[f382,f952])).
% 1.94/0.68 tff(f952,plain,(
% 1.94/0.68 spl38_74 <=> ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_74])])).
% 1.94/0.68 tff(f382,plain,(
% 1.94/0.68 ( ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f206])).
% 1.94/0.68 tff(f206,plain,(
% 1.94/0.68 ! [X0 : list(dB)] : (listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) | ~listsp(dB,it,X0))),
% 1.94/0.68 inference(ennf_transformation,[],[f122])).
% 1.94/0.68 tff(f122,plain,(
% 1.94/0.68 ! [X0 : list(dB)] : (listsp(dB,it,X0) => listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)))),
% 1.94/0.68 inference(rectify,[],[f98])).
% 1.94/0.68 tff(f98,axiom,(
% 1.94/0.68 ! [X54 : list(dB)] : (listsp(dB,it,X54) => listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X54)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_lifts__IT)).
% 1.94/0.68 tff(f950,plain,(
% 1.94/0.68 spl38_73),
% 1.94/0.68 inference(avatar_split_clause,[],[f363,f947])).
% 1.94/0.68 tff(f363,plain,(
% 1.94/0.68 t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))),
% 1.94/0.68 inference(cnf_transformation,[],[f48])).
% 1.94/0.68 tff(f48,axiom,(
% 1.94/0.68 t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_T)).
% 1.94/0.68 tff(f945,plain,(
% 1.94/0.68 spl38_72 | ~spl38_15 | ~spl38_21),
% 1.94/0.68 inference(avatar_split_clause,[],[f680,f659,f630,f943])).
% 1.94/0.68 tff(f943,plain,(
% 1.94/0.68 spl38_72 <=> ! [X0 : nat] : sP1(var(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_72])])).
% 1.94/0.68 tff(f680,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (sP1(var(X0))) ) | (~spl38_15 | ~spl38_21)),
% 1.94/0.68 inference(resolution,[],[f660,f631])).
% 1.94/0.68 tff(f941,plain,(
% 1.94/0.68 spl38_71),
% 1.94/0.68 inference(avatar_split_clause,[],[f438,f939])).
% 1.94/0.68 tff(f939,plain,(
% 1.94/0.68 spl38_71 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1 | ~sP2(X0,X1,X2))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_71])])).
% 1.94/0.68 tff(f438,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK19(X0,X1,X2),sK20(X0,X1,X2)) = X1 | ~sP2(X0,X1,X2)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f297])).
% 1.94/0.68 tff(f934,plain,(
% 1.94/0.68 spl38_70 | ~spl38_69),
% 1.94/0.68 inference(avatar_split_clause,[],[f929,f925,f931])).
% 1.94/0.68 tff(f925,plain,(
% 1.94/0.68 spl38_69 <=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_69])])).
% 1.94/0.68 tff(f929,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))) | ~spl38_69),
% 1.94/0.68 inference(forward_demodulation,[],[f927,f500])).
% 1.94/0.68 tff(f927,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))) | ~spl38_69),
% 1.94/0.68 inference(avatar_component_clause,[],[f925])).
% 1.94/0.68 tff(f928,plain,(
% 1.94/0.68 spl38_69),
% 1.94/0.68 inference(avatar_split_clause,[],[f362,f925])).
% 1.94/0.68 tff(f362,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.94/0.68 inference(cnf_transformation,[],[f8])).
% 1.94/0.68 tff(f8,axiom,(
% 1.94/0.68 pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__096IT_A_Ilift_Au_A0_J_096)).
% 1.94/0.68 tff(f908,plain,(
% 1.94/0.68 spl38_68),
% 1.94/0.68 inference(avatar_split_clause,[],[f510,f906])).
% 1.94/0.68 tff(f906,plain,(
% 1.94/0.68 spl38_68 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_68])])).
% 1.94/0.68 tff(f510,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f904,plain,(
% 1.94/0.68 spl38_67),
% 1.94/0.68 inference(avatar_split_clause,[],[f452,f902])).
% 1.94/0.68 tff(f902,plain,(
% 1.94/0.68 spl38_67 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_67])])).
% 1.94/0.68 tff(f452,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f312])).
% 1.94/0.68 tff(f312,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f164])).
% 1.94/0.68 tff(f164,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : list(dB),X2 : dB] : (foldl(dB,dB,app,X0,X1) = foldl(dB,dB,app,X2,X1) <=> X0 = X2)),
% 1.94/0.68 inference(rectify,[],[f59])).
% 1.94/0.68 tff(f59,axiom,(
% 1.94/0.68 ! [X39 : dB,X54 : list(dB),X52 : dB] : (foldl(dB,dB,app,X52,X54) = foldl(dB,dB,app,X39,X54) <=> X39 = X52)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_apps__eq__tail__conv)).
% 1.94/0.68 tff(f900,plain,(
% 1.94/0.68 spl38_66),
% 1.94/0.68 inference(avatar_split_clause,[],[f431,f898])).
% 1.94/0.68 tff(f431,plain,(
% 1.94/0.68 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f218])).
% 1.94/0.68 tff(f218,plain,(
% 1.94/0.68 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.94/0.68 inference(ennf_transformation,[],[f155])).
% 1.94/0.68 tff(f155,plain,(
% 1.94/0.68 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) => aa(nat,type,X2,X1) = X0)),
% 1.94/0.68 inference(rectify,[],[f26])).
% 1.94/0.68 tff(f26,axiom,(
% 1.94/0.68 ! [X12 : type,X13 : nat,X14 : fun(nat,type)] : (pp(aa(type,bool,typing(X14,var(X13)),X12)) => aa(nat,type,X14,X13) = X12)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_typing__elims_I1_J)).
% 1.94/0.68 tff(f896,plain,(
% 1.94/0.68 spl38_65),
% 1.94/0.68 inference(avatar_split_clause,[],[f426,f894])).
% 1.94/0.68 tff(f426,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f214])).
% 1.94/0.68 tff(f214,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 1.94/0.68 inference(ennf_transformation,[],[f151])).
% 1.94/0.68 tff(f151,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,X2)) => pp(aa(dB,bool,it,subst(X2,var(X1),X0))))),
% 1.94/0.68 inference(rectify,[],[f9])).
% 1.94/0.68 tff(f9,axiom,(
% 1.94/0.68 ! [X8 : nat,X9 : nat,X10 : dB] : (pp(aa(dB,bool,it,X10)) => pp(aa(dB,bool,it,subst(X10,var(X9),X8))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_subst__Var__IT)).
% 1.94/0.68 tff(f892,plain,(
% 1.94/0.68 spl38_64 | ~spl38_63),
% 1.94/0.68 inference(avatar_split_clause,[],[f888,f885,f890])).
% 1.94/0.68 tff(f885,plain,(
% 1.94/0.68 spl38_63 <=> ! [X2 : dB,X0 : dB,X1 : nat] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_63])])).
% 1.94/0.68 tff(f888,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),X0,X1) = X2) ) | ~spl38_63),
% 1.94/0.68 inference(forward_demodulation,[],[f886,f500])).
% 1.94/0.68 tff(f886,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2) ) | ~spl38_63),
% 1.94/0.68 inference(avatar_component_clause,[],[f885])).
% 1.94/0.68 tff(f887,plain,(
% 1.94/0.68 spl38_63),
% 1.94/0.68 inference(avatar_split_clause,[],[f423,f885])).
% 1.94/0.68 tff(f423,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : nat] : (subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2) )),
% 1.94/0.68 inference(cnf_transformation,[],[f148])).
% 1.94/0.68 tff(f148,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : nat,X2 : dB] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1),X0,X1) = X2),
% 1.94/0.68 inference(rectify,[],[f19])).
% 1.94/0.68 tff(f19,axiom,(
% 1.94/0.68 ! [X22 : dB,X23 : nat,X18 : dB] : subst(aa(nat,dB,aa(dB,fun(nat,dB),lift,X18),X23),X22,X23) = X18),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_subst__lift)).
% 1.94/0.68 tff(f883,plain,(
% 1.94/0.68 spl38_62),
% 1.94/0.68 inference(avatar_split_clause,[],[f407,f881])).
% 1.94/0.68 tff(f407,plain,(
% 1.94/0.68 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f208])).
% 1.94/0.68 tff(f208,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 1.94/0.68 inference(ennf_transformation,[],[f135])).
% 1.94/0.68 tff(f135,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : list(dB)] : (listsp(dB,it,X1) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))))),
% 1.94/0.68 inference(rectify,[],[f70])).
% 1.94/0.68 tff(f70,axiom,(
% 1.94/0.68 ! [X59 : nat,X58 : list(dB)] : (listsp(dB,it,X58) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X59),X58))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_IT_OVar)).
% 1.94/0.68 tff(f876,plain,(
% 1.94/0.68 spl38_61 | ~spl38_60),
% 1.94/0.68 inference(avatar_split_clause,[],[f872,f869,f874])).
% 1.94/0.68 tff(f869,plain,(
% 1.94/0.68 spl38_60 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_60])])).
% 1.94/0.68 tff(f872,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_60),
% 1.94/0.68 inference(forward_demodulation,[],[f870,f500])).
% 1.94/0.68 tff(f870,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) ) | ~spl38_60),
% 1.94/0.68 inference(avatar_component_clause,[],[f869])).
% 1.94/0.68 tff(f871,plain,(
% 1.94/0.68 spl38_60),
% 1.94/0.68 inference(avatar_split_clause,[],[f404,f869])).
% 1.94/0.68 tff(f404,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f132])).
% 1.94/0.68 tff(f132,plain,(
% 1.94/0.68 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 1.94/0.68 inference(rectify,[],[f107])).
% 1.94/0.68 tff(f107,axiom,(
% 1.94/0.68 ! [X95 : bool,X96 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)) | ~pp(X95) | ~pp(X96))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 1.94/0.68 tff(f867,plain,(
% 1.94/0.68 spl38_59),
% 1.94/0.68 inference(avatar_split_clause,[],[f387,f865])).
% 1.94/0.68 tff(f387,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP0(X0) | pp(aa(dB,bool,it,sK7(X0))) | listsp(dB,it,sK8(X0)) | ~sP1(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f863,plain,(
% 1.94/0.68 spl38_58),
% 1.94/0.68 inference(avatar_split_clause,[],[f454,f861])).
% 1.94/0.68 tff(f861,plain,(
% 1.94/0.68 spl38_58 <=> ! [X2 : list(dB),X0 : list(dB),X1 : dB,X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_58])])).
% 1.94/0.68 tff(f454,plain,(
% 1.94/0.68 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f165])).
% 1.94/0.68 tff(f165,plain,(
% 1.94/0.68 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 1.94/0.68 inference(rectify,[],[f61])).
% 1.94/0.68 tff(f61,axiom,(
% 1.94/0.68 ! [X51 : list(dB),X52 : dB,X54 : list(dB),X59 : nat] : foldl(dB,dB,app,var(X59),X54) != foldl(dB,dB,app,abs(X52),X51)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Var__apps__neq__Abs__apps)).
% 1.94/0.68 tff(f855,plain,(
% 1.94/0.68 spl38_57),
% 1.94/0.68 inference(avatar_split_clause,[],[f508,f853])).
% 1.94/0.68 tff(f853,plain,(
% 1.94/0.68 spl38_57 <=> ! [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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_57])])).
% 1.94/0.68 tff(f508,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f851,plain,(
% 1.94/0.68 spl38_56),
% 1.94/0.68 inference(avatar_split_clause,[],[f498,f849])).
% 1.94/0.68 tff(f498,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f339])).
% 1.94/0.68 tff(f339,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(flattening,[],[f338])).
% 1.94/0.68 tff(f338,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(nnf_transformation,[],[f190])).
% 1.94/0.68 tff(f190,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : (cons(X0,X2,X1) = cons(X0,X4,X3) <=> (X1 = X3 & X2 = X4))),
% 1.94/0.68 inference(rectify,[],[f64])).
% 1.94/0.68 tff(f64,axiom,(
% 1.94/0.68 ! [X0 : $tType,X61 : list(X0),X62 : X0,X63 : list(X0),X64 : X0] : (cons(X0,X64,X63) = cons(X0,X62,X61) <=> (X61 = X63 & X62 = X64))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_list_Oinject)).
% 1.94/0.68 tff(f847,plain,(
% 1.94/0.68 spl38_55),
% 1.94/0.68 inference(avatar_split_clause,[],[f446,f845])).
% 1.94/0.68 tff(f845,plain,(
% 1.94/0.68 spl38_55 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP3(X0,X1,X2))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_55])])).
% 1.94/0.68 tff(f446,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK24(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP3(X0,X1,X2)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f307])).
% 1.94/0.68 tff(f307,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f305,f306])).
% 1.94/0.68 tff(f306,plain,(
% 1.94/0.68 ! [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))),
% 1.94/0.68 introduced(choice_axiom,[])).
% 1.94/0.68 tff(f305,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (abs(X3) = X0 & subst(X3,X2,zero_zero(nat)) = X1) | ~sP3(X0,X1,X2))),
% 1.94/0.68 inference(rectify,[],[f304])).
% 1.94/0.68 tff(f304,plain,(
% 1.94/0.68 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP3(X2,X0,X1))),
% 1.94/0.68 inference(nnf_transformation,[],[f265])).
% 1.94/0.68 tff(f843,plain,(
% 1.94/0.68 spl38_54),
% 1.94/0.68 inference(avatar_split_clause,[],[f421,f841])).
% 1.94/0.68 tff(f421,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : nat,X1 : dB] : (var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f146])).
% 1.94/0.68 tff(f146,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : dB,X2 : dB] : var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 1.94/0.68 inference(rectify,[],[f36])).
% 1.94/0.68 tff(f36,axiom,(
% 1.94/0.68 ! [X40 : nat,X44 : dB,X45 : dB] : var(X40) != aa(dB,dB,aa(dB,fun(dB,dB),app,X45),X44)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dB_Osimps_I5_J)).
% 1.94/0.68 tff(f839,plain,(
% 1.94/0.68 spl38_53),
% 1.94/0.68 inference(avatar_split_clause,[],[f419,f837])).
% 1.94/0.68 tff(f419,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f144])).
% 1.94/0.68 tff(f144,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : dB,X2 : dB] : abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 1.94/0.68 inference(rectify,[],[f35])).
% 1.94/0.68 tff(f35,axiom,(
% 1.94/0.68 ! [X41 : dB,X42 : dB,X43 : dB] : abs(X41) != aa(dB,dB,aa(dB,fun(dB,dB),app,X43),X42)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_dB_Osimps_I8_J)).
% 1.94/0.68 tff(f834,plain,(
% 1.94/0.68 spl38_52 | ~spl38_51),
% 1.94/0.68 inference(avatar_split_clause,[],[f830,f827,f832])).
% 1.94/0.68 tff(f832,plain,(
% 1.94/0.68 spl38_52 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_52])])).
% 1.94/0.68 tff(f827,plain,(
% 1.94/0.68 spl38_51 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_51])])).
% 1.94/0.68 tff(f830,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1)) ) | ~spl38_51),
% 1.94/0.68 inference(forward_demodulation,[],[f828,f500])).
% 1.94/0.68 tff(f828,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl38_51),
% 1.94/0.68 inference(avatar_component_clause,[],[f827])).
% 1.94/0.68 tff(f829,plain,(
% 1.94/0.68 spl38_51),
% 1.94/0.68 inference(avatar_split_clause,[],[f406,f827])).
% 1.94/0.68 tff(f406,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f134])).
% 1.94/0.68 tff(f134,plain,(
% 1.94/0.68 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.94/0.68 inference(rectify,[],[f108])).
% 1.94/0.68 tff(f108,axiom,(
% 1.94/0.68 ! [X95 : bool,X96 : bool] : (pp(X96) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 1.94/0.68 tff(f824,plain,(
% 1.94/0.68 spl38_50 | ~spl38_8 | ~spl38_21),
% 1.94/0.68 inference(avatar_split_clause,[],[f683,f659,f592,f821])).
% 1.94/0.68 tff(f821,plain,(
% 1.94/0.68 spl38_50 <=> sP1(ua)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_50])])).
% 1.94/0.68 tff(f683,plain,(
% 1.94/0.68 sP1(ua) | (~spl38_8 | ~spl38_21)),
% 1.94/0.68 inference(resolution,[],[f660,f594])).
% 1.94/0.68 tff(f819,plain,(
% 1.94/0.68 spl38_49 | ~spl38_48),
% 1.94/0.68 inference(avatar_split_clause,[],[f815,f812,f817])).
% 1.94/0.68 tff(f812,plain,(
% 1.94/0.68 spl38_48 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_48])])).
% 1.94/0.68 tff(f815,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl38_48),
% 1.94/0.68 inference(forward_demodulation,[],[f813,f500])).
% 1.94/0.68 tff(f813,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl38_48),
% 1.94/0.68 inference(avatar_component_clause,[],[f812])).
% 1.94/0.68 tff(f814,plain,(
% 1.94/0.68 spl38_48),
% 1.94/0.68 inference(avatar_split_clause,[],[f405,f812])).
% 1.94/0.68 tff(f405,plain,(
% 1.94/0.68 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f133])).
% 1.94/0.68 tff(f133,plain,(
% 1.94/0.68 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 1.94/0.68 inference(rectify,[],[f109])).
% 1.94/0.68 tff(f109,axiom,(
% 1.94/0.68 ! [X95 : bool,X96 : bool] : (pp(X95) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X96),X95)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 1.94/0.68 tff(f810,plain,(
% 1.94/0.68 spl38_47),
% 1.94/0.68 inference(avatar_split_clause,[],[f385,f808])).
% 1.94/0.68 tff(f808,plain,(
% 1.94/0.68 spl38_47 <=> ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | listsp(dB,it,sK8(X0)) | ~sP1(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_47])])).
% 1.94/0.68 tff(f385,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP0(X0) | abs(sK7(X0)) = X0 | listsp(dB,it,sK8(X0)) | ~sP1(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f796,plain,(
% 1.94/0.68 spl38_46),
% 1.94/0.68 inference(avatar_split_clause,[],[f551,f793])).
% 1.94/0.68 tff(f793,plain,(
% 1.94/0.68 spl38_46 <=> pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),t))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_46])])).
% 1.94/0.68 tff(f551,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),t))),
% 1.94/0.68 inference(forward_demodulation,[],[f522,f363])).
% 1.94/0.68 tff(f522,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(i)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 inference(definition_unfolding,[],[f367,f353])).
% 1.94/0.68 tff(f367,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 inference(cnf_transformation,[],[f42])).
% 1.94/0.68 tff(f42,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_varT)).
% 1.94/0.68 tff(f791,plain,(
% 1.94/0.68 spl38_45),
% 1.94/0.68 inference(avatar_split_clause,[],[f534,f789])).
% 1.94/0.68 tff(f534,plain,(
% 1.94/0.68 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) )),
% 1.94/0.68 inference(equality_resolution,[],[f427])).
% 1.94/0.68 tff(f427,plain,(
% 1.94/0.68 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0) )),
% 1.94/0.68 inference(cnf_transformation,[],[f215])).
% 1.94/0.68 tff(f215,plain,(
% 1.94/0.68 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0)),
% 1.94/0.68 inference(ennf_transformation,[],[f152])).
% 1.94/0.68 tff(f152,plain,(
% 1.94/0.68 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 => pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 1.94/0.68 inference(rectify,[],[f25])).
% 1.94/0.68 tff(f25,axiom,(
% 1.94/0.68 ! [X12 : type,X37 : nat,X38 : fun(nat,type)] : (aa(nat,type,X38,X37) = X12 => pp(aa(type,bool,typing(X38,var(X37)),X12)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_typing_OVar)).
% 1.94/0.68 tff(f787,plain,(
% 1.94/0.68 spl38_44 | ~spl38_9 | ~spl38_21),
% 1.94/0.68 inference(avatar_split_clause,[],[f682,f659,f597,f784])).
% 1.94/0.68 tff(f784,plain,(
% 1.94/0.68 spl38_44 <=> sP1(u)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_44])])).
% 1.94/0.68 tff(f682,plain,(
% 1.94/0.68 sP1(u) | (~spl38_9 | ~spl38_21)),
% 1.94/0.68 inference(resolution,[],[f660,f599])).
% 1.94/0.68 tff(f782,plain,(
% 1.94/0.68 spl38_43),
% 1.94/0.68 inference(avatar_split_clause,[],[f497,f780])).
% 1.94/0.68 tff(f497,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f339])).
% 1.94/0.68 tff(f777,plain,(
% 1.94/0.68 spl38_42 | ~spl38_41),
% 1.94/0.68 inference(avatar_split_clause,[],[f773,f770,f775])).
% 1.94/0.68 tff(f770,plain,(
% 1.94/0.68 spl38_41 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_41])])).
% 1.94/0.68 tff(f773,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl38_41),
% 1.94/0.68 inference(forward_demodulation,[],[f771,f500])).
% 1.94/0.68 tff(f771,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) ) | ~spl38_41),
% 1.94/0.68 inference(avatar_component_clause,[],[f770])).
% 1.94/0.68 tff(f772,plain,(
% 1.94/0.68 spl38_41),
% 1.94/0.68 inference(avatar_split_clause,[],[f402,f770])).
% 1.94/0.68 tff(f402,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f130])).
% 1.94/0.68 tff(f130,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 1.94/0.68 inference(rectify,[],[f80])).
% 1.94/0.68 tff(f80,axiom,(
% 1.94/0.68 ! [X18 : dB,X9 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X9)),X18))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_beta__cases_I1_J)).
% 1.94/0.68 tff(f768,plain,(
% 1.94/0.68 spl38_40),
% 1.94/0.68 inference(avatar_split_clause,[],[f383,f766])).
% 1.94/0.68 tff(f383,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f207])).
% 1.94/0.68 tff(f207,plain,(
% 1.94/0.68 ! [X0 : dB] : (pp(aa(dB,bool,it,abs(X0))) | ~pp(aa(dB,bool,it,X0)))),
% 1.94/0.68 inference(ennf_transformation,[],[f123])).
% 1.94/0.68 tff(f123,plain,(
% 1.94/0.68 ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) => pp(aa(dB,bool,it,abs(X0))))),
% 1.94/0.68 inference(rectify,[],[f18])).
% 1.94/0.68 tff(f18,axiom,(
% 1.94/0.68 ! [X10 : dB] : (pp(aa(dB,bool,it,X10)) => pp(aa(dB,bool,it,abs(X10))))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Lambda)).
% 1.94/0.68 tff(f764,plain,(
% 1.94/0.68 spl38_39),
% 1.94/0.68 inference(avatar_split_clause,[],[f375,f761])).
% 1.94/0.68 tff(f761,plain,(
% 1.94/0.68 spl38_39 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK6))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_39])])).
% 1.94/0.68 tff(f375,plain,(
% 1.94/0.68 pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK6))),
% 1.94/0.68 inference(cnf_transformation,[],[f272])).
% 1.94/0.68 tff(f759,plain,(
% 1.94/0.68 spl38_38),
% 1.94/0.68 inference(avatar_split_clause,[],[f361,f756])).
% 1.94/0.68 tff(f756,plain,(
% 1.94/0.68 spl38_38 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_38])])).
% 1.94/0.68 tff(f361,plain,(
% 1.94/0.68 pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts))),
% 1.94/0.68 inference(cnf_transformation,[],[f16])).
% 1.94/0.68 tff(f16,axiom,(
% 1.94/0.68 pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_argsT)).
% 1.94/0.68 tff(f753,plain,(
% 1.94/0.68 spl38_37 | ~spl38_7 | ~spl38_21),
% 1.94/0.68 inference(avatar_split_clause,[],[f681,f659,f587,f750])).
% 1.94/0.68 tff(f750,plain,(
% 1.94/0.68 spl38_37 <=> sP1(t3)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_37])])).
% 1.94/0.68 tff(f681,plain,(
% 1.94/0.68 sP1(t3) | (~spl38_7 | ~spl38_21)),
% 1.94/0.68 inference(resolution,[],[f660,f589])).
% 1.94/0.68 tff(f747,plain,(
% 1.94/0.68 spl38_36),
% 1.94/0.68 inference(avatar_split_clause,[],[f547,f745])).
% 1.94/0.68 tff(f745,plain,(
% 1.94/0.68 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))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_36])])).
% 1.94/0.68 tff(f547,plain,(
% 1.94/0.68 ( ! [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)) )),
% 1.94/0.68 inference(equality_resolution,[],[f512])).
% 1.94/0.68 tff(f512,plain,(
% 1.94/0.68 ( ! [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) )),
% 1.94/0.68 inference(cnf_transformation,[],[f344])).
% 1.94/0.68 tff(f743,plain,(
% 1.94/0.68 spl38_35),
% 1.94/0.68 inference(avatar_split_clause,[],[f530,f741])).
% 1.94/0.68 tff(f741,plain,(
% 1.94/0.68 spl38_35 <=> ! [X2 : list(dB),X3 : nat] : (sP1(foldl(dB,dB,app,var(X3),X2)) | ~listsp(dB,it,X2))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_35])])).
% 1.94/0.68 tff(f530,plain,(
% 1.94/0.68 ( ! [X2 : list(dB),X3 : nat] : (sP1(foldl(dB,dB,app,var(X3),X2)) | ~listsp(dB,it,X2)) )),
% 1.94/0.68 inference(equality_resolution,[],[f388])).
% 1.94/0.68 tff(f388,plain,(
% 1.94/0.68 ( ! [X2 : list(dB),X3 : nat,X0 : dB] : (sP1(X0) | ~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f739,plain,(
% 1.94/0.68 spl38_34),
% 1.94/0.68 inference(avatar_split_clause,[],[f373,f736])).
% 1.94/0.68 tff(f373,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),a),sK5))),
% 1.94/0.68 inference(cnf_transformation,[],[f270])).
% 1.94/0.68 tff(f734,plain,(
% 1.94/0.68 spl38_33),
% 1.94/0.68 inference(avatar_split_clause,[],[f360,f731])).
% 1.94/0.68 tff(f360,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),a),t2))),
% 1.94/0.68 inference(cnf_transformation,[],[f7])).
% 1.94/0.68 tff(f7,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(shift(type,e,i,t),a),t2))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_argT)).
% 1.94/0.68 tff(f728,plain,(
% 1.94/0.68 spl38_32),
% 1.94/0.68 inference(avatar_split_clause,[],[f544,f726])).
% 1.94/0.68 tff(f544,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) )),
% 1.94/0.68 inference(equality_resolution,[],[f488])).
% 1.94/0.68 tff(f488,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4) )),
% 1.94/0.68 inference(cnf_transformation,[],[f241])).
% 1.94/0.68 tff(f241,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4)),
% 1.94/0.68 inference(ennf_transformation,[],[f184])).
% 1.94/0.68 tff(f184,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (X3 = X4 => aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1)),
% 1.94/0.68 inference(rectify,[],[f37])).
% 1.94/0.68 tff(f37,axiom,(
% 1.94/0.68 ! [X0 : $tType,X12 : X0,X14 : fun(nat,X0),X46 : nat,X13 : nat] : (X13 = X46 => aa(nat,X0,shift(X0,X14,X13,X12),X46) = X12)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_shift__eq)).
% 1.94/0.68 tff(f724,plain,(
% 1.94/0.68 spl38_31),
% 1.94/0.68 inference(avatar_split_clause,[],[f447,f722])).
% 1.94/0.68 tff(f722,plain,(
% 1.94/0.68 spl38_31 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK24(X0,X1,X2)) = X0 | ~sP3(X0,X1,X2))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_31])])).
% 1.94/0.68 tff(f447,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK24(X0,X1,X2)) = X0 | ~sP3(X0,X1,X2)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f307])).
% 1.94/0.68 tff(f720,plain,(
% 1.94/0.68 spl38_30),
% 1.94/0.68 inference(avatar_split_clause,[],[f437,f718])).
% 1.94/0.68 tff(f718,plain,(
% 1.94/0.68 spl38_30 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK18(X0,X1,X2)) = X2 | ~sP2(X0,X1,X2))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_30])])).
% 1.94/0.68 tff(f437,plain,(
% 1.94/0.68 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK18(X0,X1,X2)) = X2 | ~sP2(X0,X1,X2)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f297])).
% 1.94/0.68 tff(f707,plain,(
% 1.94/0.68 spl38_29),
% 1.94/0.68 inference(avatar_split_clause,[],[f529,f705])).
% 1.94/0.68 tff(f529,plain,(
% 1.94/0.68 ( ! [X1 : dB] : (sP1(abs(X1)) | ~pp(aa(dB,bool,it,X1))) )),
% 1.94/0.68 inference(equality_resolution,[],[f389])).
% 1.94/0.68 tff(f389,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f703,plain,(
% 1.94/0.68 spl38_28),
% 1.94/0.68 inference(avatar_split_clause,[],[f401,f701])).
% 1.94/0.68 tff(f701,plain,(
% 1.94/0.68 spl38_28 <=> ! [X0 : $tType,X1 : list(X0)] : map(X0,X0,combi(X0),X1) = X1),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_28])])).
% 1.94/0.68 tff(f401,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X1 : list(X0)] : (map(X0,X0,combi(X0),X1) = X1) )),
% 1.94/0.68 inference(cnf_transformation,[],[f129])).
% 1.94/0.68 tff(f129,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : list(X0)] : map(X0,X0,combi(X0),X1) = X1),
% 1.94/0.68 inference(rectify,[],[f99])).
% 1.94/0.68 tff(f99,axiom,(
% 1.94/0.68 ! [X0 : $tType,X78 : list(X0)] : map(X0,X0,combi(X0),X78) = X78),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_map__ident)).
% 1.94/0.68 tff(f699,plain,(
% 1.94/0.68 spl38_27),
% 1.94/0.68 inference(avatar_split_clause,[],[f393,f697])).
% 1.94/0.68 tff(f393,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (pp(aa(dB,bool,it,sK11(X0))) | ~sP0(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f283])).
% 1.94/0.68 tff(f692,plain,(
% 1.94/0.68 ~spl38_26 | spl38_4 | ~spl38_22),
% 1.94/0.68 inference(avatar_split_clause,[],[f685,f663,f574,f689])).
% 1.94/0.68 tff(f689,plain,(
% 1.94/0.68 spl38_26 <=> sP1(subst(a,u,i))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_26])])).
% 1.94/0.68 tff(f685,plain,(
% 1.94/0.68 ~sP1(subst(a,u,i)) | (spl38_4 | ~spl38_22)),
% 1.94/0.68 inference(resolution,[],[f664,f576])).
% 1.94/0.68 tff(f677,plain,(
% 1.94/0.68 spl38_25),
% 1.94/0.68 inference(avatar_split_clause,[],[f415,f675])).
% 1.94/0.68 tff(f675,plain,(
% 1.94/0.68 spl38_25 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_25])])).
% 1.94/0.68 tff(f415,plain,(
% 1.94/0.68 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f288])).
% 1.94/0.68 tff(f288,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : nat] : ((var(X0) = var(X1) | X0 != X1) & (X0 = X1 | var(X0) != var(X1)))),
% 1.94/0.68 inference(nnf_transformation,[],[f141])).
% 1.94/0.68 tff(f141,plain,(
% 1.94/0.68 ! [X0 : nat,X1 : nat] : (var(X0) = var(X1) <=> X0 = X1)),
% 1.94/0.68 inference(rectify,[],[f21])).
% 1.94/0.68 tff(f21,axiom,(
% 1.94/0.68 ! [X28 : nat,X29 : nat] : (var(X29) = var(X28) <=> X28 = X29)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dB_Osimps_I1_J)).
% 1.94/0.68 tff(f673,plain,(
% 1.94/0.68 spl38_24),
% 1.94/0.68 inference(avatar_split_clause,[],[f413,f671])).
% 1.94/0.68 tff(f671,plain,(
% 1.94/0.68 spl38_24 <=> ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_24])])).
% 1.94/0.68 tff(f413,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f287])).
% 1.94/0.68 tff(f287,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : dB] : ((abs(X0) = abs(X1) | X0 != X1) & (X0 = X1 | abs(X0) != abs(X1)))),
% 1.94/0.68 inference(nnf_transformation,[],[f140])).
% 1.94/0.68 tff(f140,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : dB] : (abs(X0) = abs(X1) <=> X0 = X1)),
% 1.94/0.68 inference(rectify,[],[f22])).
% 1.94/0.68 tff(f22,axiom,(
% 1.94/0.68 ! [X30 : dB,X31 : dB] : (abs(X31) = abs(X30) <=> X30 = X31)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_dB_Osimps_I3_J)).
% 1.94/0.68 tff(f669,plain,(
% 1.94/0.68 spl38_23),
% 1.94/0.68 inference(avatar_split_clause,[],[f400,f667])).
% 1.94/0.68 tff(f400,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X1 : X0] : (aa(X0,X0,combi(X0),X1) = X1) )),
% 1.94/0.68 inference(cnf_transformation,[],[f128])).
% 1.94/0.68 tff(f128,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : X0] : aa(X0,X0,combi(X0),X1) = X1),
% 1.94/0.68 inference(rectify,[],[f105])).
% 1.94/0.68 tff(f105,axiom,(
% 1.94/0.68 ! [X0 : $tType,X96 : X0] : aa(X0,X0,combi(X0),X96) = X96),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U)).
% 1.94/0.68 tff(f665,plain,(
% 1.94/0.68 spl38_22),
% 1.94/0.68 inference(avatar_split_clause,[],[f396,f663])).
% 1.94/0.68 tff(f396,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) | ~sP1(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f284])).
% 1.94/0.68 tff(f284,plain,(
% 1.94/0.68 ! [X0 : dB] : ((pp(aa(dB,bool,it,X0)) | ~sP1(X0)) & (sP1(X0) | ~pp(aa(dB,bool,it,X0))))),
% 1.94/0.68 inference(nnf_transformation,[],[f262])).
% 1.94/0.68 tff(f262,plain,(
% 1.94/0.68 ! [X0 : dB] : (pp(aa(dB,bool,it,X0)) <=> sP1(X0))),
% 1.94/0.68 inference(definition_folding,[],[f124,f261,f260])).
% 1.94/0.68 tff(f124,plain,(
% 1.94/0.68 ! [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)))),
% 1.94/0.68 inference(rectify,[],[f72])).
% 1.94/0.68 tff(f72,axiom,(
% 1.94/0.68 ! [X64 : dB] : (pp(aa(dB,bool,it,X64)) <=> (? [X71 : dB,X72 : dB,X73 : list(dB)] : (pp(aa(dB,bool,it,X72)) & pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X71,X72,zero_zero(nat)),X73))) & foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X71)),X72),X73) = X64) | ? [X71 : dB] : (pp(aa(dB,bool,it,X71)) & abs(X71) = X64) | ? [X69 : list(dB),X70 : nat] : (listsp(dB,it,X69) & foldl(dB,dB,app,var(X70),X69) = X64)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_IT_Osimps)).
% 1.94/0.68 tff(f661,plain,(
% 1.94/0.68 spl38_21),
% 1.94/0.68 inference(avatar_split_clause,[],[f395,f659])).
% 1.94/0.68 tff(f395,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP1(X0) | ~pp(aa(dB,bool,it,X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f284])).
% 1.94/0.68 tff(f657,plain,(
% 1.94/0.68 spl38_20),
% 1.94/0.68 inference(avatar_split_clause,[],[f359,f654])).
% 1.94/0.68 tff(f359,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(e,u),t))),
% 1.94/0.68 inference(cnf_transformation,[],[f4])).
% 1.94/0.68 tff(f4,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(e,u),t))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_uT)).
% 1.94/0.68 tff(f652,plain,(
% 1.94/0.68 ~spl38_19 | ~spl38_12 | ~spl38_17),
% 1.94/0.68 inference(avatar_split_clause,[],[f642,f638,f617,f649])).
% 1.94/0.68 tff(f649,plain,(
% 1.94/0.68 spl38_19 <=> rs = as),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_19])])).
% 1.94/0.68 tff(f638,plain,(
% 1.94/0.68 spl38_17 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : cons(X0,X2,X1) != X1),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_17])])).
% 1.94/0.68 tff(f642,plain,(
% 1.94/0.68 rs != as | (~spl38_12 | ~spl38_17)),
% 1.94/0.68 inference(superposition,[],[f639,f619])).
% 1.94/0.68 tff(f639,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (cons(X0,X2,X1) != X1) ) | ~spl38_17),
% 1.94/0.68 inference(avatar_component_clause,[],[f638])).
% 1.94/0.68 tff(f647,plain,(
% 1.94/0.68 spl38_18),
% 1.94/0.68 inference(avatar_split_clause,[],[f358,f644])).
% 1.94/0.68 tff(f644,plain,(
% 1.94/0.68 spl38_18 <=> pp(aa(type,bool,typing(ea,ua),t))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_18])])).
% 1.94/0.68 tff(f358,plain,(
% 1.94/0.68 pp(aa(type,bool,typing(ea,ua),t))),
% 1.94/0.68 inference(cnf_transformation,[],[f76])).
% 1.94/0.68 tff(f76,axiom,(
% 1.94/0.68 pp(aa(type,bool,typing(ea,ua),t))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Var_I4_J)).
% 1.94/0.68 tff(f640,plain,(
% 1.94/0.68 spl38_17),
% 1.94/0.68 inference(avatar_split_clause,[],[f417,f638])).
% 1.94/0.68 tff(f417,plain,(
% 1.94/0.68 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (cons(X0,X2,X1) != X1) )),
% 1.94/0.68 inference(cnf_transformation,[],[f142])).
% 1.94/0.68 tff(f142,plain,(
% 1.94/0.68 ! [X0 : $tType,X1 : list(X0),X2 : X0] : cons(X0,X2,X1) != X1),
% 1.94/0.68 inference(rectify,[],[f65])).
% 1.94/0.68 tff(f65,axiom,(
% 1.94/0.68 ! [X0 : $tType,X65 : list(X0),X66 : X0] : cons(X0,X66,X65) != X65),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not__Cons__self2)).
% 1.94/0.68 tff(f636,plain,(
% 1.94/0.68 spl38_16),
% 1.94/0.68 inference(avatar_split_clause,[],[f399,f634])).
% 1.94/0.68 tff(f399,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) )),
% 1.94/0.68 inference(cnf_transformation,[],[f127])).
% 1.94/0.68 tff(f127,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 1.94/0.68 inference(rectify,[],[f39])).
% 1.94/0.68 tff(f39,axiom,(
% 1.94/0.68 ! [X36 : dB,X23 : nat] : subst(var(X23),X36,X23) = X36),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_subst__eq)).
% 1.94/0.68 tff(f632,plain,(
% 1.94/0.68 spl38_15),
% 1.94/0.68 inference(avatar_split_clause,[],[f378,f630])).
% 1.94/0.68 tff(f378,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f119])).
% 1.94/0.68 tff(f119,plain,(
% 1.94/0.68 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 1.94/0.68 inference(rectify,[],[f14])).
% 1.94/0.68 tff(f14,axiom,(
% 1.94/0.68 ! [X19 : nat] : pp(aa(dB,bool,it,var(X19)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Var__IT)).
% 1.94/0.68 tff(f628,plain,(
% 1.94/0.68 spl38_14),
% 1.94/0.68 inference(avatar_split_clause,[],[f377,f626])).
% 1.94/0.68 tff(f626,plain,(
% 1.94/0.68 spl38_14 <=> ! [X0 : nat] : zero_zero(nat) = size_size(dB,var(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_14])])).
% 1.94/0.68 tff(f377,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (zero_zero(nat) = size_size(dB,var(X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f118])).
% 1.94/0.68 tff(f118,plain,(
% 1.94/0.68 ! [X0 : nat] : zero_zero(nat) = size_size(dB,var(X0))),
% 1.94/0.68 inference(rectify,[],[f90])).
% 1.94/0.68 tff(f90,axiom,(
% 1.94/0.68 ! [X40 : nat] : zero_zero(nat) = size_size(dB,var(X40))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_dB_Osize_I4_J)).
% 1.94/0.68 tff(f624,plain,(
% 1.94/0.68 spl38_13 | spl38_1 | ~spl38_11),
% 1.94/0.68 inference(avatar_split_clause,[],[f610,f606,f559,f622])).
% 1.94/0.68 tff(f559,plain,(
% 1.94/0.68 spl38_1 <=> pp(fFalse)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_1])])).
% 1.94/0.68 tff(f610,plain,(
% 1.94/0.68 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl38_1 | ~spl38_11)),
% 1.94/0.68 inference(superposition,[],[f561,f607])).
% 1.94/0.68 tff(f561,plain,(
% 1.94/0.68 ~pp(fFalse) | spl38_1),
% 1.94/0.68 inference(avatar_component_clause,[],[f559])).
% 1.94/0.68 tff(f620,plain,(
% 1.94/0.68 spl38_12),
% 1.94/0.68 inference(avatar_split_clause,[],[f357,f617])).
% 1.94/0.68 tff(f357,plain,(
% 1.94/0.68 rs = cons(dB,a,as)),
% 1.94/0.68 inference(cnf_transformation,[],[f12])).
% 1.94/0.68 tff(f12,axiom,(
% 1.94/0.68 rs = cons(dB,a,as)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Cons)).
% 1.94/0.68 tff(f608,plain,(
% 1.94/0.68 spl38_11),
% 1.94/0.68 inference(avatar_split_clause,[],[f379,f606])).
% 1.94/0.68 tff(f379,plain,(
% 1.94/0.68 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 1.94/0.68 inference(cnf_transformation,[],[f120])).
% 1.94/0.68 tff(f120,plain,(
% 1.94/0.68 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 1.94/0.68 inference(rectify,[],[f111])).
% 1.94/0.68 tff(f111,axiom,(
% 1.94/0.68 ! [X96 : bool] : (fFalse = X96 | fTrue = X96)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 1.94/0.68 tff(f604,plain,(
% 1.94/0.68 spl38_10),
% 1.94/0.68 inference(avatar_split_clause,[],[f376,f602])).
% 1.94/0.68 tff(f602,plain,(
% 1.94/0.68 spl38_10 <=> ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_10])])).
% 1.94/0.68 tff(f376,plain,(
% 1.94/0.68 ( ! [X0 : nat] : (zero_zero(nat) = dB_size(var(X0))) )),
% 1.94/0.68 inference(cnf_transformation,[],[f117])).
% 1.94/0.68 tff(f117,plain,(
% 1.94/0.68 ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 1.94/0.68 inference(rectify,[],[f69])).
% 1.94/0.68 tff(f69,axiom,(
% 1.94/0.68 ! [X40 : nat] : zero_zero(nat) = dB_size(var(X40))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_dB_Osize_I1_J)).
% 1.94/0.68 tff(f600,plain,(
% 1.94/0.68 spl38_9),
% 1.94/0.68 inference(avatar_split_clause,[],[f356,f597])).
% 1.94/0.68 tff(f356,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,u))),
% 1.94/0.68 inference(cnf_transformation,[],[f3])).
% 1.94/0.68 tff(f3,axiom,(
% 1.94/0.68 pp(aa(dB,bool,it,u))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT)).
% 1.94/0.68 tff(f595,plain,(
% 1.94/0.68 spl38_8),
% 1.94/0.68 inference(avatar_split_clause,[],[f355,f592])).
% 1.94/0.68 tff(f355,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,ua))),
% 1.94/0.68 inference(cnf_transformation,[],[f2])).
% 1.94/0.68 tff(f2,axiom,(
% 1.94/0.68 pp(aa(dB,bool,it,ua))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J)).
% 1.94/0.68 tff(f590,plain,(
% 1.94/0.68 spl38_7),
% 1.94/0.68 inference(avatar_split_clause,[],[f354,f587])).
% 1.94/0.68 tff(f354,plain,(
% 1.94/0.68 pp(aa(dB,bool,it,t3))),
% 1.94/0.68 inference(cnf_transformation,[],[f1])).
% 1.94/0.68 tff(f1,axiom,(
% 1.94/0.68 pp(aa(dB,bool,it,t3))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096)).
% 1.94/0.68 tff(f585,plain,(
% 1.94/0.68 spl38_6),
% 1.94/0.68 inference(avatar_split_clause,[],[f397,f583])).
% 1.94/0.68 tff(f583,plain,(
% 1.94/0.68 spl38_6 <=> ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_6])])).
% 1.94/0.68 tff(f397,plain,(
% 1.94/0.68 ( ! [X0 : dB,X1 : nat] : (abs(X0) != var(X1)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f125])).
% 1.94/0.68 tff(f125,plain,(
% 1.94/0.68 ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 1.94/0.68 inference(rectify,[],[f32])).
% 1.94/0.68 tff(f32,axiom,(
% 1.94/0.68 ! [X41 : dB,X40 : nat] : abs(X41) != var(X40)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dB_Osimps_I6_J)).
% 1.94/0.68 tff(f581,plain,(
% 1.94/0.68 spl38_5),
% 1.94/0.68 inference(avatar_split_clause,[],[f390,f579])).
% 1.94/0.68 tff(f579,plain,(
% 1.94/0.68 spl38_5 <=> ! [X0 : dB] : (sP1(X0) | ~sP0(X0))),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_5])])).
% 1.94/0.68 tff(f390,plain,(
% 1.94/0.68 ( ! [X0 : dB] : (sP1(X0) | ~sP0(X0)) )),
% 1.94/0.68 inference(cnf_transformation,[],[f279])).
% 1.94/0.68 tff(f577,plain,(
% 1.94/0.68 ~spl38_4),
% 1.94/0.68 inference(avatar_split_clause,[],[f348,f574])).
% 1.94/0.68 tff(f348,plain,(
% 1.94/0.68 ~pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.94/0.68 inference(cnf_transformation,[],[f114])).
% 1.94/0.68 tff(f114,plain,(
% 1.94/0.68 ~pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.94/0.68 inference(flattening,[],[f113])).
% 1.94/0.68 tff(f113,negated_conjecture,(
% 1.94/0.68 ~pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.94/0.68 inference(negated_conjecture,[],[f112])).
% 1.94/0.68 tff(f112,conjecture,(
% 1.94/0.68 pp(aa(dB,bool,it,subst(a,u,i)))),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.94/0.68 tff(f572,plain,(
% 1.94/0.68 spl38_3),
% 1.94/0.68 inference(avatar_split_clause,[],[f352,f569])).
% 1.94/0.68 tff(f352,plain,(
% 1.94/0.68 pp(fTrue)),
% 1.94/0.68 inference(cnf_transformation,[],[f102])).
% 1.94/0.68 tff(f102,axiom,(
% 1.94/0.68 pp(fTrue)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 1.94/0.68 tff(f567,plain,(
% 1.94/0.68 spl38_2),
% 1.94/0.68 inference(avatar_split_clause,[],[f351,f564])).
% 1.94/0.68 tff(f564,plain,(
% 1.94/0.68 spl38_2 <=> zero(nat)),
% 1.94/0.68 introduced(avatar_definition,[new_symbols(naming,[spl38_2])])).
% 1.94/0.68 tff(f351,plain,(
% 1.94/0.68 zero(nat)),
% 1.94/0.68 inference(cnf_transformation,[],[f100])).
% 1.94/0.68 tff(f100,axiom,(
% 1.94/0.68 zero(nat)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 1.94/0.68 tff(f562,plain,(
% 1.94/0.68 ~spl38_1),
% 1.94/0.68 inference(avatar_split_clause,[],[f349,f559])).
% 1.94/0.68 tff(f349,plain,(
% 1.94/0.68 ~pp(fFalse)),
% 1.94/0.68 inference(cnf_transformation,[],[f101])).
% 1.94/0.68 tff(f101,axiom,(
% 1.94/0.68 ~pp(fFalse)),
% 1.94/0.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 1.94/0.68 % SZS output end Proof for theBenchmark
% 1.94/0.68 % (26842)------------------------------
% 1.94/0.68 % (26842)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.94/0.68 % (26842)Termination reason: Refutation
% 1.94/0.68
% 1.94/0.68 % (26842)Memory used [KB]: 3448
% 1.94/0.68 % (26842)Time elapsed: 0.271 s
% 1.94/0.68 % (26842)Instructions burned: 422 (million)
% 1.94/0.68 % (26837)Success in time 0.308 s
%------------------------------------------------------------------------------